Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Tail Behavior of Maximum Likelihood Estimates of Cointegrating Coefficients in Error Correction Models Abstract: This paper derives exact finite sample distributions of maximum likelihood estimators of the cointegrating coefficients in error correction models. The distributions are derived for the leading case where the variables in the system are independent random walks. But important aspects of the theory, in particular the tail behavior of the distributions, continue to apply when the system is cointegrated. The reduced rank regression estimator is shown to have a distribution with Cauchy-like tails and no finite moments of integer order. The maximum likelihood estimator of the coefficients in the triangular system representation has matrix t-distribution tails with finite integer moments in order T-n+r where T is the sample size, n is the total number of variables in the system and r is the dimension of the cointegration space. These results help to explain simulation studies where extreme outliers are found to occur more frequently for the reduced rank regression estimator than for alternative asymptotically efficient procedures that are based on the triangular representation. Classification-JEL: C22, C13, C51 Keywords: Maximum likelihood, error correction model, random walk, cointegration, finite sample Note: CFP 864. Length: 13 pages Creation-Date: 199110 Number: 999 Publication-Status: Published in Econometrica (January 1994), 62(1): 73-93 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0864.pdf File-Format: application/pdf File-Size: 973 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0999.pdf File-Format: application/pdf File-Size: 325 kb Handle: RePEc:cwl:cwldpp:999 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Unit Roots Abstract: Nonstationarity is certainly one of the most dominant and enduring characteristics of macroeconomic and financial time series. It therefore seems appropriate that this feature of the data be seriously addressed both in econometric methodology and in empirical practice. However, until recently this has not been the case. Before 1980, it was standard empirical practice in econometrics to treat observed trends as simple deterministic functions of time. Nelson-Plosser (1982) challenged this practice and showed that observed trends are better modeled if one allows for stochastic trends. Since their work there has been a continuing reappraisal of trend behavior in economic methods of nonstationary time series. This essay has touched only a part of this large research field and traced only the main ideas involved in unit root modeling and statistical testing. Classification-JEL: C22, C51 Keywords: Nonstationarity, time series Length: 10 pages Creation-Date: 199110 Number: 998 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0998.pdf File-Format: application/pdf File-Size: 464 kb Handle: RePEc:cwl:cwldpp:998 Template-type: ReDIF-Paper 1.0 Author-Name: Dean Corbea Author-X-Name-First: Dean Author-X-Name-Last: Corbea Author-Name: Sam Ouliaris Author-X-Name-First: Sam Author-X-Name-Last: Ouliaris Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Reexamination of the Consumption Function Using Frequency Domain Regressors Abstract: This paper reexamines the permanent income hypothesis (PIH) in the frequency domain. Using a simple model, we demonstrate that the PIH implies the marginal propensity to consume (MPC) out of zero frequency income is unity. The PIH also implies that the MPC out of transitory (or high frequency) income is smaller than the long-run MPC. The paper employs a systems spectral regression procedure to test the PIH that accommodates stochastic trends in the consumption and income series as well as the joint dependence in these series. Monte Carlo simulations suggest that single equation techniques can produce inefficient tests of the PIH and that systems spectral regression methods provide substantially better tests. New empirical estimates of the consumption function and tests of the PIH based on systems spectral regression methods are reported for U.S. aggregate consumption and income data over the period 1948-1990. The empirical results provide partial support for the theoretical implications of the PIH in the frequency domain. Classification-JEL: D91, D12, E21, E27 Keywords: Permanent income, hypothesis, consumption, consumer economics Note: CFP 894. Length: 18 pages Creation-Date: 199110 Number: 997 Publication-Status: Published in Empirical Economics (1994), 19: 595-609 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0864.pdf File-Format: application/pdf File-Size: 863 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0997.pdf File-Format: application/pdf File-Size: 406 kb Handle: RePEc:cwl:cwldpp:997 Template-type: ReDIF-Paper 1.0 Author-Name: Imre Barany Author-X-Name-First: Imre Author-X-Name-Last: Barany Author-Name: J. Lee Author-X-Name-First: J. Author-X-Name-Last: Lee Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Classification of Two-Person Ordinal Bimatrix Games Abstract: The set of possible outcomes of a strongly ordinal bimatrix game is studied by imbedding each pair of possible payoffs as a point on the standard two-dimensional integral lattice. In particular, we count the number of different Pareto optimal sets of each cardinality; we establish asymptotic bounds for the number of different convex hulls of the point sets, for the average shape of the set of points dominated by the Pareto optimal set, and for the average shape of the convex hull of the point set. We also indicate the effect of individual rationality considerations on our results. As most of our results are asymptotic, the appendix includes a careful examination of the important case of 2 x 2 games. Classification-JEL: C72, C70 Keywords: Game theory, rationality, preferences Length: 26 pages Creation-Date: 199110 Number: 996 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0996.pdf File-Format: application/pdf File-Size: 761 kb Handle: RePEc:cwl:cwldpp:996 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Preface to Eduard Marz, Schumpeter, English Translation, Yale University Press Abstract: Eduard Marz's book was first published in German in 1983. I have read only his English translation, which he had completed with preliminary revisions, though not alas with final polishing, before his death in 1987. The book illuminates for us who knew him in America the intellectual and personal background of this fascinating immigrant. And not just for us, of course. World events and intellectual developments over the past two decades have heightened interest in Schumpeter not only among economists, but also among our social scientists and political philosophers. Indeed many people of all ages and all walks of life have discovered Schumpeter and think that his ideas can help them understand the world they live in. Classification-JEL: B31 Keywords: Economic thought, Schumpeter Length: 8 pages Creation-Date: 199110 Number: 995 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0995.pdf File-Format: application/pdf File-Size: 434 kb Handle: RePEc:cwl:cwldpp:995 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Price Flexibility and Output Stability: An Old Keynesian View Abstract: The central macroeconomic issue is the same as ever. How reliable are automatic market adjustments in maintaining full employment equilibrium in the face of aggregate demand shocks? Many modern theorists assume that nominal prices, including wages, jump instantaneously to keep supply and demand equal in all markets. No excess supply, no involuntary unemployment, can ever arise. However, since actual price adjustments take real time, greater flexibility can be destabilizing. "Real balance" effects are overrated, and the demand effects of nominal price changes are perverse. Activist macro policies are necessary, as Keynes argued, even though nominal prices are far from rigid. Classification-JEL: E12, E31, E63 Keywords: Aggregate demand, sticky prices Note: CFP 834. Length: 36 pages Creation-Date: 1991 Revision-Date: 199109 Number: 994R Publication-Status: Published in Journal of Economic Perspectives (Winter 1993), 7(1): 45-65 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0834.pdf File-Format: application/pdf File-Size: 1260 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0994-r.pdf File-Format: application/pdf File-Size: 886 kb Handle: RePEc:cwl:cwldpp:994R Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: International Currency Regimes, Capital Mobility, and Macroeconomic Policy Abstract: The structure of the international monetary system is once again a topic of great interest and controversy -- among economists, business managers, financiers, and government leaders. Many members of all these groups are acutely dissatisfied with the floating exchange rate regime that succeeded the Bretton Woods system two decades ago. Within the European Community, the Exchange Rate Mechanism has re-established a regime of "adjustable pets." After 1992 financial markets and institutions will cover the entire Community. The further step of issuing a common European currency is under serious consideration, and beyond that the more drastic step of replacing national currencies with a single European currency. These measures would still leave exchange rates among Japan, America, and the European Community free to float in currency markets. Classification-JEL: F33, F36, F31 Keywords: International monetary system, exchange rate, currency Note: CFP 895. Length: 20 pages Creation-Date: 199110 Number: 993 Publication-Status: Published in Greek Economic Review (Autumn 1993), 15(1): 1-14 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0895.pdf File-Format: application/pdf File-Size: 678 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0993.pdf File-Format: application/pdf File-Size: 527 kb Handle: RePEc:cwl:cwldpp:993 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Commentary on Irving Fisher, The Nature of Capital and Income (1906) Abstract: Schumpeter regarded "The Nature of Capital and Income" as one of the three of Fisher's contributions to general theory generally recognized, at the time Schumpeter was writing, as "of first-class importance and originality." The other two were Fisher's "Mathematical Investigations" (1982) and his statistical method for measuring the marginal utility of income (1972). Nature is the bridge, both in sequence and in logic, between the other two great works, the timeless general equilibrium theory of the 1892 dissertation and the extension of that theory to intertemporal choices in production and consumption in the theory of interest. Classification-JEL: B31, B21 Keywords: General equilibrium, economic thought Length: 11 pages Creation-Date: 199110 Number: 992 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0992.pdf File-Format: application/pdf File-Size: 424 kb Handle: RePEc:cwl:cwldpp:992 Template-type: ReDIF-Paper 1.0 Author-Name: William C. Brainard Author-X-Name-First: William C. Author-X-Name-Last: Brainard Author-Email: william.brainard@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/brainard.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: On the Internationalization of Portfolios Abstract: Portfolio theory has been an important component of open economy macroeconomic models. In those models, it is essential to distinguish among several categories of assets, both foreign and domestic, and to specify the demands and supplies. This framework has become increasingly relevant. Movements of capital across regional and national boundaries, and across currencies, have exploded in volume, thanks to the dismantling of currency and exchange controls and other financial regulations and to revolutionary economies in technologies of communication and transactions. The globalization of financial markets was stimulated by the floating exchange rate regime established in 1973. Classification-JEL: G11, F41, F21, F31 Keywords: Portfolio choice, open economy, capital mobility, exchange rate Note: CFP 840. Length: 53 pages Creation-Date: 199110 Number: 991 Publication-Status: Published in Oxford Economic Papers (1992), 44: 533-565 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0840.pdf File-Format: application/pdf File-Size: 1759 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0991.pdf File-Format: application/pdf File-Size: 1319 kb Handle: RePEc:cwl:cwldpp:991 Template-type: ReDIF-Paper 1.0 Author-Name: William Cook Author-X-Name-First: William Author-X-Name-Last: Cook Author-Name: Thomas Rutherford Author-X-Name-First: Thomas Author-X-Name-Last: Rutherford Author-Name: Herbert E. Scarf Author-X-Name-First: Herbert E. Author-X-Name-Last: Scarf Author-Email: herbert.scarf@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/scarf.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: David F. Shallcross Author-X-Name-First: David F. Author-X-Name-Last: Shallcross Title: An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming Abstract: In recent years many advances have been made in solution techniques for specially structured 0-1 integer programming problems. In contrast, very little progress has been made on solving general (mixed integer) problems. This, of course, is not true when viewed from the theoretical side: Lenstra (1981) made a major breakthrough, obtaining a polynomial-time algorithm when the number of integer variables is fixed. We discuss a practical implementation of a Lenstra-like algorithm, based on the generalized basis reduction method of Lovasz and Scarf (1988).This method allows us to avoid the ellipsoidal approximations required in Lenstra's algorithm. We report on the solution of a number of small (but difficult) examples, up to 100 integer variables. Our computer code uses the linear programming optimizer CPlex as a subroutine to solve the linear programming problems that arise. Classification-JEL: C61, C63 Keywords: Linear programming, mixed integer problems Note: CFP 906. Length: 13 pages Creation-Date: 199108 Number: 990 Publication-Status: Published in ORSA Journal of Computing (spring 1993), 5(2): 206-221 File-URL: http://cowles.econ.yale.edu/P/cp/p09a/p0906.pdf File-Format: application/pdf File-Size: 560 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0990.pdf File-Format: application/pdf File-Size: 458 kb Handle: RePEc:cwl:cwldpp:990 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: How Fast Do Old Men Slow Down? Abstract: This study uses data on men's track and field and road racing records by age to estimate the rate at which men slow down with age. For most of the running events (400 meters through the half marathon), the slowdown rate per year is estimated to be .80 percent between ages 35 and 51. At age 51 the rate begins to increase. It is 1.04 percent at age 60, 1.46 percent at age 75, and 2.01 percent at age 95. The slowdown rate is smaller for 100 meters. For the events longer than the half marathon, the rate is smaller through about age 60 and then larger after that. The slowdown rate is generally larger at all ages for the field events. Classification-JEL: J14 Keywords: Elderly Note: CFP 872. Length: 33 pages Creation-Date: 199107 Number: 989 Publication-Status: Published in Review of Economics and Statistics (1994), 76(1): 103-118 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0872.pdf File-Format: application/pdf File-Size: 1168 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0989.pdf File-Format: application/pdf File-Size: 853 kb Handle: RePEc:cwl:cwldpp:989 Template-type: ReDIF-Paper 1.0 Author-Name: William D. Nordhaus Author-X-Name-First: William D. Author-X-Name-Last: Nordhaus Author-Email: william.nordhaus@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/nordhaus.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Ecology of Markets Abstract: The notion that "everything is connected to everything else" runs through all of modern economics. Economies are connected in the production sphere through the inputs and outputs that circulate through the world; they are connected through the exchange of goods and services; and they are connected by flows of funds through which some people or nations finance the economic activity of others. It is generally believed that the great macroeconomic crises of this century -- the periodic banking panics, the Great Depression of the 1930's, the debt crisis of the 1980's, the breakdown in socialist economies of today -- occurred because the systems failed, not because of a simultaneous burst of individual economic malfunctions. Furthermore, if some future environmental apocalypse occurs, it will be the result of a failure of markets to incorporate the appropriate signals of scarcity into prices. Classification-JEL: F01, F02, O19 Keywords: Economic development, market failure, international coordination Note: CFP 808. Length: 31 pages Creation-Date: 199107 Number: 988 Publication-Status: Published in Proceedings of the National Academy of Sciences, USA (February 1992), 89: 843-850 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0808.pdf File-Format: application/pdf File-Size: 932 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0988.pdf File-Format: application/pdf File-Size: 844 kb Handle: RePEc:cwl:cwldpp:988 Template-type: ReDIF-Paper 1.0 Author-Name: Jean-Michel Grandmont Author-X-Name-First: Jean-Michel Author-X-Name-Last: Grandmont Author-Workplace-Name: Cowles Foundation, Yale University Title: Transformations of the Commodity Space, Behavioral Heterogeneity and the Aggregation Problem Abstract: The aggregation problem in demand analysis and exchange equilibrium is studied by putting restrictions on the shape of the distribution of the agents' characteristics. This is done by exploiting the finite dimensional linear structure induced on demand functions by affine transformations of the commodity space (or household equivalence scales). Increasing the degree of behavioral heterogeneity in the household sector or more specifically, making the conditional distributions in each equivalence class of demand functions fiat enough, has an important regularizing influence on aggregate budget shares: market demand has a negative dominant diagonal Jacobian matrix, aggregate excess demand has the gross substitutability property, on a large set of prices. These facts have strong consequences for the unicity and stability of equilibrium as well as for the prevalence of the weak axiom of revealed preference in the aggregate in a private ownership Walrasian exchange model. Classification-JEL: D12, D51, C43 Keywords: Aggregation, demand functions, revealed preferences Length: 48 pages Creation-Date: 199107 Number: 987 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0987.pdf File-Format: application/pdf File-Size: 1774 kb Handle: RePEc:cwl:cwldpp:987 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Bayesian Routes and Unit Roots: de rebus prioribus semper est disputandum Abstract: This paper provides detailed responses to the following 8 discussants of my paper "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends": Gary Koop and Mark Steel; Edward Leamer; In-Moo Kim and G.S. Maddala Dale J. Poirier; Peter C. Schotman and Herman K. van Dijk; James H. Stock; David Dejong and Charles H. Whiteman; and Christopher Sims. This reply puts new emphasis on the call made in the earlier paper for objective Bayesian analysis in time series; it underlines the need for a new approach, especially with regard to posterior odds testing; and it draws attention to a new methodology of Bayesian analysis developed in a recent paper by Phillips-Ploberger (1991). Some new simulations that shed light on certain comments of the discussants are proven; new empirical evidence is reported with the extended Nelson-Plosser data supplied by Schotman and van Dijk; and the new Phillips-Ploberger posterior odds test is given a brief empirical illustration. Classification-JEL: C11, C22 Keywords: Bayesian analysis, time series Note: CFP 799. Length: 52 pages Creation-Date: 199107 Number: 986 Publication-Status: Published in Journal of Applied Econometrics (1991), 6: 435-473 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0799.pdf File-Format: application/pdf File-Size: 2516 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0986.pdf File-Format: application/pdf File-Size: 1595 kb Handle: RePEc:cwl:cwldpp:986 Template-type: ReDIF-Paper 1.0 Author-Name: Christopher A. Sims Author-X-Name-First: Christopher A. Author-X-Name-Last: Sims Author-Workplace-Name: Yale University Title: Comment on 'To Criticize the Critics,' by Peter C. B. Phillips Abstract: In his paper "To Criticize the Critics" (1991), Peter Phillips discusses Bayesian methodology for time series models. The main point that Uhlig and I set out to make, however, was that careful consideration of the implications of the likelihood principle suggests that much of the recent work under the "unit root" label in the econometrics literature is being incorrectly interpreted in practice. We pointed out that time series models with possible unit roots are one of the few domains within which the implications of a likelihood principle approach to inference are difference, even in the large samples, from those of a classical hypothesis testing approach. Phillips addresses this part of our paper only indirectly. Classification-JEL: C11, C22 Keywords: Bayesian analysis, time series, unit roots Note: CFP 824. Length: 22 pages Creation-Date: 199107 Number: 985 Publication-Status: Published in Journal of Applied Econometrics (1991), 6: 423-434 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0824.pdf File-Format: application/pdf File-Size: 877 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0985.pdf File-Format: application/pdf File-Size: 599 kb Handle: RePEc:cwl:cwldpp:985 Template-type: ReDIF-Paper 1.0 Author-Name: Ariel Pakes Author-X-Name-First: Ariel Author-X-Name-Last: Pakes Author-Workplace-Name: Yale University Title: Dynamic Structural Models: Problems and Prospects. Mixed Continuous Discrete Controls and Market Interactions Abstract: This paper reviews dynamic structural econometric models with both continuous and discrete controls, and those with market interactions. Its goal is to highlight techniques which enable researchers to obtain estimates of the parameters of models with these characteristics, and then use the estimates in subsequent descriptive and policy analysis. In an attempt to increase the accessibility of structural modeling, emphasis has been laid on estimation techniques which, though consistent with the underlying structural model, are computationally simple. The extent to which this is possible depends on the characteristics of the applied problem of interest, so the paper ends up covering more than one topic. Classification-JEL: C51, C52, C31 Keywords: Dynamic model, structural model Length: 129 pages Creation-Date: 199107 Number: 984 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0984.pdf File-Format: application/pdf File-Size: 3593 kb Handle: RePEc:cwl:cwldpp:984 Template-type: ReDIF-Paper 1.0 Author-Name: David G. Pearce Author-X-Name-First: David G. Author-X-Name-Last: Pearce Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Repeated Games: Cooperation and Rationality Abstract: The paper is a survey written for the Sixth World congress of the Econometric Society. It is devoted largely to a discussion of the progress made in the last decade in understanding the structure of self-enforcing agreements in discounted supergames of complete information. Perfect and imperfect monitoring models are considered in turn, with attention given to the case of substantial impatience as well as to the various "folk theorems." The emphasis is on the features of constrained-optimal perfect equilibria, causes of inefficiency, and some relationships among different strands of the literature. The remainder of the paper is a critical and comparative consideration of recent work on renegotiation in repeated games. Classification-JEL: C71 Keywords: Repeated game, self-enforcing contracts, supergames, folk theorem Length: 43 pages Creation-Date: 199106 Number: 983 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0983.pdf File-Format: application/pdf File-Size: 1463 kb Handle: RePEc:cwl:cwldpp:983 Template-type: ReDIF-Paper 1.0 Author-Name: William D. Nordhaus Author-X-Name-First: William D. Author-X-Name-Last: Nordhaus Author-Email: william.nordhaus@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/nordhaus.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Stabilizing the Soviet Economy Abstract: The proposals in our policy memorandum on economic stabilization -- a restrictive monetary policy and a fiscal policy that eliminates the government deficit -- are shaped by our view that the Soviet Union today faces a mounting economic crisis. As we emphasized in our discussion in the policy memorandum, problems include issues of inefficient economic structures, distorted prices, large macroeconomic imbalances, divided government, and lack of popular support for steps to stabilize and restructure the economy. Classification-JEL: E61, E63, P21, P27 Keywords: Government spending, budget deficit, Soviet Union Note: CFP 802. Length: 60 pages Creation-Date: 199106 Number: 982 Publication-Status: Published in Merton J. Peck and Thomas J. Richardson, eds., What Is to Be Done?, 1991, pp. 83-115 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0802.pdf File-Format: application/pdf File-Size: 1738 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0982.pdf File-Format: application/pdf File-Size: 1353 kb Handle: RePEc:cwl:cwldpp:982 Template-type: ReDIF-Paper 1.0 Author-Name: Faruk Gul Author-X-Name-First: Faruk Author-X-Name-Last: Gul Author-Name: David G. Pearce Author-X-Name-First: David G. Author-X-Name-Last: Pearce Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Ennio Stacchetti Author-X-Name-First: Ennio Author-X-Name-Last: Stacchetti Author-Workplace-Name: Dept. of Economics, Yale University Author-Workplace-Homepage: http://www.econ.yale.edu/ Title: A Bound of the Proportion of Pure Strategy Equilibria in Generic Games Abstract: In a generic finite normal form game with 2(alpha) + 1 Nash equilibria, at least alpha of the equilibria are nondegenerate mixed strategy equilibria (that is, they involve randomization by some players). Classification-JEL: C70 Keywords: Normal form, mixed strategy, game theory Length: 12 pages Creation-Date: 199105 Number: 981 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0981.pdf File-Format: application/pdf File-Size: 402 kb Handle: RePEc:cwl:cwldpp:981 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Werner Ploberger Author-X-Name-First: Werner Author-X-Name-Last: Ploberger Title: Time Series Modelling with a Bayesian Frame of Reference: 1. Concepts and Illustrations Abstract: This paper offers a general approach to time series modeling that attempts to reconcile classical and methods. The central idea put forward to achieve reconciliation is that the Bayesian approach relies implicitly a frame of reference for the data generating mechanism that is quite different from the one that is employed in the classical approach. Differences in inferences from the two approaches are therefore to be expected unless the altered frame reference is taken into account. We show that the new frame of reference in Bayesian inference is a consequence of a change of measure that arises naturally in the application of Bayes theorem. Our paper explores this change of measure and its consequences using martingale methods. Examples are give illustrate its practical implications. No assumptions concerning stationarity or rates of convergence are required and techniques of stochastic differential geometry on manifolds are involved. Some implications for statistical testing are explored and suggest new tests, which we call Bayes model tests, for discriminating between models. Classification-JEL: C11, C22, C51, C52 Keywords: Time series, modeling, Bayesian analysis, martingale Length: 54 pages Creation-Date: 199105 Number: 980 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0980.pdf File-Format: application/pdf File-Size: 1506 kb Handle: RePEc:cwl:cwldpp:980 Template-type: ReDIF-Paper 1.0 Author-Name: Denis Kwiatkowski Author-X-Name-First: Denis Author-X-Name-Last: Kwiatkowski Author-Workplace-Name: Central Michigan University Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Peter Schmidt Author-X-Name-First: Peter Author-X-Name-Last: Schmidt Author-Workplace-Name: Michigan State University Title: Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root? Abstract: The standard conclusion that is drawn from this empirical evidence is that many or most aggregate economic time series contain a unit root. However, it is important to note that in this empirical work the unit root is set up as the null hypothesis testing is carried out ensures that the null hypothesis is accepted unless there is strong evidence against it. Therefore, an alternative explanation for the common failure to reject a unit root is simply that most economic time series are not very informative about whether or not there is a unit root; or, equivalently, that standard unit root tests are not very powerful against relevant alternatives. Classification-JEL: C12, C52 Keywords: Unit root, time series, stationarity, hypothesis testing Note: CFP 827. Length: 28 pages Creation-Date: 199105 Number: 979 Publication-Status: Published in Journal of Econometrics (1992), 54: 159-178 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0827.pdf File-Format: application/pdf File-Size: 893 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0979.pdf File-Format: application/pdf File-Size: 663 kb Handle: RePEc:cwl:cwldpp:979 Template-type: ReDIF-Paper 1.0 Author-Name: Hiro Y. Toda Author-X-Name-First: Hiro Y. Author-X-Name-Last: Toda Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Spurious Effect of Unit Roots on Exogeneity Tests in Vector Autoregressions: An Analytical Study Abstract: This paper analyzes whether inclusion of a statistically independent random walk in a vector autoregression can result in spurious inference. The problem was raised originally by Ohanian (1988). In a Monte Carlo simulation based on the VAR's estimated by Sims (1980b, 1982), Ohanian found that block exogeneity of the genuine variables with respect to an artificially generated random walk variable was rejected too often. In the present paper we attempt a full analytical study of this problem. It can be shown that if the genuine variables are nonstationary, the Wald statistic for testing the block exogeneity hypothesis does not have the usual asymptotic chi-square distribution. This result is consistent with Ohanian's finding. Furthermore, the derived asymptotic distribution is free of nuisance parameters so that we can unambiguously determine the effect of including the random walk. Interestingly, it can also be shown that if the genuine variables of the model are stationary, the asymptotic distribution is still chi-square in spite of the inclusion of the random walk. Classification-JEL: C32, C51, C52 Keywords: Random walk, exogeneity, vector autoregressions, unit roots, Wald tests Note: CFP 854. Length: 30 pages Creation-Date: 199105 Number: 978 Publication-Status: Published in Oxford Economic Papers (1993), 59: 229-255 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0854.pdf File-Format: application/pdf File-Size: 753 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0978.pdf File-Format: application/pdf File-Size: 478 kb Handle: RePEc:cwl:cwldpp:978 Template-type: ReDIF-Paper 1.0 Author-Name: Hiro Y. Toda Author-X-Name-First: Hiro Y. Author-X-Name-Last: Toda Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Vector Autoregression and Causality Abstract: This paper develops a complete limit theory for Wald tests of Granger causality in levels vector autoregression (VAR's) and Johansen-type error correction models (ECM's) allowing for the presence of stochastic trends and cointegration. Earlier work by Sims, Stock and Watson (1990) on trivariate VAR systems is extended to the general case, thereby formally characterizing the circumstances when these Wald tests are asymptotically valid as chi-square criteria. Our results for inference from unrestricted levels VAR are not encouraging. Classification-JEL: C32, C12, C52 Keywords: Error correction model, exogeneity, Granger causality, vector autoregression Note: CFP 858. Length: 51 pages Creation-Date: 199105 Number: 977 Publication-Status: Published in Econometrica (November 1993), 61(6): 1367-1393 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0858.pdf File-Format: application/pdf File-Size: 1067 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0977.pdf File-Format: application/pdf File-Size: 868 kb Handle: RePEc:cwl:cwldpp:977 Template-type: ReDIF-Paper 1.0 Author-Name: Lin Zhou Author-X-Name-First: Lin Author-X-Name-Last: Zhou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: An 'Average' Lyapunov Convexity Theorem and Some Core Equivalence Results Abstract: I prove an "average" version of the Lyapunov convexity theorem and apply it to establish some core equivalence results for an atomless economy. Classification-JEL: D51, D58, C62 Keywords: Convex, core, exchange economy Length: 18 pages Creation-Date: 199105 Number: 976 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0976.pdf File-Format: application/pdf File-Size: 695 kb Handle: RePEc:cwl:cwldpp:976 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Exactly Unbiased Estimation of First Order Autoregressive-Unit Root Models Abstract: This paper is concerned with the estimation of first-order autoregressive/unit root models with independent identically distributed normal errors. The models considered include those without an intercept, those with an intercept, and those with an intercept and time trend. The autoregressive (AR) parameter alpha is allowed to lie in the interval (-1,1], which includes the case of a unit root. Exactly median-unbiased estimators of the AR parameter alpha are proposed. Exact confidence intervals for this parameter are introduced. Corresponding exactly median-unbiased estimators and exact confidence intervals are also provided for the impulse response function and the cumulative impulse response. An unbiased model selection procedure is discussed. The procedures that are introduced are applied to several data series including real exchange rates, the velocity of money, and industrial production. Classification-JEL: C22, C13, C51 Keywords: Autoregressive process, confidence interval, time trend, model selection, unit roots Note: CFP 832. Length: 45 pages Creation-Date: 199104 Number: 975 Publication-Status: Published in Econometrica (January 1993), 61(1): 139-165 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0832.pdf File-Format: application/pdf File-Size: 1507 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0975.pdf File-Format: application/pdf File-Size: 1266 kb Handle: RePEc:cwl:cwldpp:975 Template-type: ReDIF-Paper 1.0 Author-Name: Lin Zhou Author-X-Name-First: Lin Author-X-Name-Last: Zhou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Refined Bargaining Set of an n-Person Game and Endogenous Coalition Formation Abstract: The two most fundamental questions in cooperative game theory are: When a game is played, what coalitions will be formed and what payoff vectors will be chosen? No previous solution concepts or theories in the literature provide satisfactory answers to both questions; answers are especially lacking for the first one. In this paper we introduce the refined bargaining set, which is the first solution concept in cooperative game theory that simultaneously provides answers to both of the fundamental questions. Classification-JEL: C71 Keywords: Cooperative games, game theory, bargaining coalition Note: CFP 868. Length: 23 pages Creation-Date: 199104 Number: 974 Publication-Status: Published in Games and Economic Behavior (1994), 6: 512-526 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0868.pdf File-Format: application/pdf File-Size: 769 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0974.pdf File-Format: application/pdf File-Size: 654 kb Handle: RePEc:cwl:cwldpp:974 Template-type: ReDIF-Paper 1.0 Author-Name: Nancy T. Gallini Author-X-Name-First: Nancy T. Author-X-Name-Last: Gallini Author-Name: Nancy A. Lutz Author-X-Name-First: Nancy A. Author-X-Name-Last: Lutz Author-Workplace-Name: Dept. of Economics, Yale University Author-Workplace-Homepage: http://www.econ.yale.edu/ Title: Dual Distribution in Franchising Abstract: In this paper we offer an explanation for the practice of dual distribution. the simultaneous use of franchises and company owned outlets for distributing new products. Our explanation rests on the observation that franchisors often acquire private information, not available to franchisees, on product demand through marketing efforts. Under this assumption of asymmetric information, we show that a franchisor will use both direct ownership as well as the franchise contract to convey information about a new product. This explanation for dual distribution relies neither on capital market imperfections nor upon location-specific factors, in contrast to alternative explanations advanced in the literature Testable implications of the signaling model are discussed. Classification-JEL: L11, L14, L52 Keywords: Franchises, corporations, marketing, private information Length: 33 pages Creation-Date: 199103 Number: 973 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0973.pdf File-Format: application/pdf File-Size: 1523 kb Handle: RePEc:cwl:cwldpp:973 Template-type: ReDIF-Paper 1.0 Author-Name: Lin Zhou Author-X-Name-First: Lin Author-X-Name-Last: Zhou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Strictly Fair Allocations in Large Exchange Economies Abstract: In this paper we introduce the concept of a strictly fair allocation and investigate the set of strictly fair allocations in large exchange economies. We prove that when agents' utility functions are differentiable, the set of strictly fair allocations coincides with the set of equal-income Walrasian equilibria. This is shown using both the "limit theorem" approach the "limit economy" approach. We also extend the analysis to economies that have both atoms and an atomless sector. These results substantially improve upon the existing characterizations of equal-income Walrasian equilibria in terms of both economic efficiency and economic equity. Classification-JEL: D51, D60, D58 Keywords: Exchange economy, Walrasian equilibrium, resource allocation Note: CFP 813. Length: 26 pages Creation-Date: 199103 Number: 972 Publication-Status: Published in Journal of Economic Theory (June 1992), 57(1): 160-175 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0813.pdf File-Format: application/pdf File-Size: 778 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0972.pdf File-Format: application/pdf File-Size: 657 kb Handle: RePEc:cwl:cwldpp:972 Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Arithmetic Repeat Sales Price Estimators Abstract: Repeat sales price estimators are designed to infer price indexes of infrequently sold and unstandardized assets, such as houses, based only on changes in prices of those individual assets that are observed to be sold twice. Repeat sales price estimators are proposed here that are arithmetic, and either value-weighted or equally-weighted. Moreover, variants are proposed that are interval-weighted, i.e., that correct for a form of heteroskedasticity, and that include additional regressors representing changes in hedonic variables. Some of these methods are applied to data on house prices in Atlanta, Chicago, Dallas and San Francisco 1970-1986. Classification-JEL: R31, C43 Keywords: Price index, hedonic regression, housing Note: CFP 781. Length: 26 pages Creation-Date: 199102 Number: 971 Publication-Status: Published in Journal of Housing Economics (1991), 1: 110-126 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0781.pdf File-Format: application/pdf File-Size: 880 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0971.pdf File-Format: application/pdf File-Size: 698 kb Handle: RePEc:cwl:cwldpp:971 Template-type: ReDIF-Paper 1.0 Author-Name: Andrea E. Beltratti Author-X-Name-First: Andrea E. Author-X-Name-Last: Beltratti Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Actual and Warranted Relations Between Asset Prices Abstract: Efficient markets models assert that the price of each asset is equal to the optimal forecast of its ex-post or fundamental value. These models do not imply, however, that the covariance between two asset prices is given by the covariance between the ex-post values they respectively forecast: these two covariances can even have opposite signs. However, it is possible to place bounds on the covariance between asset prices given the covariance matrix of ex-post values. We present such bounds for both covariances and correlations and show how such bounds can be tightened using information beyond the covariance matrix of ex-post values. The methods are used to examine whether the historical correlation between the U.S. and U.K. stock markets 1919-1989 is warranted. The bounds on the warranted covariance are very wide and include the actual correlation. Classification-JEL: G12, G14, G15 Keywords: Volatility, stock market, asset pricing, efficient markets, information Note: CFP 859. Length: 22 pages Creation-Date: 199102 Number: 970 Publication-Status: Published in Oxford Economic Papers (1993), 45: 387-402 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0859.pdf File-Format: application/pdf File-Size: 871 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0970.pdf File-Format: application/pdf File-Size: 506 kb Handle: RePEc:cwl:cwldpp:970 Template-type: ReDIF-Paper 1.0 Author-Name: Herbert E. Scarf Author-X-Name-First: Herbert E. Author-X-Name-Last: Scarf Author-Email: herbert.scarf@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/scarf.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Economic Equilibrium and Soviet Economic Reform Abstract: The paper, prepared for a Roundtable on Major Economic Problems in the U.S. and the U.S.S.R., discusses some aspects of price theory ñ in particular, the theory of general equilibrium -ñ which may offer some theoretical insights about the economic problems to be encountered during the transition from Socialism to private markets in the Soviet Union. Classification-JEL: P22, P23, P51 Keywords: Socialism, scale economies, general equilibrium, market structures, prices, price theory Length: 39 pages Creation-Date: 199102 Number: 969 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0969.pdf File-Format: application/pdf File-Size: 1598 kb Handle: RePEc:cwl:cwldpp:969 Template-type: ReDIF-Paper 1.0 Author-Name: Yoon-Jae Whang Author-X-Name-First: Yoon-Jae Author-X-Name-Last: Whang Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Tests of Specification for Parametric and Semiparametric Models Abstract: This paper provides a general framework for constructing specification tests for parametric and semiparametric models. The paper develops new specification tests using the general framework. In particular, specification tests for semiparametric partially linear regression, sample selection, and censored regression models are introduced. The results apply in time series and cross-sectional contexts. The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes. Keywords: Infinite dimensional nuisance parameter, semiparametric model, specification test, stochastic equicontinuity Note: CFP 844. Length: 80 pages Creation-Date: 199101 Number: 968 Publication-Status: Published in Journal of Econometrics (1993), 57: 277-318 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0844.pdf File-Format: application/pdf File-Size: 1540 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0968.pdf File-Format: application/pdf File-Size: 1895 kb Handle: RePEc:cwl:cwldpp:968 Template-type: ReDIF-Paper 1.0 Author-Name: Vassilis A. Hajivassiliou Author-X-Name-First: Vassilis A. Author-X-Name-Last: Hajivassiliou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Daniel McFadden Author-X-Name-First: Daniel Author-X-Name-Last: McFadden Title: The Method of Simulated Scores for the Estimation of LDV Models with an Application to External Debt Crisis Abstract: The method of simulated scores (MSS) is presented for estimating LDV models with flexible correlation structure in the unobservables. We propose simulators that are continuous in the unknown parameter vectors, and hence standard optimization methods can be used to compute the MSS estimators that employ these simulators. We establish consistency and asymptotic normality of the MSS estimators and derive suitable rates at which the number of simulations must use if biased simulators are used. The estimation method is applied to analyze a model in which the incidence and the extent of debt repayments problems of LDC's are viewed as optimized choices of the central authorities of the countries in a framework of credit rationing. The econometric implementation of the resulting multi-period probit and Tobit models avoids the need for high dimensional integration. Our findings show that the restrictive error structures imposed by past studies may have led to unreliable econometric results. Classification-JEL: C24, C15, C13 Keywords: Simulation model, asymptotic theory, censored model Length: 63 pages Creation-Date: 199012 Number: 967 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0967.pdf File-Format: application/pdf File-Size: 2687 kb Handle: RePEc:cwl:cwldpp:967 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Invisible Hand in Modern Macroeconomics Abstract: The Invisible Hand, one of the Great Ideas of history and one of the most influential, is Adam Smith's most important legacy to macroeconomics, as to all economics. It is particularly important today as the ultimate inspiration for the New Classical Macroeconomics and for Real Business Cycle Theory. These are intellectual movements that engage many of the best brains in the profession, especially among younger cohorts and especially in the United States. They dominate the agenda even of theorists and econometricians who are skeptical or hostile to their methods and conclusions. Classification-JEL: B22, B31 Keywords: Adam Smith, Invisible Hand, Keynes, macroeconomics, economic thought Length: 14 pages Creation-Date: 199101 Number: 966 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0966.pdf File-Format: application/pdf File-Size: 491 kb Handle: RePEc:cwl:cwldpp:966 Template-type: ReDIF-Paper 1.0 Author-Name: Herbert E. Scarf Author-X-Name-First: Herbert E. Author-X-Name-Last: Scarf Author-Email: herbert.scarf@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/scarf.