Cowles in the History of Economic Thought
Kenneth J. Arrow
Abstracted from the Cowles Fiftieth Anniversary Volume
INTRODUCTION
The topic of this paper immediately raises a serious methodological
question: In what sense can we isolate the contribution of any individual or institution
in the development of economic analysis? This is but one example of a fundamental logical
problem that applies to the study of all history, that is, the difficulty of the
counterfactual. For when you ask, "What is the influence of A (an event, an
individual, an idea) on subsequent history?," you mean to ask what would have
happened had A not been there. There is no immediately apparent way to proceed to answer
that question. Every now and then historians debate the meaning of interpretation; in
recent years the socalled new economic history has been filled with controversy over just
such issues.
Suppose the Cowles Commission and Foundation had not existed; what would be the
difference in the present state of economic analysis? This is the ideal question; but it
is clearly unanswerable. Cowles is not and was not a group isolated from the mainstream of
economics, and its contributions are today inextricably mingled with other currents.
Influences flowed into it from the worlds of economics and statistics, or at least from
selected parts of them, and in turn ideas and achievements circulated from Cowles to the
common pools of economic knowledge.
In trying to identify the importance of Cowles, we are not entirely bereft of
meaningful data. What people at Cowles did at anyone moment is identifiable. We have the
papers they published; we can find out whether the concepts in them had their genesis at
Cowles or at some earlier intellectual abode of the author. This sort of study has its
place and may be most of what is achievable. But no research institute is an island entire
of itself (It would not be appropriate to continue the quotation; it should apply to
"joyous spells as well as holy knells.")
Cowles indeed has been an institution with a frequently changing population. The
average stay of a scholar has been only a few years, though there is of course a whole
distribution of residence times. I was at Cowles for a little over two years, Gerard
Debreu spent eleven years, and Tjalling Koopmans fortyone years. Individual scholars come
from elsewhere, bringing something to Cowles, and they leave carrying a bit of the Cowles
heritage with them. The mobility that is optimal for extending the influence of Cowles
certainly makes it difficult to measure Cowles's importance.
Even apart from mobility of scholars, there is the flow of ideas and concepts to and
from an institution like Cowles. The topics studied at Cowles originated elsewhere. Some
were endogenous to economics and emerged from previous discussions in the economics
literature. General equilibrium theory, for example, might be viewed as the result of some
economists' attempts to think about what exists in the literature and to improve on it.
Other topics originated outside economics. A good example is the interest in nuclear
energy. This first appeared during Cowles's Chicago period in the project organized by Sam
Schurr and Jacob Marschak, which was the first serious attempt to study the economics of
nuclear energy. I do not know how much it influenced policy, but it was certainly the
first analysis of the subject that made any sense. It is hard now to believe the
statements made at that time by leading thinkers, such as the then president of the
University of Chicago, that with "atomic energy" (as it was then called), no one
would have to work more than an hour or two a day, so that the really imminent problem was
how to handle leisure! It took a relatively straightforward analysis by Schurr, Marschak,
Herbert Simon, and others to demonstrate that under the most optimistic premises the
effects on the economy were marginal. With the recurrence of interest in energy economics,
the work of Tjalling Koopmans and William Nordhaus and other work on closely related
environmental issues have been significant on Cowles's recent agenda.
Having seen two examples of external influences on Cowles's research, one from within
economics and one from outside, one might ask whether Cowles itself opened any brand new
fields of inquiry. Obviously, there are problems of definition and classification in such
a question, but the answer has to be, probably no. It IS not very clear, however, whether
there are many new fields of inquiry in economics at all. When one reads the historical
background, economics appears to be a remarkably conservative field. Today, for example,
we have animated arguments between the rational expectations school and neoKeynesianism
or Tobinism or whatever label is to be attached to the current versions of disequilibrium
economics. But however they are labeled, these are the same questions that Malthus and
Ricardo debated.
I am not suggesting that there have not been great improvements. But although the
analyses have changed greatly, the questions remain relatively constant. In fact, at few
times in the history of economic thought have there been radical innovations. When they
occur, they tend to be subverted after a period of time and brought back to the
mainstream. Take the striking case of Keynes's general theory. As soon as scholars at
Cowles and elsewhere began to work on it, they developed the theory in terms of individual
rational behavior. Keynes's bold severing of the connection with rational behavior was
undermined by the intellectual need to understand behavior, which we interpret as
explaining it in rational terms. Indeed, this search did supply new concepts, firmer
foundations, and more empirically correct interpretations, especially in the explanation
of consumption.
