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Arrow, Kenneth Joseph (Born 1921) K000067 Arrow, Kenneth Joseph (born 1921) Kenneth Arrow is the author of key post-Second World War innovations in economics that have made economic theory a mathematical science. The Arrow Possibility Theorem created the field of social choice theory. Arrow extended and proved the relationship of Pareto efficiency with economic general equilibrium to include corner solutions and non-differentiable pro- duction and utility functions. With Gerard Debreu, he created the Ar- row–Debreu mathematical model of economic general competitive equilibrium including sufficient conditions for the existence of market-clear- ing prices. Arrow securities and contingent commodities extend the model to cover uncertainty and provide a cornerstone of the modern theory of finance. Kenneth Arrow is a legendary figure, with an enormous range of contribu- tions to 20th-century economics, responsible for the key post-Second World War innovations in economic theory that allowed economics to become a mathematical science. His impact is suggested by the number of major ideas that bear his name: Arrow’s Theorem, the Arrow–Debreu model, the Ar- row–Pratt index of risk aversion, and Arrow securities. Four of his most distinctive achievements, all published in the brief period 1951–54, are as follows: Arrow Possibility Theorem. Social Choice and Individual Values (1951a) created the field of social choice theory, a fundamental construct in theo- retical welfare economics and theoretical political science. Fundamental Theorems of Welfare Economics. ‘An extension of the basic theorems of classical welfare economics’ (1951b) presents the First and Sec- ond Fundamental Theorems of Welfare Economics and their proofs without requiring differentiability of utility, consumption, or technology, and in- cluding corner solutions (zeroes in quantities of inputs or outputs). The Arrow– Debreu model of general economic equilibrium. ‘Existence of equilibrium for a competitive economy’ (with Gerard Debreu, 1954) creates the mathematical model of a competitive economy. The article formalizes the cross-effects between markets (effect of one market’s price on another’s de- mand and supply) and provides sufficient conditions for the existence of prices allowing decentralized market-clearing general equilibrium of a mar- ket economy. This model is central to the study of markets and welfare economics; it is now a standard of the field. Securities markets and risk-bearing. ‘Le roˆle des valeurs boursie` res pour la re´partition la meilleure du risque’ (1953) introduces the concept of a ‘con- tingent commodity’. The article formalizes the role of markets, including financial markets, insurance, and the stock market, in resource allocation; it is a cornerstone of the modern theory of finance. Personal and intellectual history Kenneth Arrow was born in New York City on 23 August 1921. He describes his family circumstances as financially comfortable during the 1920s, but ‘my father lost everything in the great depression and we were very poor for about ten years y When it came to college, my family’s poverty constrained me to attend the City College’ (Breit and Spencer, 1986, p. 45). Free tuition at City College of New York (CCNY) gave a generation of New Yorkers their start on success. 2 Arrow, Kenneth Joseph (born 1921) The searing experience of the Depression affected career ambitions. Arrow thought he should pursue the safe career of a high-school mathematics teacher. He took education courses and he had a very successful period of practice teaching in mathematics, preparing students for the New York State Regents examination. However, the roster of applicants for New York City teachers’ positions was already filled. Arrow graduated from CCNY in 1940 with the unusual combination of a mathematics major and a Bachelor of Science in Social Science. While at CCNY he studied with Alfred Tarski in a course on the calculus of relations. Arrow was a proofreader for Tarski’s Introduction to Logic (1941). He en- tered Columbia University for graduate study and received an M.A. in mathematics in June 1941. Harold Hotelling, a statistician with an appoint- ment in the economics department, was the decisive influence. Arrow notes, ‘When I took [Hotelling’s] course in mathematical economics, I realized I had found my niche’ (Breit and Spencer, 1986, p. 45). With the inducement of a fellowship in economics, Arrow transferred to the economics depart- ment for the rest of his graduate study. Arrow’s graduate work at Columbia was interrupted by the Second World War. During the war Arrow was a weather officer in the US Army Air Corps achieving the rank of Captain, working in the Long Range Forecasting Group. Arrow’s first published paper comes from that period, ‘On the op- timal use of winds for flight planning’ (1949a). The group’s principal task was to forecast the number of rainy days in air combat areas – a month in advance. The young statisticians in the Weather Division subjected the pre- diction techniques in use to statistical test against a simple null hypothesis based on historical data. Finding that prevailing techniques were not sig- nificantly more reliable than the null, the junior officers sent a memo to the General of the Air Corps suggesting that the group be disbanded. Six months later, the General’s secretary replied on his behalf: ‘The general is well aware that your forecasts are no good. However, they are required for planning purposes.’ The group remained intact. In 1946 Arrow returned to graduate study at Columbia. Harold Hotelling had by then left for the University of North Carolina’s newly formed sta- tistics department. The concern about making a living persisted. Arrow considered a non-academic career as a life insurance actuary. Tjalling Ko- opmans (at a Cowles Commission meeting in Ithaca, New York) advised him that actuarial statistics would prove unrewarding, saying, with characteristic reticence, ‘There is no music in it.’ Fortunately for economic science, Arrow followed this advice and decided to continue a research career. In 1947 Arrow joined the (now legendary – then fledgling) research group at the Cowles Commission for Research in Economics at the University of Chicago. It seemed a golden age – all the ideas of mathematical economic theory and econometrics were being newly discovered. The close friendships and collaborations among colleagues of the Cowles Commission lasted a lifetime. Arrow describes the setting as a ‘brilliant intellectual atmosphere y with eager young econometricians and mathematically inclined economists under the guidance of Tjalling Koopmans and Jacob Marschak’ (Lindbeck, 1992, p. 107). Jacob Marschak, the Cowles Commission Research Director, arranged for the Commission to administer the Sarah Frances Hutchinson Cowles Fel- lowship for women pursuing quantitative work in the social sciences (the Fellowship had originally specified a preference that fellows be women of the Episcopal Church of Seneca Falls, New York [reported in conversation with Jacob Marschak]). The fellows were Sonia Adelson (subsequently married to Arrow, Kenneth Joseph (born 1921) 3 Lawrence Klein) and Selma Schweitzer. Kenneth Arrow and Selma Schweitzer were married in 1947. Graduate study 1946–50, through Columbia, Chicago, Cowles, RAND and Stanford, included a daunting search for a worthy dissertation topic. Prospects considered and rejected included revising and restating the Tin- bergen model (Tinbergen, 1939), and revising and restating Hicks’s Value and Capital (1939). No topic seemed worthy. Then lightning struck: Arrow in- vented an entire field of economics with his dissertation ‘Social Choice and Individual Values’. The Columbia Ph.D., with Professor Albert Hart as dis- sertation advisor, was granted in 1951. As an econometrician, T. W. And- erson of Columbia (subsequently Arrow’s colleague at Stanford) was called upon to pass judgement on a draft thesis unrecognizable as economics to Ken’s advisors; Anderson pronounced the work sound. The summer of 1948 and several summers thereafter were spent at the recently formed RAND Corporation in Santa Monica, California, a major centre of the newly emerging specialities of game theory and mathematical programming. In 1949 Arrow was appointed Acting Assistant Professor of Economics and Statistics at Stanford University, and rapidly became Pro- fessor of Economics, and of Statistics, with the eventual additional title of Professor of Operations Research. He moved to Harvard in 1968 (returning regularly to Stanford for summer workshops), and rejoined the Stanford faculty in 1979. He retired in 1991. In the 1950s and 1960s at Stanford, economic theory and econometrics faculty and graduate students were located in Serra House (converted from the retirement residence of the first president of the university) under the auspices of the Institute for Mathematical Studies in the Social Sciences (IMSSS) organized under the leadership of Patrick Suppes. In his memorial remarks for his student, Walter P. Heller (1942–2001), Arrow describes the esprit de corps: ‘Economic theory backed by serious mathematical reasoning was just beginning to be recognized...Our group of faculty and students in economic theory at Serra House ... felt ourselves a community. Not an op- pressed minority, but rather a vanguard. We were taking over!’ Stanford and UC Berkeley were centres of research in statistics and eco- nomic theory. The joint Berkeley–Stanford Mathematical Economics Sem- inar met biweekly at alternate campuses. The Berkeley group included Gerard
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