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Shallcross, David F. Title: Shortest Integer Vectors Abstract: Let A be a fixed integer matrix of size m by n and consider all b for which the body is full dimensional. We examine the set of shortest non-zero integral vectors with respect to the family of norms. We show that the number of such shortest vectors is polynomial in the bit size of A, for fixed n. We also show the existence, for any n, of a family of matrices M for which the number of shortest vectors has as a lower bound a polynomial in the bit size of M of the same degree at the polynomial bound. Classification-JEL: C60, C61 Keywords: Indivisibilities, integer programming, geometry, numbers Note: CFP 848. Length: 8 pages Creation-Date: 199101 Number: 965 Publication-Status: Published in Mathematics of Operations Research (August 1993), 18(3): 517-522 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0848.pdf File-Format: application/pdf File-Size: 371 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0965.pdf File-Format: application/pdf File-Size: 232 kb Handle: RePEc:cwl:cwldpp:965 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: D.P. Tsomocos Author-X-Name-First: D.P. Author-X-Name-Last: Tsomocos Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Strategic Market Game with a Mutual Bank with Fractional Reserves and Redemption in Gold (A Continuum of Traders) Abstract: We utilize the strategic market game approach to analyze the role and function of a mutual bank with variable fractional reserves, redemption in gold and endogenous interest rate formation. We specify the conditions of enough money and its distribution. Using the continuum of traders model, we show existence and optimality for the case of no bankruptcy as well as for the case in which there exists the potentiality of bankruptcy. Finally, we analyze the relationship of the gearing ratio and the bankruptcy penalty with respect to the resulting equilibrium allocations. Classification-JEL: G33, G21, E51, E43 Keywords: Banking, interest rates, bankruptcy, credit, money supply Note: CFP 812. Length: 24 pages Creation-Date: 199012 Number: 964 Publication-Status: Published in Journal of Economics (1992), 55(2): 123-150 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0812.pdf File-Format: application/pdf File-Size: 1072 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0964.pdf File-Format: application/pdf File-Size: 470 kb Handle: RePEc:cwl:cwldpp:964 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Default and Bankruptcy in a Multistage Exchange Economy Abstract: Either lending must be secured or otherwise some form of default or bankruptcy rules are required to provide a disincentive against strategic default. When many time periods are involved, the mere specification of a penalty which is sufficient for one period of trade, is not sufficient. The complete specification of even a two period game requires that both the treatment of creditors (including seniority conditions) and the nature of the rehabilitation of the debtor must be specified. This paper explores these problems. Classification-JEL: G33, D51 Keywords: Bankruptcy, debt, credit Length: 14 pages Creation-Date: 199012 Number: 963 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0963.pdf File-Format: application/pdf File-Size: 679 kb Handle: RePEc:cwl:cwldpp:963 Template-type: ReDIF-Paper 1.0 Author-Name: Antal Balog Author-X-Name-First: Antal Author-X-Name-Last: Balog Author-Workplace-Name: Princeton University Author-Name: Imre Barany Author-X-Name-First: Imre Author-X-Name-Last: Barany Author-Workplace-Name: NYU Title: On the Convex Hull of the Integer Points Abstract: Let P_{r} denote the convex hull of the integer points in the disc of radius r. We prove that the number of vertices of P_{r} is essentially r^{2/3} as r approaches infinity. Length: 9 pages Creation-Date: 199011 Number: 962 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0962.pdf File-Format: application/pdf File-Size: 301 kb Handle: RePEc:cwl:cwldpp:962 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Jingang Zhao Author-X-Name-First: Jingang Author-X-Name-Last: Zhao Title: A Strategic Market Game of a Finite Economy with a Mutual Bank Abstract: We introduce a strategic market game for an exchange economy not having enough commodity money. We show the existence of a non-cooperative equilibrium for any finite replication economy with a mutual bank, we then show that efficient trade can be achieved in the limiting economy by expanding the money supply through the use of fractional reserves, where the commodity money is demonetized and used for reserves. The means of exchange becomes bank credit backed in part, by "gold." However, efficiency cannot be achieved in general as a non-cooperative equilibrium of a finite player game or a finite exchange economy. Note: CFP 807. Length: 22 pages Creation-Date: 199011 Number: 961 Publication-Status: Published in Mathematical Social Sciences (1991), 22: 257-274 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0807.pdf File-Format: application/pdf File-Size: 749 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0961.pdf File-Format: application/pdf File-Size: 582 kb Handle: RePEc:cwl:cwldpp:961 Template-type: ReDIF-Paper 1.0 Author-Name: Vassilis A. Hajivassiliou Author-X-Name-First: Vassilis A. Author-X-Name-Last: Hajivassiliou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Axel Borsch-Supan Author-X-Name-First: Axel Author-X-Name-Last: Borsch-Supan Author-Workplace-Name: University of Mannheim & NBER Title: Smooth Unbiased Multivariate Probability Simulators for Maximum Likelihood Estimation of Limited Dependent Variable Models Abstract: We apply a new simulation method that solves the multidimensional probability integrals that arise in maximum likelihood estimation of a broad class of limited dependent variable models. The simulation method has four key features: the simulated choice probabilities are unbiased; they are a continuous and differentiable function of the parameters of the model; they are bounded between 0 and 1; and their computation takes an effort that is nearly linear in the dimension of the probability integral, independent of the magnitudes of the true probabilities. We also show that the new simulation method produces probability estimates with substantially smaller variance than those generated by acceptance-rejection methods or by Stern's (1987) method. The simulated probabilities can therefore be used to revive the Lerman and Manski(1981) procedure of approximating the likelihood function using simulated choice probabilities by overcoming its computational disadvantages. Note: CFP 846. Length: 25 pages Creation-Date: 199009 Number: 960 Publication-Status: Published in Journal of Econometrics (1993), 58: 347-368 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0846.pdf File-Format: application/pdf File-Size: 956 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0960.pdf File-Format: application/pdf File-Size: 685 kb Handle: RePEc:cwl:cwldpp:960 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Price for the Widow's Cruse: Or the Value of an Infinitely Productive Asset Abstract: This paper considers two basic problems: The first is the necessity for introducing government money (as contrasted with individual credit) and an infinitely lived government in an overlapping generations economy. The second concerns the evaluation of the price of an infinitely productive asset in an economy without a natural discount factor. Length: 6 pages Creation-Date: 199010 Number: 959 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0959.pdf File-Format: application/pdf File-Size: 287 kb Handle: RePEc:cwl:cwldpp:959 Template-type: ReDIF-Paper 1.0 Author-Name: Rosa L. Matzkin Author-X-Name-First: Rosa L. Author-X-Name-Last: Matzkin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Least Concavity and the Distribution-Free Estimation of Non-Parametric Concave Functions Abstract: This paper studies the estimation of fully nonparametric models in which we can not identify the values of a symmetric function that we seek to estimate. I develop a method of consistently estimating a representative of a concave and monotone nonparametric systematic function. This representative possesses the same isovalue sets as the systematic function. The method proceeds by characterizing each set of observationally equivalent concave functions by a unique "least concave" representative. The least concave representative of the equivalence class to which the systematic function belongs is estimated by maximizing a criterion function over a compact set of least concave functions. I develop a computational technique to evaluate the values, at the observed points, and the gradients, at every point and up to a constant, of this least concave estimator. The paper includes a detailed description of how the method can be used to estimate three popular microeconometric models. Length: 56 pages Creation-Date: 199010 Number: 958 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0958.pdf File-Format: application/pdf File-Size: 1532 kb Handle: RePEc:cwl:cwldpp:958 Template-type: ReDIF-Paper 1.0 Author-Name: Rosa L. Matzkin Author-X-Name-First: Rosa L. Author-X-Name-Last: Matzkin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Estimation of Multinomial Models Using Weak Monotonicity Assumptions Abstract: This paper introduces a semiparametric method of estimating multinomial models that imposes extremely weak monotonicity assumptions about a function of observable characteristics. Previous methods have imposed stronger, typically parametric, conditions on this function. The only assumptions made in this paper about the function of characteristics are its monotonicity, upper-semicontinuity, and uniform boundedness. The method is applicable, among others, to polychotomous choice models. The estimation method is shown to be strongly consistent. A technique to calculate the estimator is provided. Length: 34 pages Creation-Date: 199010 Number: 957 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0957.pdf File-Format: application/pdf File-Size: 1049 kb Handle: RePEc:cwl:cwldpp:957 Template-type: ReDIF-Paper 1.0 Author-Name: Jingang Zhao Author-X-Name-First: Jingang Author-X-Name-Last: Zhao Title: The Hybrid Solutions of an n-Person Game Abstract: We introduce a solution concept intermediate between the cooperative and noncooperative solutions of an n-person game in normal form. Consider a partition p of the players, with each s in p a coalition. A joint strategy x = {x_{s}|s in p} is a hybrid solution for the partition p if, for each s in p, x_{s} is a core solution of the corresponding parametric subgame, where this game is played by the players in s and is parameterized by x_{-s}, the strategies played by all outside players. This assumes that players behave cooperatively within each coalition and competitively across coalitions. Sufficient conditions are given for a general n-person game to have hybrid solutions for any partition. Length: 21 pages Creation-Date: 199009 Number: 956 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0956.pdf File-Format: application/pdf File-Size: 827 kb Handle: RePEc:cwl:cwldpp:956 Template-type: ReDIF-Paper 1.0 Author-Name: Stephen S. Golub Author-X-Name-First: Stephen S. Author-X-Name-Last: Golub Author-Workplace-Name: Swarthmore College Title: International Diversification of Social and Private Risk: The US and Japan Abstract: This paper concerns the gains from international trade in risky assets, with an application to the United States and Japan. I examine the role of international financial markets in diversifying the risks associated with the aggregate consumption opportunities of a nation (social risk) and the risks related to individual agents' consumption opportunities (private risk). The main empirical result is that international portfolio diversification between the United States and Japan leads to small reductions in social risk but large reductions in some private risks, especially for corporate profits. Length: 33 pages Creation-Date: 199008 Number: 955 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0955.pdf File-Format: application/pdf File-Size: 1678 kb Handle: RePEc:cwl:cwldpp:955 Template-type: ReDIF-Paper 1.0 Author-Name: Lin Zhou Author-X-Name-First: Lin Author-X-Name-Last: Zhou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies Abstract: In this paper I prove that in the standard model of 2 times n (n >= 2) pure exchange economies there is no allocation mechanism that is efficient, non-inversely-dictatorial, and strategy-proof. This strengthens two previous results on this subject by Hurwicz and by Dasgupta, Hammond, and Maskin. Note: CFP 793. Length: 11 pages Creation-Date: 199009 Number: 954 Publication-Status: Published in Social Choice and Welfare (1991), 8: 247-254 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0793.pdf File-Format: application/pdf File-Size: 431 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0954.pdf File-Format: application/pdf File-Size: 284 kb Handle: RePEc:cwl:cwldpp:954 Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Andrea E. Beltratti Author-X-Name-First: Andrea E. Author-X-Name-Last: Beltratti Author-Workplace-Name: University of Turin Title: Stock Prices and Bond Yields: Can Their Co-Movements Be Explained in Terms of Present Value Models? Abstract: Real stock prices seem to overreact to changes in long-term interest rates. That is, real stock prices drop when long-term interest rates rise (and rise when they fall) more than would be implied by a rational expectationspresent value model where expectations are based on a vector autoregression. This overreaction is not associated with any overreaction to changes in the short-run inflation rate. Over the last century real stock prices have shown little reaction to changes in inflation rates, and according to the model they should show little reaction. These conclusions were reached from an analysis of annual data in the United States 1871 to 1989 and the United Kingdom 1918 to 1989. Note: CFP 833. Length: 33 pages Creation-Date: 199009 Number: 953 Publication-Status: Published in Journal of Monetary Economics (1992), 30: 25-46 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0833.pdf File-Format: application/pdf File-Size: 1050 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0953.pdf File-Format: application/pdf File-Size: 665 kb Handle: RePEc:cwl:cwldpp:953 Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Maxim Boycko Author-X-Name-First: Maxim Author-X-Name-Last: Boycko Author-Workplace-Name: USSR Academy of Sciences Author-Name: Vladimir Korobov Author-X-Name-First: Vladimir Author-X-Name-Last: Korobov Author-Workplace-Name: USSR Academy of Sciences Title: Popular Attitudes Towards Free Markets: The Soviet Union and the United States Compared Abstract: Random samples of the Moscow and New York populations were compared in their attitudes towards free markets by administering identical telephone interviews in the two countries in May, 1990. Although the Soviet respondents were somewhat less likely to accept exchange of money as a solution to personal problems, and their attitudes towards business were less warm, we found that the Soviet and American respondents were basically similar in most dimensions. Soviets showed no difference from Americans in their feelings that price increases may be unfair. There appears to be little difference between the Soviets and Americans in their concern with income inequality, in their belief in the importance of providing material incentives for hard work, and in their understanding of the workings of markets. Classification-JEL: 123 Keywords: Market prices, market clearing, rents, behavior, fairness, income distribution, inheritance, wealth, rich, speculation, profiteering, savings, government interference, incentives, envy, perestroika, public, perceptions, attitudes, survey, poll, USA, USSR, communism, socialism, capitalism, national character, values Note: CFP 787. Length: 72 pages Creation-Date: 199008 Number: 952 Publication-Status: Published in American Economic Review (June 1991), 81(3): 385-400 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0787.pdf File-Format: application/pdf File-Size: 1131 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0952.pdf File-Format: application/pdf File-Size: 1464 kb Handle: RePEc:cwl:cwldpp:952 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: David Pollard Author-X-Name-First: David Author-X-Name-Last: Pollard Author-Workplace-Name: Dept. of Statistics, Yale University Title: A Functional Central Limit Theorem for Strong Mixing Stochastic Processes Abstract: This paper shows how the modern machinery for generating abstract empirical central limit theorems can be applied to arrays of dependent variables. It develops a bracketing approximation based on a moment inequality for sums of strong mixing arrays, in an effort to illustrate the sorts of difficulty that need to be overcome when adapting the empirical process theory for independent variables. Some suggestions for further development are offered. The paper is largely self-contained. Keywords: Strong mixing, functional central limit theorem, empirical process Note: CFP 870. Length: 16 pages Creation-Date: 199009 Number: 951 Publication-Status: Published in International Statistical Review (1994), 62(1): 119-132 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0870.pdf File-Format: application/pdf File-Size: 760 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0951.pdf File-Format: application/pdf File-Size: 518 kb Handle: RePEc:cwl:cwldpp:951 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends Abstract: In two recent articles, Sims (1988) and Sims and Uhlig (1988) question the value of much of the ongoing literature on unit roots and stochastic trends. They characterize the seeds of this literature as "sterile ideas," the application of nonstationary limit theory as "wrongheaded and unenlightening" and the use of classical methods of inference as "unreasonable" and "logically unsound." They advocate in place of classical methods an explicit Bayesian approach to inference that utilizes a flat prior on the autoregressive coefficient. DeJong and Whiteman adopt a related Bayesian approach in a group of papers (1989a,b,c) that seek to reevaluate the empirical evidence from historical economic time series. Their results appear to be conclusive in turning around the earlier, influential conclusions of Nelson and Plosser (1982) that most aggregate economic time series have stochastic trends. So far, these criticisms of unit root econometrics have gone unanswered; the assertions about the impropriety of classical methods and the superiority of flat prior Bayesian methods have been unchallenged; and the empirical reevaluation of evidence in support of stochastic trends has been left without comment. This paper breaks that silence and offers a new perspective. We challenge the methods, the assertions and the conclusions of these articles on the Bayesian analysis of unit roots. Our approach is also Bayesian but we employ objective ignorance priors not flat priors in our analysis. Ignorance priors represent a state of ignorance about the value of a parameter and in many models are very different from flat priors. We demonstrate that in time series models flat priors do not represent ignorance but are actually informative (sic) precisely because they neglect generically available information about how autoregressive coefficients influence observed time series characteristics. Contrary to their apparent intent, flat priors unwittingly bias inferences toward stationary and iid alternatives where they do represent ignorance, as in the linear regression model. This bias helps to explain the outcome of the simulation experiments in Sims and Uhlig and the empirical results of DeJong and Whiteman. Under flat priors and ignorance priors this paper derives posterior distributions for the parameters in autoregressive models with a deterministic trend and an arbitrary number of lags. Marginal posterior distributions are obtained by using the Laplace approximation for multivariate integrals along the lines suggested by the author (1983) in some earlier work. The bias from the use of flat priors is shown in our simulations to be substantial; and we conclude that it is unacceptably large in models with a fitted deterministic trend, for which the expected posterior probability of a stochastic trend is found to be negligible even though the true data generating mechanism has a unit root. Under ignorance priors, Bayesian inference is shown to accord more closely with the results of classical methods. An interesting outcome of our simulations and our empirical work is the bimodal Bayesian posterior, which demonstrates that Bayesian confidence sets can be disjoint, just like classical confidence intervals that are based on asymptotic theory. The paper concludes with an empirical application of our Bayesian methodology to the Nelson- Plosser series. Seven of the fourteen series show evidence of stochastic trends under ignorance priors, whereas under flat priors on the coefficients all but three of the series appear trend stationary. The latter result corresponds closely with the conclusion reached by DeJong and Whiteman (1989b) (based on truncated flat priors) that all but two of the Nelson-Plosser series are trend stationary. We argue that the DeJong-Whiteman inferences are biased toward trend stationarity through the use of flat priors and that their inferences are fragile (i.e., not robust) not only to the prior but also to the lag length chosen in the time series specification. Keywords: Bayesian analysis, bimodal posterior density, disjoint confidence set, flat prior, fragile inference, hypergeometric function, ignorance prior, Laplace approximation, asymmetric posterior density Note: CFP 798. Length: 44 pages Creation-Date: 199007 Number: 950 Publication-Status: Published in Journal of Applied Econometrics (1991), 6: 333-364 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0798.pdf File-Format: application/pdf File-Size: 1940 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09b/d0950.pdf File-Format: application/pdf File-Size: 1120 kb Handle: RePEc:cwl:cwldpp:950 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Shortcut to LAD Estimator Asymptotics Abstract: Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator and the results of some earlier simulation studies are examined. Keywords: Autoregression, delta sequence, density estimate, domain of attraction, generalized function, generalized Taylor series, LAD estimator, stable process Note: CFP 801. Length: 20 pages Creation-Date: 199007 Number: 949 Publication-Status: Published in Econometric Theory (1991), 7: 450-463 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0801.pdf File-Format: application/pdf File-Size: 553 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0949.pdf File-Format: application/pdf File-Size: 530 kb Handle: RePEc:cwl:cwldpp:949 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Operational Algebra and Regression t-Tests Abstract: Data reduction involves a physical transition from sample data to econometric estimator and test statistic. This transition induces a mapping on the probability law of the sample, whose image is the distribution of the statistic of interest. At a general level, the mapping can often be captured by means of an operational algebra. Some methods than employ nonlinear functions of differential operators are suggested which can perform this task. The methods are related to pseudodifferential operator techniques that are used in abstract mathematics to solve systems of partial differential equations. They also generalize the fractional calculus methods developed by the author in earlier work (1984, 1985). Two examples are studied in detail. One of these deals with the feasible generalized least squares estimator and its regression t-statistic in the linear model with a non scalar error covariance matrix whose elements are functions of a finite dimensional vector of nuisance parameters. This includes a wide class of models such as general SUR systems and models with serially dependent or heterogeneous errors. Keywords: Asymptotic expansions, Fisher's series, Fourier integral operators, fractional operators, functions of operations, pseudodifferential operators, regression t-statistics Note: CFP 830. Length: 18 pages Creation-Date: 199007 Number: 948 Publication-Status: Published in Peter C.B. Phillips, ed., Models, Methods, and Applications of Econometrics, 1993, pp. 140-151 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0830.pdf File-Format: application/pdf File-Size: 566 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0948.pdf File-Format: application/pdf File-Size: 477 kb Handle: RePEc:cwl:cwldpp:948 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Mico Loretan Author-X-Name-First: Mico Author-X-Name-Last: Loretan Title: Testing Covariance Stationarity Under Moment Condition Failure with an Application to Common Stock Returns Abstract: This paper studies tests for covariance stationarity under conditions which permit failure in the existence of fourth order moments. The problem is important because many econometric diagnostics such as tests for parameter constancy, constant variance and ARCH and GARCH effects routinely rely on fourth moment conditions. Moreover, such tests have recently been extensively employed with financial and commodity market data, where fourth moment conditions may well be quite tenuous and are usually untested. This paper considers several tests for covariance stationarity including sample split prediction tests, cusum of squares tests and modified scaled range tests. When fourth moment conditions fail we show how the asymptotic theory for these tests involves functionals of an asymmetric stable Levy process, in place of conventional standard normal or Brownian bridge asymptotics. An interesting outcome of the new asymptotics is that the power of these tests depends critically on the tail thickness in the data. Thus, for data with no finite second moment, the above mentioned tests are inconsistent. Some new tests for heterogeneity are suggested that are consistent in the infinite variance case. These are easily implemented and rely on standard normal asymptotics. A consistent estimator of the maximal moment exponent of a distribution is also proposed. Again this estimator is easily implemented, has standard normal asymptotics and leads to a simple test for the existence of moments up to a given order. An empirical application of these methods to the monthly stock return data recently studied in Pagan and Schwert (1989a, 1989b) and the daily returns of the Standard and Poors 500 stock index is presented. Keywords: Asymmetric stable process, characteristic exponent, covariance stationarity, cusum of squares test, maximal moment exponent, sample split prediction test, scaled range, stable Levy bridge, stock returns Note: CFP 866. Length: 77 pages Creation-Date: 199007 Number: 947 Publication-Status: Published in Journal of Empirical Finance (1994), 1: 211-248 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0866.pdf File-Format: application/pdf File-Size: 1551 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0947.pdf File-Format: application/pdf File-Size: 1734 kb Handle: RePEc:cwl:cwldpp:947 Template-type: ReDIF-Paper 1.0 Author-Name: Herbert E. Scarf Author-X-Name-First: Herbert E. Author-X-Name-Last: Scarf Author-Email: herbert.scarf@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/scarf.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Laszlo Lovasz Author-X-Name-First: Laszlo Author-X-Name-Last: Lovasz Author-Workplace-Name: Eotvos Lorand University, Budapest Title: The Generalized Basis Reduction Algorithm Abstract: Let F(x) be a convex function defined in R^{n}), which is symmetric about the origin and homogeneous of degree 1, and let L be the lattice of integers Z^{n}. A definition of a reduced basis, b^{1},...,b^{n}, of the lattice with respect to the distance function F is presented, and we describe an algorithm which yields a reduced basis in polynomial time, for fixed n. In the special case in which the bodies {x : F(x) <= t} are ellipsoids, the definition of a reduced basis is identical with that given by Lenstra, Lenstra and Lovasz (1982) and the algorithm is the well known basis reduction algorithm. We show that the basis vector b^{1}, in a reduced basis, is an approximation to a shortest non-zero lattice point with respect to F and relate the basis vectors b^{i} to Minkowski's successive minima. The results lead to an algorithm for integer programming which executes in polynomial time for fixed n, but which avoids the ellipsoidal approximation required by Lenstra's algorithm. We also discuss the properties of a Korkine-Zolotarev basis for the lattice. Classification-JEL: 213 Keywords: Reduced basis, lattice point, integer programming Note: CFP 818. Length: 22 pages Creation-Date: 199006 Number: 946 Publication-Status: Published in Mathematics of Operations Research (August 1992), 17(3): 751-764 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0818.pdf File-Format: application/pdf File-Size: 652 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0946.pdf File-Format: application/pdf File-Size: 399 kb Handle: RePEc:cwl:cwldpp:946 Template-type: ReDIF-Paper 1.0 Author-Name: Herbert E. Scarf Author-X-Name-First: Herbert E. Author-X-Name-Last: Scarf Author-Email: herbert.scarf@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/scarf.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Shallcross, David F. Author-Workplace-Name: Thomas J. Watson Research Center, IBM Title: The Frobenius Problem and Maximal Lattice Free Bodies Abstract: Let p = (p_{1},...,p_{n}) be a vector of positive integers whose greatest common divisor is unity. The Frobenius problem is to find the largest integer f* which cannot be written as a non-negative integral combination of the p_{i}.In this note we relate the Frobenius problem to the topic of maximal lattice free bodies and describe an algorithm for n = 3. Classification-JEL: 213 Keywords: Algorithm, Frobenius problem Note: CFP 892. Length: 12 pages Creation-Date: 199006 Number: 945 Publication-Status: Published in Mathematics of Operation Research (August 1993), 18(3): 511-515 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0892.pdf File-Format: application/pdf File-Size: 287 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0945.pdf File-Format: application/pdf File-Size: 228 kb Handle: RePEc:cwl:cwldpp:945 Template-type: ReDIF-Paper 1.0 Author-Name: Eric Zivot Author-X-Name-First: Eric Author-X-Name-Last: Zivot Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis Abstract: Recently Perron (1989) has carried out tests of the unit root hypothesis against the alternative hypothesis of trend stationarity with a break in the trend occurring at the Great Crash of 1929 or at the 1973 oil price shock. His analysis covers the Nelson-Plosser macroeconomic data series as well as a post-war quarter real GNP series. His tests reject the unit root null hypothesis for most of the series. This paper takes issue with the assumption used by Perron that the Great Crash and the oil price shock can be treated as exogenous events. A variation of Perron's test is considered in which the break point is estimated rather than fixed. We argue this test is more appropriate than Perron's, since it circumvents the problem of data-mining. The asymptotic distribution of the "estimated break point" test statistic is determined. The data series considered by Perron are reanalyzed using this test statistic. The empirical results make use of the asymptotics developed for the test statistic as well as extensive finite sample corrections obtained by simulation. The effect on the empirical results of fat-tailed and temporally dependent innovations is investigated. In brief, by treating the break point as endogenous, we find that there is less evidence against the unit root hypothesis than Perron finds for many of the data series, but stronger evidence against it for several of the series, including the Nelson-Plosser industrial production, nominal GNP, and real GNP series. Classification-JEL: 210, 211, 212, 220 Keywords: Asymptotic distribution, break point, Gaussian process, macroeconomic time series, structural change, test statistic, time trend, trend stationary, unit root hypothesis, weak convergence Note: CFP 811. Length: 52 pages Creation-Date: 199005 Number: 944 Publication-Status: Published in Journal of Business and Economic Statistics (July 1992), 10(3): 251-270 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0811.pdf File-Format: application/pdf File-Size: 1810 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0944.pdf File-Format: application/pdf File-Size: 1353 kb Handle: RePEc:cwl:cwldpp:944 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Tests for Parameter Instability and Structural Change with Unknown Change Point Abstract: This paper considers tests of parameter instability and structural change with unknown change point. The results apply to a wide class of parametric models including models that satisfy maximum likelihood type regularity conditions and models that are suitable for estimation by generalized method of moments procedures. The paper considers likelihood ratio and likelihood ratio like tests, as well as asymptotically equivalent Wald and Lagrange multiplier tests. Each test implicitly uses an estimate of change point. Tests of both "pure" and "partial" structural change are discussed. Keywords: Asymptotic theory, parametric models, multiplier tests, structural change Note: CFP 845. Length: 78 pages Creation-Date: 199004 Number: 943 Publication-Status: Published in Econometrica (July 1993), 61(4): 821-856 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0845.pdf File-Format: application/pdf File-Size: 1754 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0943.pdf File-Format: application/pdf File-Size: 1945 kb Handle: RePEc:cwl:cwldpp:943 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Christopher J. Monahan Author-X-Name-First: Christopher J. Author-X-Name-Last: Monahan Title: An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator Abstract: This paper considers a new class of heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators. The estimators considered are prewhitened kernel estimators with vector autoregressions employed in the prewhitening stage. The paper establishes consistency, rate of convergence, and asymptotic truncated mean squared error (MSE) results for the estimators when a fixed or automatic bandwidth procedure is employed. Conditions are obtained under which prewhitening improves asymptotic truncated MSE. Monte Carlo results show that prewhitening is very effective in reducing bias, improving confidence interval coverage probabilities, and rescuing over-rejection of t-statistics constructed using kernel-HAC estimators. On the other hand, prewhitening is found to inflate variance and MSE of the kernel estimators. Since confidence interval coverage probabilities and over-rejection of t-statistics are usually of primary concern, prewhitened kernel estimators provide a significant improvement over the standard non-prewhitened kernel estimators. Keywords: Asymptotic theory, covariance matrix, heteroskedasticity, kernel estimator, nonparametric estimator, vector autoregression Note: CFP 814. Length: 35 pages Creation-Date: 199003 Number: 942 Publication-Status: Published in Econometrica (July 1992), 60(4): 953-966 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0814.pdf File-Format: application/pdf File-Size: 690 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0942.pdf File-Format: application/pdf File-Size: 875 kb Handle: RePEc:cwl:cwldpp:942 Template-type: ReDIF-Paper 1.0 Author-Name: Salvador Barbera Author-X-Name-First: Salvador Author-X-Name-Last: Barbera Author-Workplace-Name: Universitat Autonoma de Barcelona Author-Name: Hugo Sonnenschein Author-X-Name-First: Hugo Author-X-Name-Last: Sonnenschein Author-Workplace-Name: University of Pennsylvania Author-Name: Lin Zhou Author-X-Name-First: Lin Author-X-Name-Last: Zhou Title: Voting by Committees Abstract: Problems of social choice frequently take the following form. There are n voters and a set K = (1,2,...,k) of objects. The voters must choose a subset of K. We define a class of voting schemes called voting by committees. The main result of the paper is a characterization of voting by committees, which is the class of all voting schemes that satisfy voter sovereignty and non-manipulability on the domain of separable preferences. This result is analogous to the literature on the Groves and Clarke scheme in that it characterizes all of the non-manipulable voting schemes on an important domain. Classification-JEL: 025 Keywords: Social choice, voting, committees Note: CFP 783. Length: 19 pages Creation-Date: 199005 Number: 941 Publication-Status: Published in Econometrica (May 1991), 59(3): 595-609 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0783.pdf File-Format: application/pdf File-Size: 791 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0941.pdf File-Format: application/pdf File-Size: 589 kb Handle: RePEc:cwl:cwldpp:941 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Generic Uniform Convergence Abstract: This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for establishing asymptotic properties of estimators and test statistics. The results given here have the following attributes, (1) they extend results of Newey to cover convergence almost surely as well as convergence in probability, (2) they apply to totally bounded parameter spaces (rather than just to compact parameter spaces), (3) they introduce a set of conditions for a generic uniform law of large numbers that has the attribute of giving the weakest conditions available for iid contexts, but which apply in dependent non-identically distributed contexts as well, and (4) they incorporate and extend the main results in the literature in a parsimonious fashion. Keywords: Consistency, law of large numbers, uniform convergence, asymptotic theory, test statistics, estimators Note: CFP 810. Length: 21 pages Creation-Date: 199003 Number: 940 Publication-Status: Published in Econometric Theory (1992), 8: 241-257 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0810.pdf File-Format: application/pdf File-Size: 708 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0940.pdf File-Format: application/pdf File-Size: 575 kb Handle: RePEc:cwl:cwldpp:940 Template-type: ReDIF-Paper 1.0 Author-Name: Vittorio Grilli Author-X-Name-First: Vittorio Author-X-Name-Last: Grilli Author-Workplace-Name: Yale University Author-Name: Nouriel Roubini Author-X-Name-First: Nouriel Author-X-Name-Last: Roubini Author-Workplace-Name: NBER Title: Financial Integration, Liquidity and Exchange Rates Abstract: We present a two-country extension of Lucas' (1988) work on how cash-in-advance constraints in asset markets affect the pricing of financial assets. In the model, there is some degree of separation between the goods markets and the assets markets, and money is used for transactions in both markets. The main results of the paper are the following. First, the equilibrium level of the exchange rate depends on the share of money used for asset transactions; a greater share corresponds to a more appreciated currency. Second, under uncertainty the liquidity effects deriving from stochastic shocks to bond creation lead to an "excess" volatility of nominal exchange rates, even when the "fundamental" value of the exchange rate is constant. Third, capital controls in the form of taxes on foreign asset acquisitions tend to appreciate the exchange rate. Fourth, the maturity structure of the public debt affects the equilibrium exchange rate. In particular, a move towards a longer maturity structure will tend to depreciate the exchange rate. Classification-JEL: 431, 441, 443, 411 Keywords: Asset prices, exchange rates, financial integration, asset markets, capital controls Length: 34 pages Creation-Date: 199003 Number: 939 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0939.pdf File-Format: application/pdf File-Size: 1223 kb Handle: RePEc:cwl:cwldpp:939 Template-type: ReDIF-Paper 1.0 Author-Name: Andrew Caplin Author-X-Name-First: Andrew Author-X-Name-Last: Caplin Author-Workplace-Name: Columbia University Author-Name: Barry Nalebuff Author-X-Name-First: Barry Author-X-Name-Last: Nalebuff Author-Workplace-Name: Yale School of Management Title: Aggregation and Social Choice: A Mean Voter Theorem Abstract: A celebrated result of Black (1984a) demonstrates the existence of a simple majority winner when preferences are single-peaked. The social choice follows the preferences of the median voter's most preferred outcome beats any alternative. However, this conclusion does not extend to elections in which candidates differ in more than one dimension. This paper provides a multi-dimensional analog of the median voter result. We show that the mean voter's most preferred outcome is unbeatable according to a 64%-majority rule. The weaker conditions supporting this result represent a significant generalization of Caplin and Nalebuff (1988). The proof of our mean voter result uses a mathematical aggregation theorem due to Prekopa (1971, 1973) and Borell (1975). This theorem has broad applications in economics. An application to the distribution of income is described at the end of this paper; results on imperfect competition are presented in the companion paper [CFDP 937]. Classification-JEL: 025, 022 Keywords: Median voter, voting, social choice, elections Length: 26 pages Creation-Date: 199002 Number: 938 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0938.pdf File-Format: application/pdf File-Size: 1270 kb Handle: RePEc:cwl:cwldpp:938 Template-type: ReDIF-Paper 1.0 Author-Name: Andrew Caplin Author-X-Name-First: Andrew Author-X-Name-Last: Caplin Author-Workplace-Name: Columbia University Author-Name: Barry Nalebuff Author-X-Name-First: Barry Author-X-Name-Last: Nalebuff Author-Workplace-Name: Yale School of Management Title: Aggregation and Imperfect Competition: On the Existence of Equilibrium Abstract: We present a new approach to the theory of imperfect competition and apply it to study price competition among differentiated products. The central result provides general conditions under which there exists a pure strategy price equilibrium for any number of firms producing any set of products. This includes products with multi-dimensional attributes. In addition to the proof of existence, we provide conditions for uniqueness. Our analysis covers location models, the characteristic approach, and probabilistic choice together in a unified framework. To prove existence, we employ aggregation theorems due to Prekopa (1971) and Borell (1975). Our companion paper [CFDP 938] introduces these theorems and develops the application to super-majority voting rules. Classification-JEL: 611, 022, 511 Keywords: Imperfect competition, Bertrand equilibrium, differentiated products, prices, price competition Length: 37 pages Creation-Date: 199002 Number: 937 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0937.pdf File-Format: application/pdf File-Size: 1918 kb Handle: RePEc:cwl:cwldpp:937 Template-type: ReDIF-Paper 1.0 Author-Name: Imre Barany Author-X-Name-First: Imre Author-X-Name-Last: Barany Author-Workplace-Name: Dept. of Operations Research & Yale University Author-Name: D.G. Larman Author-X-Name-First: D.G. Author-X-Name-Last: Larman Author-Workplace-Name: University College London Title: A Colored Version of Tverberg's Theorem Abstract: The main result of this paper is that given n red, n white, and n green points in the plane, it is possible to form n vertex-disjoint triangles Delta_{1},...,Delta_{n} in such a way that the Delta_{i} has one red, one white, and one green vertex for every i = 1,...,n and the intersection of these triangles is nonempty. Classification-JEL: 213 Keywords: Geometry Length: 13 pages Creation-Date: 199002 Number: 936 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0936.pdf File-Format: application/pdf File-Size: 425 kb Handle: RePEc:cwl:cwldpp:936 Template-type: ReDIF-Paper 1.0 Author-Name: Vassilis A. Hajivassiliou Author-X-Name-First: Vassilis A. Author-X-Name-Last: Hajivassiliou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Testing Game Theoretic Models of Price-Fixing Behaviour Abstract: This paper analyzes price fixing by the Joint Executive Committee railroad cartel from 1880 to 1886 and develops tests of two game-theoretic models of tacit collusion. The first model, due to Abreu, Pearce and Stacchetti (1986), predicts that price will switch across regimes according to a Markov process. The second, by Rotemberg and Saloner (1986), postulates that price wars are more likely in periods of high industry demand. Switching regressions are used to model the firms' shifting between collusive and punishment behavior. The main econometric novelty in the estimation procedures introduced in this paper is that misclassification probabilities are allowed to vary endogenously over time. The JEC data set is expanded to include measures of grain production to be shipped and availability of substitute transportation services. Our findings cast doubt on the applicability of the Rotemberg and Saloner model to the JEC railroad cartel, while they confirm the Markovian prediction of the Abreu, et al. Model. Classification-JEL: 026, 022, 611, 615 Keywords: Tact collusion, cartels, price competition, railroads, transportation Length: 36 pages Creation-Date: 199001 Number: 935 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0935.pdf File-Format: application/pdf File-Size: 1422 kb Handle: RePEc:cwl:cwldpp:935 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Growth and Distribution: A Neoclassical Kaldor-Robinson Exercise Abstract: Kaldor's capital/labor income distribution theory relied on differential saving propensities from profits and wages. Robinson's growth models typically specified constant-coefficient technologies in which marginal productivities cannot determine distribution. Here these two insights are combined in a two-sector (capital goods, consumption goods) economy. Two technologies are available, but only as either-or alternatives. The choice of technology and the income distribution depend on the saving propensities. Steady-state consumption need not be greater when the economy is more capitalized and profit rates are lower. Classification-JEL: 111, 023 Keywords: Growth mode, technology, income distribution Note: CFP 730. Length: 19 pages Creation-Date: 199001 Number: 934 Publication-Status: Published in Cambridge Journal of Economics (1989), 13: 37-45 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0730.pdf File-Format: application/pdf File-Size: 482 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0934.pdf File-Format: application/pdf File-Size: 476 kb Handle: RePEc:cwl:cwldpp:934 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Peter Schmidt Author-X-Name-First: Peter Author-X-Name-Last: Schmidt Author-Workplace-Name: Michigan State University Title: Testing for a Unit Root in the Presence of Deterministic Trends Abstract: This paper provides a new unit root test based on an alternative parameterization which has previously been considered by Bhargava (1986). This parameterization allows for trend under both the null and the alternative, without introducing any parameters that are irrelevant under either. This is not so in the Dickey-Fuller parameterizations. The new test is extracted from the score or LM principle under the assumption that the errors are iid N(0, sigma squared (epsilon)), but our asymptotics hold under more general assumptions about the errors. Two forms of the test (a coefficient test and at t-test) are derived. Keywords: Unit root, time series, random walk, co-integration Note: CFP 820. Length: 37 pages Creation-Date: 198910 Number: 933 Publication-Status: Published in Oxford Bulletin of Economics and Statistics (1992), 54(3): 257-287 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0820.pdf File-Format: application/pdf File-Size: 1231 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0933.pdf File-Format: application/pdf File-Size: 703 kb Handle: RePEc:cwl:cwldpp:933 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Victor Solo Author-X-Name-First: Victor Author-X-Name-Last: Solo Author-Workplace-Name: Johns Hopkins University Title: Asymptotics for Linear Processes Abstract: A method of deriving asymptotics for linear processes is introduced which uses an explicit algebraic decomposition of the linear filter. The method leads to substantial simplifications in the asymptotics and offers a unified approach to strong laws and central limit theory for linear processes. Sample means and sample covariances are covered. The results also accommodate both homogeneous and heterogeneous innovations as well as innovations with undefined means and variances. Keywords: Central limit theory, asymptotic theory, linear processes Note: CFP 815. Length: 48 pages Creation-Date: 198910 Number: 932 Publication-Status: Published in Annals of Statistics (1992), 20(2): 971-1001 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0815.pdf File-Format: application/pdf File-Size: 1024 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0932.pdf File-Format: application/pdf File-Size: 750 kb Handle: RePEc:cwl:cwldpp:932 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: On the Theory of Macroeconomic Policy Abstract: Jan Tinbergen was and is of course a scientist, full of curiosity about how the world works. But his motivation has always been more than curiosity. He wants to know how the world works so that he can make it work better. Knowledge is the foundation of policy. It was natural for Tinbergen to set forth a formal theory of policy nearly fifty years ago and it was equally natural from him to relate the theory to practical problems of policy in the Netherlands and else where and to implement it and illustrate it with the help of theoretical and econometric models. Thus Tinbergen was the originator of the subject on which I propose to speak to you today. Classification-JEL: 023, 031, 113, 025 Keywords: Public policy, social welfare, macroeconomic policy Note: CFP 745. Length: 18 pages Creation-Date: 198912 Number: 931 Publication-Status: Published in De Economist (1990), 138(1): 1-14 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0745.pdf File-Format: application/pdf File-Size: 813 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0931.pdf File-Format: application/pdf File-Size: 590 kb Handle: RePEc:cwl:cwldpp:931 Template-type: ReDIF-Paper 1.0 Author-Name: Herbert E. Scarf Author-X-Name-First: Herbert E. Author-X-Name-Last: Scarf Author-Email: herbert.scarf@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/scarf.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Mathematical Programming and Economic Theory Abstract: The paper discusses the analogy between economic institutions and algorithms for the solution of mathematical programming problems. The simplex method for solving linear programs can be interpreted as a search for market prices that equilibrate the demand for factors of production with their supply. An interpretation in terms of the internal organization of the large firm is offered for Lenstra's integer programming algorithm. Classification-JEL: 213, 021 Keywords: Integer programming, prices, factors of production, algorithms Note: CFP 763. Length: 26 pages Creation-Date: 198911 Number: 930 Publication-Status: Published in Operations Research (May-June 1990), 38(3): 377-385 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0763.pdf File-Format: application/pdf File-Size: 788 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0930.pdf File-Format: application/pdf File-Size: 521 kb Handle: RePEc:cwl:cwldpp:930 Template-type: ReDIF-Paper 1.0 Author-Name: In Choi Author-X-Name-First: In Author-X-Name-Last: Choi Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Asymptotic and Finite Sample Distribution Theory for IV Estimators and Tests in Partially Identified Structural Equations Abstract: General formula for the finite sample and asymptotic distributions of the instrumental variable estimators and the Wald statistics in a simultaneous equation model are derived. It is assumed that the coefficient vectors of both endogenous and exogenous variables are only partially identified, even though the order condition for identification is satisfied. This work extends previous results in Phillips (1989) where the coefficient vector of the exogenous variables is partially identified and that of the endogenous variables is totally unidentified. The effect of partial identification on the finite sample and asymptotic distributions of the estimators and the Wald statistics is analyzed by isolating identifiable parts of the coefficient vectors using a rotation of the coordinate system developed in Phillips (1989). The pdf's of the estimators and the Wald statistics are illustrated using simulation and compared with their respective asymptotic distributions. Keywords: Instrumental variable estimator, Wald statistics, finite sample theory, simultaneous equation model Note: CFP 806. Length: 57 pages Creation-Date: 198910 Number: 929 Publication-Status: Published in Journal of Econometrics (1992), 51: 113-150 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0806.pdf File-Format: application/pdf File-Size: 1006 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0929.pdf File-Format: application/pdf File-Size: 881 kb Handle: RePEc:cwl:cwldpp:929 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Mico Loretan Author-X-Name-First: Mico Author-X-Name-Last: Loretan Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Estimating Long Run Economic Equilibria Abstract: Our subject is econometric estimation and inference concerning long-run economic equilibria in models with stochastic trends. Our interest is focused on single equation specifications such as those employed in the Error Correction Model (ECM) methodology of David Hendry (1987, 1989 inter alia) and the semiparametric modified least squares method of Phillips and Hansen (1989). We start by reviewing the prescriptions for empirical time series research that are presently available. We argue that the diversity of choices is confusing to practitioners and obscures the fact that statistical theory is clear about optimal inference procedures. Part of the difficulty arises from the many alternative time series representations of cointegrated systems. We present a detailed analysis of these various representations, the links between them, and the estimator choices to which they lead. An asymptotic theory is provided for a wide menu of econometric estimators and system specifications, accommodating different levels of prior information about the presence of unit roots and the nature of short-run dynamic adjustments. The single equation ECM approach is studied in detail and our results lead to certain recommendations. Weak exogeneity and data coherence are generally insufficient for valid conditioning on the regressors in this approach. Strong exogeneity and data coherency are sufficient to validate conditioning. But the requirement of strong exogeneity rules out most cases of interest because long-run economic equilibrium typically relates interdependent variables for which there is substantial time series feedback. One antidote for this problem in practice is the inclusion of leads as well as lags in the differences of the regressors. The simulations that we report, as well as the asymptotic theory support the use of this procedure in practice. Our results also support the use of dynamic specifications that involve lagged long-run equilibrium relations rather than lagged differences in the dependent variable. Finally, our simulations point to problems of overfitting in single equation ECM's. These appear to have important implications for empirical research in terms of size distortions that are produced in significance tests that utilize nominal critical values delivered by conventional asymptotic theory. In sum, our results indicate that the single equation ECM methodology has good potential for further development and improvement. But in comparison with the semi parametric modified least squares method of Phillips and Hansen (1989) the latter method seems superior for inferential purposes in most cases. Keywords: Co-integration, long-run equilibrium, error correction, semiparametric estimation, asymptotic theory, exogeneity Note: CFP 785. Length: 58 pages Creation-Date: 198910 Number: 928 Publication-Status: Published in Review of Economic Studies (1991), 58: 407-436 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0785.pdf File-Format: application/pdf File-Size: 1658 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0928.pdf File-Format: application/pdf File-Size: 1366 kb Handle: RePEc:cwl:cwldpp:928 Template-type: ReDIF-Paper 1.0 Author-Name: William D. Nordhaus Author-X-Name-First: William D. Author-X-Name-Last: Nordhaus Author-Email: william.nordhaus@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/nordhaus.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Alternative Approaches to the Political Business Cycle Abstract: This paper reviews the theory and evidence concerning Political Business Cycles (PBC), which are based on the obvious facts of democratic life that voters care about the economy while politicians care about power. The first section provides an overview of different approaches to political cycles, describing five models that have been used in different contexts. The next two sections review major theoretical issues, with attention to the "microfoundations" of politico-economic systems, an exploration of the implications of ideological parties for political equilibria, and a formal analysis of a number of different PBC models. The empirical sections begin with an analysis of two important empirical questions in PCB models: whether voters are ultrarational and whether parties are ideological or opportunistic. The final section then examines historical and econometric evidence to determine the importance of political cycles in macroeconomic activity. Classification-JEL: 025, 133, 321 Keywords: Business cycle, public choice, politics, political cycles, social choice Note: CFP 748. Length: 83 pages Creation-Date: 198910 Number: 927 Publication-Status: Published in Brookings Papers on Economic Activity (1989), 2: 1-68 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0748.pdf File-Format: application/pdf File-Size: 3010 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0927.pdf File-Format: application/pdf File-Size: 1989 kb Handle: RePEc:cwl:cwldpp:927 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Yoon-Jae Whang Author-X-Name-First: Yoon-Jae Author-X-Name-Last: Whang Title: Additive Interactive Regression Models: Circumvention of the Curse of Dimensionality Abstract: This paper considers series estimators of additive interactive regression (AIR) models. AIR models are nonparametric regression models that generalize additive regression models by allowing interactions between different regressor variables. They place more restrictions on the regression function, however, than do fully nonparametric regression models. By doing so, they attempt to circumvent the curse of dimensionality that afflicts the estimation of fully nonparametric regression models. In this paper, we present a finite sample bound and asymptotic rate of convergence results for the mean average squared error of series estimators that show the AIR models do circumvent the curse of dimensionality. The rate of convergency of these estimators is shown to depend on the order of the AIR model and the smoothness of the regression function, but not on the dimension of the regressor vector. Series estimators with fixed and data-dependent truncation parameters are considered. Keywords: Additive interactive regression model, cross-validation, curse of dimensionality, generalized cross-validation, mean average squared error, nonparametric estimation, nonparametric regression, series estimator Note: CFP 771. Length: 20 pages Creation-Date: 198909 Number: 925 Publication-Status: Published in Econometric Theory (1990), 6: 455-479 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0771.pdf File-Format: application/pdf File-Size: 643 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0925.pdf File-Format: application/pdf File-Size: 494 kb Handle: RePEc:cwl:cwldpp:925 Template-type: ReDIF-Paper 1.0 Author-Name: William D. Nordhaus Author-X-Name-First: William D. Author-X-Name-Last: Nordhaus Author-Email: william.nordhaus@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/nordhaus.