With this background of caution about the difficulty of my task, I want to turn to a
more specific discussion of Cowles's place in the history of economic thought. I will talk
of precursors and successors. It is easier to discuss the former than the latter for when
a concept is really successful, it spreads everywhere. I must warn you, then, of some bias
in the following accounts towards identifying the influences on Cowles as opposed to
measuring the impact of Cowles's scholars on economics.
The research undertaken at Cowles has addressed a great many topics, of which I will
examine only four. These are key issues, and they also serve to illustrate different
relations between Cowles and the general history of thought. The four topics are: the
estimation of complete models of the economy, the area of programming and general
equilibrium theory (although one might question its unity), the economics of uncertainty
and information, and the field of intertemporal choice (of the first importance, although
the number of publications is small). I shall treat the first two in some detail, the
latter two more briefly. We shall see that for some topics Cowles as an institution played
a unique role in the profession as Cowles was, for at least some period, essentially the
universe in which the discourse took place. In work on the others, Cowles played an
important part but always in a twoway interaction with other scholars in the economics
community.
The Estimation of Complete Models of the Economy
The first topic shows Cowles in its most distinctive role, with the clearest separation
from the outside world. Although this work was not started at Cowles, there was a period
of four or five years when essentially all the relevant work on both the theory and the
practice of estimating large econometric models was done there. We may compare the
development of this topic to that of a river valley. A number of streams come together
into a single river, which later branches out. But there is some length in which all the
activity flows in a single channel. In estimating complete models of the economy, that
channel was Cowles. That exclusive role does not characterize, I believe, any other
subject of largescale Cowles activity.
There are two central aspects to the estimation of complete models. One is the idea
that a meaningful economic model should be estimated using realworld data, and the second
is that the model should satisfy the logical need for a complete system. The second
question raises a methodologically interesting problem of ascribing influence — in
this case, especially to the work of Jan Tinbergen — as we shall see. One possible
point of view is that the need for a complete system is so obvious that no one can be
given credit for recognizing it. If there are a number of variables, no one can be
predicted except by having a complete system. Of course, systems may decompose, so that a
complete system may have a smaller selfcontained system embedded within it. For example,
consider classical economics as exemplified by Ricardo. The central model had a complete
system in which prices were the only variables. The classical economists therefore saw no
need to discuss quantities and, in particular, they did not recognize as elementary a
concept as a demand function.
Had they thought about it, Ricardo and others would have recognized that even if they
were right in asserting that prices could be determined in a complete system not involving
quantities, there is a larger complete system in which quantities can also be determined.
Indeed, John Stuart Mill did take this additional step, by adding demand functions,
although he was not careful enough to ensure consistency in the larger system.
The very large literature on business cycles before 1930 contained analyses of many
single relations, specifying, for example, consumption as a function of other variables,
or prices and output as functions of money supply. To someone like Irving Fisher, the need
for a complete system was so clear that it was given little explicit attention. But many
authors did not have the idea of a complete system firmly in mind, for they drew
inferences about the existence of cycles from single relations.
There is a very interesting interchange between Ragnar Frisch and John Maurice Clark in
the Journal of Political Economy for 1931 and 1932. Clark, who may be largely
forgotten today but was a major figure of that time, had been one of those who advanced
the acceleration principle as an explanation of cyclical fluctuations. Frisch argued
forcibly and persuasively that this inference could not be drawn; the existence of
cyclical fluctuations emerges from the complete system. Frisch's paper was essentially a
nonmathematical version of his classic, "Propagation Problems and Impulse Problems in
Dynamic Economics," which appeared the next year in the Festschrift for Gustav
Cassel. This presents, as far as I know, the first specified complete dynamic system.
As far as I can ascertain, the first complete model to be estimated was Tinbergen's for
the Netherlands economy, published in 1937. Although the model had been formulated before
the publication of Keynes's General Theory, it was essentially a Keynesian model.
While there were some twenty equations in all, the key equation was one in which Tinbergen
set consumption equal to wages plus a fixed share of profits. He had no difficulty
understanding all the properties of complete systems, including the role of identities,
and he introduced much of the terminology we use to this day.
Tinbergen's statistical tool was ordinary regression analysis. In this he was typical
of the emerging econometric school; their statistical outlook derived from the English
school and most especially from R.A. Fisher. What was implicit even in the work of earlier
statisticians, such as Karl Pearson, was explicit in Fisher: the necessity of formulating
an explicit statistical model of the phenomena being studied to derive the statistics
needed to estimate the model parameters. To Fisher, this meant using the method of maximum
likelihood, by which he derived regression analysis, Student's ttest, the analysis of
variance, and the many other offspring of his fertile mind.
