Research Activities, July 1, 1951 – June 30, 1952

Economics is both a descriptive and a prescriptive science. In a descriptive sense the economist studies the actual economic behavior of individuals and firms, singly or in groups, in a given environment. The prescriptive side of economics has two parts: the evaluation and selection of the most desirable social and economic objectives from among all those possible, and the evaluation and selection of the most effective means for achieving chosen objectives.

Cowles Commission research of the past year has contributed to both these areas of economics. Essential to the establishment of a prescriptive science is the delineation of objectives and their formulation in precise terms. Part of the work of the Commission, reported in Section 1 below, has been concerned with this task. Sections 2 and 3, on the other hand, report on theoretical studies of the Commission which assume some individual or social objective as given and evaluate the effectiveness of different forms of behavior or organization in accomplishing that objective under a variety of circumstances.

The descriptive phase of Cowles Commission work is covered principally in Section 4, which reports on empirical studies of actual economic behavior. Section 5 describes the development of the conceptual, statistical, and mathematical tools which serve the substantive research. Research during the year was influenced by three working conferences, two held at the Commission and one held in Washington, D.C. From October 29 to November 1, 1951, a small, intensive conference on Decision-Making under Uncertainty started off a Commission research project of the same name, initiated under a contract with the Office of Naval Research. In early January, 1952, staff members of the Commission participated in the Third Annual Logistics Conference in Washington, D.C., sponsored jointly by George Washington University and the Office of Naval Research. In April, the Commission was host to colleagues from the Bureau of Business and Economic Research of the University of Illinois and the Department of Industrial Management of the Carnegie Institute of Technology for an intensive three-day conference on Business Decision-Making. Participation in these conferences was a reflection of as well as a stimulant to, the research of the Commission during the year.

1. Formulation of Individual and Social Objectives

The traditional theory of individual choice starts with the assumption that the individual has a consistent preference (or indifference) between any two given states of life. It is often assumed that, if the states of life can be catalogued by a finite set of reference numbers (such as rates of consumption of specific goods and services), then the preference ordering can be represented by a numerical "utility function" of these numbers.

This function takes on the higher value for the preferred item in each pair of states of life under comparison, and the same value for the item in an indifferent pair. However, the number system may not be rich enough to provide a different numerical label for each set of mutually indifferent states of life. This will be the case if in the preference ordering one aspect of the state of life (say, the chance of escaping death) receives absolute priority over another aspect (say, the consumption of cigarettes). Aware of this logical possibility, known as a "lexicographic" ordering, Gerard Debreu has formulated conditions for a preference structure under which a numerical utility function does indeed exist. Visiting colleagues from the University of Michigan, the psychologist Clyde H. Coombs and the mathematician Robert M. Thrall, and an economist from Oxford University, I.M.D. Little, discussed related problems in staff meetings and seminars.

The connection between a utility function and the theory of choice is simplest in the case where the individual can by his own action choose, with certainty of attainment, any state of life (or "outcome") within a given set of states (known as his "opportunity set") and no others. If consistent and rational, he will then obviously select a state of life as good as or better than all other states open to him. The utility function obtained by observing choice in such circumstances is ordinal utility: it exhibits the fact of preference but not the strength of preference.

Cardinal utility — a procedure for expressing the preference for B over A as a multiple of that for C over A — can be constructed by observing choice in circumstances where the state of life achieved is the joint outcome of an act of choice and a chance event, unknown at the time of choice. For instance, an individual may be asked to choose between a glass of milk and a fifty-fifty chance for a cup of tea as against a cup of coffee. Axioms about individual choice that permit the construction of a cardinal utility on this basis were first developed by John von Neumann and Oskar Morgenstern. .Stimulated by a reformulation of this axiom system by Jacob Marschak, described in an earlier report (1949–1950), I.N. Herstein and John Milnor (the latter of Princeton University) developed a further simplified system of behavior axioms that leads to cardinal utility by a more direct route of deductions.

The theory of choice is further complicated if the state of life achieved is the joint outcome of a choice act and an unknown state of the world which cannot even be described by a probability distribution. Most choices made in real life are of this kind. (San Francisco was built without knowing the probability distribution of earthquakes in that location.) Each action leads to a set of possible states of life containing the outcomes of that action under all conceivable states of the world. A variety of principles have been proposed for basing a preference ordering of such sets of states of life on a given cardinal utility function of the states of life contained in these sets. These principles have been appraised by asking the question: what does each principle make one do under each of various sets of circumstances? For instance, studies by statisticians have led to principles such as preferring that choice which minimizes the maximum loss (Abraham Wald), sustained by the individual after his choice is made and thereupon the state of the world is revealed. A modification of this is the principle of minimizing the maximum regret (L.J . Savage), that is the excess of the loss actually sustained over the loss that would have been incurred had the individual known the state of the world before making his choice.

The first version ("minimax loss") of this principle seems overly conservative if applied (as we assume here) in facing a neutral nature, such as when one sails in unknown waters, or sows in unknown climate or soil. It would lead us to take costly precautions (such as earthquake-proof buildings everywhere) against catastrophes. Under the second version ("minimax regret"), as shown by Herman Chernoff (Annual Report for 1949–1950), if opportunity limits the objects of choice, the preferred course of action may depend on whether some other nonpreferred course of action is available or not. Chernoff completed the study this year after adding many new considerations. This work has led Leonid Hurwicz to propose a less conservative principle of choice, considering both the best and the worst possible outcomes, on the basis of the incomplete information given, which can be associated with each course of action.

Marschak and Roy Radner, helped by their correspondence with Erich Lehmann, have studied situations where certain available courses of action, at a given cost of observation or experimentation, reduce the range of ignorance regarding the state of the world. The requirement that the choice principle be responsive to low cost opportunities to increase available information revealed further "unreasonable" features of both versions of the minimax principle and also of Hurwicz's generalization. Radner studied the question of when it is reasonable to add observations (and thus possibly to postpone choice). He also developed the concept of a "consistent" principle of choice which, with an indefinite increase in the number of observations, would converge toward that action which would be preferred if the state of the world were known. This concept is analogous to a consistent estimate or test in statistical theory.

