A New Magnifier

Kenneth Arrow stays under the radar

Posted in 2007-08 Financial Crisis, History of economics Tagged with: , , ,

Two volumes of Paul Samuelson’s Collected Scientific Papers appeared in 1966, 129 articles, 1,831 pages, published by the MIT Press. Samuelson was only fifty-one. To some it might have seemed premature, but then some part of the point must have been shock and awe: to demonstrate how far economists had come since Harvard had destroyed the plates of Foundations of Economic Analysis.

The economist to whom the Journal of Political Economy, the University of Chicago’s flagship journal, turned to review the volumes was Kenneth Arrow, of Stanford University. He was not an obvious choice.  He had been associated with the Cowles Commission. He was left-of-center politically. He was no macroeconomist. Arrow had won the Clark medal at the age of 36, in 1957, for contributions that were mostly esoteric. Presenting the award, Chicago’s George Stigler advised him, in a stage whisper, “Say ‘Symbols fail me.’”

As befit the occasion, Arrow began ”Samuelson Collected” with a warm, teasing evocation of Samuelsonian prose ( JSTOR access required). “Paul Samuelson is omnipresent in American and even world economics; like Joyce’s Humphrey Chipden Earwicker or Melville’s Confidence Man, he appears at every turn of history and in every disguise.” Undergraduates learned from his introductory text, Arrow wrote; graduate students still read the Foundations. Esoteric specialists solicited his views, as did policymakers, central bankers, Democratic presidents, Republican businessmen, magazine and newspaper editors.

Samuelson’s papers exhibited uniform virtuosity, Arrow wrote. If anything, those dealing with macroeconomic topics — theories of income and employment, as well as his observations on money and banking – deserved extra credit for  clarity, because the concepts were still so new and “fuzzy.”

But a “tingling excitement of creative originality” accompanied his contributions to neoclassical price theory: the revealed preference approach, the emphasis on optimization over time, the attempts to show how some sets of prices must depend on others.  It was here, Arrow wrote, that Samuelson’s work rose to the level of permanent contributions. He made a dry-eyed tour of Samuelson’s triumphs.

The second section of the review contained a shrewd criticism: Samuelson seemed to have little interest in applying price theory. He is asked to lecture on “What economists know?” but doesn’t refer at any point to the allocation of resources through the price system. He had little to say about the “major scandals” of price theory of the day  – the relation between micro- and macroeconomics; the place of imperfect or monopolistic competition in the scheme of things; or the role of  transactions costs as a step towards a theory of money and of asset holdings.

For that matter, Arrow wrote, Samuelson was none too curious about the relationship of theory to economic policy. “Samuelson is one of the greatest economic theorists of all time, has written extensively and significantly on welfare economics, and is strongly interested in the practical formation of policy.”

Yet he never attempts a synthesis, and “indeed goes to some considerable pains to point out difficulties.” Samuelson’s “partial and limited” investigations into the foundations of welfare economics seemed to stem from a sense that such inquiry would  lead to “deep and paradoxical levels of feeling where the mind and the judgment chase their own tails.”  Are there no general rules for the allocation of public and private resources? For the distribution of income and wealth?  “It is not adequate to present a partial system and at the same time informal judgments not consistent with it.” In contrast, Arrow comes across as a committed utilitarian.

Arrow summed up with a final remark:

A great leader of his field is not typical of his day; but neither is he outside it.  Rather he is like a magnifying glass; not only are the accomplishments the best that the period can produce, but also the underlying concepts are brought out more sharply and separated from the mass of elementary error and shortsightedness.

Arrow is often presented as a man without a program. What wasn’t yet clear to others, though clearly Arrow knew it himself, was the extent to which he had one, and, with the help of many colleagues and students, was ready and able to put it to work. Arrow himself would become the magnifying lens of the next generation, leading the effort to create formal mathematical systems against which to map and extend economic intuition and experience. The theorist-turned-historian Jürg Niehans succinctly described the practical effect:

In the second half the twentieth century, the center of gravity in economics shifted from macroeconomics to microeconomics…. No single economist contributed more to this shift than Kenneth J. Arrow.