It was natural for econometricians to adopt the tool of regression analysis when trying
to estimate relations among variables. That tool had already been used by Gauss and
Legendre to smooth astronomical and geodetic observations, and it had been given new life
(and the name) by biometricians from Francis Galton through Karl Pearson and others.
Tinbergen therefore used regression analysis as the natural tool. He was, candidly, not
very reflective on the choice of the dependent variable. He was, however, very concerned
with the structural significance of the equations being fitted, and he was very insistent
that each equation represent what he called a direct relationship. A variable, such as
consumption, should be related only to its proximate causes as suggested by economic
theory. Thus consumption was to be related to its direct cause, income. Tinbergen did no
(conceptualize the modeling enterprise in terms of simultaneous equations; he did not ask
whether the relation he found really represented the determination of income by
consumption. Nevertheless, his choice of dependent variable certainly reflected a
commonsense viewpoint and could not be described as completely arbitrary.
It was Ragnar Frisch who was more specifically concerned with the statistical problems
that arise when the observed variables are determined by a complete system. His model has
been characterized as a descriptive model rather than a specification to which inferential
procedures could be applied. It would be more accurate to say that the model was specified
only in a roughandready way. He assumed a nearly exact relation among unobserved
variates, each of which is observed with error, and he made some quite specific
statistical assumptions; for example, the errors in variables were assumed to be
independent of each other and of the systematic parts of the variables. But his
presentation was unclear. He did not use his assumptions systematically to derive
estimates or tests of hypotheses, and he did not discuss the estimation of the complete
system but only of single relations.
Tjalling Koopmans, in his 1936 doctoral dissertation, presented a much more precise
model in which he combined Frisch's ideas with regression analysis. There were shocks, but
the variables were also subject to error. If the covariance matrix of the errors was known
( in particular, if the errors of observation of different variables were independent and
the variances of the errors known), then estimates of the regression coefficients could be
found. If the errors were independent but their variances unknown, the estimates could be
shown to lie within a generalized triangle, but nothing further could be inferred.
As the theoretical modeling efforts developed and grew more sophisticated, the
depression of the 1930s had its impact on the choice of problems that those tools should
be used to study. The Depression led, not surprisingly, to the belief among economists
that unemployment was a serious problem. Economists had not yet arrived at the doctrine
some currently espouse that all unemployment is voluntary, the result of errors and
misperceptions. In response to the observed crisis, the League of Nations mounted a major
study in two parts. Gottfried Haberler wrote an excellent critical survey of
underinvestment, underconsumption, monetary investment, and other thencurrent theories of
the business cycle. Much of this literature, as I have suggested before, advanced
hypotheses about single equations rather than attempting complete explanations. Jan
Tinbergen was commissioned to develop statistical analyses of economic fluctuations, which
eventually emerged as two volumes.
In principle, Tinbergen was to test the alternative hypotheses studied by Haberler. The
execution did not fully satisfy this criterion; many of the hypotheses were not testable,
and Tinbergen ignored others. On the other hand, Tinbergen tried to do more. He responded
to Frisch's concerns. The margins of the book are filled with bunchmaps that attempt to
test Frisch's concerns about the reliability of the statistical fits when there are errors
in the observed variables.
How influential was Tinbergen's work, in particular on the Cowles Commission in its
Chicago period? One point of view might be that what Tinbergen did was so obvious that it
cannot be ascribed any independent significance. All he did was to assemble a number of
relations suggested by the literature, fit them to the best data he could find, and use
the complete system to analyze, for example, the effects of alternative policies. The
relevant Cowles literature contains very few references to Tinbergen. In fact, that
literature contains very few references at all, and only cursory ones at that, to the work
of anyone outside the Cowles circle. The reason is clear. There was such a discontinuity
in both statistical methodology and model building that external references would be only
of historical curiosity. The sheer volume of the mathematical work and the rigor and
precision of the structure in the Cowles approach dominated the choice of citations. The
style was derived from mathematics: citations are for reference to something used, not for
historical acknowledgment.
But it would be a mistake to infer that Tinbergen's work was not influential, in spite
of the lack of references to it. It created the prototype of the next step forward; it was
the work that had to be carried out in better form. To speak of myself for a moment, one
of my first attempts at a doctoral dissertation was a redoing of the Tinbergen model. It
was foolish; I had no idea of the amount of work involved. But I made notes as to the
improvement of this equation and that. My guess is that improvement of Tinbergen's work
was a widespread dream; it was at Cowles that it was achieved.