Instead of asking for a definite principle of choice under ignorance, one may take a more detached attitude and require only that the various choices made when opportunities vary shall in some logical sense be consistent with each other. A study started earlier by Herman Rubin, indicating that this type of consistent choice pattern permits inferences about the degrees of belief (psychological probabilities) that the choosing individual associates with possible states of the world, was further advanced during the year.

It should be noted that the above criticisms of the minimax principle do not apply to its use in situations studied in the theory of games where the choosing individual does not face unknown blind forces of nature, but faces a calculating opponent who is out to win over him.

The foregoing studies are based on the assumption that an individual can choose among alternative states of life or among known probability mixtures of alternative states. Ethical judgments beyond the acceptance of individual preferences as a motive for decision-making do not arise. When one considers criteria for decision-making by groups, new problems, essentially ethical in nature, are encountered. Preferences of the individual members of a group will usually conflict to some extent and the best basis for resolving such conflicts is not intuitively clear.

Economists have frequently considered the problems of determining group preferences from individual preferences.

The Pareto criterion that there will be a group preference for one state of life over an alternative if some individuals prefer that state while none prefer the alternative has been fairly generally accepted.

Important conclusions — such as the usefulness of a price system in the allocation of resources — follow from this criterion, but many controversial issues cannot be resolved by it. The most important recent investigation of the possibility of developing stronger criteria is contained in Kenneth Arrow's book, Social Choice and Individual Values. As described in preceding annual reports, Arrow showed that if certain conditions are imposed on group preferences, such preferences can be obtained only in special cases.

Stimulated by this work, Clifford Hildreth has reconsidered the Arrow conditions and their motivation. He disagreed with Arrow's premise that a satisfactory set of group preferences could not be based on interpersonal comparisons of utility and regarded the problem as principally one of seeking ethical bases for making such comparisons. This difference led him to object to Arrow's Condition 3 (irrelevance of unavailable alternatives) and he has shown that if this condition is waived, the other conditions can be strengthened without giving rise to the difficulty that no admissible sets of group preferences exist.

Hildreth has also concluded that giving effect to individual preferences may be only one of a number of considerations on which criteria for group choice might be based. He has started to construct a more general theoretical framework in the hope that it will facilitate inclusion in the discussion of such values as individual freedom, security, equality, and other commonly cited criteria for evaluating public policies.

The following papers dealing with the formulation of objectives were those presented in staff meetings or completed or published during the year 1951–1952 by staff members or guests of the Commission. Papers marked by an asterisk are also included in the Appendix, which lists all papers published or publicly presented by staff members during the period, July 1, 1951–June 30, 1952.

2. The Pursuit of Given Objectives under Certainty

Once one or more objectives of economic behavior have been specified, the problem of how best to achieve the objective selected, or how best to strike a balance between competing objectives arises in many forms. The studies in this category are intended primarily as prescriptive, although some can better be seen as theoretical inquiries into what happens if different decision-makers pursue different individual objectives. The studies differ according to the number of individuals and the number and kinds of objectives considered, the restraints placed on the achievement of objectives by technological possibilities, and the extent to which risk or uncertainty surrounds the consequences of available actions. We shall in Section 2 review studies that assume certainty about the effects of decisions, and proceed in Section 3 to cases where risk or uncertainty is introduced.

The first group of studies (among those assuming certainty) examines static models of equilibrium in a society of utility and/or profit maximizers. It is a classical theorem of static welfare economics that a competitive market organization achieves efficiency (or "Pareto optimality") in the allocation of resources. By this is meant a state in which it is impossible, by changes in the production or in the distribution of goods, to increase any individual's utility any further without decreasing at least one other individual's utility. It has long been recognized that commodity taxes or subsidies have the effect of moving the economy away from the efficiency frontier reached by competitive organization. Various measures of the social loss associated with, such policies have been proposed. Debreu applied his coefficient of resource utilization (Annual Report for 1950–51, p. 15) to develop an improved measure of this loss. Unlike its predecessors, this measure recognizes the redistributive purpose of taxation: it compares the situation resulting from taxes and subsidies, not with the situation that would exist without these policies, but with a hypothetical situation in which the income distribution is the same as that resulting from taxes and subsidies, while their adverse allocative effects are removed.

The problem studied by Robert Strotz is a logical sequel to Debreu's measure of social loss. Accepting as a social objective, greater equality of incomes than that which would be achieved by the competitive market, he appraises alternative redistributive techniques by the extent to which they maintain allocative efficiency in the sense already explained.

The classical theorem concerning the efficiency of competitive market organization in a static economy, quoted above, depends on certain deep mathematical propositions that have only rarely been examined with the preciseness necessary in specifying technological and psychological assumptions. Mere counting of equations and unknowns is insufficient to establish the existence of a state in which each individual or firm has maximized its utility or profit at the given prices. Arrow and Debreu independently obtained, and will jointly complete, extensions and generalizations of earlier studies by Wald and by von Neumann on this fundamental problem of mathematical economics.

A closer approximation to economic reality is the aim of a second group of studies concerned with the arrangement of productive activities in space and in time. Martin Beckmann completed a study of a continuous model of transportation that he had started before joining the staff. This model assumes given continuous geographical distributions of supply and demand of a number of commodities and a given dependence of per-mile transportation cost on the location of the route. Minimization of the total transportation cost incurred in moving goods from where they are available to where they are wanted leads to a pattern of flow lines for each commodity, intersected at right angles by lines of equal price for that commodity. The price difference between two points on the same flow line equals the cost of transportation between these points. The problem of most economical return routing of empty equipment, studied separately in an earlier study by Tjalling C. Koopmans and Stanley Reiter (Cowles Commission Monograph 13, Chapter XIV), is incorporated in this study by treating equipment as one of the commodities in the model.