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Risk Analysis in Economics: An Application to University Finances Abstract: Although the theory of decision making under uncertainty has been extensively studied for a half century, applications to business applications are relatively rare. This study frames a systematic risk analysis and applies the technique to the finances of private colleges and universities. It begins by constructing budgets for colleges and universities and then analyzes the major economic factors affecting those budgets. It estimates the variability (or unpredictability) associated with each major external variable from historical data and from economic forecasts. The study finds that government-spending risks outweigh all other external stock market, interest rates, inflation, and wage trends. The paper concludes by suggesting that institutions consider the implications of exogenous uncertainties other than financial markets on their economic health. It considers the development of general "spending rules" (which would be extensions of conventional "endowment spending rules") to take into account all exogenous uncertainties. Classification-JEL: 912 Keywords: Education, risk analysis, uncertainty Length: 47 pages Creation-Date: 198909 Number: 924 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0924.pdf File-Format: application/pdf File-Size: 1794 kb Handle: RePEc:cwl:cwldpp:924 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Inflationary Expectations and Price Setting Behavior Abstract: This paper tests for the existence of expectational effects in very disaggregate price equations. Price equations are estimated using monthly data for each of 40 products. The dynamic specification of the equations is also tested, including whether the equations should be specified in level form or in change form. Two expectational hypotheses are used, one in which expectations of the aggregate price level and one in which expectations are rational. Under the first hypothesis the lag length is estimated along with the other parameters, and under the second hypothesis the lead length is estimated along with the other parameters. The results strongly support the hypothesis that aggregate price expectations affect individual pricing decisions. The results do not discriminate very well between the level and change forms of the price equation, although there is a slight edge for the level form. The lag and lead lengths are not estimated precisely, but in most cases the lag length is less than 30 months and the lead length is less than 5 months. Classification-JEL: 134, 227, 133 Keywords: Inflation, expectations, price equations, price level Note: CFP 849. Length: 21 pages Creation-Date: 198909 Number: 923 Publication-Status: Published in Review of Economics and Statistics (1993), 75(1): 8-18 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0849.pdf File-Format: application/pdf File-Size: 847 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0923.pdf File-Format: application/pdf File-Size: 716 kb Handle: RePEc:cwl:cwldpp:923 Template-type: ReDIF-Paper 1.0 Author-Name: Nancy A. Lutz Author-X-Name-First: Nancy A. Author-X-Name-Last: Lutz Author-Workplace-Name: Dept. of Economics, Yale University Author-Workplace-Homepage: http://www.econ.yale.edu/ Author-Name: Philip H. Dybvig Author-X-Name-First: Philip H. Author-X-Name-Last: Dybvig Author-Workplace-Name: Washington University at St. Louis Title: Warranties, Durability, and Maintenance: Two Sided Moral Hazard in a Continuous-Time Model Abstract: We consider the provision of an optimal warranty in a continuous-time model with two-sided moral hazard. The optimal warranty must balance the producer's durability incentive and the buyer's maintenance incentive. Too little warranty protection gives the producer too much incentive to produce low durability, while too much warranty protection gives the consumer too much incentive to neglect maintenance. The derived optimal warranty is a "block warranty" that is high for an initial block of time and zero thereafter. The first-best would be available under a very high warranty for a very short time interval, except for the incentive this would create for the consumer to abuse the product to collect the warranty. Classification-JEL: 611, 514, 026, 022 Keywords: Warranties, moral hazard, incentives, product quality Length: 18 pages Creation-Date: 198908 Number: 922 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0922.pdf File-Format: application/pdf File-Size: 952 kb Handle: RePEc:cwl:cwldpp:922 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: John B. Taylor Author-X-Name-First: John B. Author-X-Name-Last: Taylor Author-Workplace-Name: Council of Economic Advisors Title: Full Information Estimation and Stochastic Simulation of Models with Rational Expectations Abstract: A computationally feasible method for the full information maximum likelihood estimation of models with rational expectations is described in this paper. The stochastic simulation of such models is also described. The methods discussed in this paper should open the way for many more tests of the rational expectations hypothesis within macroeconomic models. Keywords: Stochastic simulation, rational expectations, maximum likelihood, macroeconomic model Note: CFP 764. Length: 22 pages Creation-Date: 198908 Number: 921 Publication-Status: Published in Journal of Applied Econometrics (1990), 5: 381-392 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0764.pdf File-Format: application/pdf File-Size: 733 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0921.pdf File-Format: application/pdf File-Size: 532 kb Handle: RePEc:cwl:cwldpp:921 Template-type: ReDIF-Paper 1.0 Author-Name: David G. Pearce Author-X-Name-First: David G. Author-X-Name-Last: Pearce Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Dilip Abreu Author-X-Name-First: Dilip Author-X-Name-Last: Abreu Author-Workplace-Name: Princeton University Author-Name: Ennio Stacchetti Author-X-Name-First: Ennio Author-X-Name-Last: Stacchetti Author-Workplace-Name: Stanford University Title: Renegotiation and Symmetry in Repeated Games Abstract: It seems reasonable to suppose that in repeated games in which communications is possible, play is determined through a process of negotiation and renegotiation as events unfold. In the absence of a satisfying theory of players' bargaining power, it is unclear how to model this process. Symmetric repeated games are an important class in which the problem is less troublesome. Whatever its source, bargaining power is presumably the same for all players in a symmetric game. We take equal bargaining power to mean that a player can mount a credible objection to a continuation equilibrium in which he receives a particular expected present discounted value, if there are other self enforcing agreements that never give any player such a low continuation value after any history. This is formalized in a solution concept called consistent bargaining equilibrium. Classification-JEL: 026 Keywords: Repeated games, negotiation, bargaining theory, symmetric game, monitoring Note: CFP 852. Length: 35 pages Creation-Date: 198905 Number: 920 Publication-Status: Published in Journal of Economic Theory (August 1993), 60(2): 217-240 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0852.pdf File-Format: application/pdf File-Size: 1196 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0920.pdf File-Format: application/pdf File-Size: 853 kb Handle: RePEc:cwl:cwldpp:920 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: An Introduction to General Equilibrium with Incomplete Asset Markets Abstract: I survey the major results in the theory of general equilibrium with incomplete asset markets. I also introduce the papers in this volume and offer a few suggestions for further work. Classification-JEL: 021 Keywords: Asset markets, incomplete markets, general equilibrium theory Note: CFP 750. Length: 52 pages Creation-Date: 198906 Number: 919 Publication-Status: Published in Journal of Mathematical Economics (1990) 19: 1-38 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0750.pdf File-Format: application/pdf File-Size: 2038 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0919.pdf File-Format: application/pdf File-Size: 1555 kb Handle: RePEc:cwl:cwldpp:919 Template-type: ReDIF-Paper 1.0 Author-Name: Rosa L. Matzkin Author-X-Name-First: Rosa L. Author-X-Name-Last: Matzkin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Nonparametric Maximum Rank Correlation Estimator Abstract: This paper presents a nonparametric and distribution-free estimator for the function h*, of observable exogenous variables, x, in the generalized regression model, y-G(h*(x), mu). The method does not require a parametric specification for either the function h* or for the distribution of the random term mu. The estimation proceeds by maximizing a rank correlation criterion (Han (1987) over a set of functions that are monotone increasing, concave, and homogeneous degree one; the function h* is assumed to belong to this set of functions. The estimator is shown to be strongly consistent. Keywords: Nonparametric, rank correlation, estimators, consistency, regression model Length: 23 pages Creation-Date: 198907 Number: 918 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0918.pdf File-Format: application/pdf File-Size: 398 kb Handle: RePEc:cwl:cwldpp:918 Template-type: ReDIF-Paper 1.0 Author-Name: Imre Barany Author-X-Name-First: Imre Author-X-Name-Last: Barany Author-Workplace-Name: Mathematical Institute, Budapest Author-Name: Roger Howe Author-X-Name-First: Roger Author-X-Name-Last: Howe Author-Workplace-Name: Dept. of Mathematics, Yale University Author-Name: Laszlo Lovasz Author-X-Name-First: Laszlo Author-X-Name-Last: Lovasz Author-Workplace-Name: Eotvos & Princeton Universities Title: On Integer Points in Polyhedra: A Lower Bound Abstract: Given a polyhedron we write P(I) for the convex hull of the integral points in P. It is know that P(I) can have at most O(fi(n-1)) vertices if P is a rational polyhedron with size fi. Here we give an example showing that P(I) can have as many as Omega (fi(n-1)) vertices. The construction uses the Dirichlet unit theorem. Classification-JEL: 213 Keywords: Polyhedra, integral points, Dirichlet unit theorem Length: 12 pages Creation-Date: 198905 Number: 917 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0917.pdf File-Format: application/pdf File-Size: 251 kb Handle: RePEc:cwl:cwldpp:917 Template-type: ReDIF-Paper 1.0 Author-Name: David F. Shallcross Author-X-Name-First: David F. Author-X-Name-Last: Shallcross Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Neighbors of the Origin for Four by Three Matrices Abstract: Scarf has defined a neighborhood system for families of integer programs where the right-hand side is allowed to vary. This system depends on a matrix A of constraint and objective function coefficients of the integer programs. This paper characterizes the set of neighbors of the origin when A is four by three; showing that it may be described as the set of integer vectors in a union of two-dimensional polyhedra, where the number of polyhedra is quadratic in the bit size of A. Classification-JEL: 213 Keywords: Integer programming, neighborhood systems Length: 11 pages Creation-Date: 198906 Number: 916 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0916.pdf File-Format: application/pdf File-Size: 274 kb Handle: RePEc:cwl:cwldpp:916 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Reconciliation of Micro and Macro Economics Abstract: It is suggested that the appropriate structure for the reconciliation of micro and macroeconomics is an infinite horizon overlapping generations (OLG) model with many finitely lived natural persons and one infinitely lived strategic player without preferences whose choice rule is determined by the periodic political choice of the finitely lived players who are alive and politically strategically active at the time of choice. This player may be interpreted as government. In the steps from the finite horizon general equilibrium (GE) model to the overlapping generations model (GGOLG) it is suggested that even without exogenous uncertainty, if economic efficiency is to be attained it is logically and technologically necessary to introduce government, government money, credit, bankruptcy and inheritance conditions. Classification-JEL: 022, 023 Keywords: Government, overlapping generations model, infinite horizon Length: 29 pages Creation-Date: 198906 Number: 915 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0915.pdf File-Format: application/pdf File-Size: 675 kb Handle: RePEc:cwl:cwldpp:915 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Game Theory Without Partitions, and Applications to Speculation and Consensus Abstract: Decision theory and game theory are extended to allow for information processing errors. This extended theory is then used to reexamine market speculation and consensus, both when all actions (opinions) are common knowledge and when they may not be. Five axioms of information processing are shown to be especially important to speculation and consensus. They are called nondelusion, knowing that you know, nested, balanced, and positively balanced. We show that it is necessary and sufficient that each agent's information processing errors be nondeluded and (1) balanced so that the agents cannot agree to disagree, (2) positively balanced so that it cannot be common knowledge that they are speculating, and (3) KTYK and nested so that agents cannot speculate in equilibrium. Each condition is strictly weaker than the next one, and the last is strictly weaker than partition information. Classification-JEL: 511, 313, 026 Keywords: Game theory, decision theory, speculation, consensus, information, common knowledge Length: 33 pages Creation-Date: 198905 Number: 914 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0914.pdf File-Format: application/pdf File-Size: 310 kb Handle: RePEc:cwl:cwldpp:914 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Capital Asset Pricing Model as a General Equilibrium with Incomplete Markets Abstract: We recast the capital asset pricing model (CAPM) in the broader context of general equilibrium with incomplete markets (GEI). In this setting we give proofs of three properties of CAPM equilibria: they are efficient, asset prices lie on a "security market line," and all agents hold the same two mutual funds. The first property requires a riskless asset, the latter two do not. We show that across all GEI only one of these three properties of equilibrium is generally valid: asset prices depend on covariances, not variances. We extend CAPM to many consumption goods in such a way that all three properties hold. But now the definition of a riskless asset depends on preferences and endowments, and so cannot be specified a priori. Classification-JEL: 313, 311, 021 Keywords: Capital asset pricing model, incomplete markets, asset prices, CAPM, general equilibrium model Note: CFP 759. Length: 34 pages Creation-Date: 198905 Number: 913 Publication-Status: Published in The Geneva Papers on Risk and Insurance Theory (May 1990), 15(1): 55-71 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0759.pdf File-Format: application/pdf File-Size: 883 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0913.pdf File-Format: application/pdf File-Size: 766 kb Handle: RePEc:cwl:cwldpp:913 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Pradeep Dubey Author-X-Name-First: Pradeep Author-X-Name-Last: Dubey Author-Workplace-Name: SUNY at Stony Brook Title: Existence of Walras Equilibrium Without a Price Player of Generalized Game Abstract: We derive the existence of a Walras equilibrium directly from Nash's theorem on noncooperative games. No price player is involved, nor are generalized games. Classification-JEL: 026 Keywords: Walras equilibrium, game theory, Nash model, noncoperative games Length: 11 pages Creation-Date: 198905 Number: 912 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0912.pdf File-Format: application/pdf File-Size: 291 kb Handle: RePEc:cwl:cwldpp:912 Template-type: ReDIF-Paper 1.0 Author-Name: Vassilis A. Hajivassiliou Author-X-Name-First: Vassilis A. Author-X-Name-Last: Hajivassiliou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Do the Secondary Markets Believe in Life After Debt? Abstract: This paper employs panel-data econometric techniques to explore the relations between measures of credit worthiness and the debt discounts on the secondary markets. It investigates empirically whether the secondary market discounts reflect a history of past repayments problems or whether they anticipate future debt crises. The answer to this question has implications about the desirability of debt relief. The main finding is that the secondary markets do not seem rapidly to absorb economic information, which suggests that they are still in their evolutionary stage and are not very efficient. The estimated models are also used to analyze issues in the international finance literature. Classification-JEL: 431, 443, 411 Keywords: Debt crisis, debt relief, international finance Length: 40 pages Creation-Date: 198905 Number: 911 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0911.pdf File-Format: application/pdf File-Size: 1019 kb Handle: RePEc:cwl:cwldpp:911 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Asymptotics for Semiparametric Econometric Models: III. Testing and Examples Abstract: This paper considers tests of nonlinear parametric restrictions in semiparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like test statistics are considered and are shown to have asymptotic chi-square distributions under the null and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios. A number of examples are given to illustrate the testing results of this paper and the estimation and stochastic equicontinuity results of the antecedents to this paper, viz. Andrews (1989b, c). Keywords: Lagrange multiplier test, likelihood ratio test, semiparametric model, semiparametric tests, Wald test, asymptotic theory Length: 53 pages Creation-Date: 198905 Number: 910 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0910.pdf File-Format: application/pdf File-Size: 1227 kb Handle: RePEc:cwl:cwldpp:910 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Asymptotics for Semiparametric Econometric Models: II. Stochastic Equicontinuity and Nonparametric Kernel Estimation Abstract: This paper presents several stochastic equicontinuity results that are useful for establishing the asymptotic properties of estimators and tests in parametric, semiparametric, and nonparametric econometric models. In particular, they can be applied straightforwardly in the estimation and testing results of Andrews (1989b). The paper takes various stochastic equicontinuity results from the probability literature, which rely on entropy conditions of one sort or another, and provides primitive conditions under which the entropy conditions hold. This yields stochastic equicontinuity results that are readily applicable in a variety of contexts. This paper also presents a number of consistency results for nonparametric kernel estimators of density and regression functions and their derivatives. These results are particularly useful in semiparametric estimation and testing problems that rely on preliminary nonparametric estimators, as in Andrews (1989b). The results allow for near epoch dependent non-identically distributed random variables, data-dependent bandwidth sequences, preliminary estimation of parameters (e.g., regression based on residuals), and nonparametric regression on index functions. Some of the results make use of the stochastic equicontinuity results of the paper. Keywords: Asymptotic results, bracketing method, empirical process, kernel estimator, nonparametric density estimator, nonparametric regression estimator, semiparametric estimator, semiparametric test, series expansion, Sobolev norm, stochastic equicontinuity Note: CFP 863. Length: 98 pages Creation-Date: 1989 Revision-Date: 199007 Number: 909R Publication-Status: Published in Econometrica, 62(1), 1994 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0863.pdf File-Format: application/pdf File-Size: 1521 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0909-r.pdf File-Format: application/pdf File-Size: 2366 kb Handle: RePEc:cwl:cwldpp:909R Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Asymptotics for Semiparametric Econometric Models: I. Estimation Abstract: This paper provides a general framework for proving the square root of T consistency and asymptotic normality of a wide variety of semiparametric estimators. The results apply in time series and cross-sectional modeling contexts. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator. The criterion function need not be differentiable. The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes. This paper also considers tests of nonlinear parametric restrictions in seimparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like tests statistics are considered. A general framework is provided for proving that these test statistics have asymptotic chi-square distributions under the null hypothesis and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios. Keywords: Asymptotic normality, empirical process, infinite dimensional nuisance parameter, Lagrange multiplier test, likelihood ratio-like test, nonparametric estimation, semiparametric estimation, semiparametric model, semiparametric test, stochastic equicontinuity, Wald test, weak convergence Note: CFP 863. Length: 100 pages Creation-Date: 1989 Revision-Date: 199008 Number: 908R Publication-Status: Published in Econometrica (January 1994), 62(1): 43-72 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0863.pdf File-Format: application/pdf File-Size: 1521 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0908-r.pdf File-Format: application/pdf File-Size: 2595 kb Handle: RePEc:cwl:cwldpp:908R Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: An Empirical Process Central Limit Theorem for Dependent Non-Identically Distributed Random Variables Abstract: This paper establishes a central limit theorem (CLT) for empirical processes indexed by smooth functions. The underlying random variables may be temporally dependent and non-identically distributed. In particular, the CLT holds for near epoch dependent (i.e., functions of mixing processes) triangular arrays, which include strong mixing arrays, among others. The results apply to classes of functions that have series expansions. The proof of the CLT is particularly simple; no chaining argument is required. The results can be used to establish the asymptotic normality of semiparametric estimators in time series contexts. An example is provided. Keywords: Central limit theorem, empirical process, Fourier series, semiparametric estimator, time series Note: CFP 792. Length: 25 pages Creation-Date: 198905 Number: 907 Publication-Status: Published in Journal of Multivariate Analysis (August 1991), 38(2): 188-203 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0792.pdf File-Format: application/pdf File-Size: 696 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0907.pdf File-Format: application/pdf File-Size: 641 kb Handle: RePEc:cwl:cwldpp:907 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Asymptotic Optimality of Generalized C_{L}, Cross-Validation, and Generalized Cross-Validation in Regression with Heteroskedastic Errors Abstract: The problem considered here is that of using a data-driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter. In contrast to other papers on this subject, we consider models with heteroskedastic errors. The results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators, nearest neighbor estimators, and local regression estimators, among others. Generalized C_{L}, cross-validation, and generalized cross-validation procedures are analyzed. Keywords: Heteroskedasticity, linear regression, nonparametric regression, model selection, asymptotic theory, cross validation Note: CFP 790. Length: 24 pages Creation-Date: 198905 Number: 906 Publication-Status: Published in Journal of Econometrics (1991), 47: 359-377 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0790.pdf File-Format: application/pdf File-Size: 752 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0906.pdf File-Format: application/pdf File-Size: 458 kb Handle: RePEc:cwl:cwldpp:906 Template-type: ReDIF-Paper 1.0 Author-Name: Truman F. Bewley Author-X-Name-First: Truman F. Author-X-Name-Last: Bewley Author-Email: truman.bewley@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/bewley.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Market Innovation and Entrepreneurship: A Knightian View Abstract: Stimulated by Frank Knight's work, "Risk, Uncertainty and Profit," I present a theory of innovation based on what I term Knightian decision theory. This theory includes a concept of uncertainty aversion, a behavioral property that makes people reluctant to undertake new unevaluatable risks. This aversion is compounded when individuals are obliged to cooperate in undertaking risks. The theory leads directly to the conclusion that innovation in business is the natural domain of individual investors with unusually low levels of uncertainty aversion. Also, it should be difficult to innovate new markets for insurance of unevaluatable risks, for the success of a new market requires that many people overcome their aversion to uncertainty and enter the market. Classification-JEL: 022, 026, 511, 514 Keywords: Decision theory, uncertainty, innovation Length: 47 pages Creation-Date: 198904 Number: 905 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0905.pdf File-Format: application/pdf File-Size: 1495 kb Handle: RePEc:cwl:cwldpp:905 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Shuntian Yao Author-X-Name-First: Shuntian Author-X-Name-Last: Yao Author-Workplace-Name: Jinan University Title: Gold, Liquidity and Secured Loans in a Multi-Stage Economy. Part II. Many Durables, Land and Gold Abstract: In a previous paper (Shubik and Yao, 1988) we examined a multistage exchange economy with m perishable goods and one infinitely durable gold used as money. We considered an economy without credit and one with one hundred percent secured loans. In this paper we consider an economy with m(1) goods which have finite lives and m(2) goods which are of infinite durability. Historically the two durables which have been prominent in economic activity have been gold and land, although one might wish to include platinum and some other items. Classification-JEL: 021, 022, 213 Keywords: Exchange economy, gold, strategic games, durables Note: CFP 770. Length: 29 pages Creation-Date: 198904 Number: 904 Publication-Status: Published in Journal of Economics (1990), 52(1): 1-23 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0770.pdf File-Format: application/pdf File-Size: 898 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0904.pdf File-Format: application/pdf File-Size: 499 kb Handle: RePEc:cwl:cwldpp:904 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Shuntian Yao Author-X-Name-First: Shuntian Author-X-Name-Last: Yao Author-Workplace-Name: Jinan University Title: The Transactions Cost of Money (A Strategic Game Analysis) Abstract: The payments system of a modern economy is a peculiar mix of technological and institutional factors. Trade takes time and involves some form of money or credit. Going to the bank or arranging credits is expensive. Baumol (1952) and Tobin (1956) address the costs of transactions. However both the Baumol and the Tobin analysis was carried out in a partial equilibrium context. Here we address the task of considering the costs of banking in a closed strategic market game. Classification-JEL: 021, 022, 213 Keywords: Strategic game, exchange economy, transaction costs Note: CFP 789. Length: 24 pages Creation-Date: 198903 Number: 903 Publication-Status: Published in Mathematical Social Sciences (1990), 20: 99-114 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0789.pdf File-Format: application/pdf File-Size: 576 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0903.pdf File-Format: application/pdf File-Size: 343 kb Handle: RePEc:cwl:cwldpp:903 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Shafer, Wayne Author-Workplace-Name: University of Southern California Title: Solving Systems of Simultaneous Equations in Economics Abstract: We show that there is a broad range of systems of simultaneous equations that arise in economics as descriptions of equilibrium that can be solved in elementary fashion via degree theory. Some of these systems are not susceptible to analysis by standard Brouwer fixed point methods. Two of our applications are to general equilibrium with incomplete markets, and to Nonconvex production with noncompetitive pricing rules. Classification-JEL: 213, 022, 021 Keywords: Simultaneous equations, incomplete markets, degree theory, general equilibrium Note: CFP 749. Length: 31 pages Creation-Date: 198910 Number: 902 Publication-Status: Published in Journal of Mathematical Economics (1990), 19: 69-93 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0749.pdf File-Format: application/pdf File-Size: 1072 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0902.pdf File-Format: application/pdf File-Size: 802 kb Handle: RePEc:cwl:cwldpp:902 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Heracles M. Polemarchakis Author-X-Name-First: Heracles M. Author-X-Name-Last: Polemarchakis Author-Workplace-Name: Columbia University Title: Observability and Optimality Abstract: Observability of an individual's excess demand function for assets and commodities as all prices and revenue vary suffices in order to recover his von Neumann-Morgenstern utility function. This is generically the case, even when the asset market is incomplete and the cardinal utility indices state dependent, as long as there are at least two commodities traded in spot markets at each state of nature. On the contrary, if the response of individuals' excess demand for assets as prices in spot commodity markets vary is not observable, recoverability fails when the asset market is incomplete. In particular, it is not possible to contradict the claim that the competitive allocation is fully optimal in spite of the incompleteness of the asset market. Classification-JEL: 021, 022 Keywords: Utility function, asset market, equilibrium allocation Note: CFP 752. Length: 21 pages Creation-Date: 198910 Number: 901 Publication-Status: Published in Journal of Mathematical Economics (1990) 19: 153-165 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0752.pdf File-Format: application/pdf File-Size: 570 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0901.pdf File-Format: application/pdf File-Size: 408 kb Handle: RePEc:cwl:cwldpp:901 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Pradeep Dubey Author-X-Name-First: Pradeep Author-X-Name-Last: Dubey Author-Workplace-Name: SUNY at Stony Brook Title: Liquidity and Bankruptcy with Incomplete Markets: Pure Exchange Abstract: We enlarge the standard model of general equilibrium with incomplete market (GEI), to incorporate liquidity constraints as well as the possibility of bankruptcy and default. A new equilibrium results, which we abbreviate GELBI (general equilibrium with liquidity, bankruptcy and incomplete markets). When the supply of bank money and bankruptcy/default penalties are taken sufficiently high (the high regime), GEI occur as GELBI. But outside the high regime many new phenomena appear: money is (almost) never neutral, it has positive value and its optimum quantity is often finite; bankruptcy and default not only occur in equilibrium but can have welfare improving consequences for everyone; there is no real indeterminacy even with financial assets. Classification-JEL: 021, 022 Keywords: Incomplete markets, general equilibrium, bankruptcy, liquidity constraints Length: 60 pages Creation-Date: 198902 Number: 900 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d09a/d0900.pdf File-Format: application/pdf File-Size: 1131 kb Handle: RePEc:cwl:cwldpp:900 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: In Choi Author-X-Name-First: In Author-X-Name-Last: Choi Author-Workplace-Name: Ohio State University Title: Testing for a Unit Root by Generalized Least Squares Methods in the Time and Frequency Domains Abstract: New time and frequency domain tests for the presence of a unit root are developed. The tests are based on generalized least squares (GLS) methods in both the time and the frequency domains. For the time domain tests, moving average processes are assumed for the error terms on the autoregression. For the frequency domain tests, general assumptions are made which allow for stationary and weakly dependent error processes. The limiting distributions of feasible GLS tests are derived under MA(1) errors in the time domain. This theory is extended to higher order moving average processes under an invertibility condition. The limiting distributions of both full and band spectrum tests in the frequency domain are also derived. All of these limiting distributions are shown to be free of nuisance parameters. Some results on test consistency are also reported. Extensive Monte Carlo simulations are performed to study the size and power of the proposed tests in finite samples. Keywords: Unit root, spectral methods, generalized least squares, asymptotic theory, Monte Carlo Note: CFP 850. Length: 78 pages Creation-Date: 198903 Number: CFP 899 Publication-Status: Published in Journal of Econometrics (1993), 59: 263-286 File-URL: http://cowles.econ.yale.edu/P/cp/p08b/p0850.pdf File-Format: application/pdf File-Size: 750 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0899.pdf File-Format: application/pdf File-Size: 1104 kb Handle: RePEc:cwl:cwldpp:899 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Mico Loretan Author-X-Name-First: Mico Author-X-Name-Last: Loretan Author-Workplace-Name: Yale University Title: The Durbin-Watson Ratio Under Infinite Variance Errors Abstract: This paper studies the properties of the von Neumann ratio for time series with infinite variance. The asymptotic theory is developed using recent results on the weak convergence of partial sums of time series with infinite variance to stable processes and of sample serial correlations to functions of stable variables. Our asymptotics cover the null of iid variates and general moving average (MA) alternatives. Regression residuals are also considered. In the static regression model the Durbin-Watson statistic has the same limit distribution as the von Neumann ratio under general conditions. However, the dynamic models, the results are more complex and more interesting. When the regressors have thicker tail probabilities than the errors we find that the Durbin-Watson and von Neumann ration asymptotics are the same. Keywords: Durbin-Watson ratio, von Neumann ratio, serial correlation, dynamic models, time series, asymptotic theory Note: CFP 772. Length: 41 pages Creation-Date: 1989 Revision-Date: 198908 Number: 898R Publication-Status: Published in Journal of Econometrics (1991), 47: 85-114 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0772.pdf File-Format: application/pdf File-Size: 955 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0898-r.pdf File-Format: application/pdf File-Size: 782 kb Handle: RePEc:cwl:cwldpp:898R Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Time Series Regression with a Unit Root and Infinite Variance Errors Abstract: Chan and Tran give the limit theory for the least squares coefficient in a random walk with the iid errors that are in the domain of attraction of a stable law. This note discusses their results and provides generalizations to the case of I(q) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. General unit root tests are also studied. It is shown that the semiparametric corrections suggested by the author for the finite variance case continue to work when the errors have infinite variance. The limit laws are expressed in terms of ratios of quadratic functionals of a stable process rather than Brownian motion. The correction terms that eliminate nuisance parameter dependencies are random in the limit and involve multiple stochastic integrals that may be written in terms of the quadratic variation of the limiting stable process. Keywords: Integrated process, unit roots, random walk, time series Note: CFP 755. Length: 27 pages Creation-Date: 1989 Revision-Date: 198908 Number: 897R Publication-Status: Published in Econometric Theory (1990), 6: 44-62 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0755.pdf File-Format: application/pdf File-Size: 561 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0897-r.pdf File-Format: application/pdf File-Size: 475 kb Handle: RePEc:cwl:cwldpp:897R Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Production Smoothing Model Is Alive and Well Abstract: Monthly data in physical units for seven industries are used to examine the production smoothing hypothesis. The results strongly support this hypothesis. Significant effects of expected future sales on current production are found for four industries, and the estimated decision equations for all seven industries imply production smoothing behavior. The previous negative results regarding the hypothesis appear to be due to the use of poor data, particularly the shipments and inventory data of the Department of Commerce. Classification-JEL: 131, 522, 514, 631 Keywords: Production smoothing, investment, inventories Note: CFP 740. Length: 21 pages Creation-Date: 198902 Number: 896 Publication-Status: Published in Journal of Monetary Economics (1989), 24: 353-370 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0740.pdf File-Format: application/pdf File-Size: 897 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0896.pdf File-Format: application/pdf File-Size: 540 kb Handle: RePEc:cwl:cwldpp:896 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Pradeep Dubey Author-X-Name-First: Pradeep Author-X-Name-Last: Dubey Author-Workplace-Name: SUNY at Stony Brook Author-Name: Siddhartha Sahi Author-X-Name-First: Siddhartha Author-X-Name-Last: Sahi Author-Workplace-Name: Princeton University Title: Repeated Trade and the Velocity of Money Abstract: There are two sources of inefficiency of strategic equilibria (SE) in market mechanisms. The first is the oligopolistic effect, which occurs when an agent can single-handedly influence prices. With a continuum of agents we get "perfect competition" and this effect is, of course, wiped out. But the inefficiency of SE's may nevertheless persist because agents are not "perfectly liquid," i.e., the constraints of the mechanism are such that they cannot carry out arbitrary trades at the market prices. Our main result is that, if enough repeated rounds of trade are permitted within a single utility period, then the liquidity problem is overcome: SE outcomes turn out to be not only efficient but, in fact, Walrasian. Classification-JEL: 021, 311 Keywords: Walrasian equilibrium, oligopoly, trading Note: CFP 842. Length: 16 pages Creation-Date: 198901 Number: 895 Publication-Status: Published in Journal of Mathematical Economics (1993), 22: 125-137 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0842.pdf File-Format: application/pdf File-Size: 587 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0895.pdf File-Format: application/pdf File-Size: 296 kb Handle: RePEc:cwl:cwldpp:895 Template-type: ReDIF-Paper 1.0 Author-Name: Rosa L. Matzkin Author-X-Name-First: Rosa L. Author-X-Name-Last: Matzkin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Nonparametric Tests of Maximizing Behavior Subject to Nonlinear Sets Abstract: This paper extends the axiomatic theory of revealed preference to choices that are generated by the maximization of a strictly concave and strictly monotone function subject to nonlinear constraint sets. I characterize finite sets of observations on choice behavior that are consistent with the maximization of a strictly concave and strictly monotone objective function. Both nonconvex and convex choice sets are considered. The analysis applies, for example, to consumers who face either regressive or progressive taxes and to households that produce commodities according to either a convex or a concave production function. For choice sets that possess convex and monotone complements, my characterization provides a nonparametric test for the maximization hypothesis. For choice sets that can be supported by unique hyperplanes at the chosen elements, the result provides a nonparametric test for the strict concavity and strict monotonicity of the maximized function. Classification-JEL: 022, 213 Keywords: Revealed preferences, nonparametric tests, monotonicity, concavity Length: 59 pages Creation-Date: 198812 Number: 894 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0894.pdf File-Format: application/pdf File-Size: 917 kb Handle: RePEc:cwl:cwldpp:894 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Reflections on Econometric Methodology Abstract: General issues about the methodology of empirical econometric research are discussed. It is argued that the most successful paradigms for applied work are the ones that have a capacity to survive and to evolve into more useful forms as these are needed. Paradigms that embrace progressive modeling principles, such as those espoused by David Hendry, seem most amenable to this criterion. It is also argued that econometric theory has a large role to play in helping us to understand the strengths and the weaknesses of a methodology and to codify what its prescriptions entail. The time series methodology of David Hendry is considered in some detail. It is shown that the Hendry methodology comes remarkable close to achieving an optimal inference procedure for long run structural relationships even though it is conducted on a single equation basis. The findings indicate that the methodology may be improved further to achieve results that are equivalent to optimal estimation. Classification-JEL: 212 Keywords: Methodology, econometrics, empirical research, structural relationships Note: CFP 727. Length: 42 pages Creation-Date: 198812 Number: 893 Publication-Status: Published in The Economic Record (December 1988), 344-359 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0727.pdf File-Format: application/pdf File-Size: 1142 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0893.pdf File-Format: application/pdf File-Size: 927 kb Handle: RePEc:cwl:cwldpp:893 Template-type: ReDIF-Paper 1.0 Author-Name: David G. Pearce Author-X-Name-First: David G. Author-X-Name-Last: Pearce Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Ennio Stacchetti Author-X-Name-First: Ennio Author-X-Name-Last: Stacchetti Author-Workplace-Name: Stanford University Title: The Interaction of Implicit and Explicit Contracts in Repeated Agency Abstract: Traditional agency theory assumes that the principal has no more information about the agent's actions than the enforcement authorities have. This is unrealistic in many settings, and in repeated models, additional information possessed by the principal changes the nature of the problem. Such information can be used in implicit, self-enforcing contracts between principal and agent, that supplement the usual explicit contracts. This paper studies the way in which the two kinds of contracts are combined in constrained efficient equilibria of the agency supergame. The agent's compensation is comprised of both guaranteed payments and voluntary bonuses from the principal. We give a simple characterization of the composition of remuneration in the optimal dynamic scheme. Classification-JEL: 022, 026 Keywords: Principal-agent theory, contracts, supergames, dynamic models Length: 30 pages Creation-Date: 198812 Number: 892 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0892.pdf File-Format: application/pdf File-Size: 572 kb Handle: RePEc:cwl:cwldpp:892 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Interaction of Implicit and Explicit Contracts in Repeated Agency Abstract: This article deals with experimental games as they pertain to game theory. As such there is a natural distinction between experimentation with abstract games devoted to testing a specific hypothesis in game theory and games with a scenario from a discipline such as economics or political science where the game is presented in the context of some particular activity. Classification-JEL: 215, 026 Keywords: Experimental economics, game theory, experimental methods Length: 37 pages Creation-Date: 198811 Number: 891 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0891.pdf File-Format: application/pdf File-Size: 1356 kb Handle: RePEc:cwl:cwldpp:891 Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Karl E. Case Author-X-Name-First: Karl E. Author-X-Name-Last: Case Author-Workplace-Name: Wellesley College Title: The Behavior of Home Buyers in Boom and Post-Boom Markets Length: 37 pages Creation-Date: 198811 Number: 890 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0890.pdf File-Format: application/pdf File-Size: 1300 kb Handle: RePEc:cwl:cwldpp:890 Template-type: ReDIF-Paper 1.0 Author-Name: Rosa L. Matzkin Author-X-Name-First: Rosa L. Author-X-Name-Last: Matzkin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models Abstract: This paper studies the problem of nonparametric identification and estimation of binary threshold-crossing and binary choice models. First, conditions are given that guarantee the nonparametric identification of both the function of exogenous observable variables and the distribution of the random terms. Second, the identification results are employed to develop strongly consistent estimation methods that are nonparametric in both the function of observable exogenous variables and the distribution of the unobservable random variables. The estimators are obtained by maximizing a likelihood function over nonparametric sets of functions. A two- step constrained optimization procedure is devised to compute these estimators. Keywords: Nonparametric models, identification, likelihood function, consistency Note: CFP 809. Length: 53 pages Creation-Date: 198809 Number: 889 Publication-Status: Published in Econometrica (March 1992), 60(2): 239-270 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0809.pdf File-Format: application/pdf File-Size: 1537 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0889.pdf File-Format: application/pdf File-Size: 952 kb Handle: RePEc:cwl:cwldpp:889 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Michael Haliassos Author-X-Name-First: Michael Author-X-Name-Last: Haliassos Author-Workplace-Name: University of Maryland Title: The Macroeconomics of Government Finance Abstract: This is a critical survey of the literature on the implications of government financial policy for economic activity. The central question is whether the choice of how to finance a given path of government expenditures (i.e., through taxes, nonmonetary debt or money creation) has any real effects. We first present measures of the budget deficit and review economists' views, over the past fifty years, of the burden of public debt, of the neutrality of money, and of fiscal and monetary policies. The earlier tradition and the recent literature differ in methodology, and we then discuss the "microfoundations" approach that dominates contemporary macroeconomics. This is followed by an evaluation of recent analyses, both theoretical and empirical, focusing on (I) the Debt Neutrality hypothesis of Robert Barro, (ii) the effects of the choice between tax- and money-financing of government expenditures, and especially the issues of monetary superneutrality and of the Fisher hypothesis, and (iii) the effects of open market operations. Classification-JEL: 322, 321, 311 Keywords: Government spending, fiscal policy, government policy, budget deficit Note: CFP 768. Length: 110 pages Creation-Date: 198810 Number: 888 Publication-Status: Published in B.M. Friedman and F.H. Hahn, eds., Handbook of Monetary Economics, Vol. 2, Elsevier Sciencem 1990, pp. 889-950 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0768.pdf File-Format: application/pdf File-Size: 4241 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0888.pdf File-Format: application/pdf File-Size: 2820 kb Handle: RePEc:cwl:cwldpp:888 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A New Proof of Knight's Theorem on the Cauchy Distribution Abstract: We offer a new and straightforward proof of F.B. Knight's [3] theorem that the Cauchy type is characterized by the fact that it has no atom and is invariant under the involution i : x -> -1/x. Our approach uses the representation X = tan theta where theta is uniform on (-pi/2,pi/2) when X is standard Cauchy. A matrix generalization of this characterization theorem is also given. Keywords: Cauchy distribution, Involution, Matrix variate, Uniform distribution Length: 6 pages Creation-Date: 1989 Number: 887 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0887.pdf File-Format: application/pdf File-Size: 136 kb Handle: RePEc:cwl:cwldpp:887 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Little Magic with the Cauchy Distribution Length: 14 pages Creation-Date: 1989 Number: 886 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0886.pdf File-Format: application/pdf File-Size: 435 kb Handle: RePEc:cwl:cwldpp:886 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Chien-fu Chou Author-X-Name-First: Chien-fu Author-X-Name-Last: Chou Title: The Power of Commitment Abstract: History has seen many examples of the lone man ñ like Christ, Luther, Gandhi, or Hitler -- who without initial wealth or position, succeeds in changing the behavior of an entire society, for good or for ill. Whence comes this power. No doubt such leaders have possessed extraordinary ability, and have formulated original ideas with great appeal which others could readily follow. But there is another striking similarity among these leaders; namely their single-minded devotion to their, ideals, and their uncompromising attitude toward those who opposed them, no matter what the personal cost. There is hardly any need to document this facet of their personalities, so widely is it known. But we cannot help recalling Gandhi's threat to starve himself to death if the fighting between Hindus and Muslims did not stop. Indeed the whole-hearted commitment of these leaders to their ideals was often reflected in their followers' commitment to them. The purpose of this paper is to show how significant is the power to make commitments, perhaps in the name of some ideal. Classification-JEL: 026 Keywords: Commitment credible threat, repeated games, game theory Length: 45 pages Creation-Date: 198809 Number: 885 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0885.pdf File-Format: application/pdf File-Size: 916 kb Handle: RePEc:cwl:cwldpp:885 Template-type: ReDIF-Paper 1.0 Author-Name: Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Adam Brandenburger Author-X-Name-First: Adam Author-X-Name-Last: Brandenburger Author-Workplace-Name: Harvard Business School Author-Name: Eddie Dekel Author-X-Name-First: Eddie Author-X-Name-Last: Dekel Author-Workplace-Name: University of California, Berkeley Title: Correlated Equilibrium with Generalized Information Structures Abstract: We study the "generalized correlated equilibria" of a game when players make information processing errors. It is shown that the assumption of information processing errors is equivalent to that of "subjectivity" (i.e., differences between the players' priors). Hence a bounded rationality justification of subjective priors is provided. We also describe the set of distributions on actions induced by generalized correlated equilibria with common priors. Classification-JEL: 026, 022 Keywords: Correlated equilibria, subjective priors, bounded rationality Note: CFP 819. Length: 21 pages Creation-Date: 1988 Revision-Date: 198908 Number: 884R Publication-Status: Published in Games and Economic Behavior (1992), 4: 182-201 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0819.pdf File-Format: application/pdf File-Size: 850 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0884-r.pdf File-Format: application/pdf File-Size: 497 kb Handle: RePEc:cwl:cwldpp:884R Template-type: ReDIF-Paper 1.0 Author-Name: Herbert E. Scarf Author-X-Name-First: Herbert E. Author-X-Name-Last: Scarf Author-Email: herbert.scarf@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/scarf.