RATIONAL DECISION-MAKING
AND ECONOMIC BEHAVIOR
19TH ANNUAL REPORT
July 1, 1950 – June 30, 1951
UNIVERSITY OF CHICAGO


The Cowles Commission for Research in Economics has as its purpose the conduct and encouragement of research in economics, finance, commerce, industry, and technology, including problems of the organization of these activities, and of society in general. Its approach is to encourage and extend the use of logical, mathematical, and statistical methods of analysis. It seeks to accomplish its purpose through research and instruction, through publication, and through other programs directed toward increasing the human resources devoted to such research.

The Commission is a not-for-profit corporation, founded in Colorado in 1932 and, since 1939, chartered under the laws of the State of Illinois. Its governing bodies are its faculty, an executive committee, and a board of trustees.

Although it is an independent research organization with members of its staff in other research centers both in the United States and abroad, the Commission is affiliated in academic matters with the University of Chicago as a component of the Division of the Social Sciences. The Commission is also affiliated with the Econometric Society, an international society for the advancement of economic theory in its relation to statistics and mathematics.

THE YEAR IN REVIEW*

*The remarks in the present section of this report provide a short survey of the activities of the Commission. Additional details on many of the topics covered will be found in the remaining sections of the report.

The year of this report is memorable in the life of the Commission because it has seen the publication of five monographs, representing the fruits of research carried on over a period of years. A brief review of these five volumes is a good way to illustrate the problems the Commission studies, the skills it brings to bear on them, the answers it seeks, and the purposes these answers may serve.

Monograph II, Economic Fluctuations in the United States, 1921–1941, was written by Lawrence R. Klein, an economist now associated with the Survey Research Center of the University of Michigan and a research consultant of the Commission. The plan of this study, which was made possible by generous grants from the Rockefeller Foundation, is to reconstruct (from the statistical records of the nation) links in the chain of events that make up business cycles. Consumers spend in accordance with their income and market prices. Incomes are determined by the spending of consumers, manufacturers, and the government. Manufacturers spend in accordance with expected sales and expected profits, which are in turn determined by prices and incomes, etc. Each of these group behavior patterns is expressed by a mathematical equation distilled from the statistics. When all is put together, the explanation one obtains does not run around in a circle, for two reasons. Some items enter only as determining factors, not as being determined: weather, population, discoveries. Also, each link takes time, and carries the explanation back to earlier periods. This year's spending is, through many links, a repercussion of last year's spending, etc. The purpose of studies of this kind is not only to explain past cycles, but also to help form judgments as to how to modify and lessen future cycles.

The methods used in distilling the equations of economic behavior from statistical records are a subject of study in themselves. Such methods are developed in Monograph 10, Statistical Inference in Dynamic Economic Models. This volume had its origin in a research conference held at the Commission in 1945. It contains contributions from many authors, all mathematical statisticians or economists, both on the Commission's staff and from other institutions. Its editor is Tjalling C. Koopmans, now director of research of the Commission.

We move from the sphere of facts and the interpretation of facts to the sphere of values in Monograph 12, Social Choice and Individual Values, by Kenneth J. Arrow, now of Stanford University and a research consultant of the Commission. How will Jack and Jill, John and Jennifer, decide whether to play bridge, canasta, or go bowling if each of them has a different idea as to which of these is his or her first, second, and third choice? If we can find some scheme of calculation which mixes their individual preferences into a social choice, more problems than that of deciding on a satisfactory evening can be solved. The representative system of government is one device constructed to deal with the problem of social choice. Arrow reduces the problem to its barest logical elements. He starts by detailing in what way a method for determining social choices should be responsive to individual preferences. He also requires that, if one of the alternatives that was not at the top of the social preference list turns out to be impossible for some reason, this should not change the alternative that is at the top as long as it remains available. From this he goes on to prove that, if people are too much at cross purposes, you cannot find a common denominator of their wishes. A minimum of agreement in the diversity of individual preferences is necessary to allow the formation of social choices. While this result is not unexpected, the book marks a new departure in the field of politics and social valuation through the manner in which it introduces and utilizes the tools of formal logic. It is one thing to expect a conclusion, and another thing to establish it.

Both valuation, expressed by the desire for efficiency and maximum production, and facts, the innumerable details of technological know-how, enter into the content of Monograph 13, Activity Analysis of Production and Alllocation, edited by Koopmans. Again originating in a conference held at the Commission, this time in June, 1949, its contributing authors include economists, mathematicians, and administrators, from the staff of the Commission, from government agencies, and from various universities. The main theme of the book is how to attain efficiency in the scheduling of production in the widest sense of these words. Wide enough, for instance, to include a theoretical appraisal (and qualified confirmation) of the efficiency of the price system and competitive markets, if these are viewed as means of decentralizing production decisions among as many decision-makers as there are business firms in the country. Wide enough, also, to include the "production" of security by the military establishment, with efficiency to be sought in this case by scientific, centralized programming of the manifold activities of this very large organization. In fact, the interest of the Air Force in this problem provided the support, through a research contract with The RAND Corporation, for the Commission's research in this area, and provided the background as well for several other contributions to this volume. The book deals with theory, applications, new mathematical tools for economists, and computational methods. Applications illustrating the theory include, besides those already mentioned, the choice of a best crop rotation plan, the efficient routing of empty ships or trucks or box cars, and predicting the effects of introducing new methods of production.

Economic Aspects of Atomic Power, an exploratory study directed by Sam H. Schurr and Jacob Marschak, combines facts with hypotheses and theories. We do not know the future trends in the techniques of generating and using energy. But we can set reasonable limits. We can, for example, estimate the lowest conceivable cost for atomic power, and derive a general picture of the scope of economic change which would result, at best, from the use of the new energy source. To explore in this manner a reasonable range of possibilities, one has to use, on the one hand, facts about the supply and cost conditions for nonatomic power throughout the world and facts about the potential demand on the part of important energy-consuming industries (such as aluminum, chlorine and caustic soda, phosphate fertilizers, cement, brick and glass, iron and steel, railroad transportation, and residential heating). On the other hand, one has to employ a theory on how cheap power can affect, in general, industrialized as well as underdeveloped areas of the world. Needless to say, the applicability of any estimates or predictions thus obtained depends on how future history will develop — especially how the production and use of the new energy will be affected by political factors.

The common thread that runs through these five volumes, and through all other investigations of the Commission, is the endeavor to construct abstract models of real situations. Abstraction means expressing and exploring the common elements in many situations while ignoring what is particular and incidental. It has been our experience that abstraction in this sense is powerful and economical, not impractical or remote.

An area in which the Commission is continuing and expanding its research program is decision-making under uncertainty. There is uncertainty about nature and uncertainty about people's actions. We give one example of each: Uncertainty about the weather affects production decisions on the farm. Uncertainty about future sales and prices (the result of other people's actions) enters into business decisions about inventory accumulation or purchases of equipment.

We need to develop an analysis, abstract at first, of efficient production decisions under uncertainty about nature. Only in this way can we see the common elements in such diverse problems as the choice of a crop insurance plan, of a system of flood control, of a policy for industrial research, and hope to arrive at good solutions.

Likewise, we must analyze decision-making under uncertainty about people. To some extent, human action is predictable. Business firms pursue profits and growth, executives pursue careers, workers and employees pursue income and favorable conditions of work, savers seek the returns and preservation of capital. Nevertheless, any one individual's action is taken in some uncertainty about what others may decide to do next. The problem of best organization of a business enterprise, of a government agency, of society as a whole, is a problem in the interplay of incentives and opportunities.

Application of ideas and insights obtained by abstract analysis requires fact-finding about technology and about behavior of people, acting individually or in organizations. Most of these facts are naturally expressed in numbers and in relationships between numbers. Analysis is needed once more to decide which facts to look for, and how to distill general conclusions from the vast mass of facts collected; in short, to make the fact-finding itself efficient.

The Cowles Commission research staff is selected from individuals trained in the application of logical reasoning to theoretical analysis of the interplay of economic motives, to the collection and interpretation of facts and data, and to relationships between numbers; that is, in that order, economists, statisticians, and mathematicians. Among its research consultants it includes a political scientist. The unifying element in the cooperation of this diversity of talents is a devotion to clearly stated logical reasoning that examines particular applications in the light of general principles. The methods of cooperation include informal discussions in small groups, circulation of memoranda for discussion in staff meetings, presentation of results in seminars and at meetings of professional associations. Research fellows from other universities in the United States and abroad, as well as advanced students of the University of Chicago, participate in these activities. The frequency of joint publications of staff members and other scholars testifies to the spirit of teamwork prevalent in the group. Supporting services to the research effort are rendered by an office staff consisting of library, computational, editorial, secretarial, and administrative personnel. The publication of five monographs in one year is the result of a considerable strengthening of the supporting services against a background of a more gradually growing research effort.