In order to provide empirical background for the problem of most efficient routing of empty railway cars in the United States, Kirk Fox has prepared data showing net surpluses of inflows over outflows of commodities carried in boxcars, for the eight quarters of 1949 and 1959, for each of twelve suitably chosen areas.

A second study by Beckmann deals with transportation on a given network of possibly congested roads. The traffic capacity of each road and the transportation cost on it, are both treated as functions of the (uniform) speed of vehicles (or trains or barges) using it. The capacities of intersections and the number of vehicles are introduced as given limiting factors. A routing of commodity and equipment flows so as to fit given availabilities of and requirements for commodities at given terminals at a minimum cost again implies a locational price pattern for each commodity. However, the price difference between two points connected by a flow of that commodity now also contains a charge for the passing of each congested road or intersection point on the way. This charge reflects the social cost that each vehicle causes by adding to congestion delays of other vehicles.

C.B. McGuire has made a study of the literature on highway and railway traffic engineering, in order to provide empirical background for the capacity and cost functions used in the network model just described. In addition, Beckmann and McGuire are studying the effects of individual choice of speeds and routes by vehicle drivers where only the cost of congestion to themselves is taken into account, which is realistic in the case of highway traffic.

In all the foregoing studies the locational distribution of productive activities is assumed to be given. To make it into a variable raises at the same time the problem of the treatment of indivisibilities in production, since the land or space input into any process of production cannot economically be made arbitrarily small. One is thus led to problems of maximizing the utilization of resources by reshuffiing (permutation) of productive activities over available elementary land or space units. A forthcoming paper by von Neumann, "The Problem of Optimal Assignment and a Certain Two-Person Game" (kindly made available to the Commission in advance of its publication in the second volume on the theory of games, A.W .Tucker, ed., Annals of Mathematics series) makes computation methods developed for the solution of games applicable to this class of problems. Beckmann considered a modified problem where transportation costs between assigned locations are taken into account.

One of the purposes of the Commission's studies in transportation and location, in which Koopmans has provided general guidance and stimulation, is to prepare the way for more realistic insight into the efficiency or inefficiency of industry's present geographical distribution and of our metropolitan concentrations of population and production. It is hoped that the efficiency aspects of various methods, modes, and degrees of dispersal of these concentrations, such as may be found desirable for reduced vulnerability in war, may also be better understood through these studies. A discussion by Jack Hirschleifer, of the RAND Corporation, of war damage insurance schemes as an incentive to dispersal, provided perspective in this connection. It is mentioned here for that reason, although it will be mentioned again under its proper classification of problems involving uncertainty.

The methods of "activity analysis," developed in Cowles Commission Monograph 13 and described in two preceding annual reports, throw new light on classical problems of international trade theory. Reiter of Stanford University completed a discussion of an example showing the effect on overall output of barriers to the movements of goods. Francois Morin, a Rotary International Fellow from the Ecole Polytechnique in Paris, France, was led to the same problem through consideration of a technical question in the stowage of goods in transportation under space and weight limitations, and developed the international trade interpretation of this problem with greater validity.

A study of the efficient arrangement of productive activities over time, started by Edmond Malinvaud when visiting the Commission as a Rockefeller Fellow in 1950–1951, was brought to completion after his return to Paris. This study extends to dynamic situations earlier results of Koopmans and Debreu concerning the criteria of efficient allocation of resources in a static economy, and the role of prices in making it possible to reach or maintain efficiency under decentralized allocative decision-making. Of considerable interest for capital and interest theory is the special case of an efficient stationary state, which differs from earlier static models in that the time structure of production processes is explicitly taken into account.

On a more practical level, Franco Modigliani and Franz Hohn of the University of Illinois, have discussed the problem of how best to distribute production over time to meet a given program of delivery dates and quantities, under various assumptions as to storage cost and the dependence of cost of production on the rate of output. Morin indicated simplifications that can be achieved in this problem by treating time as a continuous variable. Time also enters, as a label of two successive states of technology, into Debreu's application of his coefficient of resource utilization to the measurement of technological change. He proposes to represent technological change numerically by the highest proportional saving in all primary inputs which, in a hypothetical static economy, would permit the attainment of this year's standards of living if next year's technology could be substituted for this year's.

Problems of allocative efficiency under certainty as well as under uncertainty are studied from a general classificatory and analytical point of view by Hurwicz. The problem of computing an efficient state of a static economy by iterative methods is linked with the dynamic problem of determining the path whereby an economy with decentralized decision-making may approach efficiency through time. Further reference to this study will be made in the next section.

3. The Pursuit of Given Objectives under Uncertainty

The problem of inventory control in response to sales reports is one of the simplest examples of a problem in decision-making under uncertainty. Two types of uncertainty maybe distinguished here: the case of "complete information," where at least the probability distribution of future demand is known, and the case of "incomplete information," where even that is not known. The work by Arrow, Harris, and Marschak on this problem, described in our Annual Report for 1950–1951, stimulated a more complete and general mathematical study carried out by Aryeh Dvoretzky, J. Kiefer, and Jacob Wolfowitz, of Cornell University on which Dvoretzky (also of the University of Jerusalem) reported in a staff meeting. They treat the inventory problem as a special case of the general problem of how to utilize such influence as one may have on a chain of successively dependent chance events (a "stochastic process") in the outcome of which one has a definite interest. In a report to the staff on conversations with river control engineers in the Tennessee Valley Authority, Koopmans presented the problem of best balance between flood prevention and electricity generation as another control problem in this category.

