Kenneth Arrow

Last updated

Kenneth Arrow
Kenneth Arrow, Stanford University.jpg
National Medal of Science award ceremony, 2004
Born
Kenneth Joseph Arrow

(1921-08-23)23 August 1921
Died21 February 2017(2017-02-21) (aged 95)
NationalityAmerican
Institution Stanford University
Field Microeconomics
General equilibrium theory
Social choice theory
School or
tradition
Neoclassical economics
Alma mater City College of New York
Columbia University
Doctoral
advisor
Harold Hotelling
Doctoral
students
Influences
Contributions General equilibrium theory
Fundamental theorems of welfare economics
Arrow's impossibility theorem
Endogenous growth theory
Awards
Information at IDEAS / RePEc
Website healthpolicy.fsi.stanford.edu/people/kenneth_j_arrow

Kenneth Joseph Arrow (23 August 1921 – 21 February 2017) was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972.

Contents

In economics, he was a major figure in post-World War II neo-classical economic theory. Many of his former graduate students have gone on to win the Nobel Memorial Prize themselves. His most significant works are his contributions to social choice theory, notably "Arrow's impossibility theorem", and his work on general equilibrium analysis. He has also provided foundational work in many other areas of economics, including endogenous growth theory and the economics of information.

Education and early career

Arrow was born on 23 August 1921, in New York City. Arrow's mother, Lilian (Greenberg), was from Iași, Romania, and his father, Harry Arrow, was from nearby Podu Iloaiei. [5] [6] The Arrow family were Romanian Jews. [7] [8] His family was very supportive of his education. [9] Growing up during the Great Depression, he embraced socialism in his youth. He would later move away from socialism, but his views retained a left-leaning philosophy. [10]

He graduated from Townsend Harris High School and then earned a Bachelor's degree from the City College of New York in 1940 in mathematics, where he was a member of Sigma Phi Epsilon. He attended Columbia University, for his graduate studies. While there, he studied under Harold Hotelling, and was greatly influenced by him. [10] He received a Master's degree in 1941. [11] He served as a weather officer in the United States Army Air Forces from 1942 to 1946. [12]

Academic career

From 1946 to 1949 Arrow spent his time partly as a graduate student at Columbia and partly as a research associate at the Cowles Commission for Research in Economics at the University of Chicago. During that time he also held the rank of Assistant Professor in Economics at the University of Chicago and worked at the RAND Corporation in California. He left Chicago to take up the post of Acting Assistant Professor of Economics and Statistics at Stanford University. In 1951, he earned his Ph.D. from Columbia. [11] He served in the government on the staff of the Council of Economic Advisers in the 1960s with Robert Solow. [13] In 1968, he left Stanford for the position of Professor of Economics at Harvard University. It was during his tenure there that he received the Nobel Prize in Economics. [11]

Arrow returned to Stanford in 1979 and became the Joan Kenney Professor of Economics and Professor of Operations Research. He retired in 1991. As a Fulbright Distinguished Chair, in 1995 he taught Economics at the University of Siena. He was also a founding member of the Pontifical Academy of Social Sciences and a member of the Science Board of Santa Fe Institute. At various stages in his career he was a Fellow of Churchill College, Cambridge. [11]

Five of his former students have gone on to become Nobel Prize winners. These include Eric Maskin, John Harsanyi, Michael Spence and Roger Myerson. [14] A collection of Arrow's papers is housed at the Rubenstein Library at Duke University. [15]

Arrow's impossibility theorem

Arrow's monograph Social Choice and Individual Values derives from his 1951 Ph.D. thesis.

