Kenneth Arrow

One of the most prominent economic theorists of the twentieth century, Kenneth J. Arrow has made fundamental contributions to numerous fields, most of then concentrated around Neo-Walrasian general equlibrium theory and welfare economics, of which he can be considered one of the primary architects.

Kenneth Arrow was a thorough New York City product: born and raised in the city, educated at City College (CCNY) and subsequently a graduate student in mathematical statistics at Columbia under Harold Hotelling and Abraham Wald. It was at Columbia that he was nudged towards economics. Finishing his Ph.D coursework in 1942, Arrow’s subsequent dissertation was to become a decade-long affair. After a stint during World War II in the Weather Division of the USAF (which resulted in his 1949 article), Arrow returned to Columbia in 1946 and, with dissertation topic still missing, he began taking steps to move into the private sector – passing a series of actuarial examinations and searching for jobs in the insurance industry. During this time period, Arrow attended Jacob Marschak’s mathematical seminar at the New School. Harold Hotelling and Wald, exasperated at Arrow’s drifting, convinced him to join Marschak at the Cowles Commission in Chicago as a research associate in 1947.

At the Cowles Commission, Arrow absorbed much of the of the Walrasian research programme being set up under Marschak and Koopmans. Arrow wrote an article with Marschak and Harris on inventory policy and contributed a piece to the famous 1951 Koopmans-edited Cowles monograph on activity analysis.

After two highly inspiring years at Cowles, Arrow moved to the RAND Corporation, a research institute associated with the United States Air Force. He would subsequently move on to teach at Stanford – where he has remained until today, save for an interlude at Harvard from 1968 to 1979.

One of the research items at RAND was the then-novel use of game theory to analyze international conflicts and strategy. However, game theory itself presupposed the the parties possessed some sort of utility functions. For parlor games with individual people, this is acceptable, but when dealing with nations as a whole involved in strategic affairs, the question of ‘America’s’ utility and ‘Soviet Union’s’ utility was an altogether different issue. Thus, Arrow wondered, under what conditions might it be reasonable to assume that collectivities such as nations possessed nicely-behaved utility functions. At long last, a dissertation topic was found, written and subsequently published as the momentous classic, Social Choice and Individual Values (1951).

At the heart of Arrow’s 1951 dissertation was the presumption that social choice orderings could be derived from individual choice orderings in a simple axiomatic manner. Arrow’s astounding conclusion, since then referred to as the Arrow Impossibility Theorem, was that a certain set of quite acceptable axioms on social choice orderings necessarily implied that there would be a ‘dictator’ (i.e. that a single agent’s own preferences over outcomes would dominate everybody else’s). This celebrated result has since created quite an research industry in social welfare theory to which Arrow himself has contributed numerous follow-ups (e.g. 1952, 1967, 1973, 1977) which has sometimes led him far afield into the philosophy of ethics and justice (e.g. 1967, 1973, 1977, 1978).

Arrow’s dissertation was concurrently published with another formidable piece of Cowles-inspired work: his proof of the First and Second Welfare theorems in general equilibrium theory (1951). Gerard Debreu, then at Cowles, had independently proved the same theorem. Kenneth Arrow and Gerard Debreu began their famous collaboration which culminated in the celebrated Arrow-Debreu proof of existence of a competitive equilibrium (1954).

All the while, Arrow had been groping for incorporating uncertainty into a general equilibrium context. In a path-breaking article, Arrow (1953) suggested that a simple procedure would be to consider markets for ‘state-contingent’ commodities. Consequently, he demonstrated that in equilibrium with a full set of state-contingent markets, there would be an optimal allocation of risk. However, Arrow noted that a full set of state-contingent commodities might seem too unrealistic. In the same article, Arrow proposed the famous contrivance of ‘Arrow securities’, i.e. securities which paid a unit of account in a particular state and nothing otherwise. Arrow demonstrated that a full set of state-contingent commodity markets could be replaced by a considerably smaller set of Arrow securities which spanned the various possible states – and that, consequently, the optimal allocation of risk would be identical as in an Arrow-Debreu model with a full set of state-contingent markets.