In taking actions the outcome of which depends on uncertain future events, businessmen must form their best judgments regarding these events. However, since the attempt to forecast or assess uncertainty absorbs attention and effort, it is important in preparing decisions to specify for which events the anticipations really matter. These considerations led Modigliani and Hohn to formalize the concept of the relevance of anticipations about various future events to a given decision problem. In particular, their study of production scheduling over time, referred to above, led them to point out the significance of storage costs and seasonal fluctuations in demand or supply that cut down the length of the period ahead for which anticipations are relevant to present decisions. A similar concern with the cost of preparing and making a decision, and with the cost incurred at successively higher levels in setting up methods and procedures for preparing and making decisions, is found in a discussion of rational decision-making in business contributed by Charles Holt of the Carnegie Institute of Technology.

The problem of best actions in the light of given anticipations is illustrated by Harry Markowitz's discussion of portfolio selection. This is treated as a problem in minimizing variability of return for given expected average return on securities, or conversely.

In this, as in the other problems of decision-making under uncertainty mentioned so far, the analysis proceeds from the assumption of one controlling interest such as the maximization of expected profit of one firm. Actions by representatives of other interests enter in some cases as uncertain events to be predicted (such as future demand), but do not become the object of analysis. The assumption of subordination to one controlling interest is still maintained in Marschak's model of a team of two partners, but each partner has access to a different field of information. The analysis assumes as given: the cost of communication between partners (in time, money, etc.), the joint probability distribution of the two states of (correct) information, and the outcome (profit) resulting from any given pair of decisions by the two partners. The possible decisions are (1) to commit the partnership if not contacted by the other partner, (2) to abstain from commitment if not contacted, (3) to exchange information and commit, and (4) to exchange information and abstain from a commitment. The problem is to find rules of response to information for each partner that maximize the mathematical expectation of the profit.

Marschak, Karl Faxén, a visiting Rockefeller Fellow from Sweden, Beckmann, and Dvoretzky, guided by experimental computation conducted by Daniel Waterman, studied an interesting special case exemplified by an arbitrage firm in which one partner is informed of the buying price and the other of the selling price. It was shown that proceeding from less favorable to more favorable information, the best responses from each partner form the following sequence: communicate (to warn the partner); do nothing; communicate (to get information); commit; communicate (to encourage the partner). Each pair of decisions (one by each partner) will result in a certain profit or loss, as entered in the five different fields on our diagram; where the axes represent the two prices per unit of finished product. The five intervals marked on each axis represent the price ranges at which certain decisions of one partner are called for by the particular rule. Depending on the probability of various pairs of prices and on the cost of communication, some of the five price intervals may disappear. For the case when the two prices are distributed independently and with uniform probability over the same range, the best of all rules that are symmetrical with respect to the two partners were found by Kiefer and O. Orey of Cornell University, in their comments on various Cowles Commission discussion papers. Valuable comments were also received from J. Laderman of the Logistics Branch, Office of Naval Research.

The model just described contains in a highly simplified form one basic element of the theory of organization: the dispersal of information among members of an organization, and the communication procedures between them. Another element, emphasized by Herbert Simon in a Cowles Commission Seminar is the coalition character of organizations: the organization is viable as long as the distinct and individual interests of its members are best served by an agreement to follow the rules of behavior that make up the organization. Both of these elements of organization theory are recognized and elaborated in Hurwicz's analysis of information processing in resource allocation. In particular, the market economy is studied as a decentralized form of organization whereby the flow of information between "participants" (buyers and sellers) takes the form of price offers and quotations and quantities ordered.

A central problem of organization theory is how to set up the rules and incentives in such a way as to obtain "best results" in the sense of the efficiency concept described above. An example is the formulation of tax laws in such a manner as to make profit maximizing behavior of business in the face of uncertainty serve general ends of society most effectively. Beckmann and Marschak extended an earlier study of the latter into the income tax structure that will produce a given revenue with a minimum deterrent effect on risk-bearing investment. Another example is Hirschleifer's discussion, already referred to, of a war damage insurance scheme that carries incentives for the most economical degree and type of dispersal of productive activities to reduce vulnerability to air attack.

4. The Study of Actual Economic Behavior

If we ask ourselves what motivates the empirical study of economic behavior, we recognize here the same urge that motivates many other empirical sciences: the scientific curiosity that desires to explore and understand the physical, technological, human, and social environment in which life is lived. Another motivation is shared with many empirical sciences: knowledge of actual behavior is indispensable in assessing and predicting the effectiveness of policies recommended for individual or social improvement. Both motivations can be discerned in the choice of topics and methods of empirical research in economics by the economic profession generally, and at the Commission.

Through its research consultants and by other means, the Commission maintains close contact with programs of empirical work in other academic centers, This section therefore describes not only the empirical work in which the Commission itself is engaged, but also describes studies made elsewhere that have been brought into the discussions in the Commission, or with which contact has been maintained in other ways. The term "empirical work" is here to be interpreted broadly. It includes theoretical studies of the implications of assumptions made for purposes of empirical analysis.

The historical survey of the Commission's research mentioned earlier, describes the work by Lawrence R. Klein on the construction of systems of aggregative behavior equations as an aid in explaining or forecasting business fluctuations and in assessing the effect of stabilizing policies. This work is at present being continued and extended under Klein's direction at the Research Seminar in Quantitative Economics of the University of Michigan. Klein presented his program in a discussion at a staff meeting. In another discussion Donald Daly of the Department of Trade and Commerce of the Canadian Government reported on experience with similar systems applied to the Canadian economy with emphasis on the testing of forecasting methods against actual developments. In both cases this work was undertaken with the idea of utilizing additional and improved statistical data, against which to test a wider range of more detailed and refined theories in order to achieve more accurate estimation of behavior parameters. These studies have been based mostly on annual time series, in some cases on quarterly series. Fuller use of quarterly series, such as is made in a pilot study carried out jointly by Klein and Harold Barger of Columbia University (involving at present the estimation of small systems of three equations) will provide additional information. The development of electronic computing devices may make such studies possible on a larger scale.