If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial. [16]

In what he named the General Impossibility Theorem, he theorized that it was impossible to formulate a social preference ordering that satisfies all of the following conditions: [17]

  1. Nondictatorship: The preferences of an individual should not become the group ranking without considering the preferences of others.
  2. Individual Sovereignty: each individual should be able to order the choices in any way and indicate ties
  3. Unanimity: If every individual prefers one choice to another, then the group ranking should do the same
  4. Freedom From Irrelevant Alternatives: If a choice is removed, then the others' order should not change
  5. Uniqueness of Group Rank: The method should yield the same result whenever applied to a set of preferences. The group ranking should be transitive.

The theorem has implications for welfare economics and theories of justice. It was extended by Amartya Sen to the liberal paradox which argued that given a status of "Minimal Liberty" there was no way to obtain Pareto optimality, nor to avoid the problem of social choice of neutral but unequal results. [17]

General equilibrium theory

Work by Arrow and Gérard Debreu and simultaneous work by Lionel McKenzie offered the first rigorous proofs of the existence of a market clearing equilibrium. [18] For this work and his other contributions, Debreu won the 1983 Nobel Prize in Economics. [19] Arrow went on to extend the model and its analysis to include uncertainty, the stability. His contributions to the general equilibrium theory were strongly influenced by Adam Smith's Wealth of Nations .[ citation needed ] Written in 1776, The Wealth of Nations is an examination of economic growth brought forward by the division of labor, by ensuring interdependence of individuals within society. [20]

In 1974, The American Economic Association published the paper written by Kenneth Arrow, General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice, where he states:

From the time of Adam Smith's Wealth of Nations in 1776, one recurrent theme of economic analysis has been the remarkable degree of coherence among the vast numbers of individual and seemingly separate decisions about the buying and selling of commodities. In everyday, normal experience, there is something of a balance between the amounts of goods and services that some individuals want to supply and the amounts that other, different individuals want to sell. Would-be buyers ordinarily count correctly on being able to carry out their intentions, and would-be sellers do not ordinarily find themselves producing great amounts of goods that they cannot sell. This experience of balance indeed so widespread that it raises no intellectual disquiet among laymen; they take it so much for granted that they are not supposed to understand the mechanism by which it occurs. [21]

Fundamental theorems of welfare economics

In 1951, Arrow presented the first and second fundamental theorems of welfare economics and their proofs without requiring differentiability of utility, consumption, or technology, and including corner solutions. [22]

Endogenous-growth theory

Arrow was one of the precursors of endogenous growth theory, which seeks to explain the source of technical change, which is a key driver of economic growth. Until this theory came to prominence, technical change was assumed to occur exogenously – that is, it was assumed to occur outside economic activities, and was outside (exogenous) to common economic models. At the same time there was no economic explanation for why it occurred. Endogenous-growth theory provided standard economic reasons for why firms innovate, leading economists to think of innovation and technical change as determined by economic actors, that is endogenously to economic activities, and thus belong inside the model. Endogenous growth theory started with Paul Romer's 1986 paper, [23] borrowing from Arrow's 1962 "learning-by-doing" model which introduced a mechanism to eliminate diminishing returns in aggregate output. [24] A literature on this theory has developed subsequently to Arrow's work. [25]

Information economics

In other pioneering research, Arrow investigated the problems caused by asymmetric information in markets. In many transactions, one party (usually the seller) has more information about the product being sold than the other party. Asymmetric information creates incentives for the party with more information to cheat the party with less information; as a result, a number of market structures have developed, including warranties and third party authentication, which enable markets with asymmetric information to function. Arrow analysed this issue for medical care (a 1963 paper entitled "Uncertainty and the Welfare Economics of Medical Care", in the American Economic Review); [26] later researchers investigated many other markets, particularly second-hand assets, online auctions and insurance.