The Commission cooperates with various other groups through joint appointments within the University, through appointment of staff members of other institutions as research consultants of the Commission, and through participation in conferences sponsored by organizations such as the Social Science Research Council, The RAND Corporation, the George Washington University, the Office of Naval Research, the Department of the Air Force, and the National Bureau of Standards. Informal contact is maintained with other research groups such as the Agricultural Research Group at the University of Chicago, the Bureau of Business Research of the University of Illinois, the School of Industrial Administration of Carnegie Institute of Technology, and a research project conducted at the University of Michigan and sponsored jointly by the Survey Research Center and the National Bureau of Economic Research. In addition, various members of the Commission render consultative services to the Bureau of the Budget, to the Treasury Department, and to The RAND Corporation.

The Commission is affiliated with the Econometric Society, an international society for the advancement of economic theory in its relation to statistics and mathematics, and its offices serve as headquarters for that organization and for its quarterly journal, Econometrica. The Society has continued its rapid growth and now has approximately 2,435 members and nonmember subscribers, chiefly libraries, representing 73 different countries. Meetings of the Econometric Society were held in Berkeley, California; Cambridge, Massachusetts; Varese, Italy; Tokyo, Japan; and Chicago, Illinois, in 1950, and meetings are currently scheduled for Santa Monica, California; Minneapolis, Minnesota; Louvain, Belgium; Tokyo, Japan; New Delhi and Patna, India; and Boston, Massachusetts, in 1951.

The Commission has continued to benefit from the support and recognition given by the University of Chicago and the Rockefeller Foundation to its general research program, and has carried further its study of the best allocation of resources under its subcontract with The RAND Corporation. Increased support was received during the year from the Commission's founder, Mr. Alfred Cowles, and from members of the Cowles family. Starting in July, 1951, the Commission will also receive support from the Office of Naval Research through a contract to undertake research in the area of decision-making under uncertainty.

These developments have made possible a marked increase in the research effort of the Commission. What is left unresolved is the problem of assuring the long-term support of this effort, a prerequisite for a continuing increase in the scope of the effort at a rate in keeping with its potential usefulness. As a first step in coping with this problem the Commission is strengthening its organizational structure, with increased provision for long-term planning and development. It is recognized that a solution to the problem requires an increase in both human as well as financial resources which can be drawn upon for econometric research, a consideration which will claim the Commission's increased attention in the period ahead.

REPORT ON RESEARCH ACTIVITIES

It was J.R. Hicks, the Oxford economist, who said that the foundations of economic theory were, essentially, nothing but "the logic of choice." Charles Hitch, of The RAND Corporation, expressed this in another way: "Economics is about how to economize." To be economical is to choose the best use of limited opportunities and resources. Let us ask, for example, what we mean by an economical, successful business manager. The firm's own capital and its ability to borrow are limited, and so are its possibilities to determine the prices of its materials and products and to improve upon the known technology of production. A good business manager will make decisions — to borrow and build, buy and hire, produce and sell — which will result in a larger profit than that resulting from choices made by a bad manager. We apply a similar criterion when judging the efficiency of a housewife or a hospital administrator: they can make a good or a bad use of limited money. The concept of "economical" decision-making has an even wider application. Army commanders are trained to choose decisions that are likely to achieve a given objective at the smallest cost in life and materiel, or decisions that are likely to yield, at a given cost, the most desirable result. And is not our concept of an efficient party leader or diplomat similar? Finally, decisions on how to carry out a national policy are also judged by their success in achieving proclaimed goals be they security, prosperity, justice, or freedom, or any combination of these values — within limits set by the skills, habits, and natural resources of the people.

All these cases of "economical" decision-making have the same logical content. In mathematical language, their common problem is to "maximize, subject to given conditions." "Rational behavior" and "optimal behavior" are still other words for economical decision-making. To study how to choose best decisions is to study norms of behavior, not actual behavior. Abstract though such a study may seem in the first stages, its ultimate ambition is to enable people to make reasonable recommendations whenever goals and opportunities are specified. These norms are, of course, suggested by and distilled from actual practice; but they are no less valid if only a small minority of practitioners has applied them in the past. For example, certain methods of inventory control were devised some years ago by Dr. Thorton Fry and Mr. R.H. Wilson, both at that time with the Bell Telephone Laboratories, Inc. These methods, and similar ones described in business literature, exemplify rational behavior since, under certain plausible assumptions, they are likely in the long run to result in a higher profit than other inventory policies. We understand that a small number of leading concerns has, rather recently, accepted these methods and successfully reduced the rate of inventories to sales. Possibly these methods can be adapted to the uses of noncommercial institutions such as schools, hospitals, and governmental depots. In other words, though few people behave rationally, people can learn to behave that way. And this learning process may be in the public interest.

However, for the purposes of the normative studies described, knowledge of the actual behavior of men is equally important, even if that behavior is only imperfectly rational or, indeed, very far from being rational. It is of interest for two reasons. First, because (as we have just seen) actual decision-making is full of suggestions for the study of rational decision-making. Second, because the rational decision-maker has to take into account the possible irrationalities of his fellows. For example, the limited opportunities of a businessman or an army leader are determined by the actual, possibly nonrational habits of his employees, competitors, and clients, or by the prejudices of his enemy and the nerves of his own troops, as much as by the natural laws that underlie technology or weather.

Hence, the interest in people's actual behavior is not motivated only by our scientific curiosity: In order to make rational recommendations on human institutions and policies it is necessary to predict as well as we can people's actual, possibly irrational behavior. Therefore, staff members of the Cowles Commission have followed with great interest the recent attempts at empirical observation, and even experimentation, in the fields of psychology directly relevant to economic decisions and social organization — for example, Thurstone's work on consumers' choices, the experiments of Mosteller on betting and of Bavelas on the effects of "democratic" and "bureaucratic" communication networks, and the social surveys conducted at the University of Michigan. The Commission's own contribution to the study of actual behavior has for the most part consisted in statistical inference from nonexperimental observations on economic time series (prices, production, consumption, investment, etc.), which measure aggregative effects of similar decisions of large numbers of people.

Inasmuch as the tools for the study of actual behavior have been statistical, their thorough revision and adaptation for the particular purposes of the social sciences is necessary. Ideas and principles developed at the Cowles Commission regarding the statistical methods necessary in economic research have been found applicable also in sociology and psychology, essentially because of the difficulty of experimentation in all social sciences.

The Commission's workers on statistical methods have received much inspiration from and have participated in recent discussions on the logic and tools of inductive inference initiated by Jerzy Neyman and developed by the late Abraham Wald into a theory of "decision functions." The empirical investigator is a decision-maker — not less so than the businessman, the housewife, and the commander. The sample, the experiment, the statistical formula must be designed in such a way as to minimize the risk of damage caused by wrong inferences to whoever has asked the statistician's advice. This "economic" approach to statistics, which is reflected in the analogy between, say, choosing the cheapest and most effective way of sampling a city population and the most satisfactory way of operating a factory or of allocating national resources, has proved fruitful of ideas. Naturally, this way of thinking is congenial to economists. It has been decisive in some recent work on the economics of uncertainty pursued at the Cowles Commission as part of its studies on rational and actual behavior. It is also notable that, with both economics and statistics considered as the study of "maximization under given conditions," economists and statisticians are expanding their horizons in their use of mathematical tools.

In reporting on particular problems under research at the Cowles Commission we shall start with (I) normative studies — the studies of rational, or optimal, behavior. Here it will be convenient to begin with (1.a) single person decision problems, typified by certain studies in the economics of business firms, and to follow up with (1.b) multi person decision problems, which arise out of conflicts of interest or imperfect communication (for example, within or between firms) and which lead up to methods for the optimal allocation of society's resources. We shall then proceed to (2) descriptive studies of actual behavior. Finally, we will take into account studies of (3) statistical methods and (4) mathematical tools. Since there is, of course, much overlapping among these fields, the outlined order can be followed only approximately.

1. Rational Behavior

1.a. Single person decision problems. The nature and practical significance of studies in the field of optimal single-person decisions is exemplified by the work on inventory policies, mentioned above. This work was done by Kenneth J. Arrow and Jacob Marschak jointly with Theodore Harris of The RAND Corporation. Although it originated and was discussed at conferences on military logistics, the study has applications in the business field as well. If the firm knows with certainty the weekly demand for its product, it can compute the optimal storage period from the cost of handling an order, the storage cost, and the buying price. If the weekly demand is uncertain but has a known probability distribution and if the firm can set a "penalty" on any given size of unsatisfied demand (and the consequent loss of customers), then it is again possible to compute the best inventory policy, characterized in this case by the stock level at which replenishment orders should be issued and by the stock level after replenishment. If the firm does not know in advance the probability distribution of demand, it is faced with a problem in statistical decision functions, to be discussed below. Unlike the previous studies of the Cowles Commission on the demand for inventories and for cash, the recent one did not consider speculation on changing prices. A combination of the two aspects of inventory decisions would involve a joint probability distribution of future demand and future price. Such an approach would give a fuller understanding of the motivation of inventories and cash balances in a free-enterprise economy. In this connection, Karl Brunner made a critical study of a recent controversy on the logic of monetary economic theories.