At the same time, economists are to an increasing extent going beyond aggregative time series in order to obtain data richer in information which permit more powerful tests of hypotheses. They have looked for enrichment of data in the following directions in particular, singly or in combination: (a) disaggregation through the study of individual markets, (b) disaggregation by industrial classes (in the study of production relationships), (c) use of cross section data, often collected by sample surveys and concentrated on particular types of decisions, such as consumers' choice or the formation of anticipations.

The empirical work of the Commission's resident research staff has been concerned mostly with the study of individual markets. The motivation of the choice of markets for study has been not only a desire for better knowledge of these particular markets, but even more a desire to increase our knowledge of economic behavior generally by the thorough study of cases where circumstances for study are favorable. Also, studies of particular markets have been a valuable testing ground for statistical and computational methods of estimating behavior constants.

A study of certain markets with forward trading (corn, other feed grains, wheat, cotton) has been undertaken by H.S. Houthakker, with the assistance of William Dunaway, to clarify the empirical background for current theories of economic dynamics, behavior under uncertainty, and speculation. The principal variables to be explained are the level of stocks and the price spreads among different futures and between futures and cash prices. In the case of feed grains this is supplemented by a more detailed investigation of their demand structure.

Hildreth, in his association with the Agricultural Economics Research Group of the University of Chicago, is conducting a statistical study of supply and demand relationships for livestock products in the United States, assisted by Frank Jarrett. This is a semi-aggregative study in the sense that, although only one group of markets is considered, the demand and supply relations studied connect aggregate quantity and price indices for all livestock products included (ranging from cattle to eggs). The fact that these commodities are competing in demand as well as in production facilitates this aggregative procedure.

Miss Hendrieke Goris of the Netherlands Economic Institute made a progress report on her study of the United States tobacco markets, carried out while spending a fellowship period with the Commission.

The studies of Houthakker and Goris, as well as that of Hildreth and Jarrett were discussed in joint staff meetings with the Agricultural Economics Research Group.

The study of aggregative production relationships expressing balance in the rates of outputs of various industries, initiated, developed, and stimulated by Wassily Leontief of Harvard University, has grown in recent years into a field of large-scale empirical research, variously referred to as input-output analysis or interindustry economics. Ronald Shephard of The RAND Corporation described at a staff meeting his research proposal to study changes over time in input-output coefficients, in response to scale of output (increasing or decreasing returns), age distribution of capital equipment, fluctuations in output, and gradual cumulative factors such as technological change. Arrow and Robert Solow, the latter of the Massachusetts Institute of Technology, cooperated with Shephard as RAND consultants in formulating this proposal.

Klein pointed out that if input-output ratios are measured as ratios of money values of interindustry commodity flows in a given year, and if the prices underlying these value aggregates are formed in competitive markets, any observed constancy over time of these input-output ratios is compatible with the existence of production functions permitting substitution among physical inputs originating in different industries, and joint production of commodities produced by one industry. Koopmans finished an expository paper discussing results reached by various authors in Cowles Commission Monograph 13 regarding the constancy of relative prices of commodities under shifts in demand, if each commodity is produced separately in one industry, while only one scarce primary factor (e.g., labor) limits the rates of output attained by all industries.

The Commission benefited from the presentations of several pieces of research in the theory and econometrics of consumption, carried out by Michael Farrell and Houthakker at the Department of Applied Economics of the University of Cambridge, by William Hamburger as a thesis project at the University of Chicago, and by Klein at the Survey Research Center of the University of Michigan. Many of these studies made or envisaged use of data obtained from consumer surveys or budget studies.

Modigliani reported empirical findings of the research project on the role of expectations in business fluctuations, directed by him at the Bureau of Business Economics of the University of Illinois (in cooperation with the Public Opinion Research Center of the University of Chicago). This project, based on the evaluation of survey data as well as on the study of time series of recorded forecasts, ma y be expected to provide a more realistic framework for theories relating economic behavior to anticipations. The general purpose of most of the studies described in Section 4 is to provide a stronger empirical basis for the explanation of cyclical fluctuations. In a research memorandum of the Economic Institute of the University of Oslo, Trygve Haavelmo has indicated the need for econometric study of problems of long-range development and of the persistent and widening differences in economic level among different areas of the world. He has constructed and compared simple models discussing economic development in terms of a few aggregative variables such as population, production, accumulated capital, level of education and know-how, plus random disturbances. Even at this level of simplification, it is found that with the same structure of behavior as regards productive effort, capital accumulation, and human reproduction, small differences in "initial conditions" may over time lead to large discrepancies in economic level.

5. Concepts and Tools of Research

The formation of concepts and the development of research tools are an integral part of the research of the Commission. The report on progress during the year will be arranged under the categories "concept formation," statistical methods," and "mathematical tools," although no sharp boundaries separate these categories.

Simon has continued and extended his examination of the concept of causality. Besides the discussion of causal hierarchy of variables in a system of linear algebraic equations, described in our previous report, he has developed the notion of a causal ordering of propositions, defined in terms of the concepts of formal logic. While applicable to all empirical sciences, this analysis arose in connection with the study of production control systems.

Several guest speakers in staff meetings or seminars contributed to problems of concept formation. Coombs and Thrall, both of the University of Michigan, discussed ramifications of the concept of measurement ranging from mere nominal classification of objects to complete numerical measurement, and including such intermediate forms as partial ordering and complete but ordinal measurement. Menger discussed the introduction of probability into ordering relations. This will facilitate interpretation of experiments on the measurement of preferences in which the responses of individuals exhibit an element of randomness.

Those working in the application of statistical methods to econometric model construction are more and more concerned with the fact that the assumptions which specify the model are always approximations, consciously adopted to make statistical procedures applicable, but not believed to be strictly valid. On the other hand, the statistical procedures of estimation, assessment of accuracy of estimates, and testing of hypotheses are strictly valid only if the models are. We are thus faced with the problem of so-called "specification error."