Awards and honors

Arrow was awarded the John Bates Clark Medal in 1957 [27] and was elected a Fellow of the American Academy of Arts and Sciences in 1959. [28] He was the joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972 and the 1986 recipient of the von Neumann Theory Prize. [11] He was one of the recipients of the 2004 National Medal of Science, the nation's highest scientific honor, presented by President George W. Bush for his contributions to research on the problem of making decisions using imperfect information and his research on bearing risk. [4]

He has received honorary doctorates from the University of Chicago (1967), the University of Vienna (1971) the City University of New York (1972). [11] On 2 June 1995 he received an honorary doctorate from the Faculty of Social Sciences at Uppsala University, Sweden. [29] He was elected a Foreign Member of the Royal Society (ForMemRS) in 2006. [30] [4] He was elected to the 2002 class of Fellows of the Institute for Operations Research and the Management Sciences. [31]

Personal life and death

Arrow was a brother to the economist Anita Summers, uncle to economist and former Treasury Secretary and Harvard President Larry Summers, and brother-in-law of the late economists Robert Summers and Paul Samuelson. [32] In 1947, he married Selma Schweitzer, graduate in economics at the University of Chicago [33] and psychotherapist, who died in 2015; they had two children: David Michael (b. 1962), an actor, [34] and Andrew Seth (b. 1965)an actor/singer. [11]

Arrow was well known for being a polymath, possessing prodigious knowledge of subjects far removed from economics. On one occasion (recounted by Eric Maskin), in an attempt to artificially best Arrow's knowledge, the junior faculty agreed to closely study the breeding habits of gray whales – a suitably obscure topic – and discuss it in his presence. To their surprise, Arrow actually joined into the conversation. [32] [35]

Arrow died in his Palo Alto, California home on 21 February 2017 at the age of 95. [32]

Publications

Reprinted as: Arrow, Kenneth J. (1963). Social Choice and Individual Values (2nd ed.). New Haven: Yale University Press. ISBN   9780300013641.
Also available as: Arrow, Kenneth J.; Hurwicz, Leonid (1977). "Appendix: An optimality criterion for decision-making under ignorance". (online Book). Cambridge Books Online: 461–72. doi:10.1017/CBO9780511752940.015. ISBN   9780511752940.CS1 maint: ref=harv (link)
and as: Arrow, Kenneth J.; Hurwicz, Leonid (1977), "Appendix: An optimality criterion for decision-making under ignorance", in Arrow, Kenneth J.; Hurwicz, Leonid (eds.), Studies in resource allocation processes, Cambridge New York: Cambridge University Press, pp. 461–72, ISBN   9780521215220.
Including: Arrow, Kenneth J. Price-quantity adjustments in multiple markets with rising demands, pp. 3–15.
Reprinted as: Arrow, Kenneth J. (1983b), "The organization of economic activity: issues pertinent to the choice of market versus non-market allocations", in Arrow, Kenneth J. (ed.), Collected papers of Kenneth J. Arrow, volume 2: general equilibrium, Cambridge, Massachusetts: Belknap Press, pp. 133–55, ISBN   9780674137615.CS1 maint: ref=harv (link)
Also reprinted as a pdf.
Reprinted as: Arrow, Kenneth J. (1983a), "Extended sympathy and the possibility of social choice", in Arrow, Kenneth J. (ed.), Collected papers of Kenneth J. Arrow, volume 1: social Choice and justice, Cambridge, Massachusetts: Belknap Press, ISBN   9780674137608.CS1 maint: ref=harv (link)
Arrow, Kenneth J. (1983a). Collected papers of Kenneth J. Arrow, volume 1: social Choice and justice. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137608.
Arrow, Kenneth J. (1983b). Collected papers of Kenneth J. Arrow, volume 2: general equilibrium. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137615.
Arrow, Kenneth J. (1984a). Collected papers of Kenneth J. Arrow, volume 3: individual choice under certainty and uncertainty. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137622.
Arrow, Kenneth J. (1984b). Collected papers of Kenneth J. Arrow, volume 4: the economics of information. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137639.
Arrow, Kenneth J. (1985a). Collected papers of Kenneth J. Arrow, volume 5: production and capital. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137776.
Arrow, Kenneth J. (1985b). Collected papers of Kenneth J. Arrow, volume 6: applied economics. Cambridge, Massachusetts: Belknap Press. ISBN   9780674137783.
Also available online as: Arrow, Kenneth J. (2008). "Arrow's theorem". The new Palgrave dictionary of economics online, (2nd ed.) . Palgrave Macmillan: 241–245. doi:10.1057/9780230226203.0061. ISBN   978-0-333-78676-5.CS1 maint: ref=harv (link)
Also available online as: Arrow, Kenneth J. (2008). "Hotelling, Harold (1895–1973)". The new Palgrave dictionary of economics online, (2nd ed.) . Palgrave Macmillan: 73–75. doi:10.1057/9780230226203.0747. ISBN   978-0-333-78676-5.CS1 maint: ref=harv (link)

