Statistical Theory

Though there is no evidence that Samuelson persisted with the Babson- funded project after Hurwicz departed, he remained focused on statistics, a subject he taught at one point with Harold Freeman.

Samuelson also took up a suggestion made in a recent issue of Econometrica that a regression equation should be calculated, not by minimizing the sum of squared deviations from the line (the usual method), but by minimizing the sum of absolute deviations. The advantage of this method, it had been claimed, was that it was not necessary to determine whether y depended on x or vice versa: one would get the same result whichever assumption was made.¹⁸ This was, Samuelson pointed out, one of many ways in which a regression line could be calculated; and to choose between various methods, he listed six properties that might be thought desirable ones for a regression line to have and against which they could be evaluated. However, the most significant observation was that the dependence of one variable on another should matter.

If the aim of the investigation is not simply a characterization of the properties of the multivariate distribution, but rather the search for a hypothetical “true” (in some sense) linear relationship, upon which has been superimposed a distribution of errors, then no definite method of determining the regression equation can be specified until some assumptions have been made concerning the nature of the disturbing causes.

This article is not, in itself, of any great importance, but Samuelson’s argu­ments show that he was engaging closely with the emerging literature on econometric methods. He cited Tjalling Koopmans’s Linear Regression Analysis of Economic Time Series (1937), where attention had been paid to mea­surement errors in the variables. Samuelson was not clear on the nature of the errors involved (were they the result of measurement error or did errors arise because behavior was partly random?), but his arguments are consistent with

c. That is, the solutions to an equation of the form be less than one. his having still been thinking along the same lines as Koopmans. His argu­ments are also consistent with the close attention Samuelson paid to residuals when estimating a consumption function the previous year. Though he does not use such language, the idea that statistical analysis required the specifica­tion of an underlying probability model, thereby making it possible to test hypotheses rather than simply to estimate relationships, was one of the cru­cial features of arguments that a Norwegian economist, Trygve Haavelmo, who was currently on a Rockefeller Fellowship to study in the United States, put forward in a working paper, On the Theory and Measurement of Economic Relations (1941).²⁰

This paper, which was later published as a special issue of Econometrica (1944) and was very important in the history of econometrics, justified the use of statistical methods of hypothesis testing to aggregate data where no sampling was involved. Samuelson still had strong connections with Harvard, where Haavelmo had written the paper, and he was among those who received a copy when a limited number were produced in August.²¹ Like Haavelmo, Samuelson believed that empirical work in economics involved integrating economic theory with statistical methods, for without economic theory it was impossible to specify the probability model to be tested.

In the 1942—43 session, two students who had arrived in the second cohort of the PhD program, Lawrence Klein and Joseph Ullmann, felt the need for additional knowledge of statistics, and they organized a seminar series involving speakers from inside and outside MIT.^22,d Samuelson attended reg­ularly. Samuelson and Harold Freeman gave papers, as did two of their stu­dents. There were several speakers from the MIT Mathematics Department, including Norbert Wiener, who expounded ergodic theory, to the bafflement of Economics Department chair, Ralph Freeman, who attended by accident and became trapped there. Wiener had begun his talk by reminding them that they were at war and that nothing heard in the room should be repeated outside, lest it give comfort to the enemy. To this, Freeman responded after Wiener had left, “Hell, Hitler and Himmler couldn't get a word out of me even if the speaker had been a coherent lecturer.”²³

Harold Hotelling came from Columbia to survey unsolved problems in statistics, covering the foundations of statistics, statistical decision mak­ing, and computational methods. Many of these problems were tackled in other seminars. Samuelson thought the best lecturer was Abraham Wald, the Romanian statistician who with Karl Schlesinger had proved the existence of

d. Klein is discussed further in chapter 24 this volume. a competitive general equilibrium, and had been recruited to Columbia by Hotelling. He lectured on tolerance limits, a problem that was important to quality control in manufacturing. Harold Freeman applied Bayesian methods to the problem of industrial sampling—testing a batch of products to find out how many are defective, and E. B. Wilson came from Harvard to talk about contingency tables. William Feller came from Brown to talk about the theory of stochastic processes.

Perhaps the most significant paper was by Haavelmo, by then working for the Norwegian Shipping and Trade Mission, on March 30, 1943. When inviting him, Ullman explained that many of the participants in the seminar would have read On the Theory and Measurement of Economic Relations and were interested in the problem of applying Jerzy Neymann’s theory of hypothesis testing to economics.