A different approach to the problem of inventory control was taken by Herbert A. Simon. Assuming the optimal size of stocks to be known, Simon devised a rule of reaction to any given deviation from optimum. Simon's mathematical model is similar to that of a robot or "servomechanism" — for example, a thermostat that quickly counteracts any undesired change in temperature.

As a concrete example of single-person decision-making under uncertainty, Harry Markowitz chose to study the behavior of open-end investment companies because of their institutional simplicity and the availability of data. If rational, such a company is assumed to act as if it had certain beliefs, based on past experience, concerning the probabilities of returns from each available security. The company would therefore be able to compute, for each possible portfolio, the probability distribution of its total profit. Each such distribution can be characterized by numbers such as the expected, or actuarial, profit level (that is, the average of all possible profit levels, weighted by their respective probabilities), by the unpredictability of profits, as measured by their potential spread around the actuarial level, etc. An "efficient" portfolio is one that has the lowest degree of unpredictability attainable in combination with a given level of actuarial profit. Markowitz attempted to test empirically whether the portfolios actually carried by companies were efficient in this sense (see Actual Behavior).

To prefer a high to a low predictability of profits may be characteristic of investment companies and their clients. But the gambler's "taste" is for the opposite. There is, in fact, a great variety of "tastes" among investors, insurers, and risk-takers in general. Such tastes can be expressed by describing the "utilities" (degrees of satisfaction) assigned by each person to gains and losses of various sizes or to any other outcome of his action. Certain plausible definitions of rational choice imply that the person will maximize the actuarial value of utility (called "moral expectation" by eighteenth-century theorists of probability). By assuming such behavior and by tracing a plausible functional relationship between a person's initial wealth, the wealth increment, and the resulting utility, Markowitz tried to explain various phenomena related to insurance and gambling.

In the inventory and investment studies outlined above, the decision-maker was supposed to act on the basis of probabilities that are either known (for example, from long experience) or believed. Indeed, some students of the logic of probability — for example, Ramsey and de Finetti — think that no rational decision is possible without some knowledge of, or belief about, the probabilities of the alternative "states of nature" that influence the action's outcome.

Yet, many statisticians feel that, in their own practice, they have to choose a "decision function" (i.e., they have to design a sample or an experiment and derive in advance a formula relating action to observation) without any advance knowledge as to the relative probabilities of alternative states of nature. The same is true of many practical situations. In fact, only in exceptional cases (such as life insurance, games of chance, and scientific predictions based on much past experience) does the decision-maker have good information on the relevant probabilities. In the general case, such information is not available; hence moral expectation cannot be computed. Additional criteria become necessary. Thus a pessimist will assume the worst possible state of nature to be true and hence will maximize the lowest possible moral expectation; while, as pointed out by Franco Modigliani, the optimist will maximize the maximum moral expectation. Leonid Hurwicz formulated a certain compromise between the two attitudes. In general, the compromise may be slanted toward optimism or pessimism, the extent of the slant being part of a person's "tastes." Another criterion was suggested by L.J. Savage and, independently, by Jurg Niehans of Zurich: for any given state of nature define as "loss" (or "regret") the difference between the highest moral expectation that could be obtained if that state were known and the moral expectation obtained from a given action; then choose the action for which the highest loss is lower than for any other action.

In a long expository paper, Arrow reviewed the theories on risk and uncertainty of economists, statisticians, probability theorists, and philosophers. Marschak and Roy Radner constructed what is perhaps the simplest possible model for economic action under incomplete information. If you do not know the proportions of black and white balls in an urn and have to pay one nickel for each observation, how many drawings will you observe before you are willing to bet on the color of the next ball? How high will your bets be? The model helps to bring into relief some essential properties of what is loosely called "taking calculated risks." Decision-making is studied under the condition — so frequent in social and economic life — that the relevant probabilities are unknown and that the experience is enlarged in the course of the action itself, thus leading to a continual change in plans of action. The implications of the model show important weaknesses of the various criteria of choice suggested so far.

The following papers bear upon the problem of optimal single-person decisions. Some of them were published or presented in public meetings, including open academic lectures or seminars. (An asterisk indicates such papers by staff members, and additional information can be found in Appendix I.) Others were discussed in Cowles Commission staff meetings, usually on the basis of a previously circulated hectographed document. Papers appear below in the same order in which the problems are described in the text. The list does not include some of the more technical papers on statistical decision functions, which will be mentioned in the section on statistical methods:

Optimal Inventory Policy: Arrow, Harris (RAND Corporation), and Marschak
Inconsistency and Indeterminacy in Classical Economics: Brunner
An Exploration into the Use of Servomechanism Theory in the Study of Production Control: Simon
Investment Company Behavior Equations: Markowitz
A Note on Markowitz' Theory of Investment Companies: Marschak
On The Certainty Equivalence and Risk-Discount Hypotheses: Markowitz
The Utility of Wealth: Markowitz
Why "Should" Statisticians and Businessmen Maximize "Moral Expectation": Marschak
Note on "Measurable Utility": Marschak
A Simplification of the Axiomatics of Measurable Utility: Marschak
A New Theory of Probability: Degree of Confirmation and Inductive Inference: Rudolf Carnap, Department of Philosophy, University of Chicago
De Finetti's Theory of Subjective Probability with Reference to the Statistical Decision Problem: Leonard J. Savage, Committee on Statistics, University of Chicago
Recent Discussions on Utility and Probability, and the Late Frank Ramsey: Marschak
Probability in the Social Sciences: Marschak
Seminar on the Economics of Uncertainty: Marschak Rational Selection of Decision Functions: Herman Chernoff, Department of Mathematics, University of Illinois
A Class of Criteria for Decision-Making under Ignorance: Hurwicz
The Generalized Bayes-Minimax Principle: A Criterion for Decision-Making under Uncertainty: Hurwitz
Alternative Approaches to the Theory of Choice in Risk-Taking Situations: Arrow
Alternative Criteria for Economic Action under Ignorance: Marschak and Radner

1.b. Multi person decision problems. If all persons in a group have identical goals and possess identical information, the team can be treated, for the purposes of the theory of decision-making, as a single person. But diversity of interests and imperfect communication create the specifically social problem: the problem of measuring group welfare, of predicting the outcome of conflict and cooperation, and of choosing the best organizational structure. In its general form the problem is this: how to let "utility maximizing" individuals choose decisions that jointly produce the best result from the point of view of the organization as a whole. This problem exists for a large corporation in relation to its managing officers as well as to its labor force; it exists for the government in relation to its subordinate agencies. In a wider sense, the same problem exists between the government and private consumers and producers. To determine the best economic organization in this wider sense is to study the central problem of our time: the advantages and limitations of free competition and the most desirable forms and limits of governmental activity. Thus, the problems that are, in most American universities, artificially split between schools of business administration, schools of public administration, departments of political science, and departments of economics, turn out to be special applications of the same general problem, that of optimal organization.

Is it possible to rank the community's preferences, to draw its list of "priorities" on the basis of conflicting desires of individual citizens? The degrees of satisfaction of various individuals are not comparable. Benthain's "greatest happiness of the greatest number" hardly stands a logical scrutiny. Arrow's book, Social Choice and Individual Values (Cowles Commission Monograph 12), deals with these problems, and Clifford Hildreth, Markowitz, and Leo A. Goodman studied conditions which may make it possible to compute a meaningful "social welfare index."

Gerard Debreu defined a measure of inefficiency of an economic system. This measure is the maximum saving of primary resources which could be made within the existing technology without preventing any consumer from enjoying his current level of satisfaction. With the help of this measure we can assess the effect of a given technological change upon the production potential or evaluate the economic loss resulting from a given system of taxes and subsidies.

Debreu's index of inefficiency of an economic system, or its complement, the index of resource utilization, is an offshoot of his more general work on efficiency. An economic system is said to be efficient if limited resources and technical knowledge are used in such a way that no consumer's satisfaction can be further increased without hurting some fellow consumer. If production decisions are made not by a central authority but by individual firms, it can be proved that there exists a set of "efficiency prices" with the following property: if every firm chooses its inputs and outputs so as to maximize its profit computed on the basis of those prices, then the system is efficient in the sense defined above. (Edmond Malinvaud extended the concept of efficiency prices to interest rates.) Efficiency prices may be identical with those arrived at under free competition between firms. But one could also think of applying the principle to the case in which the "firms" are agencies of the government — for example, branches or units of the armed forces. Decisions on production are thus decentralized and use the initiative and knowledge of local or specialized people who strive to maximize the "efficiency profits" of the agencies in their charge, computed on the basis of "efficiency prices"; the central body is left to decide only on "prices" — that is, on the relative importance of various objectives and sacrifices.