Further reading

See also

Related Research Articles

Gary Becker American economist

Gary Stanley Becker was an American economist who received the 1992 Nobel Memorial Prize in Economic Sciences. He was a professor of economics and sociology at the University of Chicago, and was a leader of the third generation of the Chicago school of economics.

Amartya Sen Indian economist and philosopher

Amartya Kumar Sen is an Indian economist and philosopher, who since 1972 has taught and worked in the United Kingdom and the United States. Sen has made contributions to welfare economics, social choice theory, economic and social justice, economic theories of famines, decision theory, development economics, public health, and measures of well-being of countries.

Welfare economics is a branch of economics that uses microeconomic techniques to evaluate well-being (welfare) at the aggregate (economy-wide) level.

John Harsanyi Hungarian economist

John Charles Harsanyi was a Hungarian-American Nobel Prize laureate economist.

Gérard Debreu French economist and mathematician

Gérard Debreu was a French-born economist and mathematician. Best known as a professor of economics at the University of California, Berkeley, where he began work in 1962, he won the 1983 Nobel Memorial Prize in Economic Sciences.

Harold Hotelling American economist and statistician

Harold Hotelling was an American mathematical statistician and an influential economic theorist, known for Hotelling's law, Hotelling's lemma, and Hotelling's rule in economics, as well as Hotelling's T-squared distribution in statistics. He also developed and named the principal component analysis method widely used in finance, statistics and computer science.

Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a collective decision or social welfare in some sense. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Social choice theory dates from Condorcet's formulation of the voting paradox. Kenneth Arrow's Social Choice and Individual Values (1951) and Arrow's impossibility theorem in it are generally acknowledged as the basis of the modern social choice theory. In addition to Arrow's theorem and the voting paradox, the Gibbard–Satterthwaite theorem, the Condorcet jury theorem, the median voter theorem, and May's theorem are among the more well known results from social choice theory.

Hirofumi Uzawa was a Japanese economist.

Jacob Marschak American economist

Jacob Marschak was an American economist.

Lionel Wilfred McKenzie was an American economist. He was the Wilson Professor Emeritus of Economics at the University of Rochester. He was born in Montezuma, Georgia. He completed undergraduate studies at Duke University in 1939 and subsequently moved to Oxford that year as a Rhodes Scholar. McKenzie worked with the Cowles Commission while it was in Chicago and served as an assistant professor at Duke from 1948–1957. Having received his Ph.D at Princeton University in 1956, McKenzie moved to Rochester where he was responsible for the establishment of the graduate program in economics.

Leonid Hurwicz Polish-American economist and mathematician

Leonid "Leo" Hurwicz was a Polish-American economist and mathematician, known for his work in game theory and mechanism design. He originated the concept of incentive compatibility, and showed how desired outcomes can be achieved by using incentive compatible mechanism design. Hurwicz shared the 2007 Nobel Memorial Prize in Economic Sciences for his seminal work on mechanism design. Hurwicz was one of the oldest Nobel Laureates, having received the prize at the age of 90.