(George Feiwel, of the University of Tennessee, produced a two- volume Festschrift in 1987 that makes possible the otherwise nearly insurmountable task of seeing the many-sided Arrow whole. No one has done more to bring the man into focus.)

.                                              Right Time, Right Place

Arrow was born in 1921, in New York, to parents who had come to the United States as infants from Romania. He grew up in comfortable circumstances until his successful father, by then a banker, was dismissed in the Depression. For a decade thereafter, the family struggled. One of his two sisters, Anita, became an economist. She married Robert Summers, Paul Samuelson’s younger brother, and raised three sons, among them Lawrence Summers.

Arrow attended City College of New York (it was free), graduating in 1940, spent two years as a graduate student in mathematics, economics and statistics at Columbia University (his father borrowed $400 for tuition), before enlisting in the Army Air Corps. Serving in the weather service, he spent three relatively uneventful years, studying among other things flight planning.

He returned to Columbia after the war to work on his dissertation. At a meeting of the American Statistical Societies at Cornell University in 1946 he met Tjalling Koopmans, who advised him to forget about becoming an insurance company actuary. “There is no music in it,” the Dutch economists explained. The next year came an invitation to join the Cowles Commission in Chicago. There Arrow met and married Selma Schweitzer, a fellow graduate student.

Arrow’s next ten years are interesting, to say the least. I don’t have time to elaborate – maybe someday.  Here I will simply stipulate four of the broad headings under which he grouped various accomplishments when it came time to publish his papers from the period.  .

1. Social choice.  Looking for a dissertation, Arrow undertook a formal study of voting that found that no method of aggregating individual preference orderings could satisfy everyone, and all could be manipulated strategically.  For  a highly readable guide once again the invaluable William Poundstone: Gaming the Vote: Why Elections Aren’t  Fair. Social Choice and Individual Values (1951). the book that eventuated, launched a field; social choice, which has since become a vigorous community of theorists and, increasingly, practitioners. But the biggest impact of the book when it appeared in 1951 was methodological. Historian Niehans wrote, “It initiated a period in which set theory [which had been introduced by Theory of Games and Economic Behavior] rapidly replaced differential calculus as the favorite tool of mathematical economics. In addition, it demonstrated how axiomatic methods, as exemplified by John von Neumann and Oskar Morgenstern, can be used to make social theories rigorous.”

2. General equilibrium theory. Arrow’s next project was to demonstrate mathematically that Adam Smith’s original intuition of economic interdependence, formalized by Walras, was in fact a logical possibility.   For the fascinating story of  the proof that eventuated, see Finding Equilibrium: Arrow, Debreu, McKenzie and the Problem of Scientific Credit (Princeton, 2014), by Till Düppe and E. Roy Weintraub. The blueprint for a perfectly competitive  economy has been a source of insight ever since when compared to the existing world.

3. Individual choice under uncertainty.  Like Samuelson, Arrow had read the British economist John Hicks’ Value and Capital.  Hicks knew that expectations about the future were uncertain, but hadn’t found a satisfactory way to express the problem.  Arrow described mathematically a series of complete markets, corn if it rains on a certain day, corn if it doesn’t, and so on, in all directions, for all commodities, depending on the state of nature on a given day. He was characterizing futures markets that farmers had invented for themselves hundreds of years before and extending the concept into a giant idealized system of what would be, in effect, insurance against all possible eventualities. From this apparatus of “contingent claims” emerged blueprints for securities markets that were extensively put into practice in the 1970s – and, for Arrow and others, a jumping off for a series of deep meditations on individuals’ responses to risk, including a method of measuring risk aversion.

4. Recursive methods. Hardly less important to economics than the rapid importation of set theory from game theory was its adoption of dynamic programming methods, or “rocket science,” from military and computer research that took place mostly at RAND Corp. during the 1950s.  (The development of rocket science in the US is described to good effect by its American inventor, Richard Bellman, in Eye of the Hurricane: An Autobiography). Arrow spent his summers at RAND and quickly recognized that Bellman’s recursive methods (“do the best you can from where you are”) would do something for economists that neoclassical models couldn’t: namely permit the analysis of economic trade-offs in things that happen in stages (meaning nearly everything). Thereafter Arrow wrote a steady stream of papers about capital accumulation and production, culminating in a book, Public Investment, the Rate of Return, and Optimal Fiscal Policy, with Mordecai Kurz, in 1970. Along the way the skein led to an investigation of economic growth that in the early ’60s was all the rage.