There was a significant conference called at Cambridge, England, in 1938 to discuss the
draft of Tinbergen's League of Nations study. Ragnar Frisch was not actually present at
the conference, but he contributed his famous memorandum on statistical versus theoretical
relations in economic macrodynamics. The emphasis was very much, as might be expected, on
dynamic relationships. Although the paper was meant to have implications for the
interpretation of statistical relations, the core of the piece concerned deterministic
systems. His argument followed these lines: Suppose the observed data are in fact the
solution of a simultaneous system of linear difference equations. The solution is then a
combination of exponential and trigonometric functions. Suppose further that a lag
structure of fixed length is specified for one of the difference equations. The solution
has to satisfy this equation. We must necessarily be able to find one equation with the
specified number of lags such that the observed variables satisfy it. Frisch asked whether
another equation of the same form might also be satisfied by the solution. If not, the
original equation was called a coflux equation. If the solution did satisfy another
equation of the same lag form, it was called a superflux relation. (This terminology was
born and died with this paper.)
Frisch made the important point that only the coflux relations can be estimated. In a
deterministic system, this will be obvious. When random terms are added, the lack of
uniqueness will be less obvious. But dividing zero by zero, which is clearly impossible,
will be replaced by dividing one random element with mean zero by another; the
impossibility will not be obvious, but the ratio will have a very broad distribution.
The historical significance of Frisch's paper has to be judged with care. History in
general, and history of thought in particular, is always written from the perspective of
hindsight. The historian looks at today's ideas and asks whether and how clearly earlier
scholars anticipated them. There are always dangers of either under or
overinterpretation. One can elevate a sneeze into a deep anticipation or, if too precise
and fussy, always find the earlier statement to be unclear and obscure. My reading of
Frisch's paper is that he was indeed groping for the concept of identification but only
identification by specification of lag structure. He did introduce a very important point
as to the aim of empirical study; what we want to estimate are structural or, as he called
them, "autonomous" relations. To be sure, the idea had been implicit earlier. In
particular, Tinbergen's emphasis on direct relations had the same purpose, as he pointed
out in his reply to Frisch. Frisch's fundamental point, that the only autonomous relations
are the coflux relations, contains the essence of the identifiability concept.
This is not the first time that identification appears in the literature. Elmer
Working's muchcited paper of 1927 raised the same question about the statistical
estimation of demand curves. But Frisch's analysis was certainly placed in a more general
context. The next step was the famous doctoral dissertation of Trygve Haavelmo. Since
Haavelmo was Frisch's student, there was certainly some interaction between them. From
later references, though, it is clear that Frisch was not entirely pleased, since Haavelmo
shifted the basis of discussion to a pure shock model. Haavelmo put forth the idea of
finding the maximum likelihood estimates of simultaneous equations. Some preliminary ideas
already appeared in a paper of his in 1940, which discussed the problem of testing
business cycle theories by examining the observed relationships and so was very closely
related to Frisch's 1938 memorandum.
Haavelmo developed his ideas further in a brief paper in 1943; his full dissertation
was published in 1944 as a supplement to Econometrica. The identification concept
is still cloudy there but it is more clearly adumbrated. An accompanying paper by Henry B.
Mann and Abraham Wald is basically just a proof of the consistency of regression when the
independent variables are lagged endogenous variables and the disturbances are serially
uncorrelated. (I say "just," but I do not mean to imply that the analysis was
not very difficult indeed.) At the end of the Mann–Wald paper, there is a discussion
of the transformation of what amount to estimates of the reduced form back into estimates
of the structural parameters, and the question of uniqueness arises.
It was therefore a major step for Tjalling Koopmans and his associates to state once
and for all what the identification problem is and to give the order and rank criteria for
identification in linear systems. Haavelmo, building on Frisch and Tinbergen, had stated a
program; Koopmans, Herman Rubin, R.B. Leipnik, Theodore W. Anderson, Jr., Leonid Hurwicz,
and others carried out the program as far as statistical methodology goes. At the same
time, Lawrence R. Klein pursued the Tinbergen program according to the new statistical
methods and their implications and according to the macroeconomic concepts adapted from
Keynes but already mixed with microeconomic theory.