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: R. Kannan Author-X-Name-First: R. Author-X-Name-Last: Kannan Author-Workplace-Name: Carnegie-Mellon University Author-Name: Laszlo Lovasz Author-X-Name-First: Laszlo Author-X-Name-Last: Lovasz Author-Workplace-Name: Budapest & Princeton University Title: The Shapes of Polyhedra Abstract: Let A be a real matrix of size (n+d+1)xn. We assume that all n x n submatrices of A are non-singular and define the condition number C = C(A) to be the ratio of the largest n x n subdeterminant of A to the smallest in absolute value. In addition we assume that there is a positive vector pi such that (pi)A = 0. This implies that for any b, the body K(b) = 'X such that AX <= b is bounded. Let f(A) be the number of subsets of the rows of A, of cardinality n+1, for which a positive linear combination equals zero. We show that for any epsilon > 0, there exists a subset of the bodies K(b), of cardinality not larger than f(A) 1/2(log to the base 2 of (nC)/epsilon^{d}, such that every body is within epsilon of some member of the subset. Classification-JEL: 213 Keywords: Polyhedra, Banach-Mazur distance, Hubert metric, Lenstra's algorithm, integer programming, minimum Note: CFP 753. Length: 31 pages Creation-Date: 198809 Number: 883 Publication-Status: Published in Mathematics of Operations Research (May 1990), 15(2): 364-390 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0753.pdf File-Format: application/pdf File-Size: 849 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0883.pdf File-Format: application/pdf File-Size: 620 kb Handle: RePEc:cwl:cwldpp:883 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Error Correction and Long Run Equilibrium in Continuous Time Abstract: This paper deals with error correction models (ECM's) and cointegrated systems that are formulated in continuous time. Problems of representation, identification, estimation and time aggregation are discussed. It is shown that every ECM in continuous time has a discrete time equivalent model in ECM format. Moreover, both models may be written as triangular systems with stationary errors. This formulation simplifies both the continuous and the discrete time ECM representations and it helps to motivate a class of optimal inference procedures. It is further shown that long run equilibria in the continuous system are always identified in the discrete time reduced form, so that there is no aliasing problem for these coefficients. Keywords: Error correction, spectral regression, differential equations, triangular system, temporal aggregation, co-integration Note: CFP 788. Length: 40 pages Creation-Date: 1988 Revision-Date: 198907 Number: 882R Publication-Status: Published in Econometrica (July 1991), 59(4): 967-980 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0788.pdf File-Format: application/pdf File-Size: 695 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0882-r.pdf File-Format: application/pdf File-Size: 1079 kb Handle: RePEc:cwl:cwldpp:882R Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Bruce E. Hansen Author-X-Name-First: Bruce E. Author-X-Name-Last: Hansen Title: Estimation and Inference in Models of Cointegration: A Simulation Study Abstract: This paper studies the finite sample distributions of estimators of the cointegrating vector of linear regression models with I(1) variables. Attention is concentrated on the least squares (OLS) and instrumental variables (IV) methods analyzed in other recent work (Phillips and Hansen (1988)). The general preference of OLS to IV techniques suggested by asymptotic theory is reinforced by our simulations. An exception arises for cases of low signal to noise, where spurious IV techniques (so named for their use of instruments that are structurally unrelated to the model) outperform uncorrected least squares. We verify the presence of a small sample estimation bias and show that the Park-Phillips bias correction does reduce the magnitude of this problem. We also find that there is substantial distributional divergence of t-statistics from the normal, unless the Phillips-Hansen endogeneity correction is used. Finally, we apply these methods to aggregate consumption and income data. Our empirical results indicate that the endogeneity and serial dependence connections are important and lead to intuitively plausible changes in the estimated coefficients. Keywords: Co-integration, endogeneity, instrumental variables, nonstationary series, asymptotic theory Note: CFP 747. Length: 38 pages Creation-Date: 198807 Number: 881 Publication-Status: Published in Advances in Econometrics, Vol. 8, JAI Press, 1990, pp. 225-248 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0747.pdf File-Format: application/pdf File-Size: 837 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0881.pdf File-Format: application/pdf File-Size: 637 kb Handle: RePEc:cwl:cwldpp:881 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Sam Ouliaris Author-X-Name-First: Sam Author-X-Name-Last: Ouliaris Author-Workplace-Name: National U. of Singapore Author-Name: Joon Y. Park Author-X-Name-First: Joon Y. Author-X-Name-Last: Park Author-Workplace-Name: Cornell University Title: Testing for a Unit Root in the Presence of a Maintained Trend Abstract: This paper develops statistics for detecting the presence of a unit root in time series data against the alternative stationarity. Unlike most existing procedures, the new tests allow for deterministic trend polynomials in the maintained hypothesis. They may be used to discriminate between unit root nonstationarity and processes which are stationary around a deterministic polynomial trend. The tests allow for both forms of nonstationarity under the null hypothesis. Moreover, the tests allow for a wide class of weakly dependent and possibly heterogenously distributed procedures. We illustrate the use of the new tests by applying them to a number of models of macroeconomic behavior. Keywords: Unit roots, stationarity, time series, deterministic trend, co-integration Note: CFP 756. Length: 40 pages Creation-Date: 198806 Number: 880 Publication-Status: Published in B. Raj, ed., Advances in Econometrics and Modelling, 1989, pp. 7-28 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0756.pdf File-Format: application/pdf File-Size: 950 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0880.pdf File-Format: application/pdf File-Size: 673 kb Handle: RePEc:cwl:cwldpp:880 Template-type: ReDIF-Paper 1.0 Author-Name: Pradeep Dubey Author-X-Name-First: Pradeep Author-X-Name-Last: Dubey Author-Email: pradeepkdubey@yahoo.com Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Default and Efficiency in a General Equilibrium Model with Incomplete Markets Abstract: We extend the standard model of general equilibrium with incomplete markets (GEI) to allow for default. Default can be either strategic, or due to ill-fortune. Agents who default are penalized to a degree proportional to the size of their default and to penalty parameters lambda. We find that under conditions similar to those necessary to guarantee the existence of GEI equilibrium, we get the existence of GEI_{lambda} equilibrium, for any lambda > 0. We argue that default is thus reasonably modeled as an equilibrium phenomenon. Moreover, we show that more lenient lambda which encourage default may be Pareto improving because they allow for better risk spreading. When default occurs, the Modigliani-Miller theorem typically fails to hold in our framework. Length: 37 pages Creation-Date: 1988 Revision-Date: 198902 Number: 879R Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0879-r.pdf File-Format: application/pdf File-Size: 1128 kb Handle: RePEc:cwl:cwldpp:879R Template-type: ReDIF-Paper 1.0 Author-Name: Philip H. Dybvig Author-X-Name-First: Philip H. Author-X-Name-Last: Dybvig Author-Name: Jaime F. Zender Author-X-Name-First: Jaime F. Author-X-Name-Last: Zender Title: Capital Structure and dividend Irrelevance with Asymmetric Information Abstract: The Modigliani and Miller propositions on the irrelevancy of capital structure and dividends are shown to be valid in a large class of models with asymmetric information. The main assumption is that managerial compensation is chosen optimally. This differs from most recent papers on this topic, which impose by fiat a suboptimal contract. Even when imperfections internal to the firm preclude optimal investment, there is a separation between incentives and financing. We also show that making prices reflect idiosyncratic information more accurately does not make investors better off, thus negating the motivation of many of the signalling models. Classification-JEL: 313, 311, 522 Keywords: Capital structure, dividends, asymmetric information, signalling theory, investment Length: 37 pages Creation-Date: 198807 Number: 878 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0878.pdf File-Format: application/pdf File-Size: 1134 kb Handle: RePEc:cwl:cwldpp:878 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation Abstract: This paper is concerned with the estimation of covariance matrices in the presence of heteroskedasticity and autocorrelation of unknown forms. Currently available estimators that are designed for this context depend upon the choice of a lag truncation parameter and a weighting scheme. No results are available, however, regarding the choice of a lag truncation parameter for a fixed sample size, regarding data-dependent automatic lag truncation parameters, or regarding the choice of weighing scheme. In consequence, available estimators are not entirely operational and the relative merits of the estimators are unknown. Keywords: Autocorrelation, kernel estimator, spectral density, heteroskedasticity, mean squared error, covariance matrix Note: CFP 780. Length: 62 pages Creation-Date: 1988 Revision-Date: 198907 Number: 877R Publication-Status: Published in Econometrica (May 1991), 59(3): 817-858 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0780.pdf File-Format: application/pdf File-Size: 1983 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0877-r.pdf File-Format: application/pdf File-Size: 1630 kb Handle: RePEc:cwl:cwldpp:877R Template-type: ReDIF-Paper 1.0 Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Stabilization of the U.S. Economy: Evidence from the Stock Market Abstract: Until recently, economists widely believed that economic activity had become less variable in the United States following the end of World War II. Challenging this belief, new research suggests that key historical time series are spuriously volatile, a finding that is highly controversial. Data from the stock market may provide a vehicle for resolving the controversy. Economic theory relates stock prices to real activity; empirical tests also show a strong link between stock prices and activity. Financial data are accurately measured over long spans of time and hence are free of most of the measurement problems in other time series. Measures of stock prices show no stabilization in the post-World War II period relative to the pre-World War I or pre-Depression periods. These stock market data thus support the hypothesis that real activity has not been stabilized. Classification-JEL: 131, 133, 313 Keywords: Business cycle, fluctuations, stabilization, stock market, economic activity Note: CFP 724. Length: 32 pages Creation-Date: 198807 Number: 876 Publication-Status: Published in American Economic Review (December 1988), 78(5): 1067-1079 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0724.pdf File-Format: application/pdf File-Size: 813 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0876.pdf File-Format: application/pdf File-Size: 641 kb Handle: RePEc:cwl:cwldpp:876 Template-type: ReDIF-Paper 1.0 Author-Name: David G. Pearce Author-X-Name-First: David G. Author-X-Name-Last: Pearce Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Dilip Abreu Author-X-Name-First: Dilip Author-X-Name-Last: Abreu Author-Workplace-Name: Harvard University Author-Name: Paul R. Milgrom Author-X-Name-First: Paul R. Author-X-Name-Last: Milgrom Author-Workplace-Name: Stanford University Title: Information and Timing in Repeated Partnerships Abstract: In a repeated partnership game with imperfect monitoring, we distinguish among the effects of (1) shortening the period over which actions are held fixed, (2) increasing the frequency with which accumulated information is reported, and (3) reducing the amount of discounting of payoffs between successive periods. While reducing the amount of discounting generally improves incentives for cooperation, the other two changes can have the reverse effect. When the game is specified in the customary way with information reported at the end of each period of fixed action, the net effect of shortening the period length can be to destroy all incentives for cooperation, reversing the usual conclusion associated with the Folk Theorem for repeated games. Moreover, when interest rates are low, reducing the frequency of information reporting can greatly enhance the efficiency of equilibrium. Classification-JEL: 026 Keywords: Monitoring, repeated games, partnership, incentives, folk theorems Length: 37 pages Creation-Date: 198805 Number: 875 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0875.pdf File-Format: application/pdf File-Size: 679 kb Handle: RePEc:cwl:cwldpp:875 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models Abstract: This paper establishes the asymptotic normality of series estimators for nonparametric regression models. Gallant's Fourier flexible form estimators, trigonometric series estimators, and polynomial series estimators are prime examples of the estimators covered by the results. The results apply to a wide variety of estimands in the regression model under consideration, including derivatives and integrals of the regression function. The errors in the model may be homoskedastic or heteroskeclastic. The paper also considers series estimators for additive interactive regression (AIR), seimparametric regression, and semiparametric index regression models and shows them to be consistent and asymptotically normal. All of the consistency and asymptotic normality results in the paper follow from one set of general results for series estimators. Keywords: Asymptotic normality, nonparametric regression, polynomial series, semiparametric regression, series estimators Note: CFP 776. Length: 70 pages Creation-Date: 1988 Revision-Date: 198905 Number: 874R Publication-Status: Published in Econometrica (March 1991), 59(2): 307-345 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0776.pdf File-Format: application/pdf File-Size: 1789 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0874-r.pdf File-Format: application/pdf File-Size: 1604 kb Handle: RePEc:cwl:cwldpp:874R Template-type: ReDIF-Paper 1.0 Author-Name: Donald J. Brown Author-X-Name-First: Donald J. Author-X-Name-Last: Brown Author-Email: donald.brown@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/brown.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Stephen A. Ross Author-X-Name-First: Stephen A. Author-X-Name-Last: Ross Title: Spanning, Valuation and Options Abstract: We model the space of marketed assets as a Riesz space of commodities. In this setting, two alternative characterizations are given of the space of continuous options on a bounded asset, s, with limited liability. The first characterization represents every continuous option on s as the uniform limit of portfolios of calls on s. The second characterization represents an option as a continuous sum (or integral) of Arrow-Debreu securities, with respect to s. The pricing implications of these representations are explored. In particular, the Breeden-Litzenberger pricing formula is shown to be a direct consequence of the integral representation theorem. Classification-JEL: 313, 213, 311 Keywords: Securities, portfolios, assets, arbitrage, marketed assets Length: 20 pages Creation-Date: 198806 Number: 873 Publication-Status: Published in Economic Theory (1991), 1(1): 3-12 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0873.pdf File-Format: application/pdf File-Size: 646 kb Handle: RePEc:cwl:cwldpp:873 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Spectral Regression for Cointegrated Time Series Abstract: This paper studies the use of spectral regression techniques in the context of cointegrated systems of multiple time series. Several alternatives are considered including efficient and band spectral methods as well as system and single equation techniques. It is shown that single equation spectral regressions suffer asymptotic bias and nuisance parameter problems that render these regressions impotent for inferential purposes. By contrast systems methods are shown to be covered by LAMN asymptotic theory, bringing the advantages of asymptotic media unbiasedness, scale nuisance parameters and the convenience of asymptotic chi-squared tests. System spectral methods also have advantages over full system direct maximum likelihood in that they do not require complete specification of the error processes. Instead they offer a nonparametric treatment of regression errors which avoids certain methodological problems of dynamic specification and permits additional generality in the class of error processes. Keywords: ARMA Model, co-integration, error correction, LAMN family, nonparametric, spectral regression Note: CFP 796. Length: 33 pages Creation-Date: 198804 Number: 872 Publication-Status: Published in William A. Barnett, James Powell and George E. Tauchen, eds., Nonparametric And Semiparametric Methods in Econometrics and Statistics: Proceedings of the Fifth International Symposium in Economic Theory and Econometrics, Cambridge University Press, 1991, pp. 413-435 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0796.pdf File-Format: application/pdf File-Size: 844 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0872.pdf File-Format: application/pdf File-Size: 501 kb Handle: RePEc:cwl:cwldpp:872 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Shuntian Yao Author-X-Name-First: Shuntian Author-X-Name-Last: Yao Title: Gold, Liquidity and Secured Loans in a Multistage Economy. Part I: Gold as Money Abstract: A multiperiod exchange economy with gold used both as money and as jewelry is examined in this paper. The existence of Nash equilibria is proved for the market games with finitely many traders as well as the games with a continuum of traders. For market games with a continuum of traders at infinite horizon, the existence of stationary Nash equilibria has been proved under the assumption that gold is properly distributed at the beginning or a secured loan between traders is available. Classification-JEL: 021, 026, 311 Keywords: Gold, exchange economy, Nash equilibrium, trading Note: CFP 731. Length: 45 pages Creation-Date: 198803 Number: 871 Publication-Status: Published in Journal of Economics (1989), 49(3): 245-277 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0731.pdf File-Format: application/pdf File-Size: 1088 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0871.pdf File-Format: application/pdf File-Size: 715 kb Handle: RePEc:cwl:cwldpp:871 Template-type: ReDIF-Paper 1.0 Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Mark W. Watson Author-X-Name-First: Mark W. Author-X-Name-Last: Watson Author-Workplace-Name: Northwestern University & NBER Title: Sources of Business Cycle Fluctuations Abstract: What shocks account for the business cycle frequency and long run movements of output and prices? This paper addresses this question using the identifying assumption that only supply shocks, such as shocks to technology, oil prices, and labor supply affect output in the long run. Real and monetary aggregate demand shocks can affect output, but only in the short run. This assumption sufficiently restricts the reduced form of key macroeconomic variables to allow estimation of the shocks and their effect on output and price at all frequencies. Aggregate demand shocks account for about twenty to thirty percent of output fluctuations at business cycle frequencies. Technological shocks account for about one-quarter of cyclical fluctuations, and about one-third of output's variance at low frequencies. Shocks to oil prices are important in explaining episodes in the 1970's and 1980's. Shocks that permanently affect labor output account for the balance of fluctuations in output, namely, about half of its variance at all frequencies. Classification-JEL: 131, 133, 134, 023 Keywords: Business cycle, supply shocks, inflation, output, demand shocks Length: 61 pages Creation-Date: 198804 Number: 870 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0870.pdf File-Format: application/pdf File-Size: 1222 kb Handle: RePEc:cwl:cwldpp:870 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Bruce E. Hansen Author-X-Name-First: Bruce E. Author-X-Name-Last: Hansen Title: Statistical Inference in Instrumental Variables Abstract: This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions. The framework of study is based on earlier work by Phillips and Durlauf (1986) and Park and Phillips (1988, 1989). In particular, the results in these papers are extended to allow for IV regressions that accommodate deterministic and stochastic regressors as well as quite general deterministic processes in the data generating mechanism. It is found that IV regressions are consistent even when the instruments are stochastically independent of the regressors. This phenomenon, which contrasts with traditional theory for stationary time series, is a beneficial artifact of spurious regression theory whereby stochastic trends in the instruments ensure their relevance asymptotically. Problems of inference are also addressed and some promising new theoretical results are reported. These involve a class of Wald tests which are modified by semiparametric corrections for serial correlation and for endogeneity. The resulting test statistics which we term fully modified Wald tests have limiting chi-squared distributions, thereby removing the obstacles to inference in cointegrated systems that were presented by the nuisance parameter dependencies in earlier work. Interestingly, IV methods themselves are insufficient to achieve this end and an endogeneity correction is still generally required, again in contrast to traditional theory. Our results therefore provide strong support for the conclusion reached by Hendry (1986) that there is no free lunch in estimating cointegrated systems. Some simulation results are reported which seek to explore the sampling behavior of our suggested procedures. These simulations compare our fully modified (semiparametric) methods with the parametric error correction methodology that has been extensively used in recent empirical research and with conventional least squares regression. Both the fully modified and error correction methods work well in finite samples and the sampling performance of each procedure confirms the relevance of asymptotic distribution theory, as distinct from superconsistency results, in discriminating between different statistical methods. Note: CFP 743. Length: 58 pages Creation-Date: 1988 Revision-Date: 198904 Number: 869R Publication-Status: Published in Review of Economic Studies (1990), 57: 99-125 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0743.pdf File-Format: application/pdf File-Size: 1145 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0869-r.pdf File-Format: application/pdf File-Size: 904 kb Handle: RePEc:cwl:cwldpp:869R Template-type: ReDIF-Paper 1.0 Author-Name: Truman F. Bewley Author-X-Name-First: Truman F. Author-X-Name-Last: Bewley Author-Email: truman.bewley@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/bewley.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Knightian Decision Theory and Econometric Inference Abstract: In this paper I attempt to reconcile the apparent definiteness of econometric practice with the vagueness of subjective probabilities assumed in Knightian decision theory. I argue that some standard uses of classical inference are Knightian in spirit, even though the formal justification of classical methods uses the frequentist notion of probability. Classical confidence regions may be viewed as defining sets of posterior means corresponding to a standardized set of prior distributions. Tests of the null hypothesis that a parameter equals a particular value may be viewed as determining whether it is rational, from a Knightian point of view, to act as if the null hypothesis were true. This interpretation of the tests seems to correspond fairly well to practice and to the informal story told by classical statisticians. Hence, one could argue that to this extent classical statisticians act unconsciously as Knightian decision makers. If one accepts this argument, then it is of interest to know what level of uncertainty aversion corresponds to the popular 5% significance level. Keywords: Decision, theory, classical statistics, probability intervals, subjective probability, Bayesian Length: 47 pages Creation-Date: 198803 Number: 868 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0868.pdf File-Format: application/pdf File-Size: 1057 kb Handle: RePEc:cwl:cwldpp:868 Template-type: ReDIF-Paper 1.0 Author-Name: Nancy A. Lutz Author-X-Name-First: Nancy A. Author-X-Name-Last: Lutz Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Warranties as Signals Under Consumer Moral Hazard Abstract: In this paper, I examine whether and how warranties serve as signals of product quality in an environment where there are opportunities for consumer moral hazard. My model is very similar to Grossman's. A risk neutral monopolist produced a good of fixed and exogenous quality. This product is offered to a market of identical risk-averse consumers, and it can be bundled with a warranty of the monopolist's choosing. The probability that the product breaks down is a function of its quality and the effort the consumer takes in using it. This consumer effort cannot be observed by the monopolist or any third party, so that the warranty cannot be made conditional on the effort taken, and in choosing the warranty the monopolist must take the moral hazard problem into account. Classification-JEL: 026, 511, 022, 611 Keywords: Warranties, moral hazard, signalling, product quality, game theory Note: CFP 739. Length: 42 pages Creation-Date: 198803 Number: 867 Publication-Status: Published in Rand Journal of Economics (Summer 1989), 20(2): 240-255 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0739.pdf File-Format: application/pdf File-Size: 1173 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0867.pdf File-Format: application/pdf File-Size: 959 kb Handle: RePEc:cwl:cwldpp:867 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Optimal Inference in Cointegrated Systems Abstract: This paper studies the properties of maximum likelihood estimates of co-integrated systems. Alternative formulations of such models are considered including a new triangular system error correction mechanism. It is shown that full system maximum likelihood brings the problem of inference within the family that is covered by the locally asymptotically mixed normal asymptotic theory provided that all unit roots in the system have been eliminated by specification and data transformation. This result has far reaching consequences. It means that cointegrating coefficient estimates are symmetrically distributed and median unbiased asymptotically, that an optimal asymptotic theory of inference applies and that hypothesis tests may be conducted using standard asymptotic chi-squared sets. Keywords: Co-integration, error correction model, maximum likelihood, unit roots, asymptotic theory Note: CFP 777. Length: 28 pages Creation-Date: 1988 Revision-Date: 198908 Number: 866R Publication-Status: Published in Econometrica (March 1991), 59(2): 283-306 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0777.pdf File-Format: application/pdf File-Size: 1253 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0866-r.pdf File-Format: application/pdf File-Size: 844 kb Handle: RePEc:cwl:cwldpp:866R Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Characteristic Function of the Dirichlet and Multivariate F Distributions Abstract: Formulae are derived for the characteristic function of the inverted Dirichlet distribution and hence the multivariate F. The analysis involves a new function with multiple arguments that extends the confluent hypergeometric function of the second kind. This function and its properties are studied in the paper and a simple integral representation is given which is useful for numerical work. A special case connected with the multivariate t distribution is also explored. Keywords: Hypergeometric function, contour integral, differential equation, characteristic function Length: 19 pages Creation-Date: 198801 Number: 865 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0865.pdf File-Format: application/pdf File-Size: 411 kb Handle: RePEc:cwl:cwldpp:865 Template-type: ReDIF-Paper 1.0 Author-Name: Adam Brandenburger Author-X-Name-First: Adam Author-X-Name-Last: Brandenburger Author-Workplace-Name: Harvard Business School Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Common Knowledge of Summary Statistics Abstract: Consider a group of people who are asked to offer their opinions on some issue. "Business confidence" surveys are an example: groups of businessmen are often asked for their predictions of economic indicators such as growth or inflation rates. Each member of the group makes a prediction based on his or her private information, and the average prediction is then publicly announced. If the members of the group are then allowed to revise their opinions, based on whatever information they glean from the public announcement, is there any tendency for the opinions in the group to converge on a common, consensus opinion? In this note we show that under certain conditions the answer to this question is yes. Classification-JEL: 213, 025 Keywords: Common knowledge, public opinion, group behavior Length: 10 pages Creation-Date: 198802 Number: 864 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0864.pdf File-Format: application/pdf File-Size: 194 kb Handle: RePEc:cwl:cwldpp:864 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Michael Magill Author-X-Name-First: Michael Author-X-Name-Last: Magill Author-Workplace-Name: University of Southern California Author-Name: Martine Quinzii Author-X-Name-First: Martine Author-X-Name-Last: Quinzii Author-Workplace-Name: University of Southern California Author-Name: J. Dreze Author-X-Name-First: J. Author-X-Name-Last: Dreze Author-Workplace-Name: CORE Title: Generic Inefficiency of Stock Market Equilibrium When Markets Are Incomplete Abstract: A stock market is a mechanism by which the ownership and control of firms is determined through the trading of securities. It is on this market that many of the major risks faced by society are shared through the exchange of securities and the production decisions that influence the present and future supply of resources are determined. If the overall structure of markets is incomplete can the stock market be expected to perform its role of exchanging risks and allocating investment efficiently? It is this question that we seek to answer. Classification-JEL: 313 Keywords: Securities, stock market, market efficiency Note: CFP 751. Length: 53 pages Creation-Date: 198802 Number: 863 Publication-Status: Published in Journal of Mathematical Economics (1990), 19: 113-151 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0751.pdf File-Format: application/pdf File-Size: 1594 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0863.pdf File-Format: application/pdf File-Size: 1386 kb Handle: RePEc:cwl:cwldpp:863 Template-type: ReDIF-Paper 1.0 Author-Name: Richard C. Levin Author-X-Name-First: Richard C. Author-X-Name-Last: Levin Author-Email: richard.levin@yale.edu Author-Workplace-Name: Dept. of Economics, Yale University Author-Workplace-Homepage: http://www.econ.yale.edu/ Author-Name: Alvin K. Klevorick Author-X-Name-First: Alvin K. Author-X-Name-Last: Klevorick Author-Email: alvin.klevorick@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/klevorick.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Richard R. Nelson Author-X-Name-First: Richard R. Author-X-Name-Last: Nelson Author-Name: Sidney G. Winter Author-X-Name-First: Sidney G. Author-X-Name-Last: Winter Title: Appropriating the Returns from Industrial R&D Abstract: In this paper, we describe the results of an inquiry into the nature of appropriability conditions in over one hundred manufacturing industries, and we discuss how this information has been and might be used to cast light on important issues in the economics of innovation and public policy. Our data, derived from a survey of high-level R&D executives, are informed opinions about the nature of an industry's technological and economic environment rather than quantitative measures of inputs and outputs. Classification-JEL: 621, 612 Keywords: R&D, technological game, innovation, patents, public policy Note: CFP 714. Length: 79 pages Creation-Date: 198802 Number: 862 Publication-Status: Published in Brookings Papers on Economic Activity (1987), 3: 783-820 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0714.pdf File-Format: application/pdf File-Size: 1689 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0862.pdf File-Format: application/pdf File-Size: 1848 kb Handle: RePEc:cwl:cwldpp:862 Template-type: ReDIF-Paper 1.0 Author-Name: Michael J. Todd Author-X-Name-First: Michael J. Author-X-Name-Last: Todd Author-Workplace-Name: Cornell University Author-Name: Yinyu Ye Author-X-Name-First: Yinyu Author-X-Name-Last: Ye Author-Workplace-Name: Stanford University Title: A Centered Projective Algorithm for Linear Programming Abstract: We describe a projective algorithm for linear programming that shares features with Karmarkar's projective algorithm and its variants and with the path-following methods of Gonzaga, Kojima-Mizuno-Yoshise, Monteiro-Adler, Renegar, Vaidya and Ye. It operates in a primal-dual setting, stays close to the central trajectories, and converges in O(square root of n times L) iterations like the latter methods. (Here n is the number of variables and L the input size of the problem). However, it is motivated by seeking reductions in a suitable potential function as in projective algorithms, and the approximate centering is an automatic byproduct of our choice of potential function. Classification-JEL: 213 Keywords: Linear programming, Karmarkar's algorithm, algorithm Note: CFP 769. Length: 40 pages Creation-Date: 198802 Number: 861 Publication-Status: Published in Mathematics of Operations Research (August 1990), 15(3): 508-529 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0769.pdf File-Format: application/pdf File-Size: 868 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0861.pdf File-Format: application/pdf File-Size: 726 kb Handle: RePEc:cwl:cwldpp:861 Template-type: ReDIF-Paper 1.0 Author-Name: Philip H. Dybvig Author-X-Name-First: Philip H. Author-X-Name-Last: Dybvig Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Chi-fu Huang Author-X-Name-First: Chi-fu Author-X-Name-Last: Huang Author-Workplace-Name: MIT Title: Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans Abstract: A restriction to nonnegative wealth is sufficient to preclude all arbitrage opportunities in financial models that have risk neutral probabilities that are valid for all simple strategies. Imposing nonnegative wealth does not constrain agents from making the choice they would make under the standard integrability condition. This conclusion does not depend on whether the markets are complete. Classification-JEL: 313, 311 Keywords: Investments, free lunch, arbitrage, option pricing, continuous time Length: 20 pages Creation-Date: 198802 Number: 860 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0860.pdf File-Format: application/pdf File-Size: 575 kb Handle: RePEc:cwl:cwldpp:860 Template-type: ReDIF-Paper 1.0 Author-Name: Philip H. Dybvig Author-X-Name-First: Philip H. Author-X-Name-Last: Dybvig Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Increases in Risk Aversion and Portfolio Choice in a Complete Market Abstract: This note examines the effect of changes in risk aversion on the optimal portfolio choice in a complete market. It is shown that an agent who is less risk averse in the Pratt (1964) sense than another will choose a portfolio whose payoff is distributed as the other's payoff plus a nonnegative random variable plus conditional-mean-zero noise. The proof of the result uses simple first order conditions and basic results from stochastic dominance. Classification-JEL: 313, 311 Keywords: Investments, portfolio theory, stochastic dominance, risk aversion, complete markets Length: 10 pages Creation-Date: 198802 Number: 859 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0859.pdf File-Format: application/pdf File-Size: 199 kb Handle: RePEc:cwl:cwldpp:859 Template-type: ReDIF-Paper 1.0 Author-Name: John Y. Campbell Author-X-Name-First: John Y. Author-X-Name-Last: Campbell Author-Workplace-Name: Princeton University Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Stock Prices, Earnings and Expected Dividends Abstract: This paper presents estimates indicating that, for aggregate U.S. stock market data 1871-1986, a long historical average of real earnings is a good predictor of the present value of future real dividends. This is true even when the information contained in stock prices is taken into account. We estimate that for each year the optimal forecast of the present value of future real dividends is roughly a weighted average of moving average earnings and current real price, with between 2/3 and 3/4 of the weight on the earnings measure. This means that simple present value models of stock market prices can be strongly rejected. We use a vector autoregressive approach which enables us to compute the implications of this for the behavior of stock prices and returns. We estimate that log dividend-price ratios are more variable than, and virtually uncorrelated with, their theoretical counterparts given the present value models. Annual returns on stocks are quite highly correlated with their theoretical counterparts, but are two to four times as variable. Our approach also reveals the connection between recent papers showing forecastability of long-horizon returns on corporate stocks, and earlier literature claiming that stock prices are too volatile to be accounted for in terms of simple present value models. We show that excess volatility directly implies the forecastability of long-horizon returns. Classification-JEL: 313, 132, 131 Keywords: Stock market, dividends, stock prices, volatility Length: 41 pages Creation-Date: 198801 Number: 858 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0858.pdf File-Format: application/pdf File-Size: 806 kb Handle: RePEc:cwl:cwldpp:858 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Informational Content of Ex Ante Forecasts Abstract: The informational content of different forecasts can be compared by regressing the actual change in a variable to be forecasted on forecasts of the change. We use the procedure in Fair and Shiller (1987) to examine the informational content of three sets of ex ante forecasts: the American Statistical Association and National Bureau of Economic Research Survey (ASA). Data Resources Incorporated (DRI), and Wharton Economic Forecasting Associates (WEFA). We compare these forecasts to each other and to "quasi ex ante" forecasts generated from a vector autoregressive model, an autoregressive components model and a large-scale structural model (the Fair model). Classification-JEL: 132, 212 Keywords: Forecasts, ex ante forecasts, informational content Note: CFP 736. Length: 17 pages Creation-Date: 198801 Number: 857 Publication-Status: Published in Review of Economics and Statistics (May 1989), 71(2): 325-331 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0736.pdf File-Format: application/pdf File-Size: 547 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0857.pdf File-Format: application/pdf File-Size: 388 kb Handle: RePEc:cwl:cwldpp:857 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: VAR Models as Structural Approximations Abstract: This paper presents a way of estimating how accurate VAR models are likely to be for answering structural questions. Data are generated from a dynamic deterministic solution of a structural model; a VAR model is estimated using a subset of these data; and the properties of the VAR model are compared to the properties of the structural model. This procedure has the advantage of eliminating the effects of error terms, since the data are generated for a deterministic simulation. The results show that the VAR models do not seem to be good structural approximations. Length: 17 pages Creation-Date: 1987 Revision-Date: 198903 Number: 856R Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0856-r.pdf File-Format: application/pdf File-Size: 449 kb Handle: RePEc:cwl:cwldpp:856R Template-type: ReDIF-Paper 1.0 Author-Name: David G. Pearce Author-X-Name-First: David G. Author-X-Name-Last: Pearce Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Renegotiation-Proof Equilibria: Collective Rationality and Intertemporal Cooperation Abstract: Cooperation in repeated games relies on the possibility that equilibrium play following some t-period history depends on more than simply the structure of the game remaining after the first t periods, that structure being always the same. In a nondegenerate theory of renegotiation, what a player expects, and the statements he finds credible at the end of period t must be affected by the history that has transpired, and perhaps by the implicit agreement that was in force. The solution concept proposed in this paper acknowledges both these influences, while imposing a certain stationarity on beliefs regarding what renegotiation options are available: renegotiation to an equilibrium sigma will not take place if, after some history h, the continuation equilibrium sigma given h is itself vulnerable to renegotiation to sigma (in the sense that all players prefer sigma to sigma given h). Classification-JEL: 721 Keywords: Planning, natural resource Length: 33 pages Creation-Date: 198712 Number: 855 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0855.pdf File-Format: application/pdf File-Size: 631 kb Handle: RePEc:cwl:cwldpp:855 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Pradeep Dubey Author-X-Name-First: Pradeep Author-X-Name-Last: Dubey Author-Workplace-Name: SUNY at Stony Brook Title: A Note on an Optimal Garnishing Rule Abstract: A simple optimal garnishing rule to discourage strategic bankruptcy is derived. Classification-JEL: 021, 026, 611 Keywords: Garnishing, bankruptcy Note: CFP 708. Length: 3 pages Creation-Date: 198711 Number: 854 Publication-Status: Published in Economics Letters (1988), 27: 5-6 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0708.pdf File-Format: application/pdf File-Size: 74 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0854.pdf File-Format: application/pdf File-Size: 60 kb Handle: RePEc:cwl:cwldpp:854 Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Investor Behavior in the 1987-10 Stock Market Crash: Survey Evidence Abstract: Questionnaires were sent out at the time of the October 19, 1987 stock market crash to both individual and institutional investors inquiring about their behavior during the crash. Nearly 1000 responses were received. The survey results show that: 1. No news story or rumor appearing on the 19th or over the preceding weekend was responsible for investor behavior, 2. Investors' importance rating of news appearing over the preceding week showed only a slight relation to decisions to buy or sell, 3. There was a great deal of investor talk and anxiety around October 19, much more than suggested by the volume of trade, 4. Many investors thought that they could predict the market, 5. Both buyers and sellers generally thought before the crash that the market was overvalued, 6. Most investors interpreted the crash as due to the psychology of other investors, 7. Many investors were influenced by technical analysis considerations, 8. Portfolio insurance is only a small part of predetermined stop-loss behavior, and 9. Some investors changed their investment strategy before the crash. Classification-JEL: 313 Keywords: Stock market, survey, crash, investor, panic, volume Length: 43 pages Creation-Date: 198711 Number: 853 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0853.pdf File-Format: application/pdf File-Size: 1093 kb Handle: RePEc:cwl:cwldpp:853 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Multiple Regression with Integrated Time Series Abstract: Recent work on the theory of regression with integrated process is reviewed. This work is particularly relevant in economics where many financial series and macroeconomic time series exhibit nonstationary characteristics and are often well modeled individually as simple ARIMA processes. The theory makes extensive use of weak convergence methods and allows for integrated processes that are driven by quite general weakly dependent and possibly heterogeneously distributed innovations. The theory also includes near integrated time series, which have roots near unity, and cointegrated series, which move together over time but are individually nonstationary. A general framework for asymptotic analysis is given which involves limiting Gaussian functionals and extends the LAN and LAMN families of conventional asymptotic theory. An application to the Gaussian AR(1) is reported. Keywords: LAMN, LAN asymptotics, stochastic integral, unit roots, weak convergence, weak dependence Note: CFP 720. Length: 41 pages Creation-Date: 198711 Number: 852 Publication-Status: Published in Contemporary Mathematics (1988), 80: 79-105 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0720.pdf File-Format: application/pdf File-Size: 838 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0852.pdf File-Format: application/pdf File-Size: 657 kb Handle: RePEc:cwl:cwldpp:852 Template-type: ReDIF-Paper 1.0 Author-Name: Karl E. Case Author-X-Name-First: Karl E. Author-X-Name-Last: Case Author-Workplace-Name: Wellesley College Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Prices of Single Family Homes Since 1970: New Indexes for Four Cities Abstract: This paper uses data on nearly a million homes sold in four metropolitan areas -- Atlanta, Chicago, Dallas and San Francisco -- to construct quarterly indexes of existing home prices between 1970 and 1986. We propose and apply a new method of constructing such indexes which we call the method of constructing such indexes which we call the weighted repeat sales method (WRS). We believe the results give an accurate picture of the actual rate of appreciation in home prices in the four cities. The paper explains the construction of the index, discusses the results and compares them with the National Association of Realtors data on the median price of existing single family homes for the period 1981-1986. Classification-JEL: 026, 012 Keywords: Noncooperative games, agreements, repeated games Length: 53 pages Creation-Date: 198704 Number: 851 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0851.pdf File-Format: application/pdf File-Size: 1008 kb Handle: RePEc:cwl:cwldpp:851 Template-type: ReDIF-Paper 1.0 Author-Name: Siddhartha Sahi Author-X-Name-First: Siddhartha Author-X-Name-Last: Sahi Author-Name: Shuntian Yao Author-X-Name-First: Shuntian Author-X-Name-Last: Yao Title: The Noncooperative Equilibria of a Trading Economy with Complete Markets and Consistent Prices Length: 31 pages Creation-Date: 198709 Revision-Date: 198712 Number: 850R Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08b/d0850-r.pdf File-Format: application/pdf File-Size: 483 kb Handle: RePEc:cwl:cwldpp:850R Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Inventories, Investment, Inflation and Taxes Abstract: Sales today were made possible by inputs of factor services and intermediate goods at various previous dates. Prices change between the input dates and the sale date. Especially in periods of general inflation, these price movements create ambiguities in the reckoning of profits. The accounting definition used in taxing profits can have significant economic effects. Tax accounting is generally not neutral vis-a-vis general inflation. Costing inputs at their historical nominal prices (FIFO) is a real burden and disincentive, greater the higher the inflation rate. It is analogous to depreciating durable capital at historical cost. However, it may be partially, completely, or excessively offset by another non-neutrality, the deductibility of nominal interest from taxable income. This too has analogous effects on after-tax returns from fixed capital. Classification-JEL: 521, 323, 134 Keywords: Inventories, investment, inflation, taxes, depreciation Note: CFP 712. Length: 19 pages Creation-Date: 198709 Number: 849 Publication-Status: Published in A. Chikan and M.C. Lovell, eds., The Economics of Inventory Management, Elsevier Science, 1988, pp. 285-304 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0712.pdf File-Format: application/pdf File-Size: 546 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0849.pdf File-Format: application/pdf File-Size: 427 kb Handle: RePEc:cwl:cwldpp:849 Template-type: ReDIF-Paper 1.0 Author-Name: Vassilis A. Hajivassiliou Author-X-Name-First: Vassilis A. Author-X-Name-Last: Hajivassiliou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: An Aggregative Disequilibrium Model of the U.S. Labour Market Abstract: A model is presented in which aggregation over microsectors, each in different extent of disequilibrium, has implications analogous to the standard single aggregate sector switching disequilibrium model. Empirical implementation of the model of this paper is less involved than estimation of the standard model. Hence the approach here may be seen both as providing an underlying micro justification for the switching disequilibrium model, and as a computationally simpler (though statistically less efficient) technique. The model is estimated from post-war labour market quarterly data for the U.S. Manufacturing sector. We find the supply side more satisfactorily determined than in past disequilibrium studies. Length: 42 pages Creation-Date: 198707 Number: 848 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0848.pdf File-Format: application/pdf File-Size: 962 kb Handle: RePEc:cwl:cwldpp:848 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Sam Ouliaris Author-X-Name-First: Sam Author-X-Name-Last: Ouliaris Title: Asymptotic Properties of Residual Based Tests for Cointegration Abstract: This paper develops an asymptotic theory for residual based tests for cointegration. These tests involve procedures that are designed to detect the presence of a unit root in the residuals of (cointegrating) regressions among the levels of economic time series. Attention is given to the augmented Dickey-Fuller (ADF) test that is recommended by Engle-Granger (1987) and the Z(a) and Z(t) unit root tests recently proposed by Phillips (1987). Two new tests are also introduced, one of which is invariant to the normalization of the cointegrating regression. All of these tests are shown to be asymptotically similar and simple representations of their limiting distributions are given in terms of standard Brownian motion. The ADF and Z(t) tests are asymptotically equivalent. Power properties of the tests are also studied. The analysis shows that all the tests are consistent if suitably constructed but that the ADF and Z(t) tests have slower rates of divergence under cointegration than the other tests. This indicates that, at least in large samples, the Z(a) test should have superior power properties. Keywords: Co-integration, consistent tests, unit root tests, asymptotic theory, power Note: CFP 746. Length: 51 pages Creation-Date: 1987 Revision-Date: 198807 Number: 847R Publication-Status: Published in Econometrica (January 1990), 58(1): 165-193 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0746.pdf File-Format: application/pdf File-Size: 1087 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0847-r.pdf File-Format: application/pdf File-Size: 828 kb Handle: RePEc:cwl:cwldpp:847R Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations Abstract: Under general conditions the sample covariance matrix of a vector martingale and its differences converges weakly to the matrix stochastic integral from zero to one of BdB; where B is vector Brownian motion. For strictly stationary and ergodic sequences, rather than martingale differences, a similar result obtains. In this case, the limit is the same with a constant matrix, of bias terms whose magnitude depends on the serial correlation properties of the sequence. This note gives a simple proof of the result using martingale approximations. Keywords: Martingale approximations, stochastic integrals, weak convergence Note: CFP 716. Length: 9 pages Creation-Date: 198707 Number: 846 Publication-Status: Published in Econometric Theory (1988), 4: 528-533 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0716.pdf File-Format: application/pdf File-Size: 186 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0846.pdf File-Format: application/pdf File-Size: 135 kb Handle: RePEc:cwl:cwldpp:846 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Partially Identified Econometric Models Abstract: This paper studies a class of models where full identification is not necessarily assumed. We term such models partially identified. It is argued that partially identified systems are of practical importance since empirical investigators frequently proceed under conditions that are best described as apparent identification. One objective of the paper is to explore the properties of conventional statistical procedures in the context of identification failure. Our analysis concentrates on two major types of partially identified model: the classic simultaneous equations model under rank condition failures; and time series spurious regressions. Both types serve to illustrate the extensions that are needed to conventional asymptotic theory if the theory is to accommodate partially identified systems. Keywords: Gaussian functionals, identification, simultaneous equations, spurious regressions, asymptotic theory Note: CFP 728. Length: 95 pages Creation-Date: 1987 Revision-Date: 198808 Number: 845R Publication-Status: Published in Econometric Theory (1989), 5: 181-240 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0728.pdf File-Format: application/pdf File-Size: 1781 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0845-r.pdf File-Format: application/pdf File-Size: 1366 kb Handle: RePEc:cwl:cwldpp:845R Template-type: ReDIF-Paper 1.0 Author-Name: Rosa L. Matzkin Author-X-Name-First: Rosa L. Author-X-Name-Last: Matzkin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Marcel K. Richter Author-X-Name-First: Marcel K. Author-X-Name-Last: Richter Author-Workplace-Name: University of Minnesota Title: Testing Strictly Concave Rationality Abstract: We prove that the Strong Axiom of Revealed Preference tests the existence of a strictly quasiconcave (in fact, continuous, generically C(infinity), strictly concave, and strictly monotone) utility function generating finitely many demand observations. This sharpens earlier results of Afriat, Diewert, and Varian that tested ("nonparametrically") the existence of a piecewise linear utility function that could only weakly generate those demand observations. When observed demand is also invertible, we show that the rationalizing can be done in a C(infinity) way, thus extending a result of Chiappori and Rochet from compact sets to all of R(n). For finite data sets, one implication of our result is that even some weak types of rational behavior -- maximization of pseudotransitive or semitransitive preferences -- are observationally equivalent to maximization of continuous, strictly concave, and strictly monotone utility functions. Classification-JEL: 022, 213 Keywords: Nonparametric tests, revealed preference, rational choice, concave utility, strong axiom of revealed preference Note: CFP 782. Length: 20 pages Creation-Date: 198711 Number: 844 Publication-Status: Published in Journal of Economic Theory (April 1991), 53(2): 287-303 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0782.pdf File-Format: application/pdf File-Size: 670 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0844.pdf File-Format: application/pdf File-Size: 461 kb Handle: RePEc:cwl:cwldpp:844 Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: J. Huston McCulloch Author-X-Name-First: J. Huston Author-X-Name-Last: McCulloch Author-Workplace-Name: Ohio State University Title: The Term Structure of Interest Rates. U.S. Government Term Structure Data Abstract: This paper consolidates and interprets the literature on the term structure, as it stands today. Definitions of rates of return, forward rates and holding returns for all time intervals are treated here in a uniform manner and their interrelations, exact or approximate, delineated. The concept of duration is used throughout to simplify mathematical expressions. Continuous compounding is used where possible, to avoid arbitrary distinctions based on compounding assumptions. Both the theoretical and the empirical literature are treated. The attached tables by J. Huston McCulloch give term structure data for U.S. government securities 1946-1987. The tables give discount bond yields, forward rates and par bond yields as defined in the paper. The data relate to the concepts in the paper more precisely than does any previously published data series. Classification-JEL: 311, 313 Keywords: Term structure, interest rates, government securities, rates of return, forward rates, bond yields Note: CFP 766. Length: 119 pages Creation-Date: 198707 Number: 843 Publication-Status: Published in B.M. Friedman and F.H. Hahn, eds., Handbook of Monetary Economics, Vol. 1, 1990, pp. 627-715 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0766.pdf File-Format: application/pdf File-Size: 4484 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0843.pdf File-Format: application/pdf File-Size: 3482 kb Handle: RePEc:cwl:cwldpp:843 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Vassilis A. Hajivassiliou Author-X-Name-First: Vassilis A. Author-X-Name-Last: Hajivassiliou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Bimodal t-Ratios Abstract: This paper studies the sampling distribution of the conventional t-ratio when the sample comprises independent draws from a standard Cauchy (0,1) population. It is shown that this distribution displays a striking bimodality for all sample sizes and that the bimodality persists asymptotically. An asymptotic theory is developed in terms of bivariate stable variates and the bimodality is explained by the statistical dependence between the numerator and denominator statistics of the t-ratio. This dependence also persists asymptotically. These results are in contrast to the classical t statistic constructed from a normal population, for which the numerator and denominator statistics are independent and the denominator, when suitably scaled, is a constant asymptotically. Our results are also in contrast to those that are known to apply for multivariate spherical populations. In particular, data from an n dimensional Cauchy population are well known to lead to a t-ratio statistic whose distribution is classical t with n-1 degrees of freedom. In this case the univariate marginals of the population are all standard Cauchy (0,1) but the sample data involves a special form of dependence associated with the multivariate spherical assumption. Our results therefore serve to highlight the effects of the dependence in component variates that is induced by a multivariate spherical population. Some extensions to symmetric stable populations with exponent parameter alpha does not equal 1 are also indicated. Simulation results suggest that the sampling distributions are well approximated by the asymptotic theory even for samples as small as n = 20. Length: 26 pages Creation-Date: 198707 Number: 842 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0842.pdf File-Format: application/pdf File-Size: 405 kb Handle: RePEc:cwl:cwldpp:842 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Silver and Gold and Liquidity Abstract: A simple model with trade in gold is explored where the cost of liquidity is measured in terms of utility foregone by using the gold as a money or means of payment rather than for utilitarian purposes. We close with remarks on the use of both silver and gold. Length: 8 pages Creation-Date: 198706 Number: 841 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0841.pdf File-Format: application/pdf File-Size: 135 kb Handle: RePEc:cwl:cwldpp:841 Template-type: ReDIF-Paper 1.0 Author-Name: Grant H. Hillier Author-X-Name-First: Grant H. Author-X-Name-Last: Hillier Title: Joint Distribution Theory for Some Statistics Based on LIML and TSLS Abstract: In the context of a single linear structural equation under classical assumptions, we derive the joint conditional density of the LIML endogenous coefficient estimator, and the usual characteristic root arising from the LIML procedure, given the OLS estimates of the reduced form coefficients for the excluded exogenous variables. This provides the joint distributions for various combinations of the statistics commonly used for inference in this model, and is hence an important stepping stone in the analysis of these procedures. The main result also leads to a new derivation of the density of the LIML estimator itself, and provides a result which is directly comparable to earlier results for IV estimators, including OLS and TSLS. We also consider briefly the density of the LIML structural variance estimator, and the joint density of the LIML and TSLS estimators for the endogenous coefficients. Keywords: LIML, Two state least squares, density function Length: 31 pages Creation-Date: 198706 Number: 840 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0840.pdf File-Format: application/pdf File-Size: 464 kb Handle: RePEc:cwl:cwldpp:840 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Kathryn M. Dominguez Author-X-Name-First: Kathryn M. Author-X-Name-Last: Dominguez Author-Workplace-Name: Harvard University Title: Effects of the Changing U.S. Age Distribution on Macroeconomic Equations Abstract: The effects of the changing U.S. age distribution on various macroeconomic equations are examined in this paper. The equations include consumption, money demand, housing investment, and labor force participation equations. Seven groups are analyzed: 16-19, 20-24, 30-39, 40-54, 55-64, and 65+. There seems to be enough variance in the age distribution data to allow reasonably precise estimates of the effects of a number of age categories on the macro variables. The results show that, other things being equal, age groups 30-39 and 40-54 consume less than average, invest less in housing than average, and demand more money than average. Age group 55-64 consumes more and demands more money. If these estimates are right, they imply, other things being equal, that consumption and housing investment will be negatively affected in the future as more and more baby boomers enter the 30-54 age group. The demand for money will be positively affected. If, as Easterlin argues, the average wage that an age group faces is negatively affected by the percent of the population in that group, then the labor force participation rate of a group should depend on the relative size of the group. If the substitution effect dominates, people in a large group should work less than average, and if the income effect dominates, they should work more than average. The results indicate that the substitution effect dominates for women 25-54 and that the income effect dominates for men 25-54. Classification-JEL: 132, 212, 841, 824 Keywords: Econometric model, demographics, housing investment, labor force participation, consumption, money demand Note: CFP 800. Length: 33 pages Creation-Date: 198706 Number: 839 Publication-Status: Published in American Economic Review (1991), 81(5): 1276-1294 File-URL: http://cowles.econ.yale.edu/P/cp/p08a/p0800.pdf File-Format: application/pdf File-Size: 1295 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0839.pdf File-Format: application/pdf File-Size: 730 kb Handle: RePEc:cwl:cwldpp:839 Template-type: ReDIF-Paper 1.0 Author-Name: Donald J. Brown Author-X-Name-First: Donald J. Author-X-Name-Last: Brown Author-Email: donald.brown@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/brown.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://www.econ.yale.edu/ Author-Name: Charalambos Aliprantis Author-X-Name-First: Charalambos Author-X-Name-Last: Aliprantis Author-Workplace-Name: IUPUI Author-Name: Owen Burkinshaw Author-X-Name-First: Owen Author-X-Name-Last: Burkinshaw Author-Workplace-Name: IUPUI Title: Valuation and Optimality in Exchange Economies with a Countable Number of Agents Abstract: We present versions of the two fundamental welfare theorems of economics for exchange economies with a countable number of agents and an infinite dimensional commodity space. These results are then specialized to the overlapping generations model. Classification-JEL: 021, 024 Keywords: Welfare theorem, overlapping generations model, Pareto optimality, competitive equilibrium Length: 17 pages Creation-Date: 198706 Number: 838 Publication-Status: Published in C.D. Aliprantis, K.C. Border and W.A.J. Luxemburg, Positive Operators, Riesz Spaces, and Economics, Springer-Verlag, 1991 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0838.pdf File-Format: application/pdf File-Size: 520 kb Handle: RePEc:cwl:cwldpp:838 Template-type: ReDIF-Paper 1.0 Author-Name: Thomas Rutherford Author-X-Name-First: Thomas Author-X-Name-Last: Rutherford Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Implementational Issues and Computational Performance Solving Applied General Equilibrium Models with SLCP Abstract: This paper reports on an implementation of Mathiesen's sequential method for solving applied general equilibrium models. In this approach, the underlying nonlinear complementarity problem is solved by successive linearization. The paper discusses model formulation, implementation and performance. Several test problems and empirical models are used to evaluate efficiency and robustness. Classification-JEL: 213, 021, 214 Keywords: General equilibrium models, algorithm, numerical modeling Length: 34 pages Creation-Date: 198705 Number: 837 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0837.pdf File-Format: application/pdf File-Size: 589 kb Handle: RePEc:cwl:cwldpp:837 Template-type: ReDIF-Paper 1.0 Author-Name: Thomas Rutherford Author-X-Name-First: Thomas Author-X-Name-Last: Rutherford Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Modeling System for Applied General Equilibrium Analysis Abstract: Numerical modeling in the Arrow-Debreu framework has emerged as a consistent approach for economic analysis. A major disadvantage of the applied general equilibrium (AGE) framework has been the high degree of technical expertise required for formulating and solving these models. This paper describes a micro-computer for AGE modeling. The system, named MPS/GE, combines an efficient solution algorithm with an interactive user-interface. Using MPS/GE, models containing up to 300 prices and activities can be formulated and solved on an IBM PC. This makes AGE modeling accessible to a wider group of policy analysts and educators than was previously the case. Classification-JEL: 213, 214, 021 Keywords: General equilibrium, numerical, modeling, algorithm, software Length: 45 pages Creation-Date: 198705 Number: 836 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0836.pdf File-Format: application/pdf File-Size: 780 kb Handle: RePEc:cwl:cwldpp:836 Template-type: ReDIF-Paper 1.0 Author-Name: Truman F. Bewley Author-X-Name-First: Truman F. Author-X-Name-Last: Bewley Author-Email: truman.bewley@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/bewley.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Knightian Decision Theory, Part II. Intertemporal Problems Abstract: The theory of choice proposed in "Knightian Decision Theory, Part I" is here applied to intertemporal problems. An analogue of dynamic programming called maxmin programming is developed. Also, it is shown that detailed contingent planning may not be needed in order to achieve maximality, a program being maximal if no other program is preferred to it. In certain circumstances, a maximal program can be achieved by making a finite calculation in each period. This calculation ignores distant future states and could also ignore unlikely contingencies. A decision maker making such calculations would behave much like a satisficer. Classification-JEL: 022, 511, 213 Keywords: Satisficing, decision theory, dynamic programming, maxmin programming Length: 36 pages Creation-Date: 198705 Number: 835 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0835.pdf File-Format: application/pdf File-Size: 750 kb Handle: RePEc:cwl:cwldpp:835 Template-type: ReDIF-Paper 1.0 Author-Name: Donald J. Brown Author-X-Name-First: Donald J. Author-X-Name-Last: Brown Author-Email: donald.brown@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/brown.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Charalambos Aliprantis Author-X-Name-First: Charalambos Author-X-Name-Last: Aliprantis Author-Workplace-Name: IUPUI Author-Name: Owen Burkinshaw Author-X-Name-First: Owen Author-X-Name-Last: Burkinshaw Author-Workplace-Name: IUPUI Title: Equilibria in Exchange Economies with a Countable Number of Agents Abstract: The existence of equilibria is established in an overlapping generations exchange economy, where each generation lives for two periods and the commodity space is the positive cone of an infinite dimensional Riesz space. In particular, we establish the existence of equilibria in the stochastic overlapping generations model, i.e., we establish the existence of equilibria when the commodity space in each period is L_{infinity} equipped with the Mackey topology tau(L_{infinity},L_{1}). Length: 38 pages Creation-Date: 198704 Number: 834R Publication-Status: Published in Journal of Mathematical Analysis and Applications (1989), 142(1): 250-299 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0834-r.pdf File-Format: application/pdf File-Size: 1154 kb Handle: RePEc:cwl:cwldpp:834R Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Econometric Modeling as Information Aggregation Abstract: The information contained in the forecasts from two econometric models can be compared by regressing the actual change in the variable forecasted on the two forecasts of the change. We do such comparisons in this paper, where the forecasts are based only on information through the period prior to the first period of the forecast. If a model's forecast is statistically significant in such a regression, we conclude that the model captures information not in the other model whose forecast is also included in the regression. The models studied include the Fair model, vector autoregressive (VAR) models estimated by ordinary least squares, vector autoregressive models estimated with Litterman priors, and a new class of models, which we call "autoregressive components: (AC) models. The AC models divide GNP into components and estimate an autoregressive equation for each component. Our results show that the Fair model's forecasts contain information not in the forecasts of the VAR and AC models. The AC models contain no information not in the Fair model, which indicates that the Fair model uses all the useful information in the components. The VAR models contain information not in the Fair model for the four-quarter-ahead forecasts but not the one- quarter-ahead forecasts. The best AC model contains information not in the best VAR model, which indicates that there is useful information in the components that the VAR models are not using. The best VAR model contains information not in the best AC model for the four-quarter-ahead forecasts but not the one-quarter-ahead forecasts. Classification-JEL: 132, 211 Keywords: Forecasting, autoregressive components model Note: CFP 754. Length: 25 pages Creation-Date: 1987 Revision-Date: 198801 Number: 833R Publication-Status: Published in American Economic Review (June 1990), 80(3): 376-389 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0754.pdf File-Format: application/pdf File-Size: 1079 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0833-r.pdf File-Format: application/pdf File-Size: 672 kb Handle: RePEc:cwl:cwldpp:833R Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Inference in Econometric Models with Structural Change Abstract: This paper extends the classical Chow (1960) test for structural change in linear regression models to a wide variety of nonlinear models, estimated by a variety of different procedures. Wald, Lagrange multiplier-like, and likelihood ratio-like test statistics are introduced. The results allow for heterogeneity and temporal dependence of general unifying results for estimation and testing in nonlinear parametric econometric models. Keywords: Chow test, dynamic model, econometric model, Lagrange multiplier test, likelihood ratio test, structural change, Wald test, nonlinear model Note: CFP 713. Length: 60 pages Creation-Date: 198704 Number: 832 Publication-Status: Published in Review of Economic Studies (1988), 55: 615-640 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0713.pdf File-Format: application/pdf File-Size: 1334 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0832.pdf File-Format: application/pdf File-Size: 1227 kb Handle: RePEc:cwl:cwldpp:832 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Effect of Economic Events on Votes for President: 1984 Update Abstract: In previous work I have developed an equation explaining votes for president in the United States that seems to have a remarkable predictive ability. The purpose of this paper is to update this equation through the 1984 election and then use it to predict the 1988 election. Classification-JEL: 025, 212, 921, 131 Keywords: Presidential election, votes, inflation, gross national product growth, unemployment, politics, political business cycle, president Note: CFP 735. Length: 14 pages Creation-Date: 198704 Number: 831 Publication-Status: Published in Political Behavior (1988), 10(2): 168-179 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0735.pdf File-Format: application/pdf File-Size: 591 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0831.pdf File-Format: application/pdf File-Size: 309 kb Handle: RePEc:cwl:cwldpp:831 Template-type: ReDIF-Paper 1.0 Author-Name: Rosa L. Matzkin Author-X-Name-First: Rosa L. Author-X-Name-Last: Matzkin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Semiparametric Estimation of Monotonic and Concave Utility Functions: The Discrete Choice Case Abstract: This paper develops a semiparametric method for estimating the nonrandom part V(.) of a random utility function U(v, omega) - V(v) + e(omega) from data on discrete choice behavior. Here v and omega are, respectively, vectors of observable and unobservable attributes of an alternative, and e(omega) is the random part of the utility for that alternative. The method is semiparametric because it assumes that the distribution of the random parts is know up to a finite-dimensional parameter theta, while not requiring specification of a parametric form for V( ). The nonstochastic part V( ) of the utility function U( ) is assumed to be Lipschitzian and to possess a set of properties, typically assumed for utility functions. The estimator of the pair (V,theta) is shown to be strongly consistent. Keywords: Discrete choice models, nonparametric estimation, utility functions, consistency, semiparametric estimation Note: CFP 795. Length: 40 pages Creation-Date: 198704 Number: 830 Publication-Status: Published in Econometrica (September 1991), 59(5): 1315-1327 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0795.pdf File-Format: application/pdf File-Size: 593 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0830.pdf File-Format: application/pdf File-Size: 671 kb Handle: RePEc:cwl:cwldpp:830 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Game Theory. Models of Strategic Behavior and Nuclear Deterrence Abstract: This essay offers an exposition of the potential uses of game theoretic reasoning and mathematical models in the study of the prevention of nuclear war. Classification-JEL: 026, 114 Keywords: Game theory, nuclear deterrence, arms race, escalation, retaliation, threat Length: 97 pages Creation-Date: 198703 Number: 829 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0829.pdf File-Format: application/pdf File-Size: 2417 kb Handle: RePEc:cwl:cwldpp:829 Template-type: ReDIF-Paper 1.0 Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Measuring Market Power in U.S. Industry Abstract: Non-competitive conduct can be assessed by estimating the size of the markup or Lerner index achieves in a market. The markup implies a price elasticity of demand faced by the representative firm. For a given markup, non-competitive conduct that is insensitive to the value of the monopoly. To implement this measure, both the firm's and the market elasticities of demand must be estimated. Hall shows how to estimate the markup, and hence the elasticity faced by the firm, from the cyclical behavior of productivity. To estimate the market elasticity, an instrumental variables procedure exploiting a covariance restriction between productivity shocks and demand shocks is used. Results for broad sectors of private industry and for non-durable manufacturing industries display a wide range of monopoly power. Classification-JEL: 611, 022, 212 Keywords: Market power, markup, Lerner index, elasticities, monopoly power, instrumental variables Length: 37 pages Creation-Date: 198704 Number: 828 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0828.pdf File-Format: application/pdf File-Size: 736 kb Handle: RePEc:cwl:cwldpp:828 Template-type: ReDIF-Paper 1.0 Author-Name: Philip H. Dybvig Author-X-Name-First: Philip H. Author-X-Name-Last: Dybvig Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Distributional Analysis of Portfolio Choice Abstract: We compare trading in a market with receiving some particular consumption bundle, given increasing state-independent preferences and complete markets. The analysis focuses on the distributional price of the particular bundle. The distributional price is the price of the cheapest utility-equivalent bundle sold in the market. The distributional price is determined by the distributional functions of the outside bundle and the state price density. Simple portfolio performance measures illustrate the value of the approach. Unlike CAPM-based measures, these measures are valid even when superior information is the source of superior performance. Note: CFP 709. Length: 41 pages Creation-Date: 1987 Revision-Date: 198801 Number: 827R Publication-Status: Published in Journal of Business (1988), 61(3): 369-393 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0709.pdf File-Format: application/pdf File-Size: 1094 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0827-r.pdf File-Format: application/pdf File-Size: 825 kb Handle: RePEc:cwl:cwldpp:827R Template-type: ReDIF-Paper 1.0 Author-Name: Philip H. Dybvig Author-X-Name-First: Philip H. Author-X-Name-Last: Dybvig Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Inefficient Dynamic Portfolio Strategies or How to Throw Away a Million Dollars in the Stock Market Abstract: A number of portfolio strategies followed by practitioners are dominated because they are incompletely diversified over time. The Payoff Distribution Pricing Model is used to compute the cost of following undiversified strategies. Simple numerical examples illustrate the technique, and computer-generated examples provide realistic estimates of the cost of some typical policies using reasonable parameter values. The cost can be substantial and should not be ignored by practitioners. A section on generalizations shows how to extend the analysis to term structure models and other general models of returns. Note: CFP 704. Length: 39 pages Creation-Date: 1987 Revision-Date: 198801 Number: 826R Publication-Status: Published in Review of Financial Studies (Spring 1988), 1(1): 67-88 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0704.pdf File-Format: application/pdf File-Size: 971 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0826-r.pdf File-Format: application/pdf File-Size: 796 kb Handle: RePEc:cwl:cwldpp:826R Template-type: ReDIF-Paper 1.0 Author-Name: Rabah Amir Author-X-Name-First: Rabah Author-X-Name-Last: Amir Author-Workplace-Name: SUNY at Stony Brook Title: Sequential Games of Resource Extraction: Existence of Nash Equilibria Abstract: A general model for noncooperative extraction of common-property resource is considered. The main result is that this sequential game has a Nash equilibrium in stationary strategies. The proof is based on an infinite dimensional fixed-point theorem, and relies crucially on the topology of epi-convergence. A byproduct of the analysis is that Nash equilibrium strategies may be selected such that marginal propensities of consumption are bounded above by one. Classification-JEL: 026, 632, 213, 721 Keywords: Sequential games, dynamic programming, fixed point theorem, Nash equilibrium, common property, natural resources, common property Length: 26 pages Creation-Date: 198703 Number: 825 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0825.pdf File-Format: application/pdf File-Size: 496 kb Handle: RePEc:cwl:cwldpp:825 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Conditional and Unconditional Statistical Independence Abstract: Conditional independence almost everywhere in the space of the conditioning variates does not imply unconditional independence, although it may well imply unconditional independence of certain functions of the variables. An example that is important in linear regression theory is discussed in detail. This involves orthogonal projections on random linear manifolds, which are conditionally independent but not unconditionally independent under normality. Necessary and sufficient conditions are obtained under which conditional independence does imply unconditional independence. Note: CFP 705. Length: 13 pages Creation-Date: 1987 Revision-Date: 198712 Number: 824R Publication-Status: Published in Journal of Econometrics (1988), 75(2): 341-348 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0705.pdf File-Format: application/pdf File-Size: 319 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0824-r.pdf File-Format: application/pdf File-Size: 256 kb Handle: RePEc:cwl:cwldpp:824R Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Spherical Matrix Distributions and Cauchy Quotients Abstract: It is shown that matrix quotients of submatrices of a spherical matrix are distributed as matrix Cauchy. This generalizes known results for scalar ratios of independent normal variates. The derivations are simple and make use of the theory of invariant measures on manifolds. Keywords: Cauchy quotients, invariant measures, matrix variates, spherical distributions Note: CFP 729. Length: 5 pages Creation-Date: 198702 Number: 823 Publication-Status: Published in Statistics and Probability Letters (1989), 8: 51-53 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0729.pdf File-Format: application/pdf File-Size: 116 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0823.pdf File-Format: application/pdf File-Size: 99 kb Handle: RePEc:cwl:cwldpp:823 Template-type: ReDIF-Paper 1.0 Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Are Cyclical Fluctuations in Productivity Due More to Supply Shocks or Demand Shocks? Abstract: Measured productivity is strongly procyclical. Real business cycle theories suggest that actual fluctuations in productivity are the source of fluctuations in aggregate output. Keynesian theories maintain that fluctuations in aggregate output come from shocks to aggregate demand. Keynesian theories appeal to labor hoarding or off the production function behavior to explain the procyclicality of productivity. If observed productivity shocks are true productivity shocks, a function of factor prices should covary exactly with productivity. In annual data for United States industries, that function of factor prices and conventionally-measured productivity move together very closely. Moreover, their difference is uncorrelated with aggregate output. Classification-JEL: 131, 023, 825 Keywords: Business cycles, macroeconomic fluctuations, productivity, aggregate demand, factor prices Note: CFP 677. Length: 19 pages Creation-Date: 198702 Number: 822 Publication-Status: Published in AEA Papers and Proceedings (May 1987), 77(2): 118-124 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0677.pdf File-Format: application/pdf File-Size: 471 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0822.pdf File-Format: application/pdf File-Size: 390 kb Handle: RePEc:cwl:cwldpp:822 Template-type: ReDIF-Paper 1.0 Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew Author-X-Name-Last: Shapiro Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Supply Shocks in Macroeconomics Abstract: Supply shocks played an important role in macroeconomic fluctuations during the 1970's. Supply shocks are also increasingly important in Keynesian and neo-classical models of the business cycle. This paper is a short survey of these theoretical models. It also discusses the history of supply shocks in recent business cycles. Classification-JEL: 023, 131 Keywords: Supply shocks, macroeconomic fluctuations, business cycles Length: 18 pages Creation-Date: 198702 Number: 821 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0821.pdf File-Format: application/pdf File-Size: 361 kb Handle: RePEc:cwl:cwldpp:821 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Future of Social Security: One Economist's Assessment Abstract: Three interrelated issues must be faced in assessing the future of OASI. I shall discuss each in turn. Balancing Contributions and Benefits. The overriding long-run issue about OASI is the balance between the tax contributions of the young and the benefits of the old. The system is now geared to scale up benefits automatically so as to maintain the ratio of benefits to contemporaneous wages, the replacement ratio, at its historical level of roughly 40 percent. Payroll tax rates are the residual balancing item in the OASI financial equation. They have been raised steadily for years, and according to current projections they will have to be raised substantially next century if the replacement ratio is to be maintained. The generations involved, however, may at some point prefer to move to or toward a different option-freezing the tax rates and adjusting future benefits instead. This would mean that in the 21st century the benefit/wage ratio would fall; OASI benefits would still be rising in absolute purchasing power, but they would decline relative to the wages of active workers. It is not too soon to begin serious consideration of the options. Erosion of Confidence. The confidence of young workers in Social Security has eroded in recent years. Some are worried that the system will go broke. Others perceive that their rate of return on the payroll tax contributions they and their employers make will be quite low, in contrast to the interest rates they observe in financial markets today. They wonder why participation itself should be compulsory. The link between the contributions of, or on behalf of, any individual participant and his or her eventual benefits is quite loose, and quite mysterious. The system is a hybrid, mixing social retirement insurance with some intragenerational redistribution in favor of workers with low earnings. This is bound to diminish the rates of return high wage workers perceive they can earn through OASI. Old issues return anew: Should OASI be made more purely an insurance program, letting the general federal budget handle redistribution via needs-tested transfers? Should the link between contributions and benefits be actuarially fair for individual participants? Should the benefit entitlements earned by past contributions be reported regularly and clearly to participants throughout their careers? Should compulsory participation be limited to defined levels of contributions and benefits? As Robert Ball recounts in Chapter 1 of this volume, the founders of Social Security confronted these questions and compromised. Compromises, even theirs, are not graven in stone. Times, circumstances, and attitudes change. At the end of this chapter I shall sketch, as an option worth considering, a system that links contributions and benefits more explicitly and tightly. Financing Social Security. The issues just raised regarding the links between contributions and benefits for individual participants are related to questions about the financing of the system as whole. Until now Social Security has been mainly a pay-as-you-go system, using its current receipts from workers' contributions to pay its current benefits. Its trust fund, as its reserves are called, has been deliberately kept small. Under the 1983 legislation, this fund will grow to unprecedented heights relative to annual outlays over the next 15 to 20 years. Thereafter it is projected to decline, and to vanish after midcentury. A case can be made on macroeconomic grounds for a funded system in preference to pay-as-you-go. Full funding would mean a trust fund commensurate to OASI's liabilities for the future benefits accumulation of such a fund, it can be argued, would add to national saving and investment enough productive capital to yield the promised benefits. That yield might well be a higher rate of return than pay-as-you-go can offer. History cannot be rerun. A shift to funding would take nearly a half century to accomplish. Moreover, the proposal inevitably raises the question of the relation between Social Security trust funds and the overall federal budget. I shall discuss these financial issues, and in my sketch of possible reforms for the next century I shall describe how the long transition to a funded system might be managed. Classification-JEL: 915, 918, 914, 913, 921 Keywords: Social security, government expenditures, OASI, old age, elderly Length: 49 pages Creation-Date: 198702 Number: 820 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0820.pdf File-Format: application/pdf File-Size: 1125 kb Handle: RePEc:cwl:cwldpp:820 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Joon Y. Park Author-X-Name-First: Joon Y. Author-X-Name-Last: Park Author-Workplace-Name: School of Economics, Seoul National University Title: Statistical Inference in Regressions with Integrated Processes: Part 2 Abstract: This paper continues the theoretical investigation of Park and Phillips [7]. We develop an asymptotic theory of regression for multivariate linear models that accommodates integrated processes of different orders, nonzero means, drifts, time trends and cointegrated regressors. The framework of analysis is general but has a common architecture that helps to simplify and codify what would otherwise be a myriad of isolated results. A good deal of earlier research by the authors and by others comes within the new framework. Special models of some importance are considered in detail, such as VAR systems with multiple lags and cointegrated variants. Note: CFP 722. Length: 63 pages Creation-Date: 1986 Revision-Date: 198702 Number: 819R Publication-Status: Published in Econometric Theory (1989), 5: 95-131 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0722.pdf File-Format: application/pdf File-Size: 1438 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0819-r.pdf File-Format: application/pdf File-Size: 1096 kb Handle: RePEc:cwl:cwldpp:819R Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Optimal Choice of Monetary Policy Instruments in a Macroeconometric Model Abstract: It has been nearly twenty years since Poole (1970) wrote his classic article on the optimal choice of monetary policy instruments in a stochastic IS-LM model. Poole assumed that the monetary authority (henceforth called the Fed) can control the interest rate or the money supply exactly. These are the two "instruments" of monetary policy. If the aim is to minimize the squared deviation of real output from its target value, Poole showed that the choice of the optimal instrument depends on the variance of the error term in the IS function, the variance of the error term in the LM function, the covariance of the two error terms, and the size of the parameters in the two functions. Most people would probably agree that between about 1979-10 and October 1982 the Fed tried to use the money supply as its primary instrument. This attempt does not appear to have been successful in the sense that since about 1982-10 the Fed seems to have gone back to using the interest rate as its primary instrument. If the interest rate has won out, it is interesting to ask if this decision can be justified on the basis of the Poole analysis. Is the economy one in which the relevant variances, covariance, and parameters are such as to lead a la the Poole analysis, to the optimal instrument being the interest rate? The purpose of this paper is to examine this question using my United States econometric model. Are the variances, covariances, and parameters in the model such as to favor one instrument over the other, in particular the interest rate over the money supply? This question can be examined in an econometric model by the use of stochastic simulation. Interestingly enough, Poole's analysis has never been tried on an actual econometric model. The closest study in this respect is that of Tinsley and von zur Muehlen (1983), although they did not analyze the same question that Poole did. Other studies that have extended Poole's work, such as those of Turnovsky (1975) and Yoshikawa (1981), have been primarily theoretical. Classification-JEL: 311, 023, 212 Keywords: Monetary policy, money supply, interest rate, monetary authority Note: CFP 734. Length: 23 pages Creation-Date: 198701 Number: 818 Publication-Status: Published in Journal of Monetary Economics (1988), 22: 301-315 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0734.pdf File-Format: application/pdf File-Size: 778 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0818.pdf File-Format: application/pdf File-Size: 525 kb Handle: RePEc:cwl:cwldpp:818 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Financial Intermediaries Abstract: This is an essay on Financial Intermediaries written for the New Palgrave. It includes sections on national wealth, financial markets, assets, risk and regulation. Classification-JEL: 314, 310 Keywords: Financial intermediaries Length: 32 pages Creation-Date: 198701 Number: 817 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0817.pdf File-Format: application/pdf File-Size: 785 kb Handle: RePEc:cwl:cwldpp:817 Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Ultimate Sources of Aggregate Variability Abstract: What, ultimately, is different from quarter to quarter or year to year that accounts for the fact that macroeconomic variables change over these intervals? That is, which are the biggest ultimate sources, in terms we may say of tastes, technology, endowments, government policy, industrial organization, labor-management relations, speculative behavior, or the like, that change to cause this variability? There are a bewildering variety of claims in the literature for such ultimate sources. Far fewer efforts have been made to give a breakdown of the variance of macroeconomic aggregates by Pigou (1929) and Fair (1987). The nature of the evidence for such breakdowns is discussed here, and the possibility that a partial breakdown may be well-determined is put forward. An unsuccessful attempt is made to detect a component of macroeconomic fluctuations that is due to the weather. Classification-JEL: 023, 131 Keywords: Macroeconomic aggregate, variance, economic fluctuation Length: 23 pages Creation-Date: 198701 Number: 816 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0816.pdf File-Format: application/pdf File-Size: 466 kb Handle: RePEc:cwl:cwldpp:816 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Sources of Output and Price Variability in a Macroeconometric Model Abstract: There has been much recent discussion about the ultimate sources of macroeconomic variability. Shiller (1987) surveys this work, where he points out that a number of authors attribute most of output or unemployment variability to only a few sources, sometimes only one. The sources vary from technology shocks for Kydland and Prescott (1982), to unanticipated changes in the money stock for Barro (1977), to "unusual structural shifts," such as changes in the demand for produced goods relative to services, for Lilien (1982), to oil price shocks for Hamilton (1983), to changes in desired consumption for Hall (1986). (See Shiller (1987) for more references.) Although it may be that there are only a few important sources of macroeconomic variability, this is far from obvious. Economies seem complicated, and it may be that there are many important sources. The purpose of this paper is to estimate the quantitative importance of various sources of variability using a macroeconometric model. Macroeconometric models provide an obvious vehicle for estimating the sources of variability of endogenous variables. There are two types of shocks that one needs to consider: shocks to the stochastic equations and shocks to the exogenous variables. Shocks to the stochastic equations are easy to handle. They are simply draws from the postulated distribution (usually normal) of the structural error terms, the distribution upon which the estimation of the model is based. Shocks to the exogenous variables are less straightforward to handle. Since by definition exogenous variables are not modeled, it is not unambiguous what one means by exogenous-variable shock. Another possibility is to postulate that exogenous-variable shocks are the errors that forecasting services make in their forecasts of the exogenous variables. The sources of output and price variability are examined in this paper using my United States model (Fair (1984)). The procedure that was followed, which is discussed in detail in the next section, is briefly as follows. Autoregressive equations were estimated for 23 exogenous variables in the model. These variables make up all the important exogenous variables in the model (in my view). These equations were then added to the model. There are 30 structural stochastic equations in the model, and so the expanded model includes 53 stochastic equations. The 53 x 53 covariance matrix of the error terms was then estimated. In estimating this matrix the error terms in the structural equations were assumed to be uncorrelated with the error terms in the exogenous-variable equations, which means that the matrix was taken to be block diagonal (with a 30 x 30 block and a 23 x 23 block). This procedure is consistent with the assumption upon which the estimation of the model is based, namely that the exogenous variables are not correlated with the error terms in the structural equations. Classification-JEL: 023, 131, 132, 212, 134 Keywords: Output variability, price fluctuations, macroeconomic model, United States model Length: 26 pages Creation-Date: 198701 Number: 815 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0815.pdf File-Format: application/pdf File-Size: 573 kb Handle: RePEc:cwl:cwldpp:815 Template-type: ReDIF-Paper 1.0 Author-Name: Rabah Amir Author-X-Name-First: Rabah Author-X-Name-Last: Amir Author-Workplace-Name: SUNY at Stony Brook Author-Name: Siddhartha Sahi Author-X-Name-First: Siddhartha Author-X-Name-Last: Sahi Author-Workplace-Name: Princeton University Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Strategic Market Game with Complete Markets Abstract: Existence of equilibrium is proved for an exchange strategic market game with complete markets. An example of equilibrium with inconsistent prices is given. Classification-JEL: 026, 021 Keywords: Game theory, general equilibrium, exchange market, complete markets Note: CFP 757. Length: 25 pages Creation-Date: 1986 Revision-Date: 198709 Number: 814R Publication-Status: Published in Journal of Economic Theory (June 1990), 51(1): 126-143 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0757.pdf File-Format: application/pdf File-Size: 558 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0814-r.pdf File-Format: application/pdf File-Size: 394 kb Handle: RePEc:cwl:cwldpp:814R Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: International Evidence on the Demand for Money Abstract: One of the current questions in the literature on the demand for money is whether the adjustment of actual to desired money holdings is in nominal or real terms. This paper describes a simple procedure that can be used to test the nominal against the real hypothesis. The test is carried out for 27 countries. The paper also tests the structural stability of the demand for money equations and the correctness of the dynamic specification. Classification-JEL: 311, 023, 123, 212 Keywords: Money demand Note: CFP 732. Length: 17 pages Creation-Date: 198612 Number: 813 Publication-Status: Published in Review of Economics and Statistics (August 1987), 69(3): 473-480 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0732.pdf File-Format: application/pdf File-Size: 579 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0813.pdf File-Format: application/pdf File-Size: 433 kb Handle: RePEc:cwl:cwldpp:813 Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: John Y. Campbell Author-X-Name-First: John Y. Author-X-Name-Last: Campbell Title: The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors Abstract: A linearization of a rational expectations present value model for corporate stock prices produces a simple relation between the log dividend-price ratio and mathematical expectations of future log real dividend changes and future real discount rates. This relation can be tested using vector autoregressive methods. Three versions of the linearized model, differing in the measure of discount rates, are tested for United States time series 1981-1986: versions using real interest rate data. The results yield a metric to judge the relative importance of real dividend growth, measured real discount rates and unexplained factors in determining the dividend-price ratio. Classification-JEL: 313, 312, 522 Keywords: Dividend-Price ratio, rational expectations, present value, vector autoregression, dividends, stock prices, discount rate Length: 39 pages Creation-Date: 198612 Number: 812 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0812.pdf File-Format: application/pdf File-Size: 787 kb Handle: RePEc:cwl:cwldpp:812 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Joon Y. Park Author-X-Name-First: Joon Y. Author-X-Name-Last: Park Author-Workplace-Name: School of Economics, Seoul National University Title: Statistical Inference in Regressions with Integrated Processes: Part 1 Abstract: This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F-tests is explored and new transformations are introduced to deal with these dependencies. Some specializations of our theory are considered in detail. In models with strictly exogenous regressors we demonstrate the validity of conventional asymptotic theory for appropriately constructed Wald tests. These tests provide a simple and convenient basis for specification robust inferences in this context. Single equation regression tests are also studied in detail. Here it is shown that the asymptotic distribution of the Wald test is a mixture of the chi square of conventional regression theory and the standard unit root theory. The new result accommodates both extremes and intermediate cases. Keywords: Brownian motion, cointegration, integrated regressors, unit roots Note: CFP 715. Length: 50 pages Creation-Date: 1986 Revision-Date: 198708 Number: 811R Publication-Status: Published in Econometric Theory (1988), 4: 468-497 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0715.pdf File-Format: application/pdf File-Size: 1105 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0811-r.pdf File-Format: application/pdf File-Size: 861 kb Handle: RePEc:cwl:cwldpp:811R Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Interest Rate and Exchange Rate Determination Abstract: It is well known that modeling exchange rates is difficult. Meese and Rogoff's (1983) results show that a random walk model performs as well as or better than a variety of structural models, where the forecasts from the structural models are based on the actual values of the future explanatory variables. Because of these and other results, the view has become fairly widespread that structural models of exchange rates are not very good. There is, however, somewhat of a dichotomy in the literature between those who deal with small models, where the focus is almost exclusively on exchange rates, and those who deal with large macroeconometric models, where exchange rates make up only a small subset of the endogenous variables. One might have thought, for example, that in a survey like Levich's (1985) both types of models would be considered, but the large models are given only one footnote (fn. 19, p. 1001). It may be that exchange rate determination within the context of large models has not been given a sufficient hearing. Exchange rate and interest rate equations are estimated and analyzed for 17 countries in this paper. This study is part of a larger project of constructing a multicountry econometric model. One of the aims of this paper is to see if the exchange rate equations that are part of my multicountry model also suffer from the Meese and Rogoff criticism. The results show that the view that structural exchange rate models are not very good may be too pessimistic. The theory upon which the multicountry econometric model is based is outlined in Section II. The exchange rate and interest rate equations are estimated in Section III and tested in Section IV. Classification-JEL: 431, 212, 132, 313 Keywords: Interest rate, exchange rates, multicountry econometric model Length: 43 pages Creation-Date: 198612 Number: 810 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0810.pdf File-Format: application/pdf File-Size: 943 kb Handle: RePEc:cwl:cwldpp:810 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Sam Ouliaris Author-X-Name-First: Sam Author-X-Name-Last: Ouliaris Title: Testing for Cointegration Using Principal Component Measures Abstract: This paper studies cointegrated systems of multiple time series which are individually well described as integrated processes (with or without a drift). Necessary and sufficient conditions for cointegration are given. These conditions form the basis for a new class of statistical procedures designed to test for cointegration. The new procedures rely on principal components methods. They are simple to employ and they involve only the standard normal distribution. Monte Carlo simulations reported in the paper indicate that the new procedures provide simple and apparently rather powerful diagnostics for the detection of cointegration. Some empirical applications to macroeconomic data are conducted. Keywords: Latent root, spectral density matrix, time series Note: No page 2; CFP 723. Length: 38 pages Creation-Date: 1986 Revision-Date: 198707 Number: 809R Publication-Status: Published in Journal of Economic Dynamics and Control (1988), 12: 205-230 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0723.pdf File-Format: application/pdf File-Size: 1150 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0809-r.pdf File-Format: application/pdf File-Size: 818 kb Handle: RePEc:cwl:cwldpp:809R Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Kathryn M. Dominguez Author-X-Name-First: Kathryn M. Author-X-Name-Last: Dominguez Title: Forecasting the Depression: Harvard Versus Yale Abstract: Was the Depression forecastable? After the Crash, how long did it take contemporary economic forecasters to realize how severe the downturn was going to be? How long should it have taken them to come to this realization? These questions are addressed by studying the predictions of the Harvard Economic Service and Yale's Irving Fisher during 1929 and the early 1930's. The data assembled by the Harvard and Yale forecasters are subjected to modern statistical analysis to learn whether their verbal pronouncements were consistent with the data. We find that both the Harvard and Yale forecasters were systematically too optimistic, yet nothing in the data suggests that the optimum was unwarranted. Classification-JEL: 042, 031 Keywords: Depression, forecasting Note: CFP 710. Length: 38 pages Creation-Date: 198611 Number: 808 Publication-Status: Published in American Economic Review (1988), 78(4): 595-596 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0710.pdf File-Format: application/pdf File-Size: 1038 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0808.pdf File-Format: application/pdf File-Size: 942 kb Handle: RePEc:cwl:cwldpp:808 Template-type: ReDIF-Paper 1.0 Author-Name: Truman F. Bewley Author-X-Name-First: Truman F. Author-X-Name-Last: Bewley Author-Email: truman.bewley@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/bewley.