Arrow subsequently turned his attention to a new topic – the issue of ‘stability’ of competitive equilibrium with multiple markets. His interest in this topic was initiated by his work on ‘D- stability’ with McManus (1958) which was followed up by a famous article with Hurwicz (1958) on local stability. Perhaps his most famous achievement in this regard was to provide sufficient conditions (i.e. WARP) for global stability of equilibrium in an article with Block and Hurwicz (1959). His subsequent extensions and clarifications with Hurwicz (1960, 1961) outlined both the achievements and problems of stability theory.

Arrow had, in the meantime, maintained his interest in mathematical programming. With Hurwicz and Uzawa (1961), he produced a famous rather weak constraint qualification (which replaced Kuhn-Tucker’s) for obtaining the saddle-point characterization of a local solution to a non-linear programming problem. With Enthoven (1961) he produced several famous results in characterizing optimization problems when both the maximand and constraint functions are quasi-concave.

He moved concurrently into the issues of production and growth. In 1961, with Hollis Chenery, B.S. Minhas and Robert Solow, Arrow introduced the famous ‘Constant Elasticity of Substitution’ (CES) production function. In 1962, he produced two famous pieces on learning-by-doing, the predecessor of modern endogenous growth theory.

His landmark contributions continued: putting his early experience with actuarial work to good use, Arrow produced his famous 1963 paper on the medical insurance that introduced the concept of moral hazard into economics and announced the dawn of information theory. His 1965 lectures Aspects of the Theory of Risk Bearing introduced the famous “Arrow-Pratt” measure of risk-aversion as well as popularized asymmetric information and the terms moral hazard and adverse selection. Much of Arrow’s work on moral hazard, optimal insurance and optimal risk-bearing allocations was collected in his famous 1971 book, Essays in the Theory of Risk-Bearing. Arrow’s work on education and racial discrimination (1972, 1973) have since become famous classroom applications of signalling and screening mechanisms under conditions of asymmetric information.

Arrow had linked the theory of public investment with uncertainty in a famous article with Lind (1970) arguing for the risk-bearing role of government. His concern with mathematical programming and public policy led him naturally to the topic of optimal policy – in particular, to the use of optimal control theory as a guide to resource allocation, inventory policy, public investment, etc. In a series of articles with Mordecai Kurz (1969, 1970), culminating in their famous 1970 book, Arrow presented numerous applications and extensions of the then-rare use of Hamiltonians. Arrow’s famous ‘sufficiency’ conditions for an optimum generalized the Mangasarian conditions.

In 1971, Kenneth Arrow and Frank H. Hahn produced their famous treatise/textbook General Competitive Analysis (1971) which remained, until recently, a definitive treatment of Walrasian general equilibrium theory. Although research in general equilibrium have since moved in very different directions than those considered by Arrow and Hahn, it was at least partly due to their critical assessments of the treatment of money, uncertainty and stability in a G.E. context which led economists to recast these issues in different light. In 1981-3, Arrow lent his hand as co-editor of the Handbook of Mathematical Economics, which once again summarized the state of the art in G.E.

Although Arrow has produced more than a lion’s share of groundbreaking contributions to general equilibrium theory, social welfare theory, growth, production, uncertainty, information and optimal public policy, he has not rested on his laurels and continues to produce apace. For instance, his 1979 work with Radner on the theory of ‘teams’ and with Chang on the theory of natural resources (1980) has opened new avenues in the theory of organization and resource allocation. Even more recently, Arrow has teamed up with Hahn again to began tackling the issue of ‘endogenous uncertainty’ (1999).

Kenneth Arrow is perhaps one of the most respected and admired economists. In many ways, his life is exemplary in that the almost incredible success that have accompanied him have not, in any way, hardened into that arrogance and pettiness so common among professional scholars. By all accounts, Arrow ranks highly among economists and non-economists, orthodox and heterodox, for his scholarly depth, his wide-ranging interests, his personal and intellectual generosity and openness, and his consistent refusal to engage in ideological quibbling. If nothing else, Arrow is positive proof of Pushkin’s conjecture that ‘villainy and genius are two things that can never go together’ (Pushkin, 1832).