The principle of efficiency prices as a guide for decentralized policy-making in the interest of the community goes back to earlier studies, by Tjalling C. Koopmans and others. Those studies excluded from consideration the conflict of individual interests and defined as efficient an allocation of resources under which the output of a good cannot be increased further without decreasing the output of some other good. The organizational device of decentralizing decisions through efficiency prices is assumed here also. With the specific difficulty of the diversity of individual interests removed, it is in principle a simple matter to test the efficiency of an economic decision, whether it is made by one person or decentralized among many. The volume on Activity Analysis of Production and Allocation (Cowles Commission Monograph 13) was written in this spirit. In 1950–1951 conditions for efficiency were studied in a few concrete fields, mainly those related to location and transportation. George H. Borts continued his statistical study of the production technology of railroads. His preliminary results indicated constant or increasing returns to scale for the production of line-haul services, and constant or slightly decreasing returns to scale for the production of switching services. Kirk Fox and Koopmans began to collect and study data on the movement patterns for empty railroad cars. Martin J. Beckmann used hydrodynamic theorems to discuss the optimal transport flows through a closed region with a given geographic distribution of demand and supply conditions for each commodity. Koopmans studied also the efficiency aspects of dispersal of population and industry.

It takes time to make and carry out a decision. This fact is neglected in the simple, "static" model of decentralized decision-making discussed so far. Arrow and Hurwicz made a step toward greater realism. Both the organization leader who determines efficiency prices and the subordinate who determines the in- and outputs for his agency proceed by alternate steps: each reacts to the preceding move of the other. Optimal rules of action are rules that make for the quickest convergence to the optimal use of the organization's resources. The problem reduces to the mathematical one of finding the fastest iterative method for a computation. Exploratory computations were made by James G.C. Templeton.

Another realistic step was made by Simon, who introduced into organization theory the important element of uncertainty. He pointed out, for example, that the difference between a news publisher's contract with a salaried staff member and one with a free-lance contributor lies in the greater predictability of services obtained in the former case. This difference may be reflected in the relative prices of the two kinds of services.

A Difficulty in the Concept of Social Welfare: Arrow Derivation of Social Welfare Functions from Individual Utility Functions: Hildreth
Social Welfare Functions Based on Rankings: Leo J. Goodman, Department of Sociology, University of Chicago, and Markowitz The Coefficient of Resource Utilization: Debreu
Effect of Technological Change on Production Potential:* Debreu Efficiency Prices as Guides for Decentralized Decisions: Debreu The Mathematics of Welfare Economics: An Introduction:* Hurwicz
Resource Allocation and Statistical Decision Functions: Debreu An Extension of the Basic Theorems of Classical Welfare Economics: Arrow
Recent Developments in the Theory of Production: Koopmans Generalizations of Leontief's Input–Output Model:* Koopmans A Continuous Transportation Model: Beckmann
Efficiency Aspects of Dispersal of Population and Industry: Koopmans
A Gradient Method for the Lagrangian Problem: Arrow, Hurwicz, Templeton
Theory of Economic Organization: Hurwicz
A Formal Theory of the Employment Relationship: Simon A Comparison of Organization Theories: Simon
The Bargaining Problem: John F. Nash, Princeton University Theory of Cooperative and Noncooperative Games: Nash
On Some Problems in Logistics: C.B. Tompkins, George Washington University
Organization Theory in Miniature: A. Newell, RAND Corporation, and J. Kruskal, Logistics Project of the Office of Naval Research, George Washington University

2. Actual Behavior

Some of the descriptive work done during the report period is directly related to models of optimal behavior. It aims at establishing some concrete, possibly numerical, properties of the model, and measuring its deviation from reality. The work on railroad transport by Borts and by Fox and Koopmans, mentioned above, is along these lines. Markowitz' discussion of the utility function of wealth, also mentioned above, is of the same type, although it has not so far involved any statistical study. However, Markowitz' model for the optimal portfolios of investment is being submitted to elaborate statistical measurements. Taking into account a few of the more important variables usually recognized in security analysis, Markowitz derives the "belief formation equations" assumed to be used by a company in estimating the probability distribution of future returns from various securities. On this basis the set of efficient portfolios is constructed and compared with actual portfolios.

The study on expectations and business fluctuations, conducted by Modigliani at the University of Illinois, is not related to the Cowles Commission formally, but the subject matter indicates a strong mutual interest, fostered by visits and discussions. Modigliani's group is interested in the formation of expectations in industry, and has completed the analysis of the quarterly shippers' forecasts of carload requirements. As part of this project Jean Bronfenbrenner and A. Kisselgoff studied the formation and realization of capital outlay plans.

In cooperation with the Agricultural Economics Research Group of the University of Chicago and the Bureau of Agricultural Economics of the U.S. Department of Agriculture, Hildreth is conducting a study of supply and demand for live-stock products in the United States. A model has been developed to explain annual fluctuations in the amounts of all livestock products (treated as a group) produced and consumed in the United States, in the price of livestock products, and in selected economic variables. Available time series for the period 1920–1949 are being processed to obtain measurements of variables that most nearly correspond to those appearing in the model. When these are obtained, a statistical analysis of the model will be undertaken. This will include estimation of equations by alternative methods and a comparison of the results. Frank Jarrett, research associate in economics, University of Chicago, is participating in the study.

The following list, which includes contributions by guests, gives an account of work on actual behavior not listed previously in this report:

Statistical Problems and Computational Programs Suggested by the Theory of Investment Behavior: Markowitz
Interim Report of Progress of Project on Expectations and Business Fluctuations: Modigliani
Discrepancies between Actual and Anticipated Plant and Equipment for Individual Firms: Jean Bronfenbrenner
A Model of Farm Production: Hildreth
A Tentative Model of the Livestock Economy: Jarrett and Hildreth
A Report on a Two Week Visit at the Chrysler Corporation: Christ A Statistical Analysis of the Demand for Liquor in Sweden: Sten Malmquist, Uppsala, Sweden
A Measurement of Money Utility and of Functional Values of the Cost of Living Index: Isamu Yamada, Hitotsubashi University, Tokyo, Japan

3. Statistical Methods

Work was continued on Cowles Commission Monograph 14, Econometric Methods, a statement of earlier and new work on the statistical measurement of economic relationships, with emphasis on exposition. We shall mention here only contributions to this volume not described in the Commission's Report for 1949–1950. In an introductory article Marschak discusses economic measurements for policy and prediction by elaborating in detail the program outlined in "Economic Structure, Path, Policy, and Prediction," in the Commission's Five-Year Report for 1942–1946.

Simon extended the distinction between endogenous and exogenous variables into a discussion of causal ordering of variables connected by a system of relationships. In this (partial) ordering a variable lower in the hierarchy is affected by, but does not itself affect, a variable placed higher up. He then noticed and analyzed connections between the analysis of a causal hierarchy and criteria for identifiability of the relationships explaining the formation of these variables. It is worth noting that the study was inspired by Simon's interest in servomechanisms, mentioned earlier.

Hurwicz discussed both model construction and the choice of a method of estimation as a problem in decision-making under uncertainty, balancing the effects of specification errors on the usefulness of the model against the complications arising from too detailed or refined models.

Herman Chernoff and Nathan J. Divinsky completed a detailed expository description of computational procedures followed in maximum-likelihood estimation of systems of behavior equations and of subsystems or single equations thereof.

Many gaps in the statistical theory of structural equation systems are still to be filled. T.W. Anderson completed his study of exact confidence regions for coefficients of a certain type of incomplete set of linear structural equations. A similar problem was attacked by Gurland for the case, called "dynamic" by economists, in which lagged dependent variables appear. An econometric problem induced Gurland to study also the distribution of ratios of quadratic forms; this may lead to applications in other fields as well. Anderson continued his joint study with Hurwicz on models involving disturbances in equations as well as errors in observations. Hildreth revived an earlier suggestion of Wald's to base estimates on means of subsets of observations, and studied its application to models involving disturbances. He also discussed the application of statistical decision functions to the estimation of economic structure. Arnold C. Harberger examined the effect of empirical or a priori limits to the variance of disturbances upon the bias of the least-squares method; this attempt is motivated by the relative cheapness of the latter method.