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Knightian Decision Theory: Part 1 Abstract: A theory of choice under uncertainty is proposed which removes the completeness assumption from the Anscombe-Aumann formulation of Savage's theory and introduces an inertia assumption. The inertia assumption is that there is such a thing as the status quo and an alternative is accepted only if it is preferred to the status quo. This theory is one way of giving rigorous expression to Frank Knight's distinction between risk and uncertainty. Classification-JEL: 026, 022, 511 Keywords: Decision theory, Knight, theory of choice, uncertainty, inertia assumption Note: CFP 1053 Length: 54 pages Creation-Date: 198611 Number: 807 Publication-Status: Published in Decisions in Economics and Finance (2002), 25(2): 79-110 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0807.pdf File-Format: application/pdf File-Size: 1186 kb Handle: RePEc:cwl:cwldpp:807 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Unique Minimal Cash Flow Competitive Equilibrium Abstract: The exchange economy E can be reformulated as a strategic market game. In particular the point of concern here involves the introduction of a specified amount of credit or fiat money to monetize exchange. Dubey and Shubik (1979) and Shubik and Wilson (1977) have studied the possibility of introducing a fixed amount M of money to finance trade. When one formulates exchange as a game of strategy using any form of credit or fiat money where there is any possibility whatsoever that an individual will be unable to pay back that which he has borrowed, the rules of the game require that the procedure to be followed in case of default must be specified. This is not a mere institutional detail but a logical necessity. It is however reasonable to expect that one might try to design a default penalty sufficiently harsh to discourage strategic default. Classification-JEL: 021, 026 Keywords: Cash flow competitive equilibrium, strategic market games Note: CFP 702. Length: 7 pages Creation-Date: 198610 Number: 806 Publication-Status: Published in Economics Letters (1987), 27: 303-306 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0702.pdf File-Format: application/pdf File-Size: 181 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0806.pdf File-Format: application/pdf File-Size: 163 kb Handle: RePEc:cwl:cwldpp:806 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Game Theoretic Approach to the Theory of Money and Financial Institutions Abstract: This is a sketch of a game theoretic and gaming approach to the development of an appropriate microeconomic theory of money and financial institutions. The phrase "money and financial institutions" is used to stress that a theory of money alone cannot be fruitfully constructed in an institutional vacuum. The monetary and financial system of an economy are part of the socio-politico-economic control mechanism used by every state to connect the economy with the polity and society. This neural network provides the administrative means to collect taxes, direct investment, provide public goods, trade. The money measures provide a crude but serviceable basis for the accounting system which in turn, along with the codification of commercial law and financial regulation are the basis for economic evaluation and the measurement of trust and fiduciary responsibility among the economic agents. A central feature of a control mechanism is that it is designed to influence process. Dynamics is its natural domain. Equilibrium is not the prime concern, the ability to control the direction of motion is what counts. Bagehot (1962) noted that a financial instrument originally designed for one purpose may take on a life of its own and serve a different purpose. In particular most of the instruments may have been invented to facilitate trade but they provided a means for control. Money and financial institutions provide the command and control system of a modern society. The study of the mechanism, how they are formed, how they are controlled and manipulated and how their influence is measured in terms of social, political, and economic purpose pose questions not in pure economics, not even in a narrow political economy, but in the broad compass of a political economy set in the context of society. A basic purpose of the approach adopted here is to show the minimal conditions which require that financial institutions and instruments emerge as a necessary carriers of process. The thrust is for the development of a mathematical institutional economics. Classification-JEL: 311, 022, 023, 026 Keywords: Game theory, money, financial institutions, mathematical institutional economics Note: CFP 767. Length: 74 pages Creation-Date: 198611 Number: 805 Publication-Status: Published in B. M. Friedman and F.H. Hahn, eds., Handbook of Monetary Economics, Vol. 1, Elsevier Science, 1990, pp. 172-219 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0767.pdf File-Format: application/pdf File-Size: 2266 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0805.pdf File-Format: application/pdf File-Size: 1641 kb Handle: RePEc:cwl:cwldpp:805 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Enough Commodity Money and the Selection of a Unique Competitive Equilibrium Abstract: Suppose that we reformulate the exchange economy as a strategic market game. As all purchases are paid for in cash it is possible to attach precise meaning to what is meant by enough money. As the game is a single simultaneous bid and offered at m trading posts and m prices are all simultaneously determined, in essence the trading technology is completely specified. Classification-JEL: 021, 026 Keywords: Exchange economy, strategic market game; commodity money Length: 8 pages Creation-Date: 198610 Number: 804 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0804.pdf File-Format: application/pdf File-Size: 160 kb Handle: RePEc:cwl:cwldpp:804 Template-type: ReDIF-Paper 1.0 Author-Name: Vassilis A. Hajivassiliou Author-X-Name-First: Vassilis A. Author-X-Name-Last: Hajivassiliou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Temporal Dependence in Limited Dependent Variable Models: Theoretical and Monte-Carlo Results Abstract: This paper analyzes the consistency properties of classical estimators for limited dependent variables models, under conditions of serial correlation in the unobservables. A unified method of proof is used to show that for certain cases (e.g., Probit, Tobit and Normal Switching Regimes models, which are normality-based) estimators that neglect particular types of serial dependence (specifically, corresponding to the class of "mixing" processes) are still consistent. The same line of proof fails for the analogues to the above models that impose logistic distributional assumptions, thus indicating that normality plays a special role in these problems. Sets of Monte-Carlo experiments are then carried out to investigate these theoretical results. Keywords: Consistency, serial dependence, mixing processes, limited dependent variables models, probit, logit, tobit, normality Length: 38 pages Creation-Date: 198608 Number: 803 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0803.pdf File-Format: application/pdf File-Size: 941 kb Handle: RePEc:cwl:cwldpp:803 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Joon Y. Park Author-X-Name-First: Joon Y. Author-X-Name-Last: Park Author-Workplace-Name: School of Economics, Seoul National University Title: Asymptotic Equivalence of OLS and GLS in Regressions with Integrated Regressors Note: CFP 703. Length: 20 pages Creation-Date: 1986 Number: 802 Publication-Status: Published in Journal of American Statistical Association (1988), 83(401): 111-115 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0703.pdf File-Format: application/pdf File-Size: 366 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0802.pdf File-Format: application/pdf File-Size: 342 kb Handle: RePEc:cwl:cwldpp:802 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Joon Y. Park Author-X-Name-First: Joon Y. Author-X-Name-Last: Park Author-Workplace-Name: School of Economics, Seoul National University Title: On the Formulation of Wald Tests of Nonlinear Restrictions Abstract: This paper utilizes asymptotic expansions to investigate alternative forms of the Ward set of nonlinear restrictions. Some formulae for the asymptotic expansion of the distribution of the Wald statistic are provided for a general case. When specialized to the simple cases that have been studied recently in the literature, these formulae are found to explain rather well the discrepancies in sampling behavior that have been observed by other authors. It is further shown how the correction delivered by the Edgeworth expansion may be used to find transformations of the restrictions which accelerate convergence to the asymptotic distribution. Note: CFP 718. Length: 33 pages Creation-Date: 198609 Number: 801 Publication-Status: Published in Econometrica (September 1988), 56(5): 1065-1083 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0718.pdf File-Format: application/pdf File-Size: 705 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0801.pdf File-Format: application/pdf File-Size: 447 kb Handle: RePEc:cwl:cwldpp:801 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Power in Econometric Applications Abstract: This paper is concerned with the use of power properties of tests in econometric applications. Power radius and inverse power functions are defined. These functions are designed to yield summary measures of power that facilitate the interpretation of test results in practice. Simple approximations are introduced for the power radius and inverse power functions of Wald, likelihood ration, Lagrange multiplier, and Hausman tests. These approximations readily convey the general qualitative features of the power of a test. Examples are provided to illustrate their usefulness in interpreting test results. Keywords: Power function, hypothesis tests, inverse power function Note: CFP 737. Length: 54 pages Creation-Date: 198608 Number: 800 Publication-Status: Published in Econometrica (September 1989), 57(5): 1050-1090 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0737.pdf File-Format: application/pdf File-Size: 1588 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d08a/d0800.pdf File-Format: application/pdf File-Size: 1221 kb Handle: RePEc:cwl:cwldpp:800 Template-type: ReDIF-Paper 1.0 Author-Name: Imelda Yeung Powers Author-X-Name-First: Imelda Young Author-X-Name-Last: Powers Title: Limiting Distributions of the Number of Pure Strategy Nash Equilibria in n-Person Games Abstract: In this paper, we study the number of pure strategy Nash equilibria in a "random" n-person non-cooperative game in which all players have a countable number of strategies. We provide explicit expressions for the expected number of pure strategy Nash Equilibria, and show that the distribution of the number of pure strategy Nash Equilibria approaches the Poisson distribution with mean 1 as the numbers of strategies of two or more players go to infinity. Classification-JEL: 026 Keywords: Pure strategy, Nash equilibria, random n-person game, strictly and weakly ordinal game Length: 43 pages Creation-Date: 198608 Number: 799 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0799.pdf File-Format: application/pdf File-Size: 736 kb Handle: RePEc:cwl:cwldpp:799 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: On the Performance of Least Squares in Linear Regression with Undefined Error Means Abstract: This paper considers the linear regression model with multiple stochastic regressors, intercept, and errors that have undefined means. This model is of interest from a robustness perspective as a polar case. Generally, least squares estimators are inconsistent in this context. It is shown, however, that this inconsistency is restricted to the estimation of the intercept, if the regressors are highly variable. Rates of convergence of the least squares slope estimators are determined, and are shown to exceed the standard rate, n^{-1/2}, in certain contexts. The results place no restrictions on the temporal dependence of the errors, and require an unusually weak exogeneity condition between the regressors and errors. Implications of the results for robustness theory are discussed. Keywords: Least squares estimator, linear regression, stable distribution, fat-tails, consistency, robustness Length: 54 pages Creation-Date: 198607 Number: 798 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0798.pdf File-Format: application/pdf File-Size: 1005 kb Handle: RePEc:cwl:cwldpp:798 Template-type: ReDIF-Paper 1.0 Author-Name: Paul R. Milgrom Author-X-Name-First: Paul R. Author-X-Name-Last: Milgrom Author-Workplace-Name: Dept. of Economics, Yale University Author-Workplace-Homepage: http://www.econ.yale.edu/ Title: Quasirents, Influence and Organization Form Abstract: When changing jobs is costly, efficient employment arrangements are characterized by complex contracts, rather than simply wages. Under these contracts, workers are not generally fully compensated for the effects of post-employment events or decisions. As a consequence, if there is a central office executive with discretionary authority to make decisions, employees will be led to waste valuable time in attempts to influence his decisions. Efficient organization design balances these "influence costs" against the benefits of improved appraisal, coordination, and planning that such an executive can provide. Identifying influence costs requires first identifying the kinds of decisions about which employees will care. We identify several: with efficient employment contracts, employees prefer more on-the-job consumption and better opportunities to learn and display their abilities and to acquire human capital. They also prefer to occupy jobs where continuity of employment is particularly important to the employer, because such jobs carry higher wages. Applications of our perspective, which focuses on influence processes and the trade-off between influence costs and improved decisionmaking appears to have wide and fruitful application to questions or organization theory, industrial organization, contract theory, and related areas. Classification-JEL: 511 Keywords: Efficient organization design, influence costs Length: 42 pages Creation-Date: 198607 Number: 797 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0797.pdf File-Format: application/pdf File-Size: 948 kb Handle: RePEc:cwl:cwldpp:797 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Weak Convergence to the Matrix Stochastic Integral BdB Abstract: The asymptotic theory of regression with integrated processes of the ARIMA type frequently involves weak convergence to stochastic integrals of the form integral_{0}^{1}WdW, where W(r) is standard Brownian motion. In multiple regressions and vector autoregressions with vector ARIMA processes the theory involves weak convergence to matrix stochastic integrals of the form integral_{0}^{1}BdB', where B(r) is vector Brownian motion with non scalar covariance matrix. This paper studies the weak convergence of sample covariance matrices to integral_{0}^{1}BdB' under quite general conditions. The theory is applied to vector autoregressions with integrated processes. Keywords: Integrated process, invariance principle, near integrated time series; stochastic integral, vector autoregression, weak convergence Note: CFP 697. Length: 18 pages Creation-Date: 198607 Number: 796 Publication-Status: Published in Journal of Multivariate Analysis (February 1988), 24(2): 252-264 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0697.pdf File-Format: application/pdf File-Size: 320 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0796.pdf File-Format: application/pdf File-Size: 243 kb Handle: RePEc:cwl:cwldpp:796 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Pierre Perron Author-X-Name-First: Pierre Author-X-Name-Last: Perron Author-Workplace-Name: Universite of Montreal Title: Testing for a Unit Root in Time Series Regression Abstract: This paper proposes some new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey and Fuller. Some simulations are reported which provide evidence on the performance of the new tests in finite samples. Keywords: Brownian motion, noncentral distributions, weak convergence, nonparametric tests Note: CFP 706. Length: 31 pages Creation-Date: 1986 Revision-Date: 198709 Number: 795R Publication-Status: Published in Biometrika (1988), 75(2): 335-346 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0706.pdf File-Format: application/pdf File-Size: 657 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0795-r.pdf File-Format: application/pdf File-Size: 545 kb Handle: RePEc:cwl:cwldpp:795R Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: John Pound Author-X-Name-First: John Author-X-Name-Last: Pound Author-Workplace-Name: Securities & Exchange Commission Title: Survey Evidence on Diffusion of Interest Among Institutional Investors Abstract: Contagion or epidemic models of financial markets are proposed in which interest in or attention to individual stocks is spread by word of mouth. The models give alternative interpretations of the random walk character of stock prices. A questionnaire survey of institutional investors was undertaken to ascertain the relevance of such models. Questions elicited what fraction of these investors were unsystematic and allowed themselves to be influenced by word-of-mouth communications or other salient stimuli. Rough indications of the infection rate and removal rate were produced. Investors in stocks whose price had recently increased dramatically to a high P/E ratio were contrasted with a control group of investors. Classification-JEL: 313 Keywords: financial markets, stocks, word-of-mouth, random walk Length: 26 pages Creation-Date: 198605 Number: 794 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0794.pdf File-Format: application/pdf File-Size: 516 kb Handle: RePEc:cwl:cwldpp:794 Template-type: ReDIF-Paper 1.0 Author-Name: William D. Nordhaus Author-X-Name-First: William D. Author-X-Name-Last: Nordhaus Author-Email: william.nordhaus@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/nordhaus.htm Author-Workplace-Name: Dept. of Economics, Yale University Author-Workplace-Homepage: http://www.econ.yale.edu/ Title: Resources, Technology, and Development: Will the Table Be Bare When Poor Countries Get There? Abstract: This paper discusses the net effect of these two economic forces on developing countries: Is the drag to economic advance from dwindling resources outweighed by the accompanying technological advances? Or will the potential scarcity of resources during the next century on balance weigh down the pace of economic progress? Classification-JEL: 111, 721, 621 Keywords: Natural resources, economic growth, technology, resource depletion Note: CFP 660. Length: 21 pages Creation-Date: 198605 Number: 793 Publication-Status: Published in Indian Economic Review (1986), 21(2): 81-94 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0660.pdf File-Format: application/pdf File-Size: 654 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0793.pdf File-Format: application/pdf File-Size: 519 kb Handle: RePEc:cwl:cwldpp:793 Template-type: ReDIF-Paper 1.0 Author-Name: Vassilis A. Hajivassiliou Author-X-Name-First: Vassilis A. Author-X-Name-Last: Hajivassiliou Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Two Misspecification Tests for the Simple Switching Regressions Disequilibrium Model Abstract: Two specification tests for switching regimes disequilibrium models are developed. The first is an asymptotically locally optimal Lagrange multiplier test of endogeneity of a set of regressors, which takes the convenient form of a LM significance-test of certain regression residuals. The second is a Hausman specification test of the accuracy of regime classification information. Note: CFP 673. Length: 10 pages Creation-Date: 198605 Number: 792 Publication-Status: Published in Economics Letters (1986), 22: 343-348 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0673.pdf File-Format: application/pdf File-Size: 311 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0792.pdf File-Format: application/pdf File-Size: 212 kb Handle: RePEc:cwl:cwldpp:792 Template-type: ReDIF-Paper 1.0 Author-Name: Dilip Abreu Author-X-Name-First: Dilip Author-X-Name-Last: Abreu Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: David G. Pearce Author-X-Name-First: David G. Author-X-Name-Last: Pearce Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Ennio Stacchetti Author-X-Name-First: Ennio Author-X-Name-Last: Stacchetti Title: Toward a Theory of Discounted Repeated Games with Imperfect Monitoring Abstract: This paper investigates pure strategy sequential equilibria of repeated games with imperfect monitoring. The approach emphasizes the equilibrium value set and the static optimization problems embedded in external equilibria. We characterize these equilibria, and provide computational and comparative statics results. The "self-generation" and "bang-bang" propositions which were at the core of our analysis of optimal cartel equilibria [2], are generalized to asymmetric games and infinite action spaces. New results on optimal implicit reward functions include the necessity (as opposed to sufficiency) of bang-bang functions, and the nature of optimal punishment regions. Classification-JEL: 026 Keywords: Pure strategy sequential equilibria, repeated games, imperfect monitoring Note: CFP 762. Length: 34 pages Creation-Date: 198604 Number: 791 Publication-Status: Published in Econometrica (September 1990), 58(5): 1041-1063 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0762.pdf File-Format: application/pdf File-Size: 1243 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0791.pdf File-Format: application/pdf File-Size: 595 kb Handle: RePEc:cwl:cwldpp:791 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers Abstract: A basic tool of modern econometrics is a uniform law of large numbers (LLN). It is a primary ingredient used in proving consistency and asymptotic normality of parametric and nonparametric estimators in nonlinear econometric models. Thus, in a well-known review article, Burguete, Gallant, and Sousa [8, p. 162] introduce a uniform LLN with the statement: "The following theorem is the result upon which the asymptotic theory of nonlinear econometrics rests. "So pervasive is the use of uniform LLNs, that numerous authors appeal to an unspecified generic uniform LLN. Others appeal to some specific result. The purpose of this paper is to provide a generic uniform LLN that is sufficiently general to incorporate most applications of uniform LLNs in the nonlinear econometrics literature. In summary, the paper presents a result that can be used to turn state of the art pointwise LLNs into uniform LLNs over compact sets, with the addition of a single smoothness condition -- either a Lipschitz condition or a derivative condition. The latter is particularly easy to verify, and is implied by common assumptions used to prove asymptotic normality of estimators. Thus, the additional condition is not particularly restrictive. In contrast to other uniform LLNs that appear in the literature, the one given here allows the full range of heterogeneity of summands (i.e., non-identical distributions), and temporal dependence, that is available with pointwise LLNs. Keywords: Uniform law of large Numbers, consistency, nonlinear econometric models Note: CFP 693. Length: 26 pages Creation-Date: 198604 Number: 790 Publication-Status: Published in Econometrica (November 1987), 55(6): 1465-1471 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0693.pdf File-Format: application/pdf File-Size: 354 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0790.pdf File-Format: application/pdf File-Size: 534 kb Handle: RePEc:cwl:cwldpp:790 Template-type: ReDIF-Paper 1.0 Author-Name: J. Hoult Verkerke Author-X-Name-First: J. Hoult Author-X-Name-Last: Verkerke Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Defense Economics and Economic Warfare Revisited Abstract: In this paper we paint with a broad brush. Our purpose is to present an overview, a status report, and by implication, an indication of what needs to be done at this time. We first provide a survey of topics in the economics of defense and in economic warfare, then we comment on some naval aspects of these topics. Classification-JEL: 114 Keywords: Economics of defense, economic warfare Note: CFP 741. Length: 41 pages Creation-Date: 198604 Number: 789 Publication-Status: Published in Journal of Conflict Resolution (September 1989), 33(3): 480-499 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0741.pdf File-Format: application/pdf File-Size: 811 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0789.pdf File-Format: application/pdf File-Size: 1548 kb Handle: RePEc:cwl:cwldpp:789 Template-type: ReDIF-Paper 1.0 Author-Name: Steven N. Durlauf Author-X-Name-First: Steven N. Author-X-Name-Last: Durlauf Author-Workplace-Name: Stanford University Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Trends Versus Random Walks in Time Series Analysis Abstract: This paper studies the effects of spurious detrending in regression. The asymptotic behavior of traditional least squares estimators and tests are examined in the context of models where the generating mechanism is systematically misspecified by the presence of deterministic time trends. Most previous work on the subject has relied upon Monte Carlo studies to understand the issues involved in detrending data that is generated by integrated processes and our analytical results help to shed light on many of the simulation findings. Standard F tests and Hausman tests are shown to inadequately discriminate between the competing hypotheses. Durbin-Watson statistics, on the other hand, are shown to be valuable measures of series stationarity. The asymptotic properties of regressions and excess volatility tests with detrended integrated time series are also explored. Keywords: Excess volatility tests, integrated processes, misspecification, specification tests, spurious detrending Note: CFP 744. Length: 40 pages Creation-Date: 198604 Number: 788 Publication-Status: Published in Econometrica (November 1988), 56(6): 1333-1354 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0744.pdf File-Format: application/pdf File-Size: 1087 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0788.pdf File-Format: application/pdf File-Size: 817 kb Handle: RePEc:cwl:cwldpp:788 Template-type: ReDIF-Paper 1.0 Author-Name: P. Bracken Author-X-Name-First: P. Author-X-Name-Last: Bracken Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Issues Arising in Management and Control of Naval Forces Abstract: This paper takes the context of political and military command as given and considers the fundamental question of how a modern navy fits in with the usual conception of nuclear deterrence between the United States and the Soviet Union. We here summarize the major issues, questions, and conclusions from this research as they serve to provide the context for our observations on the relevance of and potential for operations research and decision sciences contributions to providing understanding and analysis for these critical and highly qualitative problems. Classification-JEL: 114, 511 Keywords: Deterrence, naval forces Length: 20 pages Creation-Date: 198604 Number: 787 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0787.pdf File-Format: application/pdf File-Size: 622 kb Handle: RePEc:cwl:cwldpp:787 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Best Median Unbiased Estimation in Linear Regression with Bounded Asymmetric Loss Functions Abstract: We first show that the Generalized Least Squares estimator is the best median unbiased estimator of the regression parameters for quite general loss functions, when the parameter space is unrestricted. Of note is the fact that this result holds without moment restrictions. Thus, the errors may have multivariate Cauchy distribution. Next, we show that a restricted GLS estimator is best median unbiased for a linear combination of the regression parameters, when that linear combination is restricted to lie in an interval. Certain other linear combinations of the parameter vector may be subject to arbitrary additional restrictions. The paper then presents best median unbiased estimators of the error variance sigma-squared, as well as monotone functions of sigma-squared, when the errors are normally distributed. If sigma-squared is constrained to lie in a finite interval, the best estimator is a censored version of its unconstrained counterpart. When sigma-square is constrained only to be positive, the best median unbiased estimator is always larger than the best mean unbiased estimator s-squared, and is approximately equal to s-squared calculated with its degrees of freedom reduced by .66. Keywords: Keywords: Generalized least squares, elliptically symmetric distribution, restricted parameter space, minimum risk, variance, estimation Note: CFP 690. Length: 28 pages Creation-Date: 198603 Number: 786 Publication-Status: Published in Journal of the American Statistical Association (September 1987), 82(399): 886-893 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0690.pdf File-Format: application/pdf File-Size: 862 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0786.pdf File-Format: application/pdf File-Size: 629 kb Handle: RePEc:cwl:cwldpp:786 Template-type: ReDIF-Paper 1.0 Author-Name: John Y. Campbell Author-X-Name-First: John Y. Author-X-Name-Last: Campbell Author-Workplace-Name: Princeton University Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Cointegration and Tests of Present Value Models Abstract: In a model where a variable Y is proportional to the present value, with constant discount rate, of expected future values of a variable y, the "spread" S - Y - qy will be stationary for some q whether or not y must be differenced to induce stationarity. Thus, Y and y are cointegrated. The model implies that S is proportional to the optimal forecast of S*, the present value of future changes in y. We use vector autoregressive methods, and recent literature on cointegrated processes, to test the model. When Y is the long-term interest rate and y the short-term interest rate, we find in postwar United States data that S behaves much like an optimal forecast of S* even though as earlier research has shown it is negatively correlated with next period's change in Y. When Y is a real stock price index and y the corresponding real dividend, using annual United States data for 1871-1986 we obtain less encouraging results for the model, although the results are sensitive to the assumed discount rate. Classification-JEL: 313 Keywords: Cointegration, present value methods, stock price index, interest rates, term structure, volatility, efficient markets Length: 41 pages Creation-Date: 198603 Number: 785 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0785.pdf File-Format: application/pdf File-Size: 855 kb Handle: RePEc:cwl:cwldpp:785 Template-type: ReDIF-Paper 1.0 Author-Name: Charalambos Aliprantis Author-X-Name-First: Charalambos Author-X-Name-Last: Aliprantis Author-Workplace-Name: Purdue University Author-Name: Donald J. Brown Author-X-Name-First: Donald J. Author-X-Name-Last: Brown Author-Email: donald.brown@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/brown.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Owen Burkinshaw Author-X-Name-First: Owen Author-X-Name-Last: Burkinshaw Author-Workplace-Name: Purdue University Title: Edgeworth Equilibria in Production Economies Abstract: An Edgeworth equilibrium is an allocation that belongs to the core of every n-fold replica of the economy. In [2] we studied in the setting of Riesz spaces the properties of Edgeworth equilibria for pure exchange economies with infinite dimensional commodity spaces. In this work, we study the same problem for economies with production. Under some relatively mild conditions we establish (among other things) that: 1. Edgeworth equilibria exist; 2. Every Edgeworth equilibrium is a quasiequilibrium; and 3. An allocation is an Edgeworth equilibrium if and only if it can be "decentralized" by a price system. Classification-JEL: 021 Keywords: Edgeworth equilibrium, Riesz spaces, production economies Note: CFP 700. Length: 42 pages Creation-Date: 198603 Number: 784 Publication-Status: Published in Journal of Economic Theory (December 1987), 43(2): 252-291 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0700.pdf File-Format: application/pdf File-Size: 1147 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0784.pdf File-Format: application/pdf File-Size: 957 kb Handle: RePEc:cwl:cwldpp:784 Template-type: ReDIF-Paper 1.0 Author-Name: John Andrew Author-X-Name-First: John Author-X-Name-Last: Andrew Author-Name: William D. Nordhaus Author-X-Name-First: William D. Author-X-Name-Last: Nordhaus Author-Email: william.nordhaus@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/nordhaus.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Share Economy: A Symposium Abstract: In 1985-06, the Yale Economics Department sponsored a half-day conference on Martin Weitzman's striking proposal that sharing would be introduced into compensation arrangements. His suggestions have received wide attention in the popular press and from economists, but the organizers believed that the suggestions were sufficiently novel and promising to warrant careful scrutiny from a wide range of points of view. The conference participants therefore examined the "share economy" from the vantage point of labor economics, capital theory, general equilibrium theory, and macroeconomics. Classification-JEL: 023 Keywords: Share economy, stagflation Length: 80 pages Creation-Date: 198602 Number: 783 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0783.pdf File-Format: application/pdf File-Size: 1961 kb Handle: RePEc:cwl:cwldpp:783 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Towards a Unified Asymptotic Theory for Autoregression Abstract: This paper develops an asymptotic theory for a first order autoregression with a root near unity. Deviations from the unit root theory are measured through a noncentrality parameter. When this parameter is negative we have a local alternative that is stationary; when it is positive, the local alternative is explosive; and when it is zero we have the standard unit root theory. Our asymptotic theory accommodates these alternatives and helps to unify earlier theory in which the unit root case appears as a singularity of the asymptotics. The general theory is expressed in terms of functionals of a simple diffusion process. The theory has applications to continuous time estimation and to the analysis of the asymptotic power of tests for a unit root under a sequence of local alternatives. Keywords: Autoregression, Brownian motion, diffusion, near-integrated process, noncentrality parameters, unit root Note: CFP 685. Length: 13 pages Creation-Date: 198602 Revision-Date: 198608 Number: 782R Publication-Status: Published in Biometrika (1987), 74: 535-547 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0685.pdf File-Format: application/pdf File-Size: 653 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0782-r.pdf File-Format: application/pdf File-Size: 517 kb Handle: RePEc:cwl:cwldpp:782R Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Regression Theory for Near-Integrated Time Series Abstract: The concept of a near-integrated vector random process is introduced. Such processes help us to work towards a general asymptotic theory of regression for multiple time series in which some series may be integrated processes of the ARIMA type, others may be stable ARMA processes with near unit roots, and yet others may be mildly explosive. A limit theory for the sample moments of such time series is developed using weak convergence and is shown to involve a simple functionals of a vector diffusion. The results suggest finite sample approximations which in the stationary case correspond to conventional central limit theory. The theory is applied to the study of vector autoregressions and cointegrating regressions of the type recently advanced by Granger and Engle (1987). A noncentral limiting distribution theory is derived for some recently proposed multivariate unit root tests. This yields some interesting insights into the asymptotic power properties of the various tests. Models with drift and near integration are also studied. The asymptotic theory in this case helps to bridge the gap between the nonnormal asymptotics obtained by Phillips and Durlauf (1986) for regressions with integrated regressors and the normal asymptotics that usually apply in regressions with deterministic regressors. Keywords: Brownian motion, cointegration, diffusion, near-integration, unit root tests Note: CFP 711. Length: 42 pages Creation-Date: 198601 Revision-Date: 198701 Number: 781R Publication-Status: Published in Econometrica (September 1988), 56(5): 1021-1043 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0711.pdf File-Format: application/pdf File-Size: 928 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0781-r.pdf File-Format: application/pdf File-Size: 698 kb Handle: RePEc:cwl:cwldpp:781R Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Monetary-Fiscal Mix: Long-Run Implications Abstract: The long-run dynamics of public deficits and debt are modeled, assuming that public debt competes with capital for limited private savings. The interest costs of the debt are endogenously determined in this market, and the deficit in other budget transactions is a constant fraction of Gross National Product. Simulations with parameter values suggested by recent United States experience show the likelihood of unstable paths, along which debt grows faster than GNP indefinitely. Classification-JEL: 023, 321 Keywords: Monetary-fiscal mix, public deficits, public debt Note: CFP 645. Length: 15 pages Creation-Date: 198601 Number: 780 Publication-Status: Published in AEA Papers and Proceedings (May 1986), 76(2): 213-218 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0645.pdf File-Format: application/pdf File-Size: 371 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0780.pdf File-Format: application/pdf File-Size: 245 kb Handle: RePEc:cwl:cwldpp:780 Template-type: ReDIF-Paper 1.0 Author-Name: Paul R. Milgrom Author-X-Name-First: Paul R. Author-X-Name-Last: Milgrom Author-Workplace-Name: Yale University Title: Auction Theory Abstract: This paper discusses two central questions: Why do auction institutions continue to be so popular after thousands of years? and What accounts for particular details, like the popularity of sealed bid and ascending-bid auctions? Classification-JEL: 022 Keywords: Auction theory, sealed-bid auctions, ascending-bid auctions Length: 53 pages Creation-Date: 198511 Number: 779 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0779.pdf File-Format: application/pdf File-Size: 1377 kb Handle: RePEc:cwl:cwldpp:779 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Polemarchakis, Heracles M. Author-Workplace-Name: Columbia University Title: Walrasian Indeterminacy and Keynesian Macroeconomics Abstract: Overlapping generations models with or without production or a portfolio demand for money display a fundamental indeterminacy. Expectations matter; and they are not, in the short run, constrained by the hypotheses of agent optimization, rational expectations, and market clearing. No short run policy analysis is possible without some explicit understanding of how agents expect the economy to respond to the policy. In this framework of perfect foresight and market clearing prices, it is possible to make Keynesian assumptions about the rigidity of money wages and the exogeneity of "animal spirits" of investors, to use the standard IS-LM apparatus, and to derive Keynesian conclusions about the short run effectiveness of policy. Alternatively, starting from difference but no less rational expectations, one can derive the "new classical" neutrality propositions. Classification-JEL: 023, 021 Keywords: Overlapping generations, perfect foresight, short run policy effectiveness Note: CFP 1120. Length: 52 pages Creation-Date: 198510 Number: 778 Publication-Status: Published in Review of Economic Studies (1986), 53: 755-779 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0778.pdf File-Format: application/pdf File-Size: 1286 kb Handle: RePEc:cwl:cwldpp:778 Template-type: ReDIF-Paper 1.0 Author-Name: Chien fu Chou Author-X-Name-First: Chien fu Author-X-Name-Last: Chou Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: On Finitely Repeated Games and Pseudo-Nash Equilibria Abstract: In this paper we propose a pseudo-Nash equilibrium for N-person games in which very simply we allow play in the last period to be arbitrary, but otherwise it must conform to the (perfect) Nash optimality criterion. Classification-JEL: 026 Keywords: Pseudo-Nash equilibrium, arbitrary last period play, overlapping generations economies, Radner's definition, "crazy equilibrium" Length: 28 pages Creation-Date: 198510 Number: 777 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0777.pdf File-Format: application/pdf File-Size: 633 kb Handle: RePEc:cwl:cwldpp:777 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Neoclassical Theory in America: J.B. Clark and Fisher Abstract: The intellectual breakthroughs that mark the neoclassical revolution in economic analysis occurred in Europe around 1870. The next two decades witnessed lively debates in which the new theory more or less absorbed or was absorbed in the classical tradition that preceded and provoked it. In the 1890s, according to Joseph A. Schumpeter (1954, p. 754) there emerged "a large expanse of common ground and ... a feeling of repose, both of which created, in the superficial observer, an impression of finality -- the finality of a Greek temple that spreads its perfect lines against a cloudless sky." Of course the temple was by no means complete. Its building and decoration continue to this day, even while its faithful throngs worship within. American economists were not present at the creation. To a considerable extent they built their own edifice independently, designing some new architecture in the process. They participated actively in the international controversies and syntheses of the period 1870-1914. At least two Americans were prominent builders of the "temple," John Bates Clark and Irving Fisher. They and others brought neoclassical theory into American journals, classrooms, and textbooks, and its analytical tools into the kits of researchers and practitioners. Eventually, for better or worse, their paradigm would dominate economic science in this country. This paper discusses their contribution. Classification-JEL: 031 Keywords: Neoclassical economics, J.B. Clark, Irving Fisher Note: CFP 636. Length: 36 pages Creation-Date: 198509 Number: 776 Publication-Status: Published in American Economic Review (December 1985), 75(6): 28-38 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0636.pdf File-Format: application/pdf File-Size: 1276 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0776.pdf File-Format: application/pdf File-Size: 875 kb Handle: RePEc:cwl:cwldpp:776 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Paul R. Milgrom Author-X-Name-First: Paul R. Author-X-Name-Last: Milgrom Author-Workplace-Name: Stanford University Title: A Theory of Hierarchies Based on Limited Managerial Attention Abstract: Our purpose in this paper is to investigate the economics of managerial organizations by focusing on the decision problem of management. Ours is a "team theory" analysis, that is, it ignores the problem of conflicting objectives among managers and focuses instead on the problem of coordinating the decisions of several imperfectly informed actors. However, unlike classical team theory, we concentrate on the choice by managers of what to know, as well as what to do, and we allow the possibility that bounded rationality limits the managers' ability to understand subtle messages. Note: CFP 794. Length: 33 pages Creation-Date: 198810 Number: 775R Publication-Status: Published in Journal of the Japanese and International Economies (1991), 5: 205-225 File-URL: http://cowles.econ.yale.edu/P/cp/p07b/p0794.pdf File-Format: application/pdf File-Size: 1092 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0775-r.pdf File-Format: application/pdf File-Size: 721 kb Handle: RePEc:cwl:cwldpp:775R Template-type: ReDIF-Paper 1.0 Author-Name: William D. Nordhaus Author-X-Name-First: William D. Author-X-Name-Last: Nordhaus Author-Email: william.nordhaus@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/nordhaus.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Forecasting Efficiency: Concepts and Applications Abstract: The question of forecasting accuracy is, of course, one that has been the subject of numerous investigations over the last two decades. The present study contributes to this line of research in two ways. First, we introduce a new concept, called "forecast efficiency," that measures the extent to which information is incorporated into forecasts. This concept is closely related to concepts of efficiency used in the analysis of stock and other financial markets. The paper proves two readily testable propositions about efficient forecasts. Second, the empirical part of the study examines forecast efficiency by looking at forecast revisions ("fixed-horizon forecasts"), rather than a series of forecasts of different events ("rolling-horizon forecasts") as is the case for most studies of forecasting. This new approach to estimation in certain circumstances will provide a more powerful test of forecast efficiency. A number of fixed-horizon forecasts are collected and these are tested for forecast efficiency. Classification-JEL: 132, 211 Keywords: Forecasting accuracy, forecast efficiency, efficient forecasts Note: CFP 692. Length: 26 pages Creation-Date: 198509 Number: 774 Publication-Status: Published in Review of Economics and Statistics (November 1987), 69(4): 667-674 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0692.pdf File-Format: application/pdf File-Size: 572 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0774.pdf File-Format: application/pdf File-Size: 403 kb Handle: RePEc:cwl:cwldpp:774 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Donald J. Brown Author-X-Name-First: Donald J. Author-X-Name-Last: Brown Author-Email: donald.brown@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/brown.