However, we must also remind ourselves that his achievements were neither the result of wild luck nor were they quickly or cheaply bought by hack work, but rather the outcome of an often painful but nonetheless continuous dedication to the task of the scholar. It is evident throughout his work that Arrow has maintained the highest standards of rigor, avoiding oversimplification and ideological rhetoric, clearly aware of and indeed actively demarcating the limits of applicability of economic theory. In so doing, has achieved and granted to us a far deeper understanding of both economics and the economic process than might otherwise have been possible.

Kenneth J. Arrow shared the Nobel prize in 1972 with another exemplary scholar, John Hicks, for his ‘pioneering contributions to general economic equlibrium theory and welfare theory’. It might be informative to recall that it was Hicks’s own Value and Capital (1939) that Arrow counts as the most influential work in his early intellectual career.

Major Works of Kenneth J. Arrow

– On the Use of Winds in Flight Planning, 1949, Journal of Meteorology
– Bayes and Minimax Solutions of Sequential Decision Problems, with D. Blackwell and M.A. Girshick, 1949, Econometrica
– A Difficulty in the Concept of Social Welfare, 1950, JPE
– Social Choice and Individual Values, 1951
– An Extension of the Basic Theorems of Classical Welfare Economics, 1951, in Neyman, editor, Proceedings of Second Berkeley Symposium
– Optimal Inventory Policy, with T. Harris and J. Marschak, 1951, Econometrica
– Little’s Critique of Welfare Economics, 1951, AER
– Mathematical Models in the Social Sciences, 1951, in Lerner and Lasswell, editors, Policy Sciences
– Alternative Proof of the Substitution Theorem for Leontief Models in the General Case, 1951, in Koopmans, editor, Activity Analysis of Production and Allocation
– Alternative Approaches to the Theory of Choice in Risk-Taking Situation, 1951, Econometrica
– The Determination of Many-Commodity Preference Scales by Two- Commodity Comparisons, 1952, Metroeconomica
– Principle of Rationality in Collective Decisions, 1952, Economie Appliquee
– Admissable Points of Convex Sets, with E.W. Barankwin and D.W. Blackwell, 1953, Contributions to the Theory of Games
– The Role of Securities in the Optimal Allocation of Risk-Bearing, 1953, Econometrie – (in 1963, RES)
– Existence of an Equilibrium for a Competitive Economy, with Gerard Debreu, 1954, Econometrica
– Import Substitution in Leontief Models, 1954, Econometrica
– A Theorem on Expectations and the Stability of Equilibrium, 1956, with A. Enthoven, Econometrica
– Reduction of Constrained Maxima to Saddle-Point Problems, with L. Hurwicz, 1956, Proceedings of the Third Berkeley Symposium
– Statistics and Economic Policy, 1957, Econometrica
– Decision Theory and Operations Research, 1957, Operations Research
– Gradient Methods for Constrained Maxima, with L. Hurwicz, 1957, Operations Research
– Utilities, Attitudes, Choices: A review note, 1958, Operations Research
– A Note on Expectations and Stability, with M. Nerlove, 1958, Econometrica
– A Note on the Dynamic Stability, with M. McManus, 1958, Econometrica
– Tinbergen on Economic Policy, 1958, JASA
– Studies in the Mathematical Theory of Inventory and Production, with S. Karlin and H.E. Scarf, 1958
– Studies in Linear and Non-Linear Programming, with L. Hurwicz and Hirofumi Uzawa, 1958
– On the Stability of Competitive Equilibrium I, with Leonid Hurwicz, 1958, Econometrica
– On the Stability of Competitive Equilibrium, II, with J.D.Block, L.Hurwicz, 1959, Econometrica
– Rational Choice Functions and Ordering, 1959, Economica
– Toward a Theory of Price Adjustment, 1959, in Abramovitz, editor, Allocation of Economic Resources
– Rational Choice Functions and Orderings, 1959, Economica
