Mathematical Economist
Samuelson had made the decision to study a lot of mathematics while in Chicago, and his teachers in mathematical economics at Harvard included Schumpeter, who encouraged the use of mathematics even though he was no mathematician himself, and Leontief.
But the person who shaped his conception of mathematical economics was the professor of Vital Statistics and part-time member of the economics department, Edwin Bidwell Wilson. “Operationalism” had been in the air in Chicago, the term being used by Henry Schultz and Paul Douglas, and it was obviously familiar at Harvard, home of its creator, physicist Percy Bridgman. But it was Wilson who guided Samuelson to the mathematical apparatus by which he was to operationalize economic theory. He introduced Samuelson to the work of Willard Gibbs, seeking to instill in him the rigor that Gibbs would have expected. Wilson stood apart from many developments in mathematics during the twentieth century, including some that were to become fashionable in economics, but he nonetheless provided Samuelson with as rigorous a training in mathematical economics as he could have obtained anywhere else.The central idea Samuelson acquired from Wilson was that seemingly different problems might have a common mathematical structure. The fact that a system involved equilibrium, whether physical, chemical, biological, or economic, might be sufficient for it to exhibit certain properties that could be derived without knowing anything about the field in question. Samuelson extended this insight—his Correspondence Principle—to the idea that one might need to assume the equilibrium was stable. This led Samuelson, guided by Wilson, to focus on linear algebra as the means by which comparative statics results could be derived in systems that might contain many variables, and to work on the theory of difference and differential equations, needed to study dynamics.
This focus on linear algebra and on difference/ differential equations set Samuelson's work apart from other important work on mathematical economics in the 1940s, such as The Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. Samuelson understood their work, but he remained a skeptic of the usefulness of game theory, and guided by Wilson, chose not to follow their approach to the use of mathematics in economics.There is an obvious parallel between Samuelson’s wartime work on ballistics and Wilson’s First World War move into aeronautics. It is not clear when Samuelson started this work, for he claimed to have worked on the problem of fire control before he entered the Radiation Laboratory full time. He taught in the mathematics department, and it is entirely plausible that, in teaching in the mathematics department in wartime, his focus was the mathematics of projectiles, to which calculus and differential equations are directly applicable. He might also have discussed the problem in the seminar run by Norbert Wiener, in which cybernetics was worked out. However, whereas Wilson went on to write a textbook in aeronautics, Samuelson ended his time in the Radiation Laboratory, impatient to return to working full time as an economist.
When he described himself, to Wheeler Loomis, the Radiation Laboratory director, as “a second-rate mathematician,” he was no doubt comparing himself with colleagues such as I. I. Rabi, Ivan Getting, and Stanislaw Ulam, realizing that in their company he would never be the star that he could be in economics. He was clearly respected by the scientists and mathematicians with whom he was working, for otherwise Rabi would never have invited him to become the official historian of the Manhattan Project to develop the atomic bomb. His response to Goldsmith’s attempts to recruit him as a consultant to the War Production Board show that, instead of choosing to immerse himself completely in science and engineering, he remained fascinated by economic problems.
He wanted to be somewhere he could excel.Given Samuelson’s commitment to operationalizing economic theory, it is no surprise that in 1940 he embarked, with Leonid Hurwicz, on an empirical project on the business cycle, focused on data analysis. This highly ambitious project clearly failed to produce the anticipated results, and Samuelson did not follow it up with other, similar projects. He was acquiring a thorough knowledge of mathematical statistics, working alongside Harold Freeman and the new cohort of economics graduate students at MIT, and could have continued a project using the methods being developed by Haavelmo and others at the Cowles Commission, but he did not. He chose not to become an econometrician in the modern sense of the term.
One reason why he remained skeptical of econometric results was E. B. Wilson, whose course had introduced him to mathematical statistics. Wilson had the mathematical expertise to engage in formal statistical or econometric modeling, and yet he is on record as admiring the work of Wesley Clair Mitchell, seeing the need for taxonomic work analogous to that involved in identifying species in biology. Theory had to be combined with close awareness of economic data. This explains why Wilson could work closely with his Harvard colleagues, Crum and Frickey, whose work Samuelson disparaged. Attaching importance to a good understanding of data (how it was constructed and what it meant) was consistent with his view that theory should not be applied unless there were evidence that doing so increased knowledge, and corresponded with his sympathy towards Stephen Leacock's skepticism of complicated mathematical theories.
Samuelson's most systematic engagement with statistics came during wartime. His work at the National Resources Planning Board (NRPB) did not involve complex formal modeling, let alone the estimation of a probability model, as advocated by Haavelmo, but did call for meticulous analysis of consumption patterns and the consequences of changes in the distribution of income.
Inference was not involved, just careful data analysis. Data were also at the forefront when Samuelson discussed the multiplier with economists in wartime Washington. He was obviously concerned with theoretical problems—such as what came to be known as the balanced budget multiplier—but data were never far away because to be usable for policy, a number needed to be attached to the multiplier. Samuelson clearly paid as much attention to the appropriate data as to getting theory right.Coming from this perspective, it should be no surprise that, faced with the exchange between Koopmans and Vining over “measurement without theory,” Samuelson would give at least partial support to Vining's defense of empiricism “against the perfectionistic-formalism of the Cowles Commission.”2 Samuelson did not share Wilson's enthusiasm for Mitchell's economics—he regarded the approach taken at the National Bureau of Economic Research as having grown decadent in the thirty years from Mitchell's first book on the business cycle to his last (with Arthur Burns). Samuelson could never have written, as Wilson had done in 1938, that he endorsed everything Mitchell had done. However, Samuelson's pragmatic use of different methods of data analysis, maintaining a distance between theorizing and data analysis, but undertaking theory while being immersed in facts, closely reflected Wilson's position.