Edward Glaeser: Remembering Samuelson, Who Forever Fused Economics with Math

[My comment: The small town of Gary, Indiana lost two of its greatest people this year: Paul A. Samuelson and Michael Jackson.]

Edward L. Glaeser is an economics professor at Harvard.

Paul Samuelson died on Sunday at the age of 94.



Yale Joel/Time & Life Pictures — Getty Images Paul A. Samuelson at M.I.T. in 1950, where he used mathematics to analyze complex economic theories.

He was an immortal among dismal scientists: one of the mighty trio, along with Kenneth Arrow and Milton Friedman, who dominated post-war economics, the great formalizer of the field.

Friedman’s policy insights may have been more radical and significant; Arrow’s genius may have produced more beautiful gems of economic theory. But it was Samuelson who gave economists our toolbox — the mathematical methods that define our field — and the magnitude of that gift made him an indispensible economist.

Samuelson grew up in Chicago and entered the University of Chicago in 1932. He was drawn to economics because of a lecture on Thomas Malthus, where a simple equation seemed to suggest that mankind was drawn inevitably toward overpopulation and starvation.

The great appeal of Samuelsonian economics would be its use of mathematics to make sense of the human condition, usually — although not always — with more success than poor, mistaken Malthus.

The University of Chicago then, as now, had remarkable economists who inspired and mentored Samuelson: the irascible Frank Knight, expert of entrepreneurship and mentor of George Stigler; the international trade expert Jacob Viner (Milton Friedman’s adviser); and Paul H. Douglas, a labor economist extraordinaire and later three-term senator from Illinois.

Samuelson ignored their advice to follow Friedman to Columbia University. He instead went to Harvard for graduate school, apparently imagining it to be some sort of bucolic Eden. In the 1930s, Cambridge was no sylvan retreat, but it was a sanctuary for European scholars, who fled the dark and gathering storms across the Atlantic. Scholarly émigrés, like Joseph Alois Schumpeter, Gottfried Haberler and Wassily Leontief, imported Austrian and German knowledge into the United States and taught the young Paul Samuelson.

Many people associate Samuelson with Keynesianism. He did, after all, make Keynes popular in the United States by writing and then selling millions of copies of a textbook that helped explain Keynes’s work. But among academic economists, Keynesianism came and went. If he were merely another Keynesian, Samuelson’s place in intellectual history would be similar to the far-more-modestly-known Alvin Hansen, another of his Harvard advisers.

The full measure of Samuelson’s influence is that he not only wrote Keynesian arithmetic, but also crafted the mathematical toolbox that would eventually crack the Keynesian orthodoxy.

When Robert Lucas, the Nobel laureate who micro-founded macroeconomics and challenged Keynes, decided to switch from history to economics, he spent a summer reading Samuelson’s Ph.D. dissertation, “The Foundations of Economic Analysis,” by “working through the first four chapters, line by line, going back to my calculus books when I needed to.” As a result, “by the beginning of fall quarter I was as good an economic technician as anyone on the Chicago faculty.”

One of the oddities of Samuelson’s academic life is that he wrote his dissertation — the seminal document of modern mathematical economics — under the tutelage of Joseph Alois Schumpeter, whose own scholarship is essentially math-free.

Perhaps the physicist and statistician Edwin Bidwell Wilson played a more crucial role in Samuelson’s intellectual arbitrage, his importation of ideas from physics into economics. Samuelson’s “Foundations,” which was finally published in 1947, is more textbook than research monograph. A smart, mathematically literate young scholar, like the young Robert Lucas, can really sit down with the book and emerge with the basic tools needed to write academic models.

Samuelson’s algebra conquered the profession, and — despite the criticism that mathematics engenders in outsiders — it is easy to understand why.

The great subjects of economics are aggregations: groups of people who interact with each other in markets. Given the complexity of group interactions, logical errors are often unexposed in written discussions. Only the cold purity of mathematical logic can make transparent the chain of reasoning from assumption to conclusion.

Mathematics doesn’t substitute for genuine insight or knowledge of the real world, but it is necessary if economists are going to craft logically coherent models of complex phenomena. While many mathematical models failed to predict the current downturn, plenty of non-mathematical seers also failed. If we ever do come to understand the vicissitudes of asset markets, that understanding will come in the form of formal mathematical analysis, ultimately inspired by Samuelson.

The start of the economists’ toolbox is the utility function — a somewhat mythical thing, which is emphatically not the same thing as happiness — that we pretend that human beings maximize.

Borrowing from others, Samuelson’s dissertation gave us a clear justification for this fictional convenience.

If people can rank outcomes in terms of their desirability, and if they choose one outcome over another, then people have preferences. (Who can disagree with that?) And if, as Samuelson taught us, those preferences follow a few simple rules, then human behavior can be described with a utility function. That conclusion allows economists to turn to Newton and optimization theory.

Samuelson’s “Foundation”s was equally important in founding production theory by importing tools from the physical sciences, like the Le Chatelier principle, where an initial shift engenders off-setting responses.

After publishing his dissertation, Samuelson’s output continued to be prodigious. In 1954, he gave us the theory of public goods, which are things, like national defense or clean air, that can be consumed by multiple people at the same time, and that no one can be effectively excluded from using. (For example, the United States army defends me and you at the same time, usually without firing a shot.) He made major contributions to international trade, such as the Stolper-Samuelson Theorem, which predicts the relationship between final goods prices and the costs of inputs — the price of labor will rise with the demand for labor-intensive goods. Samuelson crafted the overlapping-generations model, which remains a workhorse of social security scholarship and dynamic economics.

I teach the first quarter of micro-economic theory to Harvard’s Ph.D. students, and Samuelson’s presence can be felt at least five times an hour. It is impossible to teach the core skills of our discipline without constantly relying on his contributions. Samuelson may have passed, but the river of human knowledge has absorbed his scholarship fully.

No thinker could ask for more.