It is notable how statistical problems studied in connection with the measurement of economic structure have also arisen in other fields. Koopmans applied the concept of identifiability to the "latent structures" postulated by Paul Lazarsfeld, of Columbia University, to analyze and explain responses to public opinion surveys. Anderson developed models for the analysis of data reflecting changes in responses by a panel of respondents to repeated surveys.

Economists often face the peculiar statistical problem of aggregating or summarizing numerous data into a few index numbers, such as price level and total output. Debreu's coefficient of resource utilization may prove, for certain problems, more useful than some conventional aggregates such as the gross national product. In fact, as in other statistical methods, the choice of the best method of aggregation depends on its relative cost and usefulness. A set of items (prices, for example) can be partitioned into mutually exclusive subsets in a variety of ways, with a certain operation to be performed subsequently on each subset. The problem of finding, for a given cost, the most useful partition and operation is a problem in decision-making. This point of view was taken by Hurwicz, who treated the general case of uncertainty, and by Marschak, who used the inventory problem as an illustration for the case of certainty.

The following list excludes those contributions to Monograph 14:

Some Specification Problems and Applications to Econometric Problems: Hurwicz
"Possibilities" and Statistical Analysis: Hildreth
Some Remarks on Admissible Minimax Solutions of Statistical Decision Problems: Sverdrup
Bayes and Minimax Interpretations of the Maximum-Likelihood Estimation Criterion: Hurwicz
Distribution of Ratios of Quadratic Forms: Gurland
A Reconsideration of Least-Squares and Simultaneous-Equations Estimates: Harberger
Probability Models for Analyzing Time Changes in Attitudes: Anderson
Identification Problems in Latent Structure Analysis: Koopmans Introduction to Econometrics (Course Lectures): Hildreth
Statistical Problems of Model Construction (Course Lectures): Koopmans
Testing Linear Hypotheses (Course Lectures):* Gurland Theory of Statistical Estimation (Course Lectures): Gurland
The Causal Principle and the Identification Problem: Simon Aggregation as a Problem in Decision-Making under Ignorance or Uncertainty: Hurwicz
Aggregation Problems Exemplified in Optimal Inventory Policy: Marschak

4. Mathematical Tools

As mentioned in the previous report, a process of widening the horizons of economists in regard to mathematical tools used in their theories can be observed. In particular, the work on resource allocation has led away from differential calculus, called "marginal analysis" by economists and appropriated from mechanics and physics, toward the methods of point set theory, which are more abstract, more general, logically simpler, and better adapted too many problems of social science. Convex point sets have been particularly useful in expressing a more general form of the traditional assumption of increasing marginal rates of substitution in consumption, and in expressing the simplifying assumptions of constant returns to scale and additivity of production processes. More general point sets need to be studied in order to revise these assumptions to obtain greater realism. The abandonment of differentiability assumptions permits inclusion, in the analysis, of limits to physical resources or plant capacities and other technical indivisibilities, as well as consumption patterns in which the price-and-income situation induces some consumers to exclude some commodities altogether from their consumption.

Morton L. Slater studied the mathematical content of the problem of economic choice, that is, the problem of maximization under constraint. He provided mathematical advice and criticism with regard to the work of many staff members and provided expository presentations of mathematical results to economists. Visiting mathematicians addressed the staff on problems of maximization under linear inequalities. John Chipman, Debreu, and Slater explored mathematical theorems providing criteria of stability in models of international, interregional, or interindustrial economics. Templeton gave direction to the computing staff of the Commission.

Lagrange Multipliers Revisited: Slater
A Note on Motzkin's Transposition Theorem: Slater
Optimization under Constraints: A Central Economic Problem
and the Mathematical Tools for Its Solution: Slater
Mathematical Methods in the Study of Efficiency in Production: Slater
Convex Cones and the Economic Theory of Production: Koopmans
Solutions of Linear Inequalities: Theodore S. Motzkin, National Bureau of Standards at Los Angeles
Some Problems in Linear Programming: E. Barankin, University of California, Berkeley
Admissible Points of Convex Sets: Arrow and D. Blackwell, Stanford University
The Stability of Systems with Nonnegative Coefficients: Chipman
Characteristic Roots of Nonnegative Matrices: Debreu
A Theorem on Characteristic Roots: Slater

STAFF MEETINGS AND SEMINARS

The Cowles Commission has developed its research procedures with a view to benefiting from the cooperative efforts of research workers with a variety of backgrounds and training: economists who specialize either in theory, the analysis of policies, or empirical work; statisticians; mathematicians; and (among research consultants) one who specializes in political science and administrative behavior. An essential feature of this cooperation is the informal discussion which takes place among staff members at various stages of the research. Staff meetings are scheduled when an individual's research reaches a point at which criticism by the group as a whole would prove of particular value. Research memoranda are circulated in advance of such meetings to economize on the time required for presentation and to facilitate constructive criticism and appraisal of the work. At such staff meetings the resident staff is often joined by research consultants of the Commission and by advanced students and research fellows from the University of Chicago and other American or foreign academic centers. There were 42 such staff meetings held at the Cowles Commission during the period of the present report.

Of a more expository and somewhat less technical nature are the seminars which the Cowles Commission conducts throughout the year devoted to varying topics within the broad area of quantitative method. Papers are presented by research workers from this and other centers of learning and are followed by critical discussions of the material by seminar participants. The seminars have proved to be of particular value in suggesting new associations of ideas and in developing a more receptive attitude toward quantitative techniques. To facilitate this, invitations to seminars are extended to research personnel in a wide variety of fields as well as to the public and to interested graduate students.

It was possible to arrange most of the seminar sessions of the 1950–1951 period into two sequences:"Utility and Probability" (papers by Carnap, Savage, Marschak, Arrow, Chernoff, van Dantzig, and Thurstone) and "Economics of Welfare" (papers by Hurwicz, Koopmans, Slater, Debreu, and Hildreth). During the period covered by this report the following Cowles Commission seminars were held:

1950  
October 12 JOHN F. NASH, Princeton University, "The Extended Bargaining Problem"
October 26 RUDOLPH CARNAP, Department of Philosophy, University of Chicago, "A New Theory of Probability: Degree of Confirmation and Inductive Inference"
November 9 LEONARD J. SAVAGE, Committee on Statistics, University of Chicago, "De Finetti's Theory of Subjective Probability with Reference to the Statistical Decision Problem"
November 16 LLOYD A. METZLER, Department of Economics, University of Chicago, "The Pigou Effect and the Rate of Interest"
November 30 JACOB MARSCHAK, "Recent Discussions on Utility and Probability, and the Late Frank Ramsey"
December 21 KENNETH J. ARROW, "Alternative Approaches to the Theory of Choice in Risk-Taking Situations"
1951  
January 11 HAROLD T. DAVIS, "Some Implications of the Curve of Income Distribution"
January 25 HERMAN CHERNOFF, Department of Mathematics, University of Illinois, "Rational Selection of Decision Functions"
February 1 D. VAN DANTZIG, Department of Mathematics, University of Amsterdam, "On the Linking up of Probability Theory to Empirical Sciences"
February 15 LOUIS L. THURSTONE, Department of Psychology, University of Chicago, "Consumer Preferences and the Prediction of Choices"
March 1 LEONID HURWICZ, "The Mathematics of Welfare Economics: An Introduction"
March 15 T.C. KOOPMANS, "Generalizations of Leontief's Input–Output Model"
March 29 LEONID HURWICZ, "Optimization Rules in a Decentralized Economy"
April 12 MORTON L. SLATER, "Optimization under Constraints: A Central Economic Problem and the Mathematical Tools for Its Solution"
April 26 LOUIS GUTTMAN, Israel Institute of Applied Social Research, "Qualitative Data and the Theory of Scaling" (Jointly with Committee on Statistics, University of Chicago)
May 3 GERARD DEBREU, "The Efficiency of an Economic System"
May 10 CLIFFORD HILDRETH, "Derivation of Social Welfare Functions from Individual Utility Functions"
May 24 JOHN CHIPMAN, University of Chicago, "Oscillations in a Multi-Sector Economy"
June 12 M.G. KENDALL, London School of Economics, "Testing Significance in Cases Where There Is Autocorrelation in Residuals of a Time Series"

COOPERATION WITH OTHER GROUPS

The Cowles Commission and its staff members have continued to cooperate in various ways with other parts of the University of Chicago and other institutions in research of common interest.

In view of the interdisciplinary nature of the Commission's interests, close ties with other departments within the University are important for the success of its work. The Commission has several joint appointments with the Department of Economics (Hildreth, Koopmans, Marschak). It also has joint appointments with the Committee on Statistics (Gurland), with the Agricultural Economics Research Group (Hildreth), and with the Department of Mathematics (Herstein). The research results and experience of the Commission have been and are being utilized by the Agricultural Economics Group, in particular in a study conference on efficiency held in the summer of 1950. They also play an important role in the study of supply and demand for livestock products in the United States which Hildreth is conducting for the Agricultural Economics Group with the cooperation of the Bureau of Agricultural Economics of the U.S. Department of Agriculture.