Roger Myerson American mathematician

Roger Bruce Myerson is an American economist and professor at the University of Chicago. He holds the title of the David L. Pearson Distinguished Service Professor of Global Conflict Studies at The Pearson Institute for the Study and Resolution of Global Conflicts in the Harris School of Public Policy, the Griffin Department of Economics, and the College. Previously, he held the title The Glen A. Lloyd Distinguished Service Professor of Economics. In 2007, he was the winner of the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel with Leonid Hurwicz and Eric Maskin for "having laid the foundations of mechanism design theory." He was elected a Member of the American Philosophical Society in 2019.

Stanley Reiter was an American author, economist, and Emeritus Professor at Northwestern University. Reiter was a leading pioneer in the field of mechanism design.

Kotaro Suzumura Japanese economist

Kotaro Suzumura was a Japanese economist and professor emeritus of Hitotsubashi University. He graduated from Hitotsubashi University in 1966. His research interests were in social choice theory and welfare economics. He was also a Fellow of the Econometric Society.

Frank Hahn British economist

Frank Horace Hahn FBA was a British economist whose work focused on general equilibrium theory, monetary theory, Keynesian economics and monetarism. A famous problem of economic theory, the conditions under which money can have a positive value in a general equilibrium, is called "Hahn's problem" after him.

Shapley–Folkman lemma

The Shapley–Folkman lemma is a result in convex geometry with applications in mathematical economics that describes the Minkowski addition of sets in a vector space. Minkowski addition is defined as the addition of the sets' members: for example, adding the set consisting of the integers zero and one to itself yields the set consisting of zero, one, and two:

Ross Marc Starr is an American economist who specializes in microeconomic theory, monetary economics and mathematical economics. He is a Professor at the University of California, San Diego.

In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences and convex budget sets and on producers with convex production sets; for convex models, the predicted economic behavior is well understood. When convexity assumptions are violated, then many of the good properties of competitive markets need not hold: Thus, non-convexity is associated with market failures, where supply and demand differ or where market equilibria can be inefficient. Non-convex economies are studied with nonsmooth analysis, which is a generalization of convex analysis.

Prasanta Kumar Pattanaik, is emeritus professor at the Department of Economics at the University of California. He is a Fellow of the Econometric Society.

The Journal of Mathematical Economics is a bimonthly peer-reviewed academic journal of mathematical economics published by Elsevier. It covers work in economic theory which expresses economic ideas using formal mathematical reasoning. The journal was established in 1974, with Werner Hildenbrand as the founding editor-in-chief. The current editor-in-chief is Atsushi Kajii. According to the Journal Citation Reports, the journal has a 2018 5-year impact factor of 0.725.