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Comparative Statics and Local Indeterminacy in OLG Economies: An Application of the Multiplicative Ergodic Theorem Abstract: This study is an effort to give a simple measure of the local size of the equilibrium set of OLG economies in which there may be more than one good and more than one consumer per period, and in which the generations may differ across time. Classification-JEL: 021 Keywords: OLG economics, overlapping generations, equilibrium Length: 34 pages Creation-Date: 198510 Number: 773 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0773.pdf File-Format: application/pdf File-Size: 806 kb Handle: RePEc:cwl:cwldpp:773 Template-type: ReDIF-Paper 1.0 Author-Name: John Y. Campbell Author-X-Name-First: John Y. Author-X-Name-Last: Campbell Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Richard H. Clarida Author-X-Name-First: Richard H. Author-X-Name-Last: Clarida Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Term Structure of Euromarket Interest Rates: An Empirical Investigation Abstract: This paper is an empirical investigation of the predictability and comovement of risk premia in the term structure of Euromarket interest rates. We show that variables which have been used as proxies for risk premia on uncovered foreign asset positions also predict excess returns in Euromarket term structures, while variables which have been used as proxies for risk premia in the term structure also predict excess returns on taking uncovered foreign asset positions. These findings suggest that risk premia move together. We test formally the hypothesis that risk premia on uncovered 3-month EuroDM and Eurosterling deposits move in proportion to a single latent variable. We are unable to reject this hypothesis. We are also unable to reject the hypothesis that the risk premia on these three strategies and those on rolling over 1-month Eurosterling (EuroDM) deposit move in proportion to a single latent variable. The single latent variable model can be interpreted atheoretically, as a way of characterizing the extent to which predictable asset returns "move together"; or it can be interpreted as in Hansen and Hodrick (1983) and Hodrick and Srivastava (1983) as a specialization of the ICAPM in which assets have constant betas on a single, unobservable benchmark portfolio. Length: 35 pages Creation-Date: 1985 Revision-Date: 198602 Number: 772R Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0772-r.pdf File-Format: application/pdf File-Size: 808 kb Handle: RePEc:cwl:cwldpp:772R Template-type: ReDIF-Paper 1.0 Author-Name: Richard H. Clarida Author-X-Name-First: Richard H. Author-X-Name-Last: Clarida Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: International Lending and Borrowing in a Stochastic Sequence Equilibrium Abstract: The objective of this paper is to study international lending and borrowing in general equilibrium framework in which countries are subject to stochastic productivity fluctuations. The role of time preference, borrowing limits, and lump sum taxation are rigorously analyzed, yielding results which enrich those obtained in the existing literature. Classification-JEL: 441, 431 Keywords: International lending and borrowing, stochastic productivity fluctuations Length: 32 pages Creation-Date: 198505 Number: 771 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0771.pdf File-Format: application/pdf File-Size: 567 kb Handle: RePEc:cwl:cwldpp:771 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Andreu Mas-Colell Author-X-Name-First: Andreu Author-X-Name-Last: Mas-Colell Author-Workplace-Name: MSRI & Harvard University Title: Real Indeterminacy with Financial Assets Abstract: The purpose of this paper, which takes up after D. Cass (1984a, 1984b) is to find the degree of real indeterminacy inherent in models with purely financial assets. We solve the problem for the case where there are enough traders (precisely, the number of traders is larger than the number of bonds) and the asset returns structure is in general position. We find that if the number of bonds is non-zero and fewer than the number of states then, generically, the number of dimensions of real indeterminacy is S-1, one less than the number of states. There is something of a surprise in the above result, namely the dimension of real indeterminacy does not depend on the number of bonds (except in the two limit cases). Indeed one initial conjecture was S-B. This points to an intriguing qualitative discontinuity at the complete market configuration. If markets are financially complete then the model is determinate. Let just one bond be missing and the model become highly indeterminate. Thus, in this sense, the complete markets hypothesis lacks robustness. Classification-JEL: 313 Keywords: Incomplete financial markets, real indeterminacy, complete markets hypothesis Note: CFP 721. Length: 14 pages Creation-Date: 1985 Revision-Date: 198510 Number: 770R Publication-Status: Published in Journal of Economic Theory (February 1989), 47(1): 22-38 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0721.pdf File-Format: application/pdf File-Size: 851 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0770-r.pdf File-Format: application/pdf File-Size: 329 kb Handle: RePEc:cwl:cwldpp:770R Template-type: ReDIF-Paper 1.0 Author-Name: Richard H. Clarida Author-X-Name-First: Richard H. Author-X-Name-Last: Clarida Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Balance of Payments Adjustment Mechanism in a Rational Expectations Equilibrium Abstract: This paper provides a choice theoretic, general equilibrium account of the balance of payments adjustment process and the determination of national price levels in a world comprised of countries populated by rational households. Balance of payments adjustment dynamics arise in the equilibrium of this model from the precautionary saving behavior of risk-averse households who self-insure against random productivity fluctuations by accumulating, via balance of payments surpluses in productive periods, buffer stocks of domestic money which can be drawn down to finance payments deficits, and thus a less variable profile of consumption relative to output, when productivity is unexpectedly low. Precautionary saving is shown to exhibit the partial-adjustment-to-target behavior typically postulated in the monetary approach literature. The existence of a rational expectations equilibrium in which the distribution of international reserves among central banks is stationary is established. Classification-JEL: 431 Keywords: Balance of payments, adjustment dynamics, price levels Length: 25 pages Creation-Date: 198504 Number: 769 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0769.pdf File-Format: application/pdf File-Size: 490 kb Handle: RePEc:cwl:cwldpp:769 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Steven N. Durlauf Author-X-Name-First: Steven N. Author-X-Name-Last: Durlauf Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Multiple Time Series Regression with Integrated Processes Abstract: This paper develops a general asymptotic theory of regression for processes which are integrated of order one. The theory includes vector autoregressions and multivariate regressions amongst integrated processes that are driven by innovation sequences which allow for a wide class of weak dependence and heterogeneity. The models studied cover cointegrated systems and quite general linear simultaneous equations systems with contemporaneous regressor-error correlation and serially correlated errors. Problems of statistical testing in vector autoregressions and multivariate regressions with integrated processes are also studied. It is shown that the asymptotic theory for conventional tests involves major departures from classical theory and raises new and important issues of the presence of nuisance parameters in the limiting distribution theory. Keywords: Integrated process, multivariate functional CLT, asymptotic theory for stationary VAR's Note: CFP 659. Length: 43 pages Creation-Date: 198509 Number: 768 Publication-Status: Published in Review of Economic Studies (1986), 53: 473-495 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0659.pdf File-Format: application/pdf File-Size: 1118 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0768.pdf File-Format: application/pdf File-Size: 817 kb Handle: RePEc:cwl:cwldpp:768 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Fractional Matrix Calculus and the Distribution of Multivariate Tests Abstract: Fractional matrix operator methods are introduced as a new tool of distribution theory for use in multivariate analysis and econometrics. Earlier work by the author on this operational calculus is reviewed and to illustrate the use of these methods we give an exact distribution theory for a general class of tests in the multivariate linear model. This distribution theory unifies and generalizes previously known results, including those for the standard F statistic in linear regression, for Hotelling's T^{2} test and for Hotelling's generalized T^{-2} test. We also provide a simple and novel derivation of conventional asymptotic theory as a specialization of exact theory. This approach is extended to generate general formulae for higher order asymptotic expansions. Thus, the results of the paper provide a meaningful unification of conventional asymptotics, higher order asymptotic expansions and exact finite sample distribution theory in this context. Keywords: Fractional matrix calculus, multivariate tests, exact distribution theory, asymptotic expansions Note: CFP 664. Length: 23 pages Creation-Date: 198509 Number: 767 Publication-Status: Published in I.B. MacNeill and G.J. Umphrey, eds., Time Series and Econometric Modelling, Reidel, 1987, pp. 219-234 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0664.pdf File-Format: application/pdf File-Size: 519 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0767.pdf File-Format: application/pdf File-Size: 412 kb Handle: RePEc:cwl:cwldpp:767 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Uses, Value and Limitation of Game Theoretic Methods in Defense Analysis Abstract: The central contribution of game theory to defense analysis has been a language for the understanding of how to formulate and study strategic or cross-purposes optimization in situations involving two or more actors. It is suggested here in this discussion that two fundamentally different classes of application of game theory to problems in defense have emerged. The first is the application of two-person zero sum game theory to military, primarily tactical situations which for the purposes at hand can be reasonably well modeled in this manner. The second is the application of two or more person nonconstant sum game theory to strategic problems involving threat analysis, crises control and the interface between international diplomatic relations and war. Classification-JEL: 114, 026 Keywords: Game theory, war, national defense Length: 40 pages Creation-Date: 198510 Number: 766 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0766.pdf File-Format: application/pdf File-Size: 1087 kb Handle: RePEc:cwl:cwldpp:766 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Asymptotic Expansions in Nonstationary Vector Autoregressions Abstract: This paper studies the statistical properties of vector autoregressions (VAR's) for quite general multiple time series which are integrated of order one. Functional central limit theorems are given for multivariate partial sums of weakly dependent innovations and these are applied to yield first order asymptotics in nonstationary VAR's. Characteristic and cumulant functionals for generalized random processes are introduced as a means of developing a refinement of central limit theory on function spaces. The theory is used to find asymptotic expansions of the regression coefficients in nonstationary VAR's under very general conditions. The results are specified to the scalar case and are related to other recent work by the author in [17] and [19]. Keywords: Asymptotic expansions, vector autoregressions, characteristic functionals, generalized random processes Note: CFP 679. Length: 35 pages Creation-Date: 198508 Number: 765 Publication-Status: Published in Econometric Theory (1987), 3: 45-68 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0679.pdf File-Format: application/pdf File-Size: 786 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0765.pdf File-Format: application/pdf File-Size: 585 kb Handle: RePEc:cwl:cwldpp:765 Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Heracles M. Polemarchakis Author-X-Name-First: Heracles M. Author-X-Name-Last: Polemarchakis Title: Existence, Regularity, and Constrained Suboptimality of Competitive Allocations When the Asset Market Is Incomplete Abstract: Let assets be denominated in an a priori specified numeraire. Whether or not the asset is complete, a competitive equilibrium exists as long as arbitrage is possible when assets are free. Generically, the set of competitive equilibria is finite, and the equilibrium prices and allocations in the commodity spot markets are uniquely determined by the asset allocation is generically constrained suboptimal: there exists an arbitrarily small reallocation of the existing assets, which leads to a Pareto improvement in welfare when prices and allocations in the commodity spot markets adjust to maintain equilibrium. Classification-JEL: 313 Keywords: Asset markets, competitive equilibria, incomplete asset markets Note: CFP 652. Length: 62 pages Creation-Date: 198508 Number: 764 Publication-Status: Published in W. Heller, R. Starr and D. Starrett eds., Uncertainty, Information and Communication, Essays in Honor of Kenneth J. Arrow, Vol. III, Cambridge University Press, 1986, pp. 65-95 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0652.pdf File-Format: application/pdf File-Size: 1340 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0764.pdf File-Format: application/pdf File-Size: 1060 kb Handle: RePEc:cwl:cwldpp:764 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Random Cell Chi-Square Diagnostic Tests for Econometric Models: II. Theory Abstract: This paper extends the Pearson chi-square testing method to non-dynamic parametric econometric models, in particular, to models with covariates. The paper establishes the asymptotic distribution of the test statistic under the null and local alternatives, when the test statistic is based on data-dependent random cells of a general form, and on an arbitrary asymptotically normal estimator. These results are attained by extending recent probabilistic results for the weak convergence of empirical processes indexed by sets. The chi-square test that is introduced can be used to test goodness-of-fit of a parametric model, as well as to test particular aspects of the parametric model that are of interest. In the event of rejection of the null hypothesis, the test provides information concerning the direction of departure from the null. The diagnostics provided by the test are intuitive and particularly easy to interpret. Classification-JEL: 212 Keywords: Specification test, goodness-of-fit test, chi-square Note: CFP 719. Length: 64 pages Creation-Date: 1985 Revision-Date: 198606 Number: 763R Publication-Status: Published in Econometrica (November 1988), 56(6): 1419-1458 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0719.pdf File-Format: application/pdf File-Size: 1678 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0763-r.pdf File-Format: application/pdf File-Size: 1331 kb Handle: RePEc:cwl:cwldpp:763R Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Random Cell Chi-Square Diagnostic Tests for Econometric Models: I. Introduction and Applications Abstract: This paper and its sequel, Andrews [4], extend the Pearson chi-square testing method to non-dynamic parametric econometric models, in particular, models with covariates. The present paper introduced the test and discusses a wide variety of applications. Andrews [4] establishes the asymptotic properties of the test, by extending recent probabilistic results for the weak convergence of empirical processes indexed by sets. The chi-square test that is introduced can be used to test goodness-of-fit of a parametric model, as well as to test particular aspects of the parametric model that are of interest. In the event of rejection of the null hypothesis of correct specification, the test provides information concerning the direction of departure from the null. The results allow for estimation of the parameters of the model by quite general methods. The cells used to construct the test statistic my be random and can be specified in a general form. Classification-JEL: 212 Keywords: Specification, test, goodness-of-fit test, chi-square testing method Note: CFP 698. Length: 62 pages Creation-Date: 198509 Number: 762 Publication-Status: Published in Journal of Econometrics (November 1988), 37: 135-156 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0698.pdf File-Format: application/pdf File-Size: 969 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0762.pdf File-Format: application/pdf File-Size: 1342 kb Handle: RePEc:cwl:cwldpp:762 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Asymptotic Results for Generalized Wald Tests Abstract: This note presents conditions under which a quadratic form based on a g-inverted weighting matrix converges to a chi-square distribution as the sample size goes to infinity. Subject to fairly weak underlying conditions, a necessary and sufficient condition is given for this result. The result is of interest, because it is needed to establish asymptotic significance levels and local power properties of generalized Wald tests (i.e., Wald tests with singular limiting covariance matrices). Included in this class of tests are Hausman specification tests and various goodness of fit tests, among others. The necessary and sufficient condition is relevant to procedures currently in the econometrics literature, because it illustrates that some results stated in the literature only hold under more restrictive assumptions than those given. Keywords: Generalized inverse, Wald test, asymptotics, chi-square Note: CFP 694. Length: 14 pages Creation-Date: 198509 Revision-Date: 198604 Number: 761R Publication-Status: Published in Econometric Theory (1987), 3: 348-358 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0694.pdf File-Format: application/pdf File-Size: 554 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0761-r.pdf File-Format: application/pdf File-Size: 330 kb Handle: RePEc:cwl:cwldpp:761R Template-type: ReDIF-Paper 1.0 Author-Name: Roger Howe Author-X-Name-First: Roger Author-X-Name-Last: Howe Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Sections and Extensions of Concave Functions Note: CFP 683. Length: 17 pages Creation-Date: 198508 Number: 760 Publication-Status: Published in Journal of Mathematical Economics (1987), 16: 53-64 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0683.pdf File-Format: application/pdf File-Size: 342 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0760.pdf File-Format: application/pdf File-Size: 268 kb Handle: RePEc:cwl:cwldpp:760 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Many Properties of Money: A Strategic Market Game Analysis Abstract: Among the major properties of a money are that it can serve as (1) a numeraire, (2) a means of exchange, (3) a store of value, and (4) a source of liquidity. Among the lesser properties are that it should be easy to transport and identify, it should be durable, easily divisible, hard to counterfeit and easy to store. A possibly desirable property is that it is an anonymous "bearer instrument," but the price of anonymity is that it is hard to recover if it is stolen. A personal check which is bank money can be stopped and is more personal than a $100 bill. The properties of a money are systemic and strategic and are most naturally formalized by means of strategic market games. Here we concentrate on the four major properties noted above and include comments on the cost of liquidity and the role of various assets as near monies. Classification-JEL: 023, 310 Keywords: Strategic market games, properties of money Length: 19 pages Creation-Date: 198509 Number: 759 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0759.pdf File-Format: application/pdf File-Size: 461 kb Handle: RePEc:cwl:cwldpp:759 Template-type: ReDIF-Paper 1.0 Author-Name: N. Gregory Mankiw Author-X-Name-First: N. Gregory Author-X-Name-Last: Mankiw Author-Workplace-Name: MIT Author-Name: David Romer Author-X-Name-First: David Author-X-Name-Last: Romer Author-Workplace-Name: MIT Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: An Unbiased Reexamination of Stock Market Volatility Note: CFP 623. Length: 22 pages Creation-Date: 198501 Number: 758 Publication-Status: Published in Journal of Finance (July 1985), 40(3): 677-687 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0623.pdf File-Format: application/pdf File-Size: 530 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0758.pdf File-Format: application/pdf File-Size: 436 kb Handle: RePEc:cwl:cwldpp:758 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Understanding Spurious Regressions in Econometrics Abstract: This paper provides an analytical study of spurious regressions involving the levels of economic time series. As asymptotic theory is developed for regressions that relate independent random walks. It is shown that the usual t ratio significance tests do not possess limiting distributions but actually diverge as the sample size T approaches infinity. The Durbin-Watson statistic, on the other hand, converges in probability to zero. An alternative asymptotic theory is also analyzed. An alternative asymptotic theory is developed based on the concept of continuous data recording. This theory together with the large sample asymptotics that we present go a long way towards explaining the experimental results of Granger and Newbold (1974, 1977). Keywords: Spurious regressions, random walk, asymptotic theory Note: CFP 667. Length: 29 pages Creation-Date: 198507 Number: 757 Publication-Status: Published in Journal of Econometrics (1986), 33: 311-340 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0667.pdf File-Format: application/pdf File-Size: 942 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0757.pdf File-Format: application/pdf File-Size: 721 kb Handle: RePEc:cwl:cwldpp:757 Template-type: ReDIF-Paper 1.0 Author-Name: Donald J. Brown Author-X-Name-First: Donald J. Author-X-Name-Last: Brown Author-Email: donald.brown@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/brown.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Charalambos Aliprantis Author-X-Name-First: Charalambos Author-X-Name-Last: Aliprantis Author-Name: Owen Burkinshaw Author-X-Name-First: Owen Author-X-Name-Last: Burkinshaw Title: Edgeworth Equilibria Abstract: The paper studies pure exchange economies with infinite dimensional commodity spaces in the setting of Riesz dual systems. Several new concepts of equilibrium are introduced. An allocation (x_{1},...,x_{m}) is said to be a) an Edgeworth equilibrium whenever it belongs to the core of every n-fold replication of the economy; and b) an epsilon > 0 there exists some price p not equal to 0 with p omega =1 (where omega = Sigma omega_{i} is the total endowment) and with x >=_{i} x_{i} implying p times x > p times omega_{i} - epsilon. The major results of the paper are the following: Theorem I: Edgeworth equilibria exist. Theorem II: An allocation is an Edgeworth equilibrium if and only if it is an epsilon-Walrasian equilibrium. Theorem III: If preferences are proper, then every Edgeworth equilibrium is a quasi-equilibrium. Note: CFP 691. Length: 39 pages Creation-Date: 198509 Number: 756R Publication-Status: Published in Econometrica (September 1987), 55(5): 1109-1137 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0691.pdf File-Format: application/pdf File-Size: 1354 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0756-r.pdf File-Format: application/pdf File-Size: 983 kb Handle: RePEc:cwl:cwldpp:756R Template-type: ReDIF-Paper 1.0 Author-Name: Rabah Amir Author-X-Name-First: Rabah Author-X-Name-Last: Amir Title: A Characterization of Globally Optimal Paths in the Non-Classical Growth Model Abstract: We show that the monotonicity property of optimal paths (or, equivalently, the uniform boundedness of the marginal propensity of consumption by unity) is a necessary condition for local (as well as for global) optimality, and is also sufficient for local optimality, but not for global optimality. We also show that the well-known properties of the value function -- continuity and monotonicity -ñ are sufficient (along with the above conditions) to guarantee global optimality. In other words, if at any stock level, a local non-global maximizer is selected, a discontinuity in the value function will be observed. We suggest that the previous literature on this problem has not distinguished between local and global maxima, and consequently has not attempted to derive conditions that uniquely characterize global optimality. This is the major aim of this paper, and we hope to have provided some insight towards a systematic approach to non-convex dynamic optimization. Classification-JEL: 111 Keywords: Non-convex dynamic optimization, optimality Length: 33 pages Creation-Date: 198505 Number: 754 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0754.pdf File-Format: application/pdf File-Size: 553 kb Handle: RePEc:cwl:cwldpp:754 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Enough Gold in a Society Without and With Money-Lenders Abstract: If an exchange economy is modeled as a strategic market game with one commodity serving as a money, then if there is no credit available and if all traders are insignificant in size, so that an individual does not influence prices, the noncooperative equilibria (NEs) of the game will coincide with the competitive equilibria of the exchange economy provided that there is enough money to facilitate trade. The meaning of "enough money" is that the NEs are interior. In other words the constraint that an individual cannot spend more of the means of payment than he holds is not binding on any individual's plans. The condition on enough money is characterized both by the total amount of money in the system and its distribution. It is possible that an economy may not have enough money no matter how it is distributed; it is also possible that a redistribution will give rise to interior solutions. These statements are made precise and illustrated by means of specific examples. If there is enough money but it is maldistributed it is shown that a loan market "100 per cent backed by gold" will bring efficiency. Classification-JEL: 021 Keywords: Strategic market game, noncooperative equilibria, enough money, money Length: 21 pages Creation-Date: 198506 Number: 753 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0753.pdf File-Format: application/pdf File-Size: 448 kb Handle: RePEc:cwl:cwldpp:753 Template-type: ReDIF-Paper 1.0 Author-Name: Peter J. Hammond Author-X-Name-First: Peter J. Author-X-Name-Last: Hammond Author-Workplace-Name: Stanford University Author-Name: P. Kane Author-X-Name-First: P. Author-X-Name-Last: Kane Author-Workplace-Name: University of Tsukuba Author-Name: Myrna Holtz Wooders Author-X-Name-First: Myrna Holtz Author-X-Name-Last: Wooders Author-Workplace-Name: University of Toronto Title: Mass-Economies with Vital Small Coalitions; the F-Core Approach Abstract: A mass-economy is one with many, many agents where each agent is negligible and each trading group is also negligible with respect to the mass-economy. Feasible allocations are those which are virtually attainable by trades only among members of coalitions contained in feasible ("measure-consistent") partitions of the agent set. A feasible allocation is in the core, called the f-core, if it cannot be improved upon by any finite coalition. We show that in a private goods economy with indivisibilities and without externalities, the f-core, the A-core (Aumann's core concept) and the Walrasian allocations coincide. In the presence of widespread externalities, the f-core and the Walrasian allocations coincide but the definition of the A-core is problematic. The conceptual significance of these results will be discussed. Classification-JEL: 021 Keywords: Continuum economies, finite coalitions, core equivalence, equilibrium existence Length: 32 pages Creation-Date: 198505 Number: 752 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0752.pdf File-Format: application/pdf File-Size: 656 kb Handle: RePEc:cwl:cwldpp:752 Template-type: ReDIF-Paper 1.0 Author-Name: Siddhartha Sahi Author-X-Name-First: Siddhartha Author-X-Name-Last: Sahi Author-Workplace-Name: Princeton University Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Model of a Sudden-Death Field-Goal Football Game as a Sequential Duel Abstract: This paper introduces a highly simplified version of "sudden-death" scoring. The basic game is as follows. With equal probability the teams toss to see who gets the ball. The team with the ball can either run or try to kick a field goal. The first team to score wins the game. Classification-JEL: 114, 026 Keywords: Tactical combat, war and defense, football, sequential dual Note: CFP 707. Length: 15 pages Creation-Date: 198505 Number: 751 Publication-Status: Published in Mathematical Social Sciences (1988), 15: 205-215 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0707.pdf File-Format: application/pdf File-Size: 298 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0751.pdf File-Format: application/pdf File-Size: 208 kb Handle: RePEc:cwl:cwldpp:751 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Numeraire, Money and the Missing Degree of Freedom Abstract: The prime purpose of this article is to illustrate some basic problems in the modelling of strategic market games with a single means of exchange or with complete markets. A simple example involving three types of traders trading in three commodities serves to make the points clear. Classification-JEL: 026 Keywords: Strategic market games, numeraire, single means of exchange Length: 13 pages Creation-Date: 198505 Number: 750 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07b/d0750.pdf File-Format: application/pdf File-Size: 276 kb Handle: RePEc:cwl:cwldpp:750 Template-type: ReDIF-Paper 1.0 Author-Name: Paul R. Milgrom Author-X-Name-First: Paul R. Author-X-Name-Last: Milgrom Author-Workplace-Name: Yale University Author-Name: John Roberts Author-X-Name-First: John Author-X-Name-Last: Roberts Author-Workplace-Name: Stanford University Title: Relying on the Information of Interested Parties Abstract: We investigate the conventional wisdom that competition among interested parties attempting to influence a decision maker by providing verifiable information brings out all the relevant information. We find that, if the decision maker is strategically sophisticated and well informed about the relevant variables and about the preferences of the interested party or parties, competition may be unnecessary; while if the decision maker is unsophisticated or not well informed, competition is not generally sufficient. However, if the interested parties' interests are sufficiently opposed, or if the decision maker is seeking to advance the parties' decision maker's need for prior knowledge about the relevant variables and for strategic sophistication. In other settings, only the combination of competition among information providers and a sophisticated skepticism is sufficient to allow defective decision making. Classification-JEL: 026, 612, 613 Keywords: Law and economics, regulation, persuasion games, revelation games, lobbying, strategic information transmission, adversary system Length: 35 pages Creation-Date: 198505 Number: 749 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0749.pdf File-Format: application/pdf File-Size: 715 kb Handle: RePEc:cwl:cwldpp:749 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Some Three Person Games in Coalitional Form for Teaching and Experimentation Abstract: Since 1973 I have used several three person games in coalitional form for both teaching and experimental purposes. They have been run in primarily a normative mode. The individuals have been asked to act as judges called upon to recommend a division of assets among three players. The basic use of these games has been to help to raise questions about context and solution concepts in cooperative game theory. Since 1980 the three basic games noted below have been used with five more or less similar groups of students at Yale. The games, their didactic purpose and the results from the normative suggestions as to how the players should be rewarded are noted here and then these results are compared with previous games. Furthermore, some extra sensitivity analysis problems are noted. Classification-JEL: 026, 012 Keywords: Game theory, cooperative game solutions, sensitivity analysis problems Length: 16 pages Creation-Date: 198505 Number: 747 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0747.pdf File-Format: application/pdf File-Size: 336 kb Handle: RePEc:cwl:cwldpp:747 Template-type: ReDIF-Paper 1.0 Author-Name: Mamoru Kaneko Author-X-Name-First: Mamoru Author-X-Name-Last: Kaneko Author-Workplace-Name: University of Tsukuba Title: An Axiomatization of Utility and Subjective Probability Based on Objective Probability Abstract: This paper provides an axiomatic model based on an extraneous random device generating objective probabilities for the derivation of expected utilities and subjective probabilities. Four basic axioms fully determine a real-valued utility function and a finitely additive subjective probability measure. The restrictions of these axioms to lotteries depending only upon events of the random device yield the von Neumann-Morgenstern axioms. Classification-JEL: 026, 022 Keywords: Real-world event, auxiliary event, objective probabilities, subjective probabilities, von Neumann-Morgenstern axioms Length: 26 pages Creation-Date: 198504 Number: 746 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0746.pdf File-Format: application/pdf File-Size: 567 kb Handle: RePEc:cwl:cwldpp:746 Template-type: ReDIF-Paper 1.0 Author-Name: Russell Cooper Author-X-Name-First: Russell Author-X-Name-Last: Cooper Author-Name: John Andrew Author-X-Name-First: John Author-X-Name-Last: Andrew Title: Coordinating Coordination Failures in Keynesian Models Abstract: This paper focuses on the importance of strategic complementarity in agents' payoff functions as a basis for macroeconomic coordination failures. We first analyze an abstract game and find that inefficient equilibria and a multiplier process may arise in the presence of strategic complementarities (essentially positively sloped reaction curves). We then place additional economic content on complementarities arising from production functions, matching technologies and commodity demand functions in a multi-sector economy. Classification-JEL: 023 Keywords: Coordination, multipliers, strategic complementarity, Keynesian Length: 37 pages Creation-Date: 198504 Revision-Date: 198507 Number: 745R Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0745-r.pdf File-Format: application/pdf File-Size: 785 kb Handle: RePEc:cwl:cwldpp:745R Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Use of Simple Games to Illustrate Concepts and to Provide Experimental Evidence Abstract: This paper is devoted to a discussion of several simple experimental games used in a series of lectures on game theory. The prime purpose of these games was to raise questions and illustrate problems in the construction of game theoretical models in the social sciences. The students were asked to make choices or to give opinions as to what imputation should be recommended as a solution in a cooperative game. Classification-JEL: 026 Keywords: Game theory, cooperative game solutions, strategic form, extensive form Length: 39 pages Creation-Date: 198505 Number: 744 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0744.pdf File-Format: application/pdf File-Size: 780 kb Handle: RePEc:cwl:cwldpp:744 Template-type: ReDIF-Paper 1.0 Author-Name: N. Gregory Mankiw Author-X-Name-First: N. Gregory Author-X-Name-Last: Mankiw Author-Workplace-Name: Harvard University Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Title: Do We Reject Too Often? Small Sample Bias in Tests of Rational Expectations Abstract: We examine the small sample properties of tests of rational expectations models. We show using Monte Carlo experiments that these tests can be extremely biased toward rejection for sample sizes typical in applied research. These biases are important when the time series examined are highly autoregressive. We also show that these tests are even more biased with detrended data. We present correct small sample critical values for our canonical problem. Classification-JEL: 131, 211 Keywords: Rational expectations, non-stationary time series, detrending, small sample bias Note: CFP 637. Length: 20 pages Creation-Date: 198504 Number: 743 Publication-Status: Published in Economics Letters (1986), 20: 139-145 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0637.pdf File-Format: application/pdf File-Size: 314 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0743.pdf File-Format: application/pdf File-Size: 378 kb Handle: RePEc:cwl:cwldpp:743 Template-type: ReDIF-Paper 1.0 Author-Name: Bengt Holmstrom Author-X-Name-First: Bengt Author-X-Name-Last: Holmstrom Author-Name: Paul R. Milgrom Author-X-Name-First: Paul R. Author-X-Name-Last: Milgrom Title: Aggregation and Linearity in the Provision of Intertemporal Incentives Abstract: One of the main findings of the principal-agent literature has been that incentive schemes should be sensitive to all information that bears on the agent's actions. As a manifestation of this principle, incentive schemes tend to take quite complex (non-linear) forms. In contrast, real world schemes are often based on aggregate information with a rather simple structure. This paper considers the optimality of linear schemes that use only aggregated information. The hypothesis is that linear schemes are to be expected in situations where the agent has a rich set of actions to choose from, because richness in action choice allows the agent to circumvent highly nonlinear schemes. We show that optimal compensation schemes are indeed linear functions of appropriate accounting aggregates in a multi-period model where the agent can observe and respond to his own performance over time. Furthermore, when profits evolve according to a controlled Brownian motion (with the agent at the controls) the optimal compensation scheme is linear in profits. The optimal scheme can be computer as if the principal could only choose among linear rules in a corresponding static problem. Applications of this ad hoc principle appear quite promising and are briefly illustrated. Classification-JEL: 025 Keywords: Intertemporal incentives, linear incentive schemes Length: 55 pages Creation-Date: 198508 Number: 742 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0742.pdf File-Format: application/pdf File-Size: 1319 kb Handle: RePEc:cwl:cwldpp:742 Template-type: ReDIF-Paper 1.0 Author-Name: Adrian Pagan Author-X-Name-First: Adrian Author-X-Name-Last: Pagan Title: Two Stage and Related Estimators and Their Applications Abstract: Applied econometric research frequently encounters the difficulty that estimation of the parameters of interest is complex owing to the presence of incidental parameters. It is tempting therefore to try to circumvent the difficulties by proceeding in two stages. In the first, some estimates are made of the incidental parameters. In the second, these estimates are treated as though they were population values, leading to a large reduction in the dimension of the unknown parameter space, possibly even down to that of the parameters of interest only. The properties of such a staged process (particularly as they relate to issues arising from the consistency and efficiency of the estimator and the provision of reliable inference), applications involving the presence of current and future anticipations, an alternative estimator, and diagnostic tests are all discussed in this paper. Keywords: Two stage estimators, censored data, anticipation Length: 45 pages Creation-Date: 198504 Number: 741 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0741.pdf File-Format: application/pdf File-Size: 1079 kb Handle: RePEc:cwl:cwldpp:741 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Time Series Regression with a Unit Root Abstract: This paper studies the random walk in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t-statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984). Note: CFP 674. Length: 43 pages Creation-Date: 198504 Revision-Date: 198602 Number: 740R Publication-Status: Published in Econometrica (March 1987), 55(2): 277-301 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0674.pdf File-Format: application/pdf File-Size: 1070 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0740-r.pdf File-Format: application/pdf File-Size: 884 kb Handle: RePEc:cwl:cwldpp:740R Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Distribution of FIML in the Leading Case Abstract: In a recent article (1984a) Phillips showed that the distribution of the limited information maximum likelihood (LIML) estimator of the coefficients of the endogenous variables in a single structural equation is multivariate Cauchy in the leading (totally unidentified) case. The purpose of the present note is to show that the same result holds for the full information maximum likelihood (FIML) estimator. Our proof relies on the theory of invariant measures on a Stiefel manifold. This approach provides a major simplification of the derivation of the LIML result given in the earlier article and extends to the FIML case without difficulty. We start by illustrating its use for LIML. Keywords: Distribution theory, Stiefel manifold, invariant measure, FIML, LIML Note: CFP 638. Length: 8 pages Creation-Date: 198504 Number: 739 Publication-Status: Published in International Economic Review (February 1986), 27(1): 239-243 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0638.pdf File-Format: application/pdf File-Size: 200 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0739.pdf File-Format: application/pdf File-Size: 164 kb Handle: RePEc:cwl:cwldpp:739 Template-type: ReDIF-Paper 1.0 Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: N. Gregory Mankiw Author-X-Name-First: N. Gregory Author-X-Name-Last: Mankiw Author-Workplace-Name: MIT Title: Risk and Return: Consumption Beta Versus Market Beta Abstract: Much recent work emphasizes the joint nature of the consumption decision and the portfolio allocation decision. In this paper, we compare two formulations of the Capital Asset Pricing Model. The traditional CAPM suggests that the appropriate measure of an asset's risk is the covariance of the asset's return with the market return. The consumption CAPM, on the other hand, implies that a better measure of risk is the covariance with aggregate consumption growth. We examine a cross-section of 464 stocks and find that the beta measured with respect to a stock market index outperforms the beta measured with respect to consumption growth. Classification-JEL: 313, 921 Keywords: Capital asset pricing model, consumption, risk, portfolio theory Note: CFP 657. Length: 30 pages Creation-Date: 198501 Number: 738 Publication-Status: Published in Review of Economics and Statistics (August 1986), 68(3): 453-458 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0657.pdf File-Format: application/pdf File-Size: 583 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0738.pdf File-Format: application/pdf File-Size: 626 kb Handle: RePEc:cwl:cwldpp:738 Template-type: ReDIF-Paper 1.0 Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Title: Capital Utilization and Capital Accumulation: Theory and Evidence Abstract: A firm may acquire additional capital input by purchasing new capital or by increasing the utilization of its current capital. The margin between capita accumulation and capital utilization is studied in a model of dynamic factor demand where the firm chooses capital, labor, and their rates of utilization. A direct measure of capital utilization -- the work week of capital -- is incorporated into the theory and estimates. The methodology advocated by Hansen and Singleton (1982) is used to obtain estimates of the model's parameters. This methodology allows the firm's decision problem to depend on expected values of future endogenous and exogenous functional form or the distribution of shocks to the system. The estimates imply that capital stock is costly to adjust while the work week of capital is essentially costless to adjust. Hence, the work week of capital overshoots the steady state when innovations in policy or other shocks change the demand for capital. Short run variation in the demand for capital is met by changing utilization. Long run variation is met by changing the stock. The estimated response of the capital stock to changes in its price and in the required rate of return is substantial and it takes place more quickly than found in other estimates. These results provide an important challenge to the view that input prices and required rates of return are empirically unimportant in models of the demand for capital. Classification-JEL: 131, 641 Keywords: Investment, capacity utilization, capital, labor demand Note: CFP 662. Length: 54 pages Creation-Date: 198501 Number: 736 Publication-Status: Published in Journal of Applied Econometrics (1986), 1: 211-234 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0662.pdf File-Format: application/pdf File-Size: 1449 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0736.pdf File-Format: application/pdf File-Size: 1181 kb Handle: RePEc:cwl:cwldpp:736 Template-type: ReDIF-Paper 1.0 Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Title: The Dynamic Demand for Capital and Labor Abstract: A model of the dynamically interrelated demand for capital and labor is specified and estimated. The estimates are of the first-order conditions of the firm's problem rather than of the closed-form decision rules. This use of the first-order conditions allows a random rate of return and a flexible specification of the technology. The estimates do not imply the very slow rates of adjustment displayed in other, related estimates of the demand for capital. Because adjustment is estimated to be rapid, there is, contrary to the standard view, scope for factor-prices to affect investment at relatively high frequencies. Classification-JEL: 131, 641 Keywords: Investment, capital, labor demand Note: CFP 650. Length: 34 pages Creation-Date: 198401 Number: 735 Publication-Status: Published in Quarterly Journal of Economics (August 1986), 513-542 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0650.pdf File-Format: application/pdf File-Size: 1405 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0735.pdf File-Format: application/pdf File-Size: 789 kb Handle: RePEc:cwl:cwldpp:735 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Note on the Unbiasedness of Feasible GLS, Quasi-Maximum Likelihood, Robust Adaptive, and Spectral Estimators of the Linear Model Abstract: This note presents a set of conditions on the defining functions of regression parameter estimators of the linear model. These conditions guarantee that the estimators are symmetrically distributed about the true parameter value, and hence are median unbiased, provided the conditional distribution of the vector of errors is symmetric given the matrix of regressors. The symmetry result holds even if the regression parameters are subject to linear restrictions. If the estimators posses one or more moments, then the symmetry result also implies mean unbiasedness. Similar conditions are provided that establish the property of origin (or shift) equivariance for the estimators. Common feasible GLS, quasi-ML, robust, adaptive, and spectral estimators are seen easily to satisfy the requisite conditions. Keywords: Unbiasedness, linear model, parameter estimators Note: CFP 658. Length: 30 pages Creation-Date: 198412 Revision-Date: 198508 Number: 734R Publication-Status: Published in Econometrica (May 1985), 54(3): 687-698 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0658.pdf File-Format: application/pdf File-Size: 732 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0734-r.pdf File-Format: application/pdf File-Size: 711 kb Handle: RePEc:cwl:cwldpp:734R Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Games with Perceptive Commanders But Less Perceptive Subordinates Abstract: We introduce a model of the 2 x 2 games played by agents or subordinates of the players. We assume that each agent or subordinates of the players. We assume that each agent is not as perceptive as his commander in that he can make only two distinctions among the four outcomes whose value can be distinguished by the commanders. Classification-JEL: 026 Keywords: Game theory, agents, commanders, subordinates Length: 13 pages Creation-Date: 198412 Number: 733 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0733.pdf File-Format: application/pdf File-Size: 303 kb Handle: RePEc:cwl:cwldpp:733 Template-type: ReDIF-Paper 1.0 Author-Name: Pierre Perron Author-X-Name-First: Pierre Author-X-Name-Last: Perron Author-Workplace-Name: Yale University Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Testing the Random Walk Hypothesis: Power Versus Frequency of Observation Abstract: Power functions of tests of the random walk hypothesis versus stationary first order autoregressive alternatives are tabulated for samples of fixed span but various frequencies of observation. For a t-test and normalized test, power is found to depend, for a substantial range of parameter values, more on the span of the data in time than on the number of observations. For a runs test, power rapidly declines as the number of observations is increased beyond a certain point. Classification-JEL: 313 Keywords: Random walk, unit roots, power function, efficient markets hypothesis Length: 28 pages Creation-Date: 198412 Number: 732 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0732.pdf File-Format: application/pdf File-Size: 466 kb Handle: RePEc:cwl:cwldpp:732 Template-type: ReDIF-Paper 1.0 Author-Name: Sam Ouliaris Author-X-Name-First: Sam Author-X-Name-Last: Ouliaris Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Exact Distribution of the Wald Statistic: The Non-Central Case Abstract: This paper extends earlier results, which were reported in [7], to include non null distributions. As in [7], attention is concentrated on the Wald statistic for testing general linear restrictions on the coefficients in the multivariate linear model. The results of the present paper encompass the null distributions derived in [7] and generalize all previously known results for such statistics as the standard regression F test and Hotelling's T^{2} test. Keywords: Wald statistic, noncentral quadratic forms, distribution theory, matrix fractional calculus Length: 13 pages Creation-Date: 198411 Number: 731 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0731.pdf File-Format: application/pdf File-Size: 212 kb Handle: RePEc:cwl:cwldpp:731 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Note on Enough Money in a Strategic Market Game with Complete or Fewer Markets Abstract: This paper discusses the notion of "enough money" in strategic market games. In an economy with one money, m-1 markets and no credit, in order to be able to achieve efficient trade there must be "enough money" held by all traders. In essence "enough money" means that the noncooperative equilibrium solutions to a strategic market game is interior, in other words it is not considered by lack of liquidity. For simplicity two specific market mechanisms are described to illustrate the relationship between market structure and liquidity. Classification-JEL: 020 Keywords: Enough money in trade, price system, market structure Note: CFP 632. Length: 10 pages Creation-Date: 198411 Number: 730 Publication-Status: Published in Economics Letters (1985), 19: 231-235 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0632.pdf File-Format: application/pdf File-Size: 189 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0730.pdf File-Format: application/pdf File-Size: 211 kb Handle: RePEc:cwl:cwldpp:730 Template-type: ReDIF-Paper 1.0 Author-Name: Bengt Holmstrom Author-X-Name-First: Bengt Author-X-Name-Last: Holmstrom Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: I. Ricard Author-X-Name-First: I. Author-X-Name-Last: Ricard Author-Workplace-Name: Navarra University, Spain Author-Name: Joan Costa Author-X-Name-First: Joan Author-X-Name-Last: Costa Author-Workplace-Name: Navarra University, Spain Title: Managerial Incentives and Capital Management Abstract: In Holmstrom (1982) an example is given, which shows that a manager's concern for the value of his human capital will lead to a natural incongruity in risk-preferences between himself and the owners, even when no effort considerations are involved. In this paper we present a formal model of this channel of incongruity based on learning about managerial talent. We also explore the nature of an optimal incentive contract in the case where the manager may withhold but not misrepresent information about investment returns. The optimal contract is an option on the manager's human capital value with a possible bonus for investing. The optimal investment rule accepts fewer investments than under the cost of capital -- a commonly observed real world feature. Another phenomena the model helps explain is the extensive use of capital budgeting and rationing schemes in place of linear or non-linear price decentralization, which are shown to be less efficient modes of allocation. Classification-JEL: 026, 851, 512 Keywords: Incentives, managerial incentives, capital budgeting Length: 54 pages Creation-Date: 198411 Number: 729 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0729.pdf File-Format: application/pdf File-Size: 1129 kb Handle: RePEc:cwl:cwldpp:729 Template-type: ReDIF-Paper 1.0 Author-Name: Herbert E. Scarf Author-X-Name-First: Herbert E. Author-X-Name-Last: Scarf Author-Email: herbert.scarf@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/scarf.