Informal contact has been continued with various centers of empirical work. Through Modigliani the Commission remains in touch with the study on expectations and business fluctuations conducted at the Bureau of Business Research of the University of Illinois. Through Klein and others the Commission similarly maintains contact with the collection and analysis of survey data on consumer behavior conducted at the University of Michigan under the auspices of the Survey Research Center and the National Bureau of Economic Research. Further insight into problems of empirical research has been gained through the continued consultative activities of Hildreth with agricultural research workers in other institutions.

A number of research conferences during the year were the occasion of particularly fruitful cooperation between the Commission and other groups. Several staff members (Arrow, Hurwicz, Koopmans, Marschak, Slater) took part in a conference on logistics at The RAND Corporation in Santa Monica, California, in the summer of 1950. Marschak participated in a second conference on logistics held in Washington, DC, in January, 1951, under the joint auspices of The George Washington University and the Logistics Branch of the Office of Naval Research. In April the Social Science Research Council sponsored a conference in Princeton on the measurement of technological change. Debreu, Hurwicz, and Koopmans took part in that conference, as well as in a symposium on linear inequalities and programming held in Washington, DC, in June. The latter conference was organized jointly by the Department of the Air Force and the National Bureau of Standards. Integration of the research being undertaken at the Cowles Commission with that of Carnegie Institute of Technology in their Air Force project on intra-firm behavior and their Controllership Foundation project on decentralization of accounting organization was the subject of another June conference. This was held at Pittsburgh and was attended by Hurwicz, Koopmans, Marschak, and Simpson, and by Simon and other members of the Carnegie staff.

Certain staff members (Anderson, Arrow, Marschak) served as consultants to The RAND Corporation during the year in addition to Hurwicz and Simon who, as consultants of the Commission, are engaged in research being undertaken by the Commission under contract with The RAND Corporation. Hurwicz provided consultative services to the U.S. Bureau of the Budget on problems connected with inter-industry studies. Hildreth was a consultant to the Office of the Technical Staff of the U.S. Treasury on estimating the effects of excise taxes on demand, supply, and revenue.

Links are established with various institutions through members of their staffs acting as research consultants of the Cowles Commission. The number in this category increased during the year and now includes Carnegie Institute of Technology, Columbia University and its Bureau of Applied Social Research, The Johns Hopkins University, Northwestern University, Stanford University, the University of Illinois, the University of Michigan and its Survey Research Center, the University of Oslo, and the University of Toronto.

PAPERS AND MONOGRAPHS

The results of research by members of the Commission's staff are published in two series, Cowles Commission Papers and Cowles Commission Monographs, as well as in occasional separate form.

The policy was adopted at the end of 1943 of having reprints of papers by members of the Commission's research staff bound in special covers as Cowles Commission Papers, New Series (for econometric research), and Cowles Commission Special Papers. A list of these papers is given in Appendix III. Two papers (Nos. 36 and 39) were issued during the period covered by this report. Nos. 32, 33, and 34 are in preparation and will be issued in the latter part of 1951, along with ten papers to be published shortly after the period of this report. A limited supply is available of those papers which are marked by an asterisk, and copies will be furnished to individuals who request particular items.

A complete list of the monographs published by the Cowles Commission is included in Appendix IV. Published at the beginning of the report period were Monograph 10, Statistical Inference in Dynamic Economic Models, edited by Tjalling C. Koopmans; Monograph 11, Economic Fluctuations in the United States, 1921–1941, by Lawrence R. Klein; and an unnumbered monograph, Economic Aspects of Atomic Power, by Sam H. Schurr, Jacob Marschak, et al. During the latter part of the report period two further monographs were published: Monograph 12, Social Choice and Individual Values, by Kenneth J. Arrow, and Monograph 13, Activity Analysis of Production and Allocation, edited by Tjalling C. Koopmans.

Two monographs are in manuscript stage: Monograph 14, Econometric Methods, edited by Hood and Koopmans, a less technical presentation of some of the contents of Monograph 10, together with results of further research in methods; and a monograph on introductory econometrics being prepared by Marschak and Christ on the basis of a lecture series presented earlier. The latter monograph will be of interest to a broader readership than the other, recently published monographs.

RELATED TEACHING

The University of Chicago offers a wide variety of courses in econometrics, mathematical economics, economic theory, and statistics. Staff members of the Cowles Commission participate in the teaching activities of the University, especially in these fields. The courses offered by the Department of Economics or by the Committee on Statistics (not all given every year) that are particularly relevant to the area of interest of the Commission are listed in Appendix II.

STAFF NEWS

The current period has again been one of considerable research activity, travel, and publication for members of the Commission's staff. Some indication of these activities has been given in the section on cooperation with other groups and by the lists of papers cited in the text of the report on research. Information about papers and lectures published or presented outside of staff meetings during the period is given in Appendix I. Other items of staff news are given in the present section, which brings up to date the biographical sketches of staff members in earlier reports of the Cowles Commission.

The terms "research associate" and "research assistant" are used to denote staff members who are resident and devote part or all of their time to the research work of the Cowles Commission. The term "research consultant" is used to designate staff members who are generally nonresident and cooperate in the work of the Commission by participating in staff meetings, by correspondence, or in other ways. Only active members are retained on the list of the staff of the Commission.

Gerard Debreu continued as a research associate of the Commission throughout the period in connection with the study of the theory of resource allocation conducted for The RAND Corporation. In June, 1951, he was appointed assistant professor in the Cowles Commission.

Nathan J. Divinsky left the Commission in July, 1950, to become assistant professor of mathematics at Ripon College, and was succeeded by James G.C. Templeton as supervisor of the computational work of the Commission. Templeton obtained his B.A. in applied mathematics at the University of Toronto in 1947 and his A.M. in mathematics at Princeton University in 1949. Prior to joining the Cowles Commission as a research associate he spent three years at Princeton University as a graduate student in mathematical physics and mathematical statistics and as an assistant in instruction and research. In the summer of 1949 he attended the Institute for Numerical Analysis at Los Angeles.

John Gurland continued under his joint appointment as assistant professor in the Cowles Commission and assistant professor of statistics in the Committee on Statistics.

Clifford Hildreth, associate professor in the Cowles Commission and research associate (associate professor) in the Department of Economics, carried forward his research for the Commission, presented an introductory course in econometrics, and directed the study of livestock products mentioned earlier. In addition, Hildreth served as chairman of the program committee for the meeting of the Econometric Society in Chicago in December, 1950. In June of this year he consulted with the Treasury Department on estimating effects of excise taxes.

William C. Hood, a consultant to the Commission, returned for a short period as research associate. He took leave from his position as assistant professor at the University of Toronto to spend May and June of 1951 in Chicago in connection with the writing and co-editing (with Koopmans) of Monograph 14. At Toronto he taught mathematical economics in the Department of Economics, presented a course in statistical analysis in the Institute of Business Administration, and participated in a Mathematics Department seminar on the theory of games.

Leonid Hurwicz joined the Commission on a full-time basis in October, 1950, as research associate and visiting professor and remained through January, 1951. He provided the research leadership for the project on the theory of resources allocation during Koopmans' absence, and temporarily assumed Koopmans' teaching duties in the Department of Economics of the University of Chicago. He is now research professor of economics and mathematical statistics at the University of Illinois but, effective in September, he will become professor of economics and mathematics in the School of Business Administration at the University of Minnesota. He continues his association with the Cowles Commission as a research consultant.

Of major interest was the visit of the director of research, Tjalling C. Koopmans, to leading European centers of research and instruction in econometrics, from August, 1950, to January, 1951. This trip was made possible by a grant from the Rockefeller Foundation to the University of Chicago, and occurred during Koopmans' tenure as president of the Econometric Society. The contacts made can be judged from the groups sponsoring his various lectures (see Appendix I). Upon returning from Europe, Koopmans again engaged in teaching at the University of Chicago, where he is professor of economics, and in co-editing and writing for Cowles Commission Monograph 14, described elsewhere in this report. He served as a member of the Social Science Research Council committee on the social implications of atomic energy and technological change. He is a member of the Council of the Econometric Society for 1951, and participated in arranging the program for the Minneapolis meeting of the Society. Also during the year he was appointed correspondent member of the Royal Dutch Academy of Sciences in Amsterdam.

Harry Markowitz continued as a research fellow of the Cowles Commission and as a fellow of the Social Science Research Council.