There is one curious pattern in the development of simultaneousequations estimation
that also occurred in the development of general equilibrium theory and linear
programming: a tendency to move from the dynamic to the static. To a considerable extent
in Tinbergen, and almost exclusively in Frisch, the explanatory variables were lagged
endogenous variables. The Mann–Wald proof of consistency was confined to the same
case. It took some time for economists to realize that the arguments were applicable if
some of the predetermined variables were exogenous. Indeed, the difficulties of the
consistency proof arise mostly from the lagged endogenous variables, and the extension is
relatively simple, though not entirely trivial. Similarly, the identification criteria
depend on the specification of the predetermined variables, whether they are exogenous or
lagged endogenous. The dynamic elements that were prominent in the motivation of the
research turned out to be secondary in the final logical structure.
Programming and General Equilibrium Theory
In the second major field discussed here, programming and general equilibrium theory,
Cowles played an influential role, but it was never the sole channel of intellectual flow.
The concept of programming originated outside of economics. There was, however, a relevant
history in economics — namely, in the fixed — coefficients model of
productionthat was not fully exploited. The fixedcoefficients model is very traditional
in economics, though even Ricardo had examples of alternative methods of production. Later
in the 19th century, the idea of alternative methods of production in the form of the
smooth production function was developed by Stuart Wood, John Bates Clark, Léon Walras
(explicitly in the later editions of the Eléments but clearly suggested even in
the first edition of 1874), and Philip Wicksteed. But there were always some economists
who held out against the possibilities of complete substitution. Vilfredo Pareto always
had great reservations, and Nicholas GeorgescuRoegen in the 1930s was following Pareto by
writing about "limitational factors"; instead of smooth isoquants, there could
be barriers beyond which substitution was not possible at any level, e.g., a minimum
amount of pig iron in the production of steel.
John von Neumann, in a famous paper presented to the Princeton Mathematics Club in
1932, though not published until 1937, had a perfectly clear and general activity analysis
model. There were finitely many activities, each with fixed coefficients, but alternative
activities for producing the same goods. Activities could even have multiple outputs. What
I suggested this idea to him is very unclear. The only economics he seems to have read, to
judge from his references, is Gustav Cassel's Theory of Social Economy. But
Cassel's formulation has only fixed coefficients of production and indeed in a very
primitive way; it does not even allow for circular flows. Perhaps the activity analysis
formulation of production was simply obvious to a genius like von Neumann.
Later, and independently of both the economics tradition and von Neumann, Marshall Wood
and George Dantzig in the Air Force Controller's office, operating under the practical
impact of wartime planning, were concerned with timephased programs; again they
formulated the model in terms of alternative linear activities, each with fixed
coefficients. (Note that Wood and Dantzig started with dynamic models just as von Neumann
had; only later did the more general formulations switch to a static framework.)
Linear activity analysis may be a concept like complete systems; if one thinks hard
enough about the problem, one is bound to come to it. There were, after all, two more
independent sources, L.V. Kantorovich's work in the Soviet Union, starting about 1939, and
Tjalling Koopmans's work on the transportation problem for the Combined Allied Shipping
Boards in World War II. Kantorovich gave a characterization of the solution, first for the
transportation problem and then for linear programming in general, but not an effective
method of solution in general. Koopmans, drawing upon analogies from physics, produced a
perfectly constructive solution for the transportation problem.
Perhaps the only common element in the efforts of von Neumann, Wood and Dantzig,
Kantorovich, and Koopmans was that each was a mathematician's reaction to practical
problems. As we all know, Dantzig's simplex method provided the effective solution for
linear programming in general. The reasons for its excellent performance in practice are,
however, still somewhat mysterious.
Linear programming and its generalizations were applied very rapidly, in business and
in military logistics. Programming methods have also been extensively applied within
economics itself, in such areas as economic development and the analysis of specific
industries. The great change in computer capabilities at this appropriate moment was
crucial, as indeed it was in the development of large econometric models.
In contrast to the multiple origins of linear programming, general equilibrium theory
was invented once by Leon Walras. One may ask how anyone could possibly have thought
differently. It is indeed just a special case of the need for modeling complete systems.
Nevertheless, no one did impose this condition until Walras, and many economists to this
day reject it as too complex to serve as a basis for analysis. Walras had a slogan,
repeated in different contexts: the system is determinate when the number of equations
equals the number of unknowns. It is fortunate for
the development of existence theorems for general equilibrium that differential
topology was unknown in the early 1950s. If the tools had been available to us, we would
simply have written down a few appropriate transversality conditions and then said that
Walras was really right all the time.
The possibility of nonexistence was raised during the 1930s in papers by Hans Neisser
and Heinrich von Stackelberg, and corresponding attempts to prove existence followed.