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Neighborhood Systems for Production Sets with Indivisibilities Note: CFP 648. Length: 42 pages Creation-Date: 198410 Number: 728 Publication-Status: Published in Econometrica (May 1986), 54(3): 507-532 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0648.pdf File-Format: application/pdf File-Size: 1099 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0728.pdf File-Format: application/pdf File-Size: 830 kb Handle: RePEc:cwl:cwldpp:728 Template-type: ReDIF-Paper 1.0 Author-Name: Russell Cooper Author-X-Name-First: Russell Author-X-Name-Last: Cooper Title: Expansionary Government Policy in an Economy with Commodity and Labor Abstract: This paper considers a model in which all exchange is mediated by contracts. The analysis explores the indexation of labor and commodities contracts to observable variations in government spending financed by money creation. In one of the many equilibria, prices and nominal wages are shown to be independent of current money shocks. Except in the extreme equilibrium exhibiting full indexation, policy shocks will generate correlated movements in output and employment over time. The analysis thus suggests an inverse relationship between indexation of contracts and persistence of policy effects. Classification-JEL: 311 Keywords: Labor contracts, money shocks Length: 24 pages Creation-Date: 198410 Number: 727 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0727.pdf File-Format: application/pdf File-Size: 563 kb Handle: RePEc:cwl:cwldpp:727 Template-type: ReDIF-Paper 1.0 Author-Name: Dilip Abreu Author-X-Name-First: Dilip Author-X-Name-Last: Abreu Author-Name: David G. Pearce Author-X-Name-First: David G. Author-X-Name-Last: Pearce Author-Name: Ennio Stacchetti Author-X-Name-First: Ennio Author-X-Name-Last: Stacchetti Title: Optimal Cartel Equilibria with Imperfect Monitoring Abstract: There exist optimal symmetric equilibria in the Green-Porter model [5, 8] having an elementary intertemporal structure. Such an equilibrium is described entirely by two subsets of price space and two quantities, the only production levels used by firms in any contingency. The central technique employed in the analysis is the reduction of the repeated game to a family of static games. Classification-JEL: 611, 026 Keywords: Optimal symmetric cartel equilibria, cartels, imperfect monitoring Note: CFP 656. Length: 27 pages Creation-Date: 198410 Number: 726 Publication-Status: Published in Journal of Economic Theory (June 1986), 39(1): 251-269 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0656.pdf File-Format: application/pdf File-Size: 738 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0726.pdf File-Format: application/pdf File-Size: 619 kb Handle: RePEc:cwl:cwldpp:726 Template-type: ReDIF-Paper 1.0 Author-Name: Matthew D. Shapiro Author-X-Name-First: Matthew D. Author-X-Name-Last: Shapiro Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: N. Gregory Mankiw Author-X-Name-First: N. Gregory Author-X-Name-Last: Mankiw Author-Workplace-Name: MIT Title: Trends, Random Walks, and Tests of the Permanent Income Hypothesis Abstract: Recent studies find that consumption is excessively sensitive to income. These studies assume that income is stationary around a deterministic trend. The data, however, do not reject the hypothesis that disposable income is a random walk with drift. If income is indeed a random walk, then the standard testing procedure is greatly biased toward finding excess sensitivity. Moreover, if income is borderline stationary, this procedure is also seriously biased. Classification-JEL: 131, 211, 921 Keywords: Non-stationary time series, detrending, permanent income hypothesis, small sample bias Note: CFP 628. Length: 15 pages Creation-Date: 198409 Number: 725 Publication-Status: Published in Journal of Monetary Economics (1985), 16: 165-174 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0628.pdf File-Format: application/pdf File-Size: 427 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0725.pdf File-Format: application/pdf File-Size: 563 kb Handle: RePEc:cwl:cwldpp:725 Template-type: ReDIF-Paper 1.0 Author-Name: Donald J. Brown Author-X-Name-First: Donald J. Author-X-Name-Last: Brown Author-Email: donald.brown@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/brown.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Geoffrey M. Heal Author-X-Name-First: Geoffrey M. Author-X-Name-Last: Heal Author-Workplace-Name: Columbia University Author-Name: M. Ali Khan Author-X-Name-First: M. Ali Author-X-Name-Last: Khan Author-Workplace-Name: University of Illinois Author-Name: Rajiv Vohra Author-X-Name-First: Rajiv Author-X-Name-Last: Vohra Author-Workplace-Name: Brown University Title: On a General Existence Theorem for Marginal Cost Pricing Equilibria Abstract: We report a generalization of recent results on the existence of marginal cost pricing equilibria (MCPE) in economies with an increasing returns to scale industry. Our result makes no ad hoc assumptions which force the equilibrium to be on the efficiency frontier of the aggregate production possibility set. We also present an additional condition under which our MCPE are productivity efficient in the aggregate. Note: CFP 653. Length: 20 pages Creation-Date: 198412 Number: 724 Publication-Status: Published in Journal of Economic Theory (April 1986), 38(2): 371-379 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0653.pdf File-Format: application/pdf File-Size: 389 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0724.pdf File-Format: application/pdf File-Size: 421 kb Handle: RePEc:cwl:cwldpp:724 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: An Everywhere Convergent Series Representation of the Distribution of Hotelling's Generalized T_{0}^{2} Abstract: A new series representation of the exact distribution of Hotelling's generalized T_{0}^{2}statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the noncentral distributions. Earlier results by Constantine [1], which are convergent on the interval [0,1), are also derived quite simply from our formulae. Keywords: Hotelling's T_{0}^{2}, exact distribution, invariant polynomials, everywhere convergent series Note: CFP 675. Length: 17 pages Creation-Date: 1983 Revision-Date: 198603 Number: 723R Publication-Status: Published in Journal of Multivariate Analysis (April 1987), 21(2): 238-249 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0675.pdf File-Format: application/pdf File-Size: 302 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0723-r.pdf File-Format: application/pdf File-Size: 277 kb Handle: RePEc:cwl:cwldpp:723R Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Exact Distribution of the Wald Statistic Abstract: This paper derives the exact distribution of the Wald statistic for testing general linear restrictions on the coefficients in the multivariate linear model. This generalizes all previously known results including those for the standard F statistic in linear regression, for Hotelling's T^{2} test and for Hotelling's generalized T_{0}^{2} test. Conventional classical assumptions of normally distributed errors and nonrandom exogenous variables are employed. Keywords: Matrix fractional calculus, Wald statistic, distribution theory Note: CFP 654. Length: 19 pages Creation-Date: 198409 Number: 722 Publication-Status: Published in Econometrica (July 1986), 54(4): 881-895 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0654.pdf File-Format: application/pdf File-Size: 549 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0722.pdf File-Format: application/pdf File-Size: 300 kb Handle: RePEc:cwl:cwldpp:722 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: R.C. Reiss Author-X-Name-First: R.C. Author-X-Name-Last: Reiss Title: Testing for Serial Correlation and Unit Roots Using a Computer Function Routine Bases on ERA's Abstract: This paper initiates a research program to provide computer function routines that can be used to deliver critical values or significance levels for statistical tests. These routines are easily integrated into existing econometric software and can be made available on a user call basis. The mathematical formulae underlying these approximants belong to the family of extended rational approximants (ERA's) introduced in '15. The first part of this paper extends the algebraic theory of ERA's to distribution function approximation. Composite functional approximants are also developed to treat the parameter multidimensionally that is common in practical application. The second part of the paper reports a detailed application of the approach to the distribution of the serial correlation coefficient under spherical Gaussian errors. The formulae we extract are error-corrected Edgeworth approximants that yield at least three decimal place accuracy over the entire distribution for all sample sizes (T >= 4). These approximants can be used to mount a variety of tests, including tests for serial correlation and unit roots. Further extension of this work to higher order serial correlation coefficients that are used in the Box-Jenkins model identification process are discussed in the conclusion. Keywords: Rational approximation, serial correlation, computer function routines, critical values Note: CFP 642. Creation-Date: 198409 Number: 721 Publication-Status: Published in Advances in Statistical Analysis and Statistical Computing, Vol. 1, JAI Press, 1985, pp. 1-50 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0642.pdf File-Format: application/pdf File-Size: 1781 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0721.pdf File-Format: application/pdf File-Size: 1265 kb Handle: RePEc:cwl:cwldpp:721 Template-type: ReDIF-Paper 1.0 Author-Name: Victor Ginsburgh Author-X-Name-First: Victor Author-X-Name-Last: Ginsburgh Author-Workplace-Name: Universite Libre de Bruxelles Author-Name: Ludo Van der Heyden Author-X-Name-First: Ludo Author-X-Name-Last: Van der Heyden Author-Workplace-Name: Yale School of Organization & Management Title: General Equilibrium with Wage Rigidities: An Application to Belgium Abstract: This paper concerns an application to the Belgian economy of general equilibrium analysis in the presence of downward real wage rigidities. The model aims at explaining the short-run impact of recent income and exchange policies upon employment in Belgium. Mathematical programming techniques are used to compute equilibria. Note: CFP 633. Length: 28 pages Creation-Date: 198408 Number: 720 Publication-Status: Published in Mathematical Programming Study (1985), 23: 23-39 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0633.pdf File-Format: application/pdf File-Size: 721 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0720.pdf File-Format: application/pdf File-Size: 590 kb Handle: RePEc:cwl:cwldpp:720 Template-type: ReDIF-Paper 1.0 Author-Name: Robert J. Shiller Author-X-Name-First: Robert J. Author-X-Name-Last: Shiller Author-Email: robert.shiller@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shiller.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Stock Prices and Social Dynamics Abstract: The empirical evidence that is widely interpreted as supporting the efficient markets theory in finance actually does not rule out the possibility that changing fashions or fads among investors have an important influence on prices in financial markets. A model of the impact of such fashions on prices is proposed and used in an exploratory data analysis of the aggregate United States Stock Market in the 20th century. Classification-JEL: 313 Keywords: Efficient markets, speculative bubbles, fashions, fads Note: CFP 616. Length: 74 pages Creation-Date: 198410 Number: 719R Publication-Status: Published in Brookings Papers on Economic Activity (1984), 2: 457-510 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0616.pdf File-Format: application/pdf File-Size: 948 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0719-r.pdf File-Format: application/pdf File-Size: 1560 kb Handle: RePEc:cwl:cwldpp:719R Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Use of Expected Future Variables in Macroeconometric Models Abstract: A more sophisticated expectational hypothesis than is traditionally used in the specification of macroeconometric models is tested in this paper. Economic agents are assumed to use a vector of variables Z_{t} in forming their expectations for periods t+1 and beyond. These expectations may or may not be rational in the Muth sense. The results provide some evidence in favor of the more sophisticated hypothesis, but they are not strong enough to allow much weight to be put on the hypothesis as yet. The evidence in favor of the hypothesis is strongest for households' response to future wages and prices in their consumption and labor supply decisions and for the Fed's response to future inflation rates. The sensitivity of the policy properties of my macroeconometric model to the more sophisticated hypothesis is also examined in the paper. The properties are not sensitive for a policy action in which government expenditures are changed. They are somewhat sensitive for an action in which personal tax rates are changed. In the latter case the properties are also sensitive to whether or not the policy action is anticipated. Classification-JEL: 212, 023 Keywords: Macroeconometric models, expectations, macro policy, rational expectations Length: 34 pages Creation-Date: 1984-05 Number: 718 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0718.pdf File-Format: application/pdf File-Size: 800 kb Handle: RePEc:cwl:cwldpp:718 Template-type: ReDIF-Paper 1.0 Author-Name: William D. Nordhaus Author-X-Name-First: William D. Author-X-Name-Last: Nordhaus Author-Email: william.nordhaus@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/nordhaus.htm Author-Workplace-Name: Dept. of Economics, Yale University Author-Workplace-Homepage: http://www.econ.yale.edu/ Author-Name: Steven N. Durlauf Author-X-Name-First: Steven N. Author-X-Name-Last: Durlauf Title: Empirical Tests of the Rationality of Economic Forecasters: A Fixed Horizons Approach Abstract: This paper examines the behavior of 4 major forecasters and the forecast consensus. We employ a new technique of "Fixed Horizon" models. This technique analyzes the sequence of adjustments of a series of forecasts of the same event. We first demonstrate that these forecast adjustment sequences should fluctuate randomly under rationality. We then examine approximately 1200 forecast adjustments over the 1978-1982 period to examine the statistical properties of forecast adjustments. The evidence clearly demonstrates that there are marked and significant elements of statistical rationality for these major forecasters. Information shocks are processed slowly. The pattern of adjustments is consistent with forecasters being adverse to "Inconsistency," i.e., large rapid changes in forecasts. There also may be evidence that forecasters move towards a consensus in hero-like fashion. Classification-JEL: 132 Keywords: Forecast efficiency, forecast adjustments Length: 40 pages Creation-Date: 198408 Revision-Date: 198505 Number: 717R Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0717-r.pdf File-Format: application/pdf File-Size: 820 kb Handle: RePEc:cwl:cwldpp:717R Template-type: ReDIF-Paper 1.0 Author-Name: Russell Cooper Author-X-Name-First: Russell Author-X-Name-Last: Cooper Author-Name: T.W. Ross Author-X-Name-First: T.W. Author-X-Name-Last: Ross Author-Workplace-Name: University of Chicago & Carleton University Title: Product Warranties and Double Moral Hazard Abstract: This paper explores a model of warranties in which moral hazard problems play a key role. The goal is to understand the important characteristics of warranties including their provision of incomplete insurance and the relationship between product quality and coverage. We analyze a model in which buyers and sellers take actions which affect a product's performance. Since these actions are not cooperatively determined, an incentives problem arises. We characterize the optimal warranty contract and undertake comparative statics to determine the predicted correlation of warranty coverage and product quality. Note: CFP 630. Length: 24 pages Creation-Date: 198408 Number: 716 Publication-Status: Published in Rand Journal of Economics (Spring 1985), 16(1): 103-113 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0630.pdf File-Format: application/pdf File-Size: 658 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0716.pdf File-Format: application/pdf File-Size: 469 kb Handle: RePEc:cwl:cwldpp:716 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Strategic Market Games: A Dynamic Programming Application to Money, Banking and Insurance Abstract: A series of models (kept simple in order to stress the structure of the models and the nature of the questions) are described and problems are posed pertaining to a dynamic economy with various possibilities for the issuance of fiat money, credit and insurance. Classification-JEL: 311, 315 Keywords: Strategic market games, dynamic programming, fiat money, credit Note: CFP 661. Length: 22 pages Creation-Date: 198410 Number: 715 Publication-Status: Published in Mathematical Social Sciences (1986), 12: 265-278 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0661.pdf File-Format: application/pdf File-Size: 565 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0715.pdf File-Format: application/pdf File-Size: 492 kb Handle: RePEc:cwl:cwldpp:715 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Plausible Outcomes for Games in Strategic Form Abstract: This is the first projected series of papers on solutions to games in matrix and extensive form. Classification-JEL: 026 Keywords: Game theory, matrix form, extensive form Length: 34 pages Creation-Date: 198408 Number: 714 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0714.pdf File-Format: application/pdf File-Size: 791 kb Handle: RePEc:cwl:cwldpp:714 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Many Approaches to the Study of Monopolistic Competition Abstract: It is suggested here that there are many highly different purposes for the study and application of theories of oligopolistic competition, monopolistic competition, and allied topics. This paper sets the different purposes and questions in context, then makes criticisms and suggestions as to where to go from here. Classification-JEL: 611 Keywords: Monopolistic competition, oligopolistic competition Note: CFP 641. Length: 31 pages Creation-Date: 198408 Number: 713 Publication-Status: Published in European Economic Review (1985), 27: 97-114 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0641.pdf File-Format: application/pdf File-Size: 983 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0713.pdf File-Format: application/pdf File-Size: 835 kb Handle: RePEc:cwl:cwldpp:713 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Bracken, J. Author-Name: Tulowitzki, Haviv Title: Nuclear Warfare, C_{3}I and First and Second Scenarios (A Sensitivity Analysis) Length: 31 pages Creation-Date: 198408 Number: 712 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0712.pdf File-Format: application/pdf File-Size: 644 kb Handle: RePEc:cwl:cwldpp:712 Template-type: ReDIF-Paper 1.0 Author-Name: James Tobin Author-X-Name-First: James Author-X-Name-Last: Tobin Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Mean-Variance Approach to Fundamental Valuations Note: CFP 603. Length: 17 pages Creation-Date: 1984 Number: 711R Publication-Status: Published in The Journal of Portfolio Management (Fall 1984) File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0603.pdf File-Format: application/pdf File-Size: 441 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0711-r.pdf File-Format: application/pdf File-Size: 323 kb Handle: RePEc:cwl:cwldpp:711R Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Stability Comparisons of Estimators (5/1985 and 11/1985) Abstract: This paper investigates a property of estimators called stability. The stability exponent of an estimator is defined to be a measure of the effect of any single observation in the sample on the realized value of the estimator. High stability is often desirable for robustness against misspecification and against highly variable observations. Stability exponents are determined and compared for a wide variety of estimators and econometric models. They are found to depend on the maximal moment exponent (i.e., the number of finite moments) of the estimator's influence curve. Since it is possible often to construct estimators with specified influence curves, estimators with different stability exponents can be construed. Note: CFP 663. Length: 54 pages Creation-Date: 198407 Revision-Date: 198511 Number: 710R Publication-Status: Published in Econometrica (September 1986), 54(5): 1207-1235 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0663.pdf File-Format: application/pdf File-Size: 1450 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0710-r2.pdf File-Format: application/pdf File-Size: 1242 kb Handle: RePEc:cwl:cwldpp:710R2 Template-type: ReDIF-Paper 1.0 Author-Name: Paul R. Milgrom Author-X-Name-First: Paul R. Author-X-Name-Last: Milgrom Author-Name: John Roberts Author-X-Name-First: John Author-X-Name-Last: Roberts Author-Workplace-Name: Stanford University Title: Price and Advertising Signals of Product Quality Abstract: We present a signalling model, based on ideas of Phillip Nelson, in which both the introductory price and the level of directly "uninformative" advertising or other dissipative marketing expenditures are choice variables and may be used as signals for the initially unobservable quality of a newly introduced experience good. Repeat purchases play a crucial role in our model. Classification-JEL: 026, 611, 530 Note: CFP 676. Length: 28 pages Creation-Date: 198406 Number: 709 Publication-Status: Published in Journal of Political Economy (1986), 94(4): 796-821 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0676.pdf File-Format: application/pdf File-Size: 1113 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0709.pdf File-Format: application/pdf File-Size: 910 kb Handle: RePEc:cwl:cwldpp:709 Template-type: ReDIF-Paper 1.0 Author-Name: Paul R. Milgrom Author-X-Name-First: Paul R. Author-X-Name-Last: Milgrom Title: Job Discrimination, Market Forces and the Invisibility Hypothesis Abstract: The Invisibility Hypothesis holds that the job skills of disadvantaged workers are not easily discovered by potential new employers, but that promotion enhances visibility and alleviates this problem. Then, at a competitive labor market equilibrium, firms profit by hiding talented disadvantaged workers in low level jobs. Consequently, those workers are paid less on average and promoted less often than others with the same education and ability. As a result of the inefficient and discriminatory wage and promotion policies, disadvantaged workers experience lower returns to investments in human capital than other workers. Length: 40 pages Creation-Date: 1984 Revision-Date: 1985 Number: 708R Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0708-r.pdf File-Format: application/pdf File-Size: 1168 kb Handle: RePEc:cwl:cwldpp:708R Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Estimated Trade-Offs Between Unemployment and Inflation Length: 32 pages Creation-Date: 198406 Number: 707 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0707.pdf File-Format: application/pdf File-Size: 835 kb Handle: RePEc:cwl:cwldpp:707 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Cooperative Form, the Value and the Allocation of Joint Costs and Benefits Note: CFP 634. Length: 41 pages Creation-Date: 198405 Number: 706 Publication-Status: Published in H. Peyton Young, ed., Cost Allocation, Elsevier Science, 1985, pp. 79-94 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0634.pdf File-Format: application/pdf File-Size: 1004 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0706.pdf File-Format: application/pdf File-Size: 1038 kb Handle: RePEc:cwl:cwldpp:706 Template-type: ReDIF-Paper 1.0 Author-Name: Richard H. Clarida Author-X-Name-First: Richard H. Author-X-Name-Last: Clarida Title: Consumption, Liquidity Constraints and Asset Accumulation in the Presence of Random Income Fluctuations Abstract: Recent empirical research, Flavin (1981), Hagashi (1982), has rejected the certainty-equivalent formulation of permanent income hypothesis, Hall (1978). These findings are often attributed to households' inability to borrow completely against expected future labor income. This paper is a theoretical investigation of optimal consumption behavior under risk aversion, random income fluctuations, and borrowing restrictions. Our principle objective is to establish the existence and to investigate the properties of the stationary probability distribution which characterizes the asymptotic behavior of consumption under these conditions. Classification-JEL: 023 Keywords: Permanent income hypothesis, optimal consumption behavior Note: CFP 689. Length: 24 pages Creation-Date: 198405 Revision-Date: 198507 Number: 705R Publication-Status: Published in Economic Review (June 1987), 28(2): 339-351 File-URL: http://cowles.econ.yale.edu/P/cp/p06b/p0689.pdf File-Format: application/pdf File-Size: 467 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0705-r.pdf File-Format: application/pdf File-Size: 395 kb Handle: RePEc:cwl:cwldpp:705R Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Lewis Alexander Author-X-Name-First: Lewis Author-X-Name-Last: Alexander Title: A Comparison of the Michigan and Fair Models: Further Results Abstract: This paper examines the equation-by-equation accuracy of the Michigan and Fair model using the method in Fair (1980). Emphasis is placed on examining the possible misspecification of the equations. In an earlier study, Fair and Alexander (1984), we used the method to examine the accuracy of the complete models. In the present study we are interested in the accuracy of the individual equations when considered in isolation from the rest of the model. Length: 26 pages Creation-Date: 198405 Number: 704 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0704.pdf File-Format: application/pdf File-Size: 640 kb Handle: RePEc:cwl:cwldpp:704 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Lewis Alexander Author-X-Name-First: Lewis Author-X-Name-Last: Alexander Title: A Comparison of the Michigan and Fair Models Length: 41 pages Creation-Date: 198404 Number: 703 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0703.pdf File-Format: application/pdf File-Size: 1038 kb Handle: RePEc:cwl:cwldpp:703 Template-type: ReDIF-Paper 1.0 Author-Name: Richard H. Clarida Author-X-Name-First: Richard H. Author-X-Name-Last: Clarida Author-Name: Diane Coyle Author-X-Name-First: Diane Author-X-Name-Last: Coyle Author-Workplace-Name: Harvard University Title: Conditional Projection by Means of Kalman Filtering Abstract: We establish that the recursive, state-space methods of Kalman filtering and smoothing can be used to implement the Doan, Litterman, and Sims (1983) approach to econometric forecast and policy evaluation. Compared with the methods outlined in Doan, Litterman, and Sims, the Kalman algorithms are more easily programmed and modified to incorporate different linear constraints, avoid cumbersome matrix inversions, and provide estimates of the full variance-covariance matrix of the constrained projection errors which can be used directly, under standard normality assumptions, to test statistically the likelihood and internal consistency of the forecast under study. Length: 12 pages Creation-Date: 198404 Number: 702 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0702.pdf File-Format: application/pdf File-Size: 271 kb Handle: RePEc:cwl:cwldpp:702 Template-type: ReDIF-Paper 1.0 Author-Name: Richard H. Clarida Author-X-Name-First: Richard H. Author-X-Name-Last: Clarida Title: On the Stochastic Steady-State Behavior of Optimal Asset Accumulation in the Presence of Random Wage Fluctuations and Incomplete Markets Abstract: We establish rigorously the existence and properties of the stationary probability distribution which characterizes the accumulation of non-contingent financial claims by a risk averse individual who confronts random wage fluctuations and incomplete insurance markets. We show that there exists a unique, almost-everywhere continuous stationary cumulative distribution function which characterizes the accumulation of non-contingent financial claims in a stochastic steady-state. This distribution is shown to possess a single mass point coinciding with the non-negative, finite borrowing limit faced by the individual. We establish that the stationary distribution which characterizes the asset accumulation of low time preference individuals is at least as large, in the sense of first-degree stochastic dominance, as that of individuals with higher rates of time preference. We prove that, so long as individuals are allowed to borrow in amounts which can be repayed with probability one, additive differences in the probability distribution governing random wage earnings imply inversely proportional additive differences in the stationary probability distributions which govern the accumulation of non-contingent financial claims. Length: 31 pages Creation-Date: 198404 Number: 701 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0701.pdf File-Format: application/pdf File-Size: 565 kb Handle: RePEc:cwl:cwldpp:701 Template-type: ReDIF-Paper 1.0 Author-Name: Christophe Chamley Author-X-Name-First: Christophe Author-X-Name-Last: Chamley Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A General Equilibrium Expression of the Paradox of Thrift Abstract: A model is presented which is derived from some observations of Keynes on the nature of capital. The allocation of investment is analyzed in two economies with random demand shocks which are identical except for the types of markets. In the first, the combination of an asset and forward markets realizes the complete set of markets. In the second, the forward markets are replaced by spot markets. Consumers and entrepreneurs are rational and markets clear. A clear definition of the paradox of thrift is proposed and its existence is proven. The substitution of spot markets for forward markets generates fluctuations of the aggregate variables. The equilibrium with fluctuations is not always a constrained Pareto optimum. Length: 43 pages Creation-Date: 198405 Number: 700 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d07a/d0700.pdf File-Format: application/pdf File-Size: 935 kb Handle: RePEc:cwl:cwldpp:700 Template-type: ReDIF-Paper 1.0 Author-Name: Christophe Chamley Author-X-Name-First: Christophe Author-X-Name-Last: Chamley Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Optimal Taxation of Capital Income in Economies with Identical Private and Social Discount Rates Abstract: The optimal capital income tax is analyzed in the framework of intertemporal efficient taxation. The relation between the zero tax in the long-run and the equality between private and social discount rates is emphasized. The properties of the dynamic second best path described for a specific example (convergence to a steady state and values of the capital income tax in the transition). The case where wealth is a specific utility argument is also considered. Length: 33 pages Creation-Date: 198404 Number: 699 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0699.pdf File-Format: application/pdf File-Size: 651 kb Handle: RePEc:cwl:cwldpp:699 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Zero-One Result for the Least Squares Estimator Abstract: The least squares estimator for the linear regression model is shown to converge to the true parameter vector either with probability one or with probability zero under weak conditions on the dependent random variable and regressor variables. No additional conditions are placed on the errors. The dependent and regressor variables are assumed to be weakly dependent -- in particular, to be strong mixing. The regressors may be fixed or random and must exhibit a certain degree of independent variability. No further assumptions are needed. The model considered allows the number of regressors to increase without bound as the sample size increases. The proof proceeds by extending Kolmogorov's 0-1 law for independent random variables to strong mixing random variables. Note: CFP 621. Length: 13 pages Creation-Date: 198403 Number: 698 Publication-Status: Published in Econometric Theory (1985), 1: 85-96 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0621.pdf File-Format: application/pdf File-Size: 529 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0698.pdf File-Format: application/pdf File-Size: 291 kb Handle: RePEc:cwl:cwldpp:698 Template-type: ReDIF-Paper 1.0 Author-Name: Donald W.K. Andrews Author-X-Name-First: Donald W.K. Author-X-Name-Last: Andrews Author-Email: donald.andrews@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/andrews.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Robust Estimation of Location in a Gaussian Parametric Model: II Abstract: This paper extends the results of Andrews (1984) which considers the problem of robust estimation of location in a model with stationary strong mixing Gaussian parametric distributions. Three neighbourhood systems are considered, each of which contains the Hellinger neighbourhoods used in Andrews (1984). Optimal robust estimators for this dependent random variable model are found to be bounded influence estimators with optimal psi functions which are very nearly of Huber shape. These estimators are quite robust against different "amounts" of dependence, and against lack of dependence. To generate the optimal estimators a minimax asymptotic risk criterion is used, where minimaxing is done over neighbourhoods of the parametric Gaussian distributions. The neighbourhood systems include distributions of strong mixing processes. They allow for deviations from stationarity and from the Gaussian structure of dependence. In addition, deviations from the normal univariate parametric distributions are allowed within the neighbourhoods defined by (i) epsilon_{n}-contamination, (ii) variational metric distance, and (iii) Kolmogorov metric distance. Note: CFP 725. Length: 47 pages Creation-Date: 198403 Number: 697 Publication-Status: Published in Advances in Econometrics, Vol. 7, JAI Press, 1988, pp. 3-44 File-URL: http://cowles.econ.yale.edu/P/cp/p07a/p0725.pdf File-Format: application/pdf File-Size: 1651 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0697.pdf File-Format: application/pdf File-Size: 881 kb Handle: RePEc:cwl:cwldpp:697 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: A Note on Biology, Time and the Golden Rule Length: 6 pages Creation-Date: 198403 Number: 696 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0696.pdf File-Format: application/pdf File-Size: 147 kb Handle: RePEc:cwl:cwldpp:696 Template-type: ReDIF-Paper 1.0 Author-Name: Richard H. Clarida Author-X-Name-First: Richard H. Author-X-Name-Last: Clarida Author-Name: Benjamin M. Friedman Author-X-Name-First: Benjamin M. Author-X-Name-Last: Friedman Author-Workplace-Name: Harvard University Title: The Behavior of U.S. Short-Term Interest Rates Since 1979-10 Abstract: Short-term interest rates in the United States have been "too high" since 1979-10 in the sense that both unconditional and conditional forecasts, based on an estimated vector autoregression model summarizing the prior experience, underpredict short-term interest rates during this period. Although a non-structural model cannot directly answer the question of why this has been so, comparisons of alternative conditional forecasts point to the post-1979-10 relationship between the growth of real income and the growth of real money balances as closely connected to the level and pattern of short-term interest rates. This finding is consistent with the authors' macroeconomic model, that the high average level of interest rates has been due to a combination of slow growth of (nominal) money supply and continuing price inflation, which together have kept real balances small in relation to prevailing levels of economic activity. Classification-JEL: 311 Keywords: Short term interest rates Note: CFP 596. Length: 20 pages Creation-Date: 198603 Number: 695 Publication-Status: Published in Journal of Finance (July 1984), 39(3): 671-682 File-URL: http://cowles.econ.yale.edu/P/cp/p05b/p0596.pdf File-Format: application/pdf File-Size: 729 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0695.pdf File-Format: application/pdf File-Size: 503 kb Handle: RePEc:cwl:cwldpp:695 Template-type: ReDIF-Paper 1.0 Author-Name: Richard H. Clarida Author-X-Name-First: Richard H. Author-X-Name-Last: Clarida Title: Current Account, Exchange Rate, and Monetary Dynamics in a Stochastic Equilibrium Model Abstract: We construct a simple stochastic open-economy macro-economic model from the decision rules of rational optimizing agents, solving explicitly for the relationship between the model's deep parameters, and the variance-covariance matrix of equilibrium returns on domestic and foreign assets. We use the model to study the dynamic relationship between exchange rate changes and current account flows in response to domestic monetary shocks, to establish the conditions under which exchange rate depreciations accompany current account deficits, and to investigate the link between time preference, risk aversion, and the dynamic exchange rate and current account response to monetary disturbances. The model generates current account time series which exhibit persistent deviations from balance, even for the special case in which domestic and foreign shocks are purely transitory. Classification-JEL: 431, 023 Keywords: Current account, monetary shocks Length: 31 pages Creation-Date: 198410 Number: 694 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0694.pdf File-Format: application/pdf File-Size: 650 kb Handle: RePEc:cwl:cwldpp:694 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Effects of Expected Future Government Deficits on Current Economic Activity Length: 21 pages Creation-Date: 198402 Number: 693 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0693.pdf File-Format: application/pdf File-Size: 495 kb Handle: RePEc:cwl:cwldpp:693 Template-type: ReDIF-Paper 1.0 Author-Name: Ray C. Fair Author-X-Name-First: Ray C. Author-X-Name-Last: Fair Author-Email: ray.fair@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/fair.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Excess Labor and the Business Cycle Note: CFP 601. Length: 14 pages Creation-Date: 198402 Number: 692 Publication-Status: Published in American Economic Review (March 1985), 75(1): 239-245 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0601.pdf File-Format: application/pdf File-Size: 488 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0692.pdf File-Format: application/pdf File-Size: 314 kb Handle: RePEc:cwl:cwldpp:692 Template-type: ReDIF-Paper 1.0 Author-Name: Russell Cooper Author-X-Name-First: Russell Author-X-Name-Last: Cooper Title: Insurance, Flexibility and Non-contingent Trades Abstract: This paper considers non-contingent trades through either forward markets or simple contracts. The point of the inquiry is to understand the costs and benefits of trades of this nature. We focus on the tradeoff between insurance (a benefit) and the loss of flexibility in decisions (a cost) as determining properties of trading in forward markets. This tradeoff is also used to explore contract length. Length: 33 pages Creation-Date: 198402 Number: 691 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0691.pdf File-Format: application/pdf File-Size: 628 kb Handle: RePEc:cwl:cwldpp:691 Template-type: ReDIF-Paper 1.0 Author-Name: Truman F. Bewley Author-X-Name-First: Truman F. Author-X-Name-Last: Bewley Author-Email: truman.bewley@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/bewley.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Fiscal and Monetary Policy in a General Equilibrium Model Length: 91 pages Creation-Date: 198401 Number: 690 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0690.pdf File-Format: application/pdf File-Size: 1791 kb Handle: RePEc:cwl:cwldpp:690 Template-type: ReDIF-Paper 1.0 Author-Name: Ludo Van der Heyden Author-X-Name-First: Ludo Author-X-Name-Last: Van der Heyden Title: On a Variable Dimension Algorithm for the Linear Complementarity Problem Abstract: In an earlier paper we presented a variable dimension algorithm for solving the linear complementarity problem (LCP). We now extend the class of LCP's that can be solved by this algorithm to include LCP's with copositive plus coefficient matrices. The extension, inspired by Lemke [1965], is obtained by introducing an artificial dimension and by applying the variable dimension algorithm to the enlarged LCP. Note: CFP 511. Length: 12 pages Creation-Date: 198401 Number: 689 Publication-Status: Published in Mathematical Programming (1980), 19: 328-346 File-URL: http://cowles.econ.yale.edu/P/cp/p05a/p0511.pdf File-Format: application/pdf File-Size: 763 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0689.pdf File-Format: application/pdf File-Size: 185 kb Handle: RePEc:cwl:cwldpp:689 Template-type: ReDIF-Paper 1.0 Author-Name: Russell Cooper Author-X-Name-First: Russell Author-X-Name-Last: Cooper Author-Name: Thomas W. Ross Author-X-Name-First: Thomas W. Author-X-Name-Last: Ross Author-Workplace-Name: University of Chicago & Carleton University Title: Monopoly Provision of Product Quality with Uninformed Buyers Abstract: This essay is concerned with a monopolist's incentives to provide a high quality goods when some of its customers cannot observe quality prior to purchase. We show that if all buyers have the same tastes for quality, the monopolist will not try to take advantage of the poorly informed. When tastes differ, however, some quality randomization may become profitable as a means to loosen binding self-selection constraints. The profitability of randomization is shown to depend upon the relative degrees of risk aversion of the buyers and on the convexity of the firm's cost of quality function. We view our results as pointing to some potential benefits from imperfect quality control. Length: 19 pages Creation-Date: 198401 Revision-Date: 198411 Number: 688R Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0688-r.pdf File-Format: application/pdf File-Size: 404 kb Handle: RePEc:cwl:cwldpp:688R Template-type: ReDIF-Paper 1.0 Author-Name: Cynthia Van Hulle Author-X-Name-First: Cynthia Author-X-Name-Last: Van Hulle Title: Net Present Value Maximization and Imperfections in the Loan Market: A Note Abstract: There seems to be some confusion in the literature whether or not imperfections in the lending-borrowing market, and in particular, differences in lending and borrowing rates, would destroy shareholder unanimity. The purpose of this note is to show that imperfections in this market are not really relevant to stockholder agreement concerning the optimality of the net present value rule. To do this, the paper uses a new criterion guaranteeing unanimity and which basically only requires that investors are sufficiently competitive, i.e., spanning or the notion of firm competition recently proposed by L. Makowiski [9] generally turn out to be unnecessary for shareholder agreement. In Section 1 a version of the state preference model and some of its properties which are well know, are quickly reviewed. Section 2 deals with the unanimity issue and, as an illustration of the findings, the certainty case is considered in some detail in Section 3. Note: Length: 16 pages Creation-Date: 198401 Number: 687 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0687.pdf File-Format: application/pdf File-Size: 363 kb Handle: RePEc:cwl:cwldpp:687 Template-type: ReDIF-Paper 1.0 Author-Name: Ramon Marimon Author-X-Name-First: Ramon Author-X-Name-Last: Marimon Title: Stochastic Equilibrium and Turnpike Property: The Discounted Case Abstract: The existence of the modified golden rule and the turnpike property are proved for a multi-sector stochastic growth model. The (exogenous) stochastic environment is represented by a stationary stochastic process that influences preferences, technology and resources. A social planner maximizes the expected sum of discounted utilities. The conditions required in order to obtain these results, are the natural strengthening of the stability conditions of the deterministic case. As in the deterministic case, the discount factor must be close to one in order to guarantee the almost sure (and in the mean) convergence of optimal interior programs. It is proved that all optimal interior programs converge to each other. This fact is used to prove the existence of a unique optimal stationary program (the modified golden rule). These results imply that all optimal interior programs converge to the stationary program (the turnpike property). Length: 91 pages Creation-Date: 1983 Number: 686 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0686.pdf File-Format: application/pdf File-Size: 1579 kb Handle: RePEc:cwl:cwldpp:686 Template-type: ReDIF-Paper 1.0 Author-Name: Cynthia Van Hulle Author-X-Name-First: Cynthia Author-X-Name-Last: Van Hulle Title: Dominance and Shareholder Unanimity: A New Approach Length: 38 pages Creation-Date: 198312 Number: 685 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0685.pdf File-Format: application/pdf File-Size: 936 kb Handle: RePEc:cwl:cwldpp:685 Template-type: ReDIF-Paper 1.0 Author-Name: Donald J. Brown Author-X-Name-First: Donald J. Author-X-Name-Last: Brown Author-Email: donald.brown@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/brown.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Geoffrey M. Heal Author-X-Name-First: Geoffrey M. Author-X-Name-Last: Heal Author-Workplace-Name: Columbia University Title: The Optimality of Regulated Pricing: A General Equilibrium Analysis Note: This also includes CFDP 684A, An Optimal Tax Rule for Average Cost Pricing. CFP 612. Length: 28 pages Creation-Date: 198312 Number: 684 Publication-Status: Published in Lecture Notes in Economics and Mathematical Systems, Vol. 244, Advances in Equilibrium Theory, Springer-Verlag, 1985, pp. 43-54 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0612.pdf File-Format: application/pdf File-Size: 448 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0684.pdf File-Format: application/pdf File-Size: 576 kb Handle: RePEc:cwl:cwldpp:684 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Finite Sample Econometrics Using ERA's Abstract: The paper considers approximate distribution theory as a way to deliver practical improvements over asymptotic methods. Trials of the adequacy of asymptotic series based approximations are conducted and the results exhibit the need for further improvements. An alternative approach is suggested which utilizes a family of extended rational approximants (ERA's). ERA's build on the strength of primitive exact theory or asymptotic series; they allow us to blend information from diverse analytic numerical and experimental sources. The ultimate objective of the approach is to incorporate directly into software constructive functional approximants relevant to statistical practice. An illustration is provided. Note: CFP 605. Length: 28 pages Creation-Date: 198311 Number: 683 Publication-Status: Published in Journal of Japan Statistical Society (1984), 14(2): 107-124 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0605.pdf File-Format: application/pdf File-Size: 809 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0683.pdf File-Format: application/pdf File-Size: 515 kb Handle: RePEc:cwl:cwldpp:683 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Exact Distribution of the Stein-Rule Estimator Note: CFP 594. Length: 11 pages Creation-Date: 1983 Number: 682 Publication-Status: Published in Journal of Econometrics (1984), 25: 123-131 File-URL: http://cowles.econ.yale.edu/P/cp/p05b/p0594.pdf File-Format: application/pdf File-Size: 296 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0682.pdf File-Format: application/pdf File-Size: 256 kb Handle: RePEc:cwl:cwldpp:682 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Exact Distribution of Exogenous Variable Coefficient Estimators Abstract: This paper derives the exact probability density function of the instrumental variable (IV) estimator of the exogenous variable coefficient vector in a structural equation containing n+1 endogenous variables and N degrees of overidentification. A leading case of the general distribution that is more amenable to analysis and computation is also presented. Conventional classical assumptions or normally distributed errors and nonrandom exogenous variables are employed. Note: CFP 602. Length: 15 pages Creation-Date: 198307 Number: 681 Publication-Status: Published in Journal of Econometrics (1984), 26: 387-398 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0602.pdf File-Format: application/pdf File-Size: 318 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0681.pdf File-Format: application/pdf File-Size: 274 kb Handle: RePEc:cwl:cwldpp:681 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: The Exact Distribution of Zellner's SUR Abstract: This paper derives the exact finite sample distribution of the two-stage GLS (generalized least squares) estimator in a multivariate linear model with general linear parameter restrictions. This includes the seemingly unrelated regression (SUR) model as a special case and generalizes presently known exact results for the latter system. The usual classical assumptions are made concerning nonrandom exogenous variables and normally distributed errors. Note: CFP 625. Length: 17 pages Creation-Date: 198308 Number: 680 Publication-Status: Published in Econometrica (July 1985), 53(4): 745-756 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0625.pdf File-Format: application/pdf File-Size: 448 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0680.pdf File-Format: application/pdf File-Size: 286 kb Handle: RePEc:cwl:cwldpp:680 Template-type: ReDIF-Paper 1.0 Author-Name: Peter C.B. Phillips Author-X-Name-First: Peter C.B. Author-X-Name-Last: Phillips Author-Email: peter.phillips@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/phillips.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: On University Education in Econometrics: Remarks on an Article by Eric R. Sowey Length: 9 pages Creation-Date: 198309 Number: 679 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0679.pdf File-Format: application/pdf File-Size: 268 kb Handle: RePEc:cwl:cwldpp:679 Template-type: ReDIF-Paper 1.0 Author-Name: Martin Shubik Author-X-Name-First: Martin Author-X-Name-Last: Shubik Author-Email: martin.shubik@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/shubik.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Shlomo Weber Author-X-Name-First: Shlomo Author-X-Name-Last: Weber Title: A Note on the 'Corelessness' of Antibalance of a Game Note: CFP 644. Length: 17 pages Creation-Date: 1983 Revision-Date: 1984 Number: 678R Publication-Status: Published in International Journal of Game Theory (1986), 15(1): 9-20 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0644.pdf File-Format: application/pdf File-Size: 394 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0678-r.pdf File-Format: application/pdf File-Size: 311 kb Handle: RePEc:cwl:cwldpp:678R Template-type: ReDIF-Paper 1.0 Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Heracles M. Polemarchakis Author-X-Name-First: Heracles M. Author-X-Name-Last: Polemarchakis Author-Workplace-Name: Columbia University Title: Intertemporally Separable Overlapping Generations Economies Note: CFP 606. Length: 12 pages Creation-Date: 198309 Number: 677 Publication-Status: Published in Journal of Economic Theory (December 1984), 34(2): 207-215 File-URL: http://cowles.econ.yale.edu/P/cp/p06a/p0606.pdf File-Format: application/pdf File-Size: 368 kb Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0677.pdf File-Format: application/pdf File-Size: 280 kb Handle: RePEc:cwl:cwldpp:677 Template-type: ReDIF-Paper 1.0 Author-Name: Pradeep Dubey Author-X-Name-First: Pradeep Author-X-Name-Last: Dubey Author-Email: pradeepkdubey@yahoo.com Author-Name: Mamoru Kaneko Author-X-Name-First: Mamoru Author-X-Name-Last: Kaneko Title: Information Patterns and Nash Equilibria in Extensive Games Length: 48 pages Creation-Date: 198308 Number: 676 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0676.pdf File-Format: application/pdf File-Size: 708 kb Handle: RePEc:cwl:cwldpp:676 Template-type: ReDIF-Paper 1.0 Author-Name: Jeremy I. Bulow Author-X-Name-First: Jeremy I. Author-X-Name-Last: Bulow Author-Workplace-Name: Stanford University Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Title: Strategic Resource Extraction: When Easy Doesn't Do It Length: 53 pages Creation-Date: 198303 Number: 675 Price: None File-URL: http://cowles.econ.yale.edu/P/cd/d06b/d0675.pdf File-Format: application/pdf File-Size: 894 kb Handle: RePEc:cwl:cwldpp:675 Template-type: ReDIF-Paper 1.0 Author-Name: Jeremy I. Bulow Author-X-Name-First: Jeremy I. Author-X-Name-Last: Bulow Author-Workplace-Name: Stanford University Author-Name: John Geanakoplos Author-X-Name-First: John Author-X-Name-Last: Geanakoplos Author-Email: john.geanakoplos@yale.edu Author-Homepage: http://cowles.econ.yale.edu/faculty/geanakoplos.htm Author-Workplace-Name: Cowles Foundation, Yale University Author-Workplace-Homepage: http://cowles.econ.yale.edu/ Author-Name: Paul D. Klemperer Author-X-Name-First: Paul D. Author-X-Name-Last: Klemperer Author-Workplace-Name: Stanford University & St. Catherine's College Title: Multimarket Oligopoly Abstract: Actions a firm takes in one market may affect its profitability in other markets, beyond any joint economies or diseconomies in production. The reason is that an action in one market, by changing marginal costs in a second market, may change competitors' strategies in that second market. We show how to calculate the strategic consequences in market 2, of a change in conditions in market 1 or of a firm's action in market 1. Qualitatively, the same results hold for both simultaneous markets and sequential markets: whether a