Thus by the time he was forty, when he spent several months at the Council of Economic Advisers in Washington, DC, to witness policy-making first hand, Arrow had put his stamp on four broad areas, any one of which would have qualified him for the profession’s highest honors.

He was only six years younger than Samuelson, but where the MIT economist had completed his most important work before World War II, Arrow’s accomplishments began only in the superheated intellectual atmosphere of the postwar era. By the time that Arrow sat down to review Samuelson, it was well understood, at least by insiders, that the younger man represented the future of the profession.

Arrow spent 1963-64 at Churchill College, Cambridge University. He returned to Stanford for a couple of years but found the best students were still going to the eastern schools. He spent the fall term of 1966 at MIT and afterwards announced he would take offers.  There was spirited bidding; presumably Columbia and perhaps Chicago made offers as well. To this day the details are not known.

Harvard won. Still suffering from Samuelson’s defection twenty-five years before, it was seeking to rebuild its economics department. Perhaps more to the point, it had the intellectual resources and was developing the pretensions of the World’s Greatest University. Arrow moved to Cambridge in the summer of 1968.

.                                                A Whole New Leg

Moving to Harvard was a bonanza for Arrow – and for economics. For one thing, there was the work Arrow brought with him – not the growth theory he had done so much as a new paper on the economics as health care. Commissioned as an exercise in using high theory as a tool in empirical work, “Uncertainty and the Welfare Economics of Medical Care” may have been the first article in the American Economic Review, the flagship journal of the profession, to prove its theorems in an appendix.

The paper itself, however, was completely accessible to non-economists.  Using the contingent-claims apparatus, Arrow contrasted the ideal of perfect competition with the actual state of the market, and showed that institutions for dealing with uncertainty were ubiquitous. Two problems in particular stood out.  Arrow borrowed terms from the actuarial science that he had studied as a 20-year-old. The first was “moral hazard,” meaning the temptation to do the wrong thing; the second was “adverse selection,” meaning the tendency of the least healthy patients to buy more insurance, thereby increasing costs and driving healthy patients out of the system; or, conversely, the ability of the insurance company to identify high-risk patients and keep them out of the system. Measured against the Arrow-Debreu-McKenzie ideal, the problem of asymmetric information stood out in sharp relief.

Then came a bombshell in the form of a paper called “The Market for Lemons: Quality Uncertainty and the Market Mechanism” from an MIT PhD teaching at the University of California at Berkeley.  George Akerlof had tried for three years to get a journal to accept his argument that, in some circumstances, suspicion of the motives of sellers might cause the market for used cars to shut down.  When, in 1970, Arrow students at Harvard’s Quarterly Journal of Economics accepted the paper as essentially correct, the effect was electric.  The problem of asymmetric information had been confirmed. Akerlof put his basic insight this way thirty years later, accepting a share of the 2001 Nobel Prize.

Bring a sad old nag to market.

Put a live eel down her throat.

She will be frisky.

Bring a high strung stallion to the ring.

Give him a bucket of beer.

He will be mellow.

These are the tricks.

On one side of the market are the tricksters.

The other side avoids the tricksters.

In the extreme, markets totally collapse.

And the good may lose out as well as the bad.

Economists went to work to understand why the worst didn’t happed most of the time. A whole new wing began to develop under the heading of principal-agent relationship, much of it emanating from Arrow’s Harvard seminars. Here is the formulation Jean-Jacques Laffont gave the simplest version in 2003, summing up thirty-five years of work by dozens of scholars in the field.