There is a good account of this period in a paper by E. Roy Weintraub. A crucial
suggestion was made by one of my favorite characters, Karl Schlesinger, an amateur
economist, a Viennese banker who had received a Ph.D. in economics in 1914 under
BöhmBawerk. Schlesinger perceived that the difficulties raised by Neisser and by von
Stackelberg in Cassel's formulation of general equilibrium theory could be resolved if one
added to the usual definitions of equilibrium (equality of supply and demand on all
markets for scarce goods) a statement that whether a good is free or scarce is itself an
economic matter. More specifically, supply may exceed demand at zero price. Schlesinger
felt that a mathematician was needed to prove existence under these assumptions. He
approached Karl Menger (not the economist, but his son, a wellknown mathematician who
later occasionally attended Cowles Commission seminars in Chicago). Menger, in turn,
referred Schlesinger to a young unemployed mathematician named Abraham Wald. (Wald was
either Romanian or Hungarian, according to one's national outlook. He was born in a town
that was Hungarian at the time but later was ceded to Romania. The Hungarians interested
in general equilibrium theory like to claim Wald for one of theirs.)
Wald produced a proof of the existence of general equilibrium, which is reviewed in
Gerard Debreu's paper in this volume. About twenty years later, under the impact of new
work in combinatorial topology and especially its application to John Nash's equilibrium
point concept, Lionel McKenzie, Gerard Debreu, and I were independently stimulated to
renewed work on existence. Here is one clear case of Robert K. Merton's "multiple
discoveries"; the tools were available, the field was ripe, and the existence
theorems were going to be proved by someone.
A key step in unifying and diffusing the developments in linear programming and
relating them to the theory of general equilibrium was the conference on activity analysis
organized by Koopmans and held in 1949. This has been regarded by all those in the field,
not only the Cowles group, as a decisive event. The exchange of ideas was crucial, as
Dantzig has testified in his reminiscences. The papers at the conference called scholars'
attention to each other; they clarified the concepts and laid a firm foundation for future
work. The first proof of the validity of the simplex method was among its most important
products. For the development of general equilibrium theory, the most important paper was
Koopmans's in which he developed the theory of production from linear activity analysis.
This synthesized all the previous lines of study — fixed coefficients, circular
flows, smooth production functions. It was the first time that the relations between
resource limitations and the boundedness of the social production possibility set, on the
one hand, and between the convexity of that set and the linearity assumptions about
individual activities, on the other, were set forth clearly. These two results were
crucial in the proofs of existence.
As the conference symbolized, the strands in the development of programming and related
areas crossed the boundary of Cowles, and this pattern persisted in subsequent
developments. Existence of equilibrium was studied by McKenzie outside of Cowles, by
Debreu at Cowles, and by myself who might be regarded at that stage as half in and half
out. If we look at the development of programming, an important step was Philip Wolfe's
solution for quadratic programming, where complementarity theory first appeared. A series
of developments followed with the formulation of the linear complementarity problem by
Dantzig and Richard Cottle and its subsequent use by Carleton Lemke and Richard Howson to
find the equilibrium points of bimatrix games. By a process described in Debreu's paper at
this symposium, this led to Herbert Scarf's fundamental contribution of an algorithm for
finding the general equilibrium of an economy. The existence theorem had been made
genuinely constructive. From then on, the sequence of influences fanned out, both in the
development of new algorithms and into the new field of applied general equilibrium
theory. John Shoven, John Whalley, and more recently Timothy Kehoe and a number of others
have been studying serious practical problems of energy, economic development, taxation,
and so forth in a correct and consistent general equilibrium framework.
Uncertainty and Information
I have concentrated on two of the four main areas of interaction between Cowles and the
general stream of economic thought, the methodology and practice of large econometric
models and programming and general equilibrium analysis. I will cover the remaining two
topics, uncertainty and information, and intertemporal choice, more briefly.
The history of the economics of uncertainty has been rather episodic. There has been
extensive discussion of both foundations and applications. The original paper of Daniel
Bernoulli (1738!) not only advanced the expected utility hypothesis but also discussed the
demand for insurance. His explanation for the purchase of marine insurance, which is
actuarially unfair, was thoroughly modern. It was portfolio diversification; insurance
payments were negatively correlated with shipping gains.