Two ways of dealing with this problem are being explored and will no doubt be pursued further in the future. One method is to study the performance of inference processes derived to fit one particular model if the observations are generated by some other model belonging to a wider class of models. A conceptual basis for this approach to the specification problem is laid in Hurwicz's study of, the consequences of incorrect specification. Studies by Stephen. Allen and Jean Bronfenbrenner of particular cases of specification error have been mentioned in previous reports, and will be included in the forthcoming Cowles Commission Monograph 14, Studies in Econometric Method. In the same category is John Gurland's study of the effects of serial correlation in the disturbances in behavior equations, and of incorrect specification of the stochastic process that generates these disturbances. The importance of a particular type of "specification error," that of incorrectly treating certain variables as exogenous, was emphasized at the Boston meeting of the Econometric Society by Guy Orcutt of Harvard University in a paper of which William Hood was a discussant. Subsequently, Koopmans contributed a written discussion of Orcutt's paper to a panel discussion, to be printed with that paper in the Review of Economics and Statistics.

Another approach is the development of more flexible statistical inference procedures, which are perhaps less efficient or powerful for a narrowly specified model, but which are valid with determinable accuracy within a wider range of assumptions. Stimulated by earlier work of Wald in this direction, Hildreth has studied methods of estimating coefficients of simultaneous equation systems by means of suitably chosen subsets of the observations.

At the same time, the development and presentation of statistical methods for given parametrically defined models has been continued. Koopmans and Hood completed an expository presentation (for Monograph 14) of the application of the maximum-likelihood method of estimation to linear equation systems with normally distributed disturbances. They considered various cases with regard to the utilization or disregard of a priori knowledge as to which variables occur in each equation. T.W. Anderson contributed a suggestion toward computationally' economical methods for utilizing this type of a priori knowledge. Allen discussed methods for the simultaneous utilization of cross-section and time-series data.

Two guest speakers, G.S. Watson, of the University of Australia, and Ulf Grenander, on leave from the University of Stockholm while associated with the Committee on Statistics of the University of Chicago, discussed the estimation of regression coefficients in cases where the disturbances are serially correlated. This and similar problems involving intertemporal dependence of observations provided the motivation for Gurland's research into the distribution of quadratic forms in random variables, and the ratios of such forms.

Erling Sverdrup's study of statistical decision problems and their solution by the minimax principle, mentioned in the Annual Report for 1949–1950, was brought to completion after his return to the University of Oslo. This study includes a discussion of prediction problems as a special class of statistical decision problems.

Progress was made in several directions toward generalization and simplification in making available mathematical tools to economists. In studies of the interaction of various parts of the economy, frequent use is made of matrices of which all elements are positive or zero. Herstein located and translated a paper by Helmut Wielandt of the University of Mainz giving a concise treatment of the properties of such matrices. Jointly with Debreu he introduced further clarity and simplification by the use of a "fixed-point theorem" and gave a unified treatment of matrix properties scattered through the literature. Additional properties were derived and applied by John Chipman of Harvard University, who participated in research discussions of the Commission while a fellow of the Department of Economics of the University of Chicago. Debreu and Marschak cooperated in developing a proof of the central theorem relating to two-person zero-sum games which appeals to geometrical intuition. A computation method for the solution of such games was presented by Howard Raiffa of the University of Michigan.

The problem of maximization of a function (such as utility or profits) under constraints (of budget or technology) is basic to much of economic theory. If differentiability is assumed, this problem reduces to that of finding a maximum of a quadratic function under linear restrictions. Conditions for such a maximum are well known to economists but satisfactory proofs are hard to find. Debreu provided a concise and complete proof, which was published in Econometrica. Clarification of mathematical tools resulted also from Debreu's work on the existence of a saddle point and of an equilibrium point, referred to in Section 2 above.

The problems of location theory associated with indivisibilities, referred to in Section 2, have led to a renewed interest in the study of permutations and functions of permutations. A somewhat related problem — to define and find the combinatorial rank of a matrix — was discussed by Simon in connection with his work on causal hierarchy of variables.

Besides giving mathematical advice to the group on a variety of problems, Herstein is writing an exposition, from the mathematician's view point, of mathematical methods and tools used or of use in economics. Waterman has supplied direction to the computation staff of the Commission.

Office, Library, and Computation Laboratory

Supporting Staff (1951–1952)

Administration
    Helen Docekal, Administrative Secretary
    Marilyn Holmes King,* Dolores Mosher, Financial Secretary

General Office
    Miye Rata, Office Supervisor
    Lorraine Kirk,* Lucette Miller,* Maureen Murphy, Iris Ross, Secretaries
    Betty Livingston, Distrihuting and Technical Typing

Editorial
    Ruth Skinner, Editorial Secretary
    Charlece Harsten Saunders,* June Novick,* Jane Diller, Assistant Editorial Secretary
    Jane Novick, Editorial Consultant

Library
    J. Myron Jacobstein, Librarian

Computation Laboratory
    Francis Bobkoski, Donald Bratton, Billy Foster,
    Totaro Miyashita, Michael Morely, Jean Smolak,*
    Vera Stepan Pless,* Jagna Zahl, Hyman Zell,* Mathematical Technicians

*Staff departures prior to June 30, 1952.

The library, offices, and computation laboratory are located in the Social Science Building on the University of Chicago quadrangles, A staff of approximately nine full-time and a, varying number of part-time persons provides a variety of supporting services for the research staff, resident guests, and advanced students associated with the Cowles Commission, Several of the staff also perform related functions for the Econometric Society which shares the offices of the Commission.