Jacob Marschak, who is a research associate of the Commission and professor of economics at the University of Chicago, took part in various outside activities during the period. He cooperates in the editing of the Journal of Political Economy, is a member of the editorial board of the Journal of Human Relations, and, starting in 1951, has been a member of the board of editors of Metroeconomica. Marschak served on the program committee for the Harvard meeting of the Econometric Society in September, 1950. Together with Hurwicz he represented the Econometric Society on the intersociety committee on the mathematical training of social scientists. He is a consultant for The RAND Corporation.

William B. Simpson, the assistant director of research of the Commission, served as acting research director during Koopmans' absence. He was appointed executive director of the Commission as of July 1, 1951. He was re-elected secretary of the Econometric Society by the Council of the Society. He continued as managing editor of Econometrica, and in June, 1951, was designated co-editor of that journal. An account of the work of the Econometric Society during the period is given in a later section of this report.

Morton L. Slater was actively engaged in mathematical research on the study of resource allocation as a research associate of the Cowles Commission (with the rank of assistant professor).

Erling Sverdrup, a fellow of the Rockefeller Foundation and a research fellow of the Cowles Commission, continued his association with the group through November, 1950. He has since been acting professor of actuarial mathematics and mathematical statistics at the University of Oslo, Norway.

Several changes occurred among research assistants of the Cowles Commission. Gerhard Stoltz completed his work as a research assistant on the resources allocation study in the summer of 1950, moved to Stanford University, and has now returned to the University of Oslo, Norway. Kirk Fox was appointed research assistant in November, 1950, and Roy Radner in March, 1951. Fox was in the United States Navy submarine service from 1943 to 1946, after which he attended the University of Chicago, where he received a B.S. in mathematics in June, 1948. Just before joining the Commission, Fox held the position of economic research assistant at the Northern Trust Company Bank of Chicago. He will be engaged in the application of linear programming techniques to the transportation industry, as well as in the performance of various administrative and editorial duties for the Commission. Concurrently he is teaching introductory and intermediate statistics at the Northwestern University School of Commerce. Radner studied at the University of Chicago from 1944 to 1945 under a William Cook scholarship, receiving his Ph.B. with honors. After three years with the army he returned to the University and undertook graduate work in mathematics, obtaining an M.S. degree in 1951. He continues his preparation in statistics concurrently with his work for the Commission.

The research consultant staff was increased during the year by the addition of Carl Christ in September, 1950, Stephen G. Allen in December, and Lawrence R. Klein in May. Christ was with the Commission as a research associate and as a fellow of the Social Science Research Council until mid-September, at which time he became an assistant professor of political economy at the Johns Hopkins University. He is currently collaborating with Marschak on the preparation of a Cowles Commission monograph on introductory econometrics. Allen and Klein were both members of the Commission's research staff in previous periods. Allen is currently a research associate of the Applied Mathematics and Statistics Laboratory at Stanford University. Klein is on the staff of the Survey Research Center at the University of Michigan and is a research associate of the National Bureau of Economic Research.

Various research consultants of the Cowles Commission, in addition to those mentioned above, were active during the year. T.W. Anderson, who is associate professor of mathematical statistics at Columbia University, continued his teaching and acted as executive officer for the Department of Mathematical Statistics at Columbia from November, 1950. He was appointed to the Board of Governors of the Bureau of Applied Social Research of Columbia University. He was elected a fellow of the Econometric Society in 1950. Anderson continued as editor of the Annals of Mathematical Statistics and was a member of the Executive Committee and Council of the Institute of Mathematical Statistics, and of a number of committees. He served as a representative of the Institute on the committee on mathematical training of social scientists. He is a consultant to The RAND Corporation.

Kenneth J. Arrow, a research consultant both to the Cowles Commission and to The RAND Corporation, is associate professor of economics and statistics at Stanford University. He was program chairman for the Berkeley meeting of the Econometric Society in 1950 and currently is on the program committee for the meeting in Santa Monica.

Harold T. Davis, professor of mathematics at Northwestern University, continued as chairman of the department at that institution. He is an associate editor of Econometrica and was a member of the program committee for the Chicago meeting of the Econometric Society.

Trygve Haavelmo is professor of economics at the University of Oslo, where he presented courses in econometric methods, statistics, and economic theory during the year. He is a consultant to the University Institute of Economics, Oslo, as well as to the Cowles Commission.

Franco Modigliani continued to devote the major portion of his time to the study on expectations and business fluctuations, of which he is director, at the University of Illinois. He is associate professor at the Bureau of Economics and Business Research. His other activities during the period included presentation of a course on the methods of mathematical economics, membership on the executive committee of the Conference on Research in Income and Wealth, National Bureau of Economic Research, and on the committee organizing the conference on short term projections to be held under the auspices of the National Bureau of Economic Research at the University of Michigan in September.

Herbert A. Simon continued as professor of administration and head of the Department of Industrial Management at Carnegie Institute of Technology. He is engaged in research as a consultant of the Cowles Commission on its study on resource allocation, and in projects at Carnegie Institute, one sponsored by the U.S. Air Force on intra-firm behavior and the other by the Controllership Foundation on the centralization and decentralization of accounting organization. Simon is currently a member of the program committee for the Boston meeting of the Econometric Society in December, 1951.

GUESTS

As in other years, the Cowles Commission has benefited from the presence of advanced students and research fellows from this and other research centers. This has both stimulated the work of the Commission and aided in spreading the results of its research.

To the extent that its resources permit, the Commission has accorded office, library, and other research facilities to its guests, a fact which has intensified the advantages gained from these periods of resident cooperation. The following are among those who were associated with the Commission in this manner during the year.

Martin J. Beckmann, formerly of the University of Freiburg, Germany, and currently a post-doctoral fellow in political economy at the University of Chicago, participated actively in the research program of the Commission during the year. He joins the Commission as a research associate as of July, 1951, to undertake research on the theory of best locational distribution of industry in connection with the study on resource allocation. George H. Borts, a Fellow of the Social Science Research Council for 1949–1950, continued as a guest of the Commission until the late summer of 1950, at which time he became assistant professor of economics at Brown University. The Commission has continued to provide computational facilities for the research he initiated while at Chicago. Karl Brunner, of the Handelshochschule, St. Gallen, Switzerland, was with the Commission under a grant from the Rockefeller Foundation throughout most of the period from January, 1950, through June, 1951. He will join the economics faculty of the University of California at Los Angeles. John Chipman, a Canadian holder of a post-doctoral fellowship in the department of economics at the University of Chicago, also participated with the staff of the Commission in its research activities. In September he will assume teaching duties at Harvard University. The Fulbright fellowship program and the Institute of International Education cooperated in bringing Siro Lombardini to the University of Chicago. He maintained contact with the work of the Commission from his arrival in October, 1950, until June, 1951, at which time he returned to Italy to join the faculty of the University of Milan. Edmond Malinvaud, of the Institut National de la Statistique et des Etudes Economiques, Paris, was with the Commission as a Rockefeller Fellow from July, 1950, through June, 1951, and was an active participant in the research group. Sten Malmquist, Statistical Institute of the University of Uppsala, Sweden, was in residence at the Commission as a guest from November, 1950, through March, 1951. Isamu Yamada visited the Commission in March and April, 1951, under the auspices of the Ministry of Education of the Japanese government. He returns to his post as professor of econometrics at Hitotsubashi University, Tokyo.

The Cowles Commission also benefited from the occasional contributions of numerous other research workers and from the brief visits of a number of distinguished guests in addition to those mentioned above. Reference to some of these visits can be found in the report on research activities and in the list of seminars.

OFFICE AND LIBRARY

The activities of the Cowles Commission, and of the Econometric Society which shares its offices, are carried out with the aid of a supporting staff of approximately ten full-time and several part-time persons. Miss Helen Docekal, who joined the staff in January, 1949, is Administrative Secretary and as such is responsible for various administrative matters as well as the supervision of the office. The publication programs of the Commission and of the Econometric Society are the concern of Mrs. Jane Novick, Editorial Secretary. J. Myron Jacobstein became Librarian of the Cowles Commission early in 1951. A Financial Secretary, Miss Marilyn Holmes, was also added to the staff during the year. The balance of the group includes mathematical technicians, editorial assistants, book-keepers, secretaries, and technical typists.

The offices and library of the Cowles Commission are located in the Social Science Research Building on the quadrangles of the University of Chicago, overlooking the Midway Plaisance. The Commission has a working library specializing in material pertinent to its investigations, particularly in the fields of quantitative economics, statistics, mathematics, economic theory, and descriptive data. Additions to the library during the period covered by this report total 279 books, 311 pamphlets, and 150 bound volumes of journals. The total collection consists of 2,728 books, 5,547 pamphlets, and 744 bound journal volumes representing 162 different journals, of which 139 are currently received. In addition, the library of the late Professor Henry Schultz, which contains 950 books and 1,750 pamphlets, is kept in the Commission's offices. The library is open to members of the Department of Economics as well as to advanced students by arrangement.