Neither Jevons nor Marshall ever discussed portfolio diversification, though it would
certainly not have been beyond their mathematical powers. Further, both showed awareness
of Bernoulli's paper. The widespread acceptance of ordinalism in the 1930s complicated
matters; it was a little hard to discuss maximizing expected utility when the utility
function itself had no cardinal significance. Jacob Marschak, before he came to Cowles,
made some efforts to construct an ordinal theory of choice under uncertainty. He assumed a
preference ordering in the space of parameters of probability distributionsin the
simplest case, the space of the mean and the variance. He also considered the possibility
that preferences might depend on the skewness (the third moment) of the distribution. From
this formulation to the analysis of portfolio selection in general is the shortest of
steps, but one not taken by Marschak. He derived only a special case of portfolio
selection, the demand for money taken as a certain alternative to risky investment.
Marschak later (1949) explored briefly the implications of an alternative view of
behavior, the maximin theory of Abraham Wald, for the demand for money. The postwar
period, in which this work was done, was one of intensive discussion of foundations for
behavior under uncertainty, an outgrowth of the searches by Jerzy Neyman, Egon S. Pearson,
Wald, and Leonard J. Savage for foundations for the practice of statistics and by John von
Neumann and Oskar Morgenstern for the behavior of individuals in games. To summarize
briefly, there was a phase, initiated by Neyman and Pearson and developed more fully by
Wald, in which a distinction was drawn between those uncertainties that were representable
by probabilities and those that were not. For decision making when probabilities could not
be used to represent uncertainties, Wald's criterion was maximization of the minimum
possible gain.
The work of von Neumann and Morgenstern and later of Savage restored the confidence of
economists in expected utility theory by showing that the theory could be reinterpreted in
ordinalist terms, as reflecting only observed behavior satisfying certain additional
rationality postulates appropriate to choice under uncertainty. Marschak (1950) and
Herstein and Milnor (1953) gave careful expositions that convinced doubters. Inhibitions
about use of the expected utility hypothesis were lifted, and more applied research
encouraged.
In particular, the theory of portfolio diversification emerged. Dickson H. Leavens, a
member of the Cowles Commission staff, who combined research and administrative roles,
used probability theory to demonstrate to a practical audience that diversification, while
it would not improve the mean, could greatly reduce the spread. He did not use a specific
measure of spread but simply exhibited the distributions in an example. (I am indebted to
Harry Markowitz for this reference.)
The modern history of the subject of portfolio theory starts, of course, with Harry
Markowitz's work at Cowles. Markowitz did not, in fact, use an expectedutility
formulation but rather minimized the variance for given mean. This is a problem in
parametric quadratic programming; not only can the problem be formulated, but it is
explicitly solvable. Subsequently, Tobin derived the meanvariance tradeoff as a special
case of expectedutility theory and gave renewed vigor to the derivation of the demand for
money from risk aversion. At that point, the floodgates were down, and the literature
poured forth at Cowles and elsewhere.
Statistical theory can be regarded as an economics of information. The economic aspect,
the tradeoff between accuracy and sampling cost, had been given some stress by more
practical statisticians, particularly Dodge, Romig, Shewhart, and others associated with
the Bell Laboratories, and was made explicit by Wald, especially in connection with the
development of sequential analysis. But it was Marschak's papers of 1954 and 1955 that
made explicit the role of information in economic behavior and organization. Specifically,
he considered the economic problems in the acquisition of information and the role of
transmission of information from one individual to another in a cooperative organization.
It is to these papers that the subsequent explosion in the economics of information, again
both at Cowles and elsewhere, can be traced.
Intertemporal Choice
Finally, I want to consider a field that has developed almost exclusively at Cowles,
which has had little impact, but which I regard as of great importance: intertemporal
choice and the necessity of impatience. Understanding these issues is essential for the
development of a satisfactory capital theory, which concerns why people save and why they
invest. And the motivation of saving and investment is, in turn, a key problem in any
modern economy.
That the rate of return is positive has not only factual but also moral implications,
since the legitimacy of income from capital is at stake. A number of 19th century writers,
such as Nassau Senior, John Stuart Mill, and Alfred Marshall invoked the grounds of
abstinence or waiting to explain the need to reward saving. Jevons followed Bentham in
postulating explicitly that future utilities count less than present ones, but his
discussion of capital does not seem to make use of this insight.
It was Eugen von BöhmBawerk who gave the first systematic account (excessively
systematic) of capital theory. He presented three "grounds" for the existence of
a positive rate of interest. The first is the diminishing marginal utility of income; if
the individual expects to be richer in the future and therefore have a lower marginal
utility of income, a positive rate of interest is needed to induce savings. The second
reason is pure time preference. The third is the positive marginal productivity of
capital, which is of a different logical order than the first two. As was later pointed
out, if the first two reasons did not operate, the third would not operate either, since
capital would be accumulated to the point where its marginal productivity was zero or even
less. It is the first two grounds — the diminishing marginal utility of income and
pure time preference — that relate to preference orders over present and future
goods.