Library

The library of the Cowles Commission is maintained primarily to assist in the research carried on by the Commission. As this research transcends the boundaries of conventional fields of inquiry, it has been advantageous to have the diverse subjects which are relevant to the studies of the Commission brought together and organized in one collection. The collection covers the fields of quantitative economics, economic theory, statistics, mathematics, descriptive data, and bibliography. To a lesser extent, it also has material on psychology, sociology, theory of communication and organization, and related topics, In view of the library's close proximity to the University of Chicago libraries, particular emphasis has been placed on journals, pamphlets, reprints, documents, and other materials that are not available through usual library sources.

During the past year the library has been recatalogued and reclassified according to the rules of the American Library Association and the Library of Congress. This integrates the various materials in the Cowles Commission collection under one system and provides conformity with the arrangement of the University of Chicago libraries. Additions to the library during 1951–52. total 287 books, 419 pamphlets, and 118 bound volumes of journals. The collection consists of 3,015 books, 5,966 pamphlets, and 862 bound journal volumes. Currently 141 journals are being received from 19 different countries. Many reprints of articles of interest are received from journals that primarily specialize in subjects outside the field of the Commission, permitting the library to have in its collection nearly all articles that touch on or relate to its research. The library also contains the collection of the late Professor Henry Schultz, consisting of 950 books and 1,750 pamphlets; a particularly valuable addition to the library since many of the books and articles are out of print and unavailable elsewhere in Chicago.

The library is open to members of the Department of Economics as well as to advanced students by arrangement.

Computation Laboratory

The computation laboratory employs the equivalent of four full-time computers whose work is confined for the most part to standard desk calculators. Most of the computers employed by the Commission have training in mathematics or statistics and for this reason can follow standardized outlines for "maximum-likelihood" and "least-squares" estimation. Daniel Waterman, research associate, directs the activities of the laboratory.

The work of the laboratory is, however, much more diverse than that of the usual statistical computing group. In the last year it has been engaged in such work as the computation of sets of orthogonal polynomials, testing the convergence of various series representations of distribution functions, the evaluation and maximization of certain definite integrals, and estimation of behavior equations.

Computation tasks expected during the next year will include the inversion of high-order matrices, which cannot be performed economically on desk calculators. Provision is therefore being made for the use of digital electronic computers belonging to outside agencies. The availability of such machines will make it possible to utilize complex estimating techniques which are not feasible at this time.

The Econometric Society

The principal activities of the Econometric Society, an international society for the advancement of economic theory in its relation to statistics and mathematics, consist of the publication of a journal, Econometrica, and the arrangement of scientific meetings in various parts of the world. In these and other activities in which the Econometric Society has engaged, it has enjoyed the advantages of a close association with the Cowles Commission through sharing office facilities and through the participation of members of the Commission's staff; an association which was the outgrowth of early ties and common sympathies set forth in detail in the "History of the Cowles Commission" which is included in this report.

The Fellows represent the highest authority of the Society. They are 94 in number, including residents of 18 different countries. In 1951 a revision of the rules for election of new Fellows was put into effect which facilitates consideration of the qualifications of candidates. Six new Fellows were elected in the current year: T. Barna, G. Darmois, H.S. Houthakker, J.J. Polak, O. ReiersØl, and J. Tobin.

The Fellows elected the following members of the Society to the Council for 1952: C. Bresciani-Turroni of Italy, J. Tinbergen of the Netherlands, and T.C. Koopmans and Wassily Leontief of the United States. The Council includes in addition the officers of the Society and Colin Clark, Australia; R.G.D. Allen and J.R. Hicks, England; Ragnar Frisch, Norway; Herman O.A. Wold, Sweden; and Griffith C. Evans and Simon Kuznets, United States.

The officers of the Society in 1951 were R.G.D. Allen, London School of Economics, president; Paul A. Samuelson, Massachusetts Institute of Technology, vice-president; and two members of the Commission, William B. Simpson and Alfred Cowles, as secretary and treasurer, respectively. The Council elected René Roy of the Institut de Statistique de l'Université de Paris to be vice-president in 1952, Samuelson was elected president, and Simpson and Cowles were re-elected to their respective offices. In May, Simpson submitted to the Council his resignation as secretary of the Society to become effective at the end of the fiscal year, upon completion of four years in office.

A total of 243 individuals were elected to membership during the fiscal year ending September 30, 1952. This brought membership in the Society to 1741, double the membership four years earlier. The number of countries represented increased to 64. Although the number of members outside Europe and North America continues to be small, the highest rates of growth in membership strength are found respectively in Central and South America, Asia, Africa, and Australasia and Oceania. Since 1949 a geographical index of members and subscribers has been published in the October issue of Econometrica.

A policy of encouraging meetings of the Econometric Society in additional parts of the world and of seeking the appointment of broadly representative program committees wherever possible has been followed in recent years. In 1951, for example, approximately 50 members participated in planning and arranging the seven meetings of the Society. Papers and formal discussions totaling 171 in number were presented at its sessions. Many more members participated through attendance, some serving as session chairmen or offering informal discussion. Other members had access to the proceedings through abstracts published in Econometrica.

In August, 1951, the West Coast regional meeting of the Econometric Society was held at the RAND Corporation in Santa Monica in conjunction with the Southern California Economic Association. In 1952 it was held at the University of Oregon in Eugene, June 19–21, in conjunction with the American Mathematical Society, Biometric Society, Institute of Mathematical Statistics, and Mathematical Association of America.

The American summer meeting of the Econometric Society was held at the University of Minnesota in September, 1951, in conjunction with the meetings of the American Mathematical Society, Mathematical Association of America, Institute of Mathematical Statistics, and Section A of the American Association for the Advancement of Science. This year the joint summer meeting with the mathematical groups was held at Michigan State College in East Lansing, September 2–5.

The American winter meeting of the Society is usually held at the same time and place as the meetings of the American Economic Association, American Statistical Association, Institute of Mathematical Statistics, and other components of the Allied Social Science Associations, and some joint sessions are arranged. This was held in Boston in 1951. The 1952. meeting with the social science organizations will be held in Chicago, December 27–29. The European meeting of the Econometric Society was held at Louvain, Belgium, in 1951, and this year at Cambridge, England, August 13–15.