– Competitive Stability under Weak Gross Substitutability: the Euclidian distance approach, with L. Hurwicz, 1960, IER
– The Work of Ragnar Frisch, Econometrician, 1960, Econometrica
– Some Remarks on the Equilibria of Economic Systems, with L. Hurwicz, 1960, Econometrica
– Constraint Qualifications in Non-Linear Programming, with L. Hurwicz and H. Uzawa, 1961, Naval Research Logistics Quarterly
– Quasi-Concave Programming, with A.C. Enthoven, 1961, Econometrica
– Capital-Labor Substitution and Economic Efficiency, with H.B. Chenery, B.S. Minhas and R.M. Solow, 1961, REStat
– Additive Logarithmic Demand Functions and the Slutsky Relations, 1961, RES
– Competitive Stability under Weak Gross Substitutability: Nonlinear price adjustment and adaptive expectations, 1962, IER
– The Economic Implications of Learning by Doing, 1962, AER
– Economic Welfare and the Allocation of Resources for Innovation, 1962, in Nelson, editor, The Rate and Direction of Inventive Activity
– Uncertainty and the Welfare Economics of Medical Care, 1963, AER
– Utility and Expectation in Economic Behavior, 1963, in Koch, editor, Psychology
– Optimal Capacity Policy, the Cost of Capital and Myopic Decision Rules, 1964, Annals of Institute of Statistical Mechanics
– Aspects of the Theory of Risk-Bearing, 1965
– Discounting and Public Investment Criteria, 1966, Water Research
– Values and Collective Decision Making, 1967, in Laslett and Runcimann, editors, Philosophy, Politics and Society
– The Place of Moral Obligation in Preference Systems, 1967, in Hook, editor, Human Values and Economic Policy
– Optimal Capital Policy with Irreversible Investment, 1968, in Wolfe, editor, Value, Capital and Growth
– Applications of Control Theory to Economic Growth, 1968, Mathematics of Decision Sciences
– Economic Equilibrium, 1968, IESS
– The Organization of Economic Activity: Issue pertinent to the choice of market versus nonmarket allocations, 1969, Analysis and Evalution of Public Expenditures
– Optimal Public Investment Policy and Controllability with Fixed Private Savings Ration, with M. Kurz 1969, JET
– Optimal Growth with Irreversible Investment in a Ramsey Model, with M. Kurz 1970, Econometrica
– Uncertainty and the Evaluation of Public Investment Decisions, with R.C. Lind, 1970, AER
– Public Investment, the Rate of Return and Optimal Fiscal Policy, 1970, with M. Kurz
– A Utilitarian Approach to the Concept of Equality in Public Expenditures, 1971, QJE
– The Value and Demand for Information, 1971, in McGuire and Radner, editors, Decision and Organization
– Expositions of the Theory of Choice under Uncertainty, 1971, in McGuire and Radner, editors, Decision and Organization
– Essays in the Theory of Risk-Bearing, 1971
– General Competitive Analysis, with F.H.Hahn, 1971
– The Firm in General Equilibrium Theory, 1971, in Marris and Wood, editors, The Corporate Economy
– Problems in Resource Allocation in United States Medical Care, 1972, in Kunz and Fehr, editors, Challenge of Life
– Models of Job Discrimination, 1972, in Pascal, editor, Ractial Discrimination in Economic Life
– Some Models of Race in the Labor Market, 1972, in Pascal, editor, Ractial Discrimination in Economic Life
– Cost-Theoretical and Demand-Theoretical Approaches to the Theory of Price Determination, with D. Starrett, 1973, in Hicks and Weber, editors, Carl Menger and the Austrian School of Economics
– Some Ordinalist-Utilitarian Notes on Rawls’s Theory of Justice, 1973, J of Philosophy
– Higher Education as a Filter, 1973, JPublicE
– The Theory of Discrimination, 1973, in Aschenfelter and Rees, editors, Discrimination in Labor Markets
– Formal Theories of Social Welfare, 1973, in Wiener, editor, Dictionary of the History of Ideas
– Social Responsibility and Economic Efficiency, 1973, Public Policy