When Party A delegates a task to Party B  who does not have the same objectives and who has or acquires private information about the cost of this task, Party A worries about the incentives of Party B. Private information can essentially be of the moral hazard (or hidden action) type… or the adverse selection (or hidden information) type….  To induce Party B to carry out the task, Party A offers an implicit or explicit contract. … What is the optimal structure of the contract that principal should offer the agent ?…

Then in 1972, Arrow’s friend and collaborator Leonid Hurwicz, of the University of Minnesota, proclaimed still another line of inquiry.  In “The Design of Mechanisms for Resource Allocation,” given at Arrow’s invitation to the meetings of the American Economic Association, Hurwicz’s paper said that thanks to developments in fields as diverse as computer science, public administration, game theory and control theory, it had become possible to think seriously about designing whole new economic systems.

It was pure Arrow.  As theorist Hugo Sonnenschein put it years later, for Samuelson the economic system was for the most part a given.  For Arrow, and others of his ilk, it was a matter of choice.

.                                                                Prize Diplomacy

The same year, 1972, the Royal Swedish Academy of Sciences awarded their new Nobel Prize in economic sciences jointly to Arrow and Hicks.

Only in October 1969 had the Swedes given their new prize for the first time, an award not included in Alfred Nobel’s hand-drawn will of 1895. (He had specified prizes in the dominant sciences of the day – physics, chemistry, and medicine or physiology – as well as literature and peace ) The Central Bank of Sweden had funded the program. Within a few years controversy about it was such that the Academy and the Nobel Foundation agreed that they would never create another.   But from the beginning, economists and others had thought long and hard about establishing the authority of the new award.

Thus the first prize was awarded for the development of econometrics, to Ragnar Frisch, of Norway, and Jan Tinbergen, of the Netherlands. The second prize recognized macroeconomics; it went to Paul Samuelson alone.  The third, for the creation of national income accounting, was given to Simon Kuznets, of the National Bureau of Economic Research and Harvard University.  The fourth prize, to Arrow and Hicks, was seen as a prize for mathematical economics.

From the beginning, it was not a popular award.  It became less so as time went on.  (Hicks died in 1989.) Arrow is modern; Hicks was old-fashioned.  Arrow’s contributions were many-sided and continuing; Hicks was spent his later years seeking to preserve the legacy of Keynes. Arrow was thoroughly original, Hicks was thought by some to have insufficiently acknowledged his debt to the  great Swedish economist Knut Wicksell. But both men had the virtue of having done with general equilibrium theory, and therefore each being hard to explain. And the value of including a British economist among the early winners (Hicks taught briefly hailed originally from in South Africa) need hardly be explained.

This, then, plus the generally esoteric nature of his contributions, is why Arrow had cast such a light shadow across the landscape of economics in the popular imagination. He doesn’t appear in Robert Heilbroner’s great history of economics through the first half of the twentieth century, The Worldly Philosophers, hardly surprising for a sturdy vessel whose keel was laid in 1953. Arrow isn’t so much as mentioned in William Breit and Roger Ransom’s excellent The Academic Scribblers, either, not even in its revised third edition, in 1998.   Nor is he included in Leonard Silk’s The Economists, in 1976  (profiles of Samuelson, Friedman, Wassily Leontief, Kenneth Boulding and John Kenneth Galbraith.)

Not until Niehans’ A History of Economic Theory: Classic Contributions 1720-1980 (Johns Hopkins, 1994) does Arrow get a lucid explication, eighteen pages  – but  then only as “an economist’s economist’s economist” (sic) who, with his one-time collaborator Gerard Debreu (“a mathematician’s economist”) attracted different type of talent to graduate work.

It doesn’t seem to bother Arrow. He’ll turn 94 on August 23.  He is still married to Selma Scheweitzer; still actively edits, with his Stanford colleague Timothy Bresnahan, the Annual Review of Economics; still goes to conferences; sees old friends and makes new ones.  His 1972 Nobel lecture, a sustained argument for the practice of combining high theory with empirical work, at one key juncture pointed to the future:

Once the broad approach to the analysis of existence was set, it could be applied in many directions.  One was the analysis of models which represented in one way or another imperfections in the competitive system.  The requirement of proving an existence theorem in each case leads to the need for a rigorous spelling out of assumptions, a requirement which seems to be proving very fruitful. Much of this work is going on now, in such areas as the analysis of futures markets, expectations, and monetary theory.

It was, of course, Arrow who would furnish the tools.