The Japanese meeting of the Econometric Society was held at the Tokyo University of Commerce, in 1951. This year the meeting is scheduled for November 1–3 at Nagoya University as a joint meeting with the Society of Theoretical Economics. Arrangements were concluded with the Japanese Science Council for Dr. Takuma Yasui to attend the year-end professional meetings in the United States as the official delegate of the Japanese branch of the Society.

In December, 1951, joint sessions of the Society were held in New Delhi with the International Statistical Institute and in Patna in conjunction with the Indian Economic Conference. Participation is now being planned in the All-India Economic Conference to be held at Travancore University in Trivandrum, December 26–30, and in a meeting of the statistical section of the Indian Science Congress to be held at Lucknow, January 2–8,1953.

In April, 1952, a questionnaire was sent to all members of the Econometric Society in Mexico, Central and South America, .and adjoining Caribbean areas to determine the extent of interest in the institution of regular meetings of the Society in the Latin American countries. On the basis of the response which was received, meetings in Mexico City, Mexico; Rio de Janeiro, Brazil; and Santiago, Chile, are under consideration for 1953.

A report on the present status of econometric teaching at the university level was prepared for the Econometric Society by Gerhard Tintner in early 1952. Conducted under provisions of a contract between the Society and UNESCO, the study forms part of UNESCO's general inquiry into teaching in the social sciences and will be published in that connection. Because of the short interval in which the report was to be prepared, major reliance was placed Upon questionnaires sent members and institutions teaching econometrics in eight countries specified by UNESCO. The survey included Egypt, France, India, Mexico, Poland, Sweden, the United Kingdom, and the United States.

The Econometric Society is Cooperating informally with the Training Center for Economic and Financial Statistics which is being established in Santiago, Chile, by the Inter American Statistical Institute and Pan American Union as part of the technical assistance program of the United Nations. A consultative panel has been appointed by the Society which will be available on a continuing basis to assist in designing a set of courses appropriate to the objectives of the Center's program. No formal connection will exist, however, between the Society and the Center or its Sponsoring agencies. Calvert L. Dedrick, Lester S. Kellogg, William G. Madow, and Gerhard Tintner will serve on the panel.

During the year the Econometric Society continued its affiliations with the International Statistical Institute, the American Association for the Advancement of Science, the division of mathematics of the National Research Council, and the Allied Social Science Associations. It also maintained its informal contacts with the International Economic Association. The Society is on the consultative register of the Economic and Social Council of the United Nations and steps have been taken to complete a consultative relationship with UNESCO. The Econometric Society continued to be represented on an intersociety committee studying the mathematical training appropriate for social scientists.

On recommendation of the secretary, the Council approved the creation of an institutional (nonvoting) membership status. Academic or nonacademic institutions subscribing a specified amount or more in support of the activities of the Society will receive two copies of each publication of the Society and may designate representatives to attend its meetings. A committee will report to the Council within two years as to the experience gained with institutional memberships and as to any addition to the constitution of the Society as may then seem desirable.

During 1951, Volume 19 of Econometrica was published, consisting of four quarterly issues totaling 573 pages. The twentieth year volume being published in 1952 will include 806 pages. This brings the journal to double the size it had prior to 1949. The journal is now being mailed to over 2700 individuals and libraries in 72 different countries. A 160-page supplement edited by Kirk Fox is in preparation containing a twenty-year author index and analytical subject guide to Econometrica. The Cowles Commission gave support to the indexing project in the form of salaries paid the editor of the index and his assistants.

Arrangements were made for the publication of a Japanese translation of Trygve Haavelmo's "The Probability Approach in Econometrics," Econometrica, Vol. 12, Supplement, July, 1944, which is in preparation by Isamu Yamada of Hitotsubashi University, Tokyo. Royalties from the sale of the edition will be used for the purchase of econometric materials for presentation to libraries in Japan.

Ragnar Frisch continued as editor of Econometrica and William B. Simpson as co-editor. The following persons were appointed as associate editors during the year to assist in arranging the refereeing of articles: Nicholas Georgescu-Roegen, Vanderbilt University; Edmond C. Malinvaud, Institut National de la Statistique et des Etudes Economiques; and J.R. Stone, Cambridge University. John R. Hicks, Oxford University, participated until 1952. Other associate editors include Harold T. Davis, Northwestern University; Kenneth O. May, Carleton College; J. Tinbergen, Netherlands School of Economics; Gerhard Tintner, Iowa State College; James Tobin, Yale University; and Herman O.A. Wold, University of Uppsala.

Econometrica began carrying a book review section, edited by Gerhard Tintner, starting with the July, 1951, issue. The journal arranged translations of articles underlying the development of econometrics to make these contributions generally accessible. During the year Mrs. Ruth Skinner succeeded Mrs. Jane Novick as editorial secretary. Mrs. Jane Diller was appointed assistant editorial secretary in June.

Other activities of the Society during the year included the establishment of an emeritus membership status, completion of a project on collation of definitions of econometrics and further work on the preparation of encyclopedia and dictionary entries, and efforts directed toward securing support for an international survey of facilities related to the quantitative approach to economics. The desirability was also explored of arranging for a publication channel for occasional contributions not suitable for either book or journal publication.

Miss Helen Docekal continued as administrative secretary during the year. Mrs. Dolores Mosher succeeded Mrs. Marilyn Holmes King as financial secretary in June, 1952. The following individuals served as financial agents of the Society in their respective countries: R.G.D. Allen, England; Francesco Brambilla, Italy; Jacques Dumontier, France; J.C. du Plessis, Union of South America; Ragnar Frisch, Norway; N.S.R. Sastry, India; J. Tinbergen, The Netherlands; and Isamu Yamada, Japan.

Contents

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