References

  1. Andrea Prat's CV
  2. PROFILE: Nancy Stokey.(Accessed September 2016)
  3. Kenneth Joseph Arrow (2017). On Ethics and Economics: Conversations with Kenneth J. Arrow. Routledge. pp. 12, 33. ISBN   978-1-138-67606-0.
  4. 1 2 3 "Professor Kenneth Arrow ForMemRS, elected 2006". London: Royal Society. Archived from the original on 17 November 2015.
  5. "Premiat Nobel cu origini românești, Doctor Honoris Causa al Universității "Al. I. Cuza" din Iași". Jurnalul.ro. Archived from the original on 1 November 2014. Retrieved 1 November 2014.
  6. Arrow and the Foundations of the Theory of Economic Policy
  7. Abu N.M. Wahid (2002). Frontiers of Economics: Nobel Laureates of the Twentieth Century. Greenwood Publishing. p. 5. ISBN   0-313-32073-X.
  8. Steven Pressman (1999). Fifty major economists: Business & Economics. Routledge Publishing. p. 177. ISBN   0-415-13480-3.
  9. "American Jewish Recipients of the Nobel Prize". Fau.edu. Retrieved 1 November 2014.
  10. 1 2 "Econ Journal Watch – Ideological Profiles of the Economics Laureates". Econjwatch.org. Retrieved 1 November 2014.
  11. 1 2 3 4 5 6 7 "Kenneth J. Arrow – Biographical". Nobelprize.org. Retrieved 1 November 2014.
  12. "Kenneth J. Arrow, MA, PhD". Stanford University. Retrieved 1 November 2014.
  13. "American President". Millercenter.org. Archived from the original on 2 November 2014. Retrieved 1 November 2014.
  14. John B. Shoven. "Kenneth Arrow Contributions to Economics" (PDF). Siepr.stanford.edu. Retrieved 1 November 2014.
  15. "Kenneth J. Arrow Papers, 1939–2009". Rubenstein Library, Duke University.
  16. Kenneth Arrow, "A Difficulty in the Concept of Social Welfare" (1950).
  17. 1 2 Morreau, Michael (1 January 2016). "Arrow's Theorem". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. Retrieved 25 February 2017.
  18. Mas-Colell, Andreu; Whinston, Michael D.; Green, Jerry R. (1995). Microeconomic Theory. New York: Oxford University Press. pp. 691–93. ISBN   0-19-507340-1.
  19. "Gerard Debreu – Biographical". www.nobelprize.org. Retrieved 25 February 2017.
  20. Smith, Adam, and Andrew S. Skinner. The wealth of nations. London: Penguin Books, 1999. Print.
  21. Arrow, Kenneth (1974). "General Economic Equilibrium: Purpose, Analytic Techniques, Collective Choice". American Economic Review . 64 (3): 253–72. JSTOR   1808881.
  22. "Kenneth Arrow (1921– )". Concise Encyclopedia of Economics. Liberty Fund. 2008. Retrieved 18 June 2017.
  23. Romer, Paul M. (1986). "Increasing Returns and Long-Run Growth" (PDF). Journal of Political Economy . 94 (5): 1002–37. doi:10.1086/261420. JSTOR   1833190.
  24. Arrow, Kenneth J. (1962). "The Economic Implications of Learning by Doing". Review of Economic Studies . 29 (3): 155–73. doi:10.2307/2295952. JSTOR   2295952.
  25. Barro, Robert J.; Sala-i-Martin, Xavier (2004). Economic Growth (2nd ed.). Cambridge: MIT Press. pp. 212–20. ISBN   0-262-02553-1.
  26. "Uncertainty and the Welfare Economics of Medical Care" (PDF).Cite journal requires |journal= (help)
  27. "John Bates Clark Medal". American Economic Association. Retrieved 25 February 2017.
  28. "Book of Members, 1780–2010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 25 April 2011.
  29. Honorary Doctors of the Faculty of Social Sciences
  30. Velupillai, K. Vela (2019). "Kenneth Joseph Arrow. 23 August 1921—21 February 2017". Biographical Memoirs of Fellows of the Royal Society. 67: 9–28. doi: 10.1098/rsbm.2019.0002 .
  31. Fellows: Alphabetical List, Institute for Operations Research and the Management Sciences, archived from the original on 10 May 2019, retrieved 9 October 2019
  32. 1 2 3 Weinstein, Michael M. (21 February 2017). "Kenneth Arrow, Nobel-Winning Economist Whose Influence Spanned Decades, Dies at 95". New York Times . Retrieved 21 February 2017.
  33. Heller, Walter P.; Starr, Ross M.; Starrett, David A., eds. (1986). "Kenneth J. Arrow". Social Choice and Public Decision Making: Essays in Honor of Kenneth J. Arrow, Volume I. Cambridge University Press. p. xiv. ISBN   0-521-30454-7.
  34. David Arrow on IMDb
  35. Arrow, Kenneth Joseph (2012). Social choice and individual values. Yale University Press. ISBN   9780300179316. OCLC   837682848.
Awards
Preceded by
Simon Kuznets
Laureate of the Nobel Memorial Prize in Economics
1972
Served alongside: John R. Hicks
Succeeded by
Wassily Leontief