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Kenneth Arrow RIP

February 22, 2017 - 21:16 -- Admin

Kenneth Arrow was, with Paul Samuelson, one of the two greatest economists that the world has known since at least the time of Lord Keynes.  I read of his death at age 95 this evening.  An astonishing man, he wrote on a myriad of aspects of modern economics and he wrote well and with great insight. A great applied mathematician he was also a skillful craftsman of the English (and French) languages. A   profound intellect, he influenced a whole generation of economists.

Simply put: I idolized the guy.

His early work did three things. First, he concerned himself with welfare economics and with the possibility of making social judgements that “reasonably” reflected individual values.  His famous “impossibility theorem” showed that, in general, this was not possible.  To make social judgements you needed to act illiberally – for example, by behaving as a dictator.  His second major early strand of work (with Gerard Debreu) proved that with reasonable individual preferences and production technologies a market-clearing, competitive equilibrium existed in competitive markets. This idea, traceable to the thinking of Adam Smith, was one of the most profound observations in modern economics.  A very deep result it drew on convex set theory and deep results in combinatorial topology notably the Kakutani fixed point theorem that had been suggested by the work of John von Neumann.  (It is impossible not to use weaker analytical methods since the existence of a competitive equilibrium implies the Kakutani fixed point theorem).  The third strand of work involved establishing the welfare properties of a competitive equilibrium.  The “First Theorem of Welfare Economics” (that a competitive equilibrium is Pareto Efficient) is a straightforward application of the definition of a competitive equilibrium.  The “Second Theorem of Welfare Economics”  showed that any sought after Pareto Efficient allocation of resources (for example, one that was equitable) could be realized as a competitive equilibrium after making transfers of resources among agents and then allowing them to trade.  It is an astonishingly insightful result (drawing on the theory of separating hyperplanes in convex set theory) that provides the intellectual basis for social democracy – for using markets after making transfers to those in need.  Many of these results are collected in a book written with Frank Hahn (“General Competitive Analysis”) where he carefully demarcates the strengths and weaknesses of these arguments.

Arrow understood the intellectual need to understand the claim that free markets could work and that they had potentially good characteristics.  This is probably the major intellectual achievement of modern economics. But Arrow spent a lifetime analyzing the strong assumptions that were necessary to make these results work. Among these assumptions were that no externalities occurred  (no pollution, no congestion), no increasing returns to scale (so no natural monopolies), no public goods (which you could neither effectively price nor would you want to price even if you could) and, most critically of all, no imperfections in the availability of information. He provided a firm basis for analyzing these “market failures” and for devising ways to address them.  Arrow was a master of modern economic theory but knew the critical foundational assumptions required to make simple generalizations work.

I have his 6 volumes of “Collected Works” at home.  It is impossible, and indeed meaningless, to try to summarize them in a short blog post.  I’ll pick a few things that I found important in my own economic studies that involved his work.  Arrow was a major student of finance and was one of the early theorists to introduce securities and risk into models of competitive equilibrium.  Arrow founded much of the core work on the “stability” of competitive systems –  this literature looked not only whether an equilibrium existed but also whether real economies would approach such equilibria starting off in a disequilibrium state.  I think it is not an exaggeration to say Arrow was the major early figure to focus on the economics of uncertainty and information – he studied insurance, gambling, education markets, health markets  (he founded “health economics”) as well as organization behaviour as a way of addressing moral hazard and adverse selecting – perhaps the major issues in what economists would now describe as comprising the analytical core of “management science” namely, “agency theory”.

I spent most of my own career working on applied optimal control theory and dynamic optimization. This theory I learned from lecture notes (and a book) on optimal economic growth written by Kenneth Arrow and Mordecai Kurz.  Again a substantial body of mathematical literature that Arrow exposited and applied in economics. His work withn Kurz remains underappreciated in the profession.

One paper that I regard as really pioneering was co-written by Kenneth Arrow and Anthony Fisher. It concerned environmental conservation under risk when current decisions had irreversible consequences.  With characteristic brilliance, this problem was solved using dynamic programming. Simply put when there are opportunities to learn in a risky environment and when decisions are irreversible, the benefits from development must exceed the costs by a “quasi-option value” that reflected the potential value of new information.  This provided a basis for the “conservation movement”,  not based on hand-waving and slogans, but on rigorous analysis.  I spent about a decade of my life studying such problems.

Arrow was keenly interested in modern thinking about a host of issues in politics (e.g. Rawls, Nozick) and most particularly in the history of economic thought.  He was generous in recognizing the work of others and particularly of the classical economists like Adam Smith. His knowledge of philosophy, of ethics and of mathematics was immense.

Arrow pursued what were initially idiosyncratic endeavors. For example, in the early stages of his career, Arrow studied meteorology and, in the 1940s, became aware of the likely problem of climate change.  He remained interested in climate economics and served on important public committees concerned with this issue.

If I could close with one of my favorite Arrow characteristics it was that he wrote well.  He was an international class mathematician as well as an economist but his writings are clear and easier than most to follow.  He always articulates the terms of the problem he is investigating well,  provides a literature survey that does in a genuine way situate a problem in the literature and exposits his approach to a solution with clarity and without either preposterous notation or intellectual demands that make it incomprehensible to mere mortals.  (That is a possibly inappropriate polemical slight of much modern economic modeling).

I was fortunate to meet Arrow (and his wife Selma) twice in Australia. He liked Australia and was an engaging pleasant person. He was an exciting man who made a room buzz with his intelligence and insight.   RIP Kenneth Arrow – a great modern thinker,  a good and remarkable man.