Path Breaker

• Author: Janet Stotsky
• Position: was until recently an Advor in the IMF's Office of Budget and Planning and is now a consultant on fiscal policies, women and development, and development macroeconomics.

Kenneth J. Arrow's path-breaking contributions to economic theory in the years after World War II are the cornerstones of the work of successive generations of theoretical and applied scholars across the economics profession.

The late economic theorist Frank Hahn, alluding to Shakespeare’s description of Julius Caesar, once said that his colleague Arrow “‘bestrides the world like a colossus’ . . . . There is hardly any area of our subject which he has not illuminated and often profoundly changed,” demonstrated perhaps by the disparate economic concepts with his name attached—such as the Arrow-Debreu model, the Arrow impossibility theorem, and Arrow securities.

Although Arrow’s first love was mathematics and mathematical statistics, he ended up an economist for a very economic reason. He ran out of money while a graduate student in mathematical statistics at Columbia University just before World War II, and the economics department offered him financial aid.

The highest bidder

Harold Hotelling, an economist, taught some of the statistics courses and “gave a course in mathematical economics” that Arrow said he took “out of curiosity.” But because it began to hook him on economics, when his cash ran down Arrow approached Hotelling. The economist told Arrow that he had no influence over the math department’s financial awards, but he could help him if he switched to economics. “So I switched to economics. People get very shocked by this. I said, ‘You’re all economists—why shouldn’t I go to the highest bidder?’” he recalled in a recent interview in his office at Stanford University, where he spent most of his professional life.

That move to the economics department started a career during which he would share a Nobel Prize for economics in 1972—at 51, the youngest economist ever to win one. The Nobel committee cited the work of Arrow and British economist John Hicks in two areas: general equilibrium theory, which seeks to explain how prices are set across an economy, and welfare theory, which analyzes the optimal allocation of goods and services in an economy. But the Nobel committee also noted that both economists had made important contributions in other areas.

That is clearly true of Arrow, who has studied what happens when one side in a transaction knows more than the other, showed how technical change can arise from economic activity, and introduced the idea of risk and uncertainty to equilibrium analysis. He has also made contributions to the economic analysis of racial discrimination and health care. Moreover, in his first major foray into economic analysis, his doctoral dissertation, Arrow essentially invented the field of social choice theory, which looks at how individual preferences are aggregated into social choice decisions, such as in voting.

In nearly all his endeavors Arrow introduced mathematical rigor and was a major influence in making economic theory as mathematically oriented as it is today.

The son of immigrants from Romania, Arrow was born in New York City in 1921. Like many in his generation, he was strongly affected by the dislocations of growing up during the Great Depression. His father’s comfortable living as a banker was upended and the family moved frequently as his father’s income rose and fell. “I wound up going to school in a lot of different places,” he recalled. But the family finally settled back in New York, where he attended Townsend Harris, a three-year public high school (“you did that by staying an extra hour a day in class”). There the mathematics bug bit him. When he graduated from high school in 1936, “we were still very poor . . . so the only real chance of going to college” was the tuition-free City College of New York (CCNY).

Like many young people who experienced the ravages of the Depression, “I was concerned about getting a job . . . . The question was, where could I get a secure job? And there was one obvious one—being a high school teacher of mathematics.” As a result he majored in math and education, although he found education courses “not very inspiring.”

No jobs teaching math

And, as would happen several years later at Columbia, mathematics did not come through for Arrow. There was such a backlog of applicants who had passed the exam for...