– Rawls’s Principle of Just Saving, 1973, Swedish JE
– General Economic Equilibrium: Purpose, analytic techniques, collective choice, 1974, AER
– The Limits of Organization, 1974
– Limited Knowledge and Economic Analysis, 1974, AER
– Optimal Insurance and Generalized Deductibles, 1974, Scandavian Actuarial Journal
– Thorstein Veblen as an Economic Theorist, 1975, American Economist
– Vertical Integration and Communication, 1975, Bell JE
– The Genesis of Dynamic Systems Governed by Metzler Matrices, 1976, Mathematical Economics and Game Theory
– Quantity Adjustment in Resource Allocation: A statistical interpretation, 1976, in Grierson, editor, Public and Urban Economics
– The Viability and Equity of Capitalism, 1976
– Theoretical Issues in Health Insurance, 1976
– Studies in Resource Allocation Processes, with L. Hurwicz, 1977
– Extended Sympathy and the Possibility of Social Choice, 1977, AER
– Current Developments in the Theory of Social Choice, 1977, Social Research
– Nozick’s Entitlement Theory of Justice, 1978, Philosophia
– Risk Allocation and Information: Some recent theoretical developments, 1978, Geneva Papers on Risk and Insurance
– The Future and Present in Economic Life, 1978, Economic Inquiry
– Jacob Marschak’s Contributions to the Economics of Decision and Information, 1978, AER
– The Property Rights Doctrine and Demand Revelation under Incomplete Information, 1979, in Boskin, editor, Economics and Human Welfare
– Allocation of Resources in Large Teams, with R. Radner, 1979, Econometrica
– The Trade-Off Between Growth and Equity, 1979, in Greenfield et al., editors, Theory for Economic Efficiency
– Real and Nominal Magnitudes in Economics, 1980, J of Financial and Quantitative Analysis
– Optimal Pricing, Use and Exploration of Uncertain Natural Resource Stocks, with S.L. Chang, 1980, in Liu, editor, Dynamic Optimization and Mathematical Economics
– Futures Markets: Some theoretical perspectives, 1981, J of Futures Markets
– Pareto Efficiency with Costly Transfers, 1981, in Los, editor, Studies in Economic Theory and Practice
– Optimal and Voluntary Income Distribution, 1981, in Rosefielde, editor, Economic Welfare and Economics of Soviet Socialism
– Editor, Handbook of Mathematical Economics, Volumes I- III, 1981-1986, with M.D. Intriligator – intro & contents
– Risk Perception in Psychology and Economics, 1982, Economic Inquiry
– Why People Go Hungry: Review of Sen, 1982
– Collected Papers of Kenneth J. Arrow, seven volumes, 1983-5
– Behavior under Uncertainty and its Implications for Policy, 1983, in Stigum and Wenstop, editors, Foundations of Utility and Risk Theory
– Team Thery and Decentralized Resource Allocation, 1983, in Desai, editor, Marxism, Central Planning and the Soviet Union
– The Potentials and Limits of the Market in Resource Allocation, 1985, in Feiwel, editor, Issues in Contemporary Microeconomics and Welfare
– Distributive Justice and Desirable Ends of Economic Activity, 1985, in Feiwel, editor, Issues in Contemporary Microeconomics and Welfare
– Informational Structure of the Firm, 1985, AER
– Agency and the Market, 1986, in Arrow and Intriligator, editors, Handbook of Mathematical Economics, Vol. III
– Methodological Individualism and Social Knowledge, 1994, AER
– Foreword, 1994, to W.B. Arthur, Increasing Returns and Path Dependence in the Economy
– Some General Observations on the Economics of Peace and War, 1994, ECAAR Japan
– Judgemental Cuts in Consumer Price Indexation Are a Bad Idea, with R. Solow and J. Tobin, 1997, FAS
– Notes on Sequence Economies, Transaction Costs and Uncertainty, with F.H. Hahn , 1999, JET
– How to Grow: Review of Olson, 2000, Washington Monthly
– Globalization and its Implications for International Security, 2000, ECAAR seminar

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