ORGANIZATIONAL STRUCTURE

An important development of the recent period has been the emergence of the faculty of the Cowles Commission as a self-governing body. More general supervision over the academic affairs of the Commission lies with the executive committee. This consisted, during the report period, of the Dean of the Division of the Social Sciences (Ralph W. Tyler), the Chairman of the Department of Economics (Theodore W. Schultz), the President of the Cowles Commission for Research in Economics, the Director of Research (as Chairman), and the Assistant Director of Research. The administrative affairs of the Commission were under the supervision of a committee consisting of the last three mentioned above.

New bylaws and statutes of the Commission, as well as amendments to the articles of incorporation, were formulated during the year to provide for organizational changes made desirable by the recent growth of the Commission and to better prepare the organization to meet the problems of the future. The new provisions will go into effect in the latter part of 1951 and will be published in full in the twentieth-year report of the Commission. Among other things, these provide for increased lay and professional representation on the board of directors of the Cowles Commission, for integration of the executive committee into the formal corporate structure, for appointment of a committee on investments and a committee on development, for realignment of responsibilities among the principal officers, and for statutes relating to the research staff, faculty, academic advisory committees, and the supporting staff. The executive committee as reconstituted will include the Chairman of the Board, the Executive Director, the Director of Research, the Treasurer, the Chairman of the Department of Economics, and the Dean of the Division of the Social Sciences of the University, and two directors not affiliated with the University who shall be elected by the board of directors.

While strengthening its own independent corporate structure and continuing its activities on both a national and international scale, the Cowles Commission also retains its valued association with the University of Chicago. The Commission is affiliated with the University in that the research activities of the Commission are integrated with other research and teaching activities of the University in the following ways: through participation of academic officials of the Division of the Social Sciences of the University in the ruling bodies of the Commission, through representation of the Commission on the executive committee of the Division of the Social Sciences of the University, through adherence to University procedures in the appraisal and appointment of members of the Commission's staff to the faculty and staff of the University, and through support provided by the University in the form of office facilities, salaries, and provision of tenure for academic appointees.

FINANCIAL SUPPORT

Acknowledgment is made to the Rockefeller Foundation and the University of Chicago for financial assistance in the Commission's research on the econometric foundations of rational economic policy. The study on the theory of allocation of resources is conducted on a cost basis under a subcontract with The RAND Corporation. Starting in July, 1951, the Commission's research in the area of decision-making under uncertainty will receive support through a contract with the Office of Naval Research.

As in previous years, a substantial contribution toward the support of the Commission has been made by its founder, Mr. Alfred Cowles, and by members of the Cowles family. The extent of this contribution was significantly increased in amount during the period of this report.

Several guests and members of the research staff have held fellowships from the Rockefeller Foundation, the Social Science Research Council, or the University of Chicago.

PRESENT NEEDS AND FUTURE PROSPECTS

Of major concern to the Cowles Commission is the problem of building up the human as well as the financial resources which must be drawn upon if the research effort of the group is to keep pace with the potential usefulness of econometric research.

For the immediate future the limitation is mainly financial, namely, that of providing additional long-term support which can form the basis for the commitments involved in adding major staff members from the existing pool of research workers.

Taking a longer view, the problem is one of developing additional human resources which can be utilized for research and teaching in this and related areas. This requires an increase in mathematical and statistical ability and interest in the economics profession and in the social sciences generally, and the removal of barriers to the exchange of information within the profession, between professions, and internationally.

The Cowles Commission is seeking support to attack this long-range problem through a fellowship program, a conference program, an extended publication program, and a study program aiming at recommendations for the improvement of communication referred to above.

Apart from the needs and prospects mentioned above there is the long-run objective of securing an endowment which would assure to the Commission a permanent source of income. There is also a pressing need for additional space, both for the rapidly growing research group and supporting staff of the Commission and for the interested group of advanced students and research fellows which is attracted to the Commission from centers of learning throughout the world.

THE ECONOMETRIC SOCIETY

The Cowles Commission offices have continued to serve as headquarters of the Econometric Society, an international society for the advancement of economic theory in its relation to statistics and mathematics.

Several members of the Cowles Commission staff hold offices in the Society. Tjalling C. Koopmans was president of the Econometric Society during 1950, after which he continued as a member of the Council. William B. Simpson was re-elected secretary of the Econometric Society and continued as managing editor of Econometrica. In June, 1951, he was designated co-editor of the journal. He has been active in organizing the various meetings of the Society. Alfred Cowles continued as treasurer of the Society and also as business counsel for Econometrica. Harold T. Davis is an associate editor of the Journal.

Various members of the staff served on program committees or presented papers or discussion in connection with the meetings of the Society. Others are members of an intersociety committee on the mathematical training of social scientists, which was an outgrowth of a symposium arranged by the Econometric Society in 1949. One member of the Commission, T.W. Anderson, was elected a Fellow of the Econometric Society during the year.

The practice of holding a regional meeting of the Econometric Society on the West Coast was initiated in 1950 with sessions on the Berkeley campus of the University of California, August 1–5, in conjunction with the second Berkeley Symposium on Mathematical Statistics and Probability and the meeting of the Institute of Mathematical Statistics. In 1951 the West Coast meeting will be held at The RAND Corporation in Santa Monica, August 2–4.

Starting in September, 1948, the practice was adopted of holding the American summer meeting of the Econometric Society in conjunction with the meetings of the American Mathematical Society, Mathematical Association of America, and Institute of Mathematical Statistics, with emphasis being placed upon papers of a mathematical and technical nature. These meetings were held at the University of Wisconsin in 1948 and at the University of Colorado in 1949. In 1950 the Econometric Society met at Harvard University concurrently with the International Congress of Mathematicians. This year the meeting is scheduled for the University of Minnesota, in Minneapolis, September 4–7.

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 Cleveland in 1948, in New York City in 1949, and in Chicago in 1950. On occasion sessions are also held jointly with Section K of the American Association for the Advancement of Science, with which section the Econometric Society is affiliated. Sessions of the Econometric Society are open to all its members as well as to the members of the other organizations and the general public. Attendance at particular sessions ranges from 25 to over 300. The 1951 meeting with the social science organizations will be held in Boston, December 26–29.

The European meeting of the Econometric Society was held at Colmar, France, in 1949 and at Varese, Italy, in 1950. It is planned this year for Louvain, Belgium, September 12–14.

The first Japanese meeting of the Econometric Society was held October 8–9, 1950, at the Tokyo University of Commerce, at which time a Japanese branch of the Society was organized. Sessions are again planned for 1951, possibly in conjunction with the meetings of the Japanese Economic Association and Japanese Statistical Association.

A preliminary meeting of persons interested in econometrics took place in India in December for purposes of planning meetings of the Society in that country. Present plans call for a joint session with the International Statistical Institute in New Delhi, December 10, 1951, and a meeting in Patna, India, within the period December 24–30, 1951, in conjunction with the meeting of the Indian Economic Association.

The representation of South American countries in the Econometric Society increased markedly during the period of this report, and consideration is being given to inaugurating annual meetings in South America.

The Econometric Society continued its affiliation with the International Statistical Institute during the year. The Council of the Society also approved entering into an informal co-operative relationship with the newly organized International Economic Association. The Society was represented by observers at the first meeting of that organization in Monaco in September, 1950, at which a round-table on the problem of long-term international economic balance was also held. It will also be represented at a forthcoming round-table conference on the teaching of economics. The Society is on the consultative register of the Economic and Social Council of the United Nations, and is undertaking steps to complete a consultative relationship to UNESCO. In response to an invitation from the National Research Council the Society has become associated with that organization through nomination of a representative to its division of mathematics.

During 1950, Volume 18 of Econometrica was published, consisting of four quarterly issues totaling 464 pages. Effective with the April, 1951, issue a book review editor was appointed, and the number of associate editors was increased to assist in arranging for the refereeing of materials submitted for publication.

Other activities of the Society during the year included amendment of the constitution to provide henceforth for ex-officio Council membership for one year for the retiring president, revision of the rules for the election of fellows of the Society, cooperation with the intersociety study committee on the mathematical training mentioned above, establishment of a project for the collation of definitions of econometrics and preparation of encyclopedia and dictionary entries, and the formulation of a proposed international survey of facilities related to the quantitative approach to economics.

The active mailing list of the Econometric Society as of September 30, 1951, the end of the current fiscal year for the Society, will include approximately 1,554 members and 881 nonmember subscribers, chiefly libraries. About Boo of the membership joined the Society since June, 1949, a fact which is indicative of the rapid growth which the Society has recently experienced. About one half of the members and subscribers are in the United States and the remainder are in 72 other countries.

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