All subsequent discussions ran in these terms. Irving Fisher was, as always, very
clear, but his discussion ran exclusively in terms of twoperiod models. It is clear that
these were regarded as paradigms for models with longer horizons, but he did not squarely
confront the problems that arise when the future is much longer (ideally, infinitely
longer) than the present. Frank Ramsey seems to be the first to have given an explicit
analysis of savings with infinite horizons. But he did not believe in time discounting; he
shared with a number of other English economists the idea that discounting is immoral. In
his model, then, the pure rate of time preference was zero, and utility was separable over
consumption in different time periods. Nevertheless, an optimal path existed.
It is curious that Ramsey's paper on optimal savings and his other economics paper, on
optimal taxation, took so long to influence economic analysis. They appeared in a leading
journal and were very well written. Their mathematics may have been a little advanced for
the day, but even the mathematically sophisticated, such as Harold Hotelling, John R.
Hicks, and the early Paul Samuelson do not seem to have been aware of Ramsey's work. Both
of these papers were suddenly revived in the 1950s. With regard to the one on optimal
savings, Tjalling Koopmans, Christian
von Weizsäcker, and others wrote important papers, in which Ramsey's model was
reinterpreted for a growing economy, where the steady state of zero marginal productivity
of capital was replaced by the golden rule.
These papers on optimal growth did not, however, reexamine the foundations of the
theory of intertemporal choice. That task was undertaken separately by Koopmans and
continued by Koopmans, Diamond, and Williamson. They raised the general question: Suppose
we do not assume additivity over time but instead only posit a general ordering over
consumptions streams that go out to infinity. They imposed a number of specific conditions
on the ordering, particularly a stationarity condition — that the ordering of
programs beginning at any time not depend on the time or upon past consumption — and
a continuity condition. Then, as they showed, there must be impatience in the following
sense: Start with two consumption programs, and find their utility difference. Then
construct two new programs, formed by having the same consumption in the first period and
then each of the two previous programs delayed by one time unit. The utility difference
between the two new programs must be less than the original utility difference. These
papers are, in my judgment, of fundamental importance, but as far as I know they had
essentially no followup until the paper, again written at Cowles, by Brown and Lewis, who
investigated the same issue from a different but related perspective.
One basic issue in all this work is the meaning of continuity in infinitedimensional
spaces. In finitedimensional commodity spaces, the topology is always Euclidean; any
reasonable topology is equivalent to that. In infinitedimensional spaces, there are
different topologies whose plausibility is not so immediately apparent. There is one key
assumption, introduced by Koopmans, that of sensitivity, which specifies that consumption
in anyone period should matter. This property does not hold for the zerodiscount case, in
which, effectively, the longrun average is maximized, and no single decision matters.
Since intertemporal choice with an infinite horizon is most naturally interpreted as
intergenerational choice, using that criterion would permit imposing any sacrifice, no
matter how large, on the initial generation if it would lead to an infinite stream of
returns, no matter how small. Such a criterion for intergenerational choice is neither
moral nor practical.
Hence, if we have both sensitivity and continuity, it must be true that the far distant
future cannot count very much. In different ways, this intuition has been formalized by
Koopmans and associates and by Brown and Lewis. This is a profoundly important point,
recently discussed by some philosophers, especially in the context of disposal of
radioactive waste. One view sometimes expressed is that a harm to someone a thousand years
hence counts equally with a harm imposed today. Though this formulation puts the
nondiscounting view in the most favorable light, I myself believe that the arguments for
discounting just given are equally compelling in this case also.
Concluding Remarks
In the study of the topics I have covered, the first and fourth are the ones in which
Cowles played a unique part; it was, at least for some period, the entire universe in
which discourse took place. One of these topics, large econometric models, has had a
profound effect on both economic analysis and what perhaps may be termed the engineering
side of economics, prediction and policy analysis. Work on the other subject,
intertemporal choice theory, has had relatively little application thus far. For the other
two topics, programming and general equilibrium theory and the economics of uncertainty
and information, Cowles played an important part, but always in twoway interaction with
others in the economics community. The channels of influence are subtle and complex, but,
however it is analyzed, the Cowles contribution is striking and permanent.
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