Klein, one of the seminar organizers and Samuelson’s PhD student, quickly took note of Haavelmo’s analysis and used it in a paper he published later that year.²⁶ Its effect on Samuelson is less clear, though he had been among the early readers of Haavelmo’s 1941 manuscript and clearly under­stood the arguments involved. When he recalled the seminar many years later, he wrote of how it had changed econometrics. “His [Haavelmo’s] MIT lecture,” Samuelson wrote, was not “a routine review” but was “a first revela­tion of what was to be a major stimulus for the Chicago Cowles group.”^27,e He went on to say that, when explaining the problems involved in estimat­ing simultaneous equations, Haavelmo had taken his (Samuelson’s) version

e. The Cowles Commission, based at the University of Chicago from 1938 to 1955, was to play a major role in developing modern econometric methods along the lines laid down by Haavelmo in the early 1940s.

of the multiplier-accelerator model as his example and shown that what they “would have” done before his talk was, in general, wrong.^f

Given that Samuelson and Hurwicz had tried to estimate a model of the business cycle, and that it would have been natural to have started with Samuelson’s own model, it is tempting to conjecture that what “we would have” done before Haavelmo’s talk was what Samuelson and Hurwicz had been trying to do two years earlier (though spectral analy­sis would have been something different).

During the 1942—43 academic year, Samuelson published two further papers in the Annals and in the Proceedings of the National Academy of Sciences, edited by Wilson since 1915, on mathematical problems that, although they arose in statistics, might appear in any field where matrix algebra was used. In one, he developed a method suggested by his friend, the chemist E. Bright Wilson, for computing the roots of a characteristic equation of a matrix.²⁸ The other proposed a method for determining latent vectors of a matrix.²⁹ The Annals of Mathematical Statistics also published a paper, “Fitting Gram- Charlier Series,” that was closely related to (if not the same as) the one he had presented to the statistics seminar that year.³⁰

Following up on a suggestion made several years earlier by Wilson, this paper attempted to simplify and bring together two ways of representing a probability distribution. This attracted the attention of Lotka, who pointed out that the expansions of a probability distribution Samuelson had been using were similar to one he was using to represent birth and death rates in a population.³¹ He noted that the field of possible applications of such functions was very broad. Of potentially even broader application was a fifth mathematical paper, also published in Wilson’s Proceedings of the National

f. What they would have done was to calculate two ordinary least squares regression equations—of consumption on lagged income and of investment on the change in income (or capital stock on income).

g. Samuelson later wrote, “Econometrics was never the same after [Haavelmo’s] famous Supplement,” the 118-page article, published as a supplement to Econometrica, in which he provided the most complete statement of these ideas (Haavelmo 1944; Samuelson 1991b, p.

Academy of Sciences, in which Samuelson proposed a new method of interpola­tion.³² These papers all tackled problems arising in mathematical statistics that were also important in analyzing dynamic economic models.

The breadth of Samuelson’s reading in statistics and the confidence with which he was prepared to criticize others’ work at this time are illustrated by a review of The Analysis of Economic Time Series by Harold Davis (1941), a mathematician associated with the Cowles Commission since its founda­tion. Samuelson found material to praise in the book, including three of the chapters on statistical theory and the chapter dealing with the equation of exchange (the quantity theory of money). However, beyond that, though his review was at all times polite, he offered a critique of what was a long (620-page) technical volume. Samuelson criticized in detail the remain­ing four chapters on statistical theory: methods Davis was advocating were inferior to other methods found in the literature; Davis had failed to con­sider the efficiency of statistical tests he was using; and Davis had not taken account of important new work, notably “the modern theories of estimation and distribution associated with Fisher and Neymann.”³³ As for the eco­nomic applications, Samuelson opined that Davis’s comparative advantage lay in statistics, and clearly he was not impressed by his “economic time series” theory of history that forecast when revolutions were likely to occur. Samuelson’s criticisms of the chapter on income distribution showed his familiarity with recent empirical literature. The review closed with the self­confident remark that he had focused on the book’s shortcomings “because economic statisticians do not always have the necessary technical equipment to ferret out points of difficulty in a book that nonetheless contained ‘many solid contributions.’ ”

This review was probably discussed when Samuelson encountered Davis at a conference the following year, for after such a substantial review, Davis might well have felt they had a lot to talk about. Their conversation prompted Samuelson to write a letter to Harold Freeman, in October 1944. Headed “Memorandum to H. A. Freeman,” it read,

Ours has been a beautiful friendship. But enough is enough. I hope you will not think that I have a prejudice against practical men—on the contrary, some of my best friends are practical men. And I’ll go so far as to say that every department can afford to tolerate one such. But you introduce one practical man into the department and he will bring another, and another, and another. Moreover, his friends will be practical men, and one will be forced to utilize valuable time in talk­ing to such practical men.

You will gather that I have been besieged for hours (or was it days?) by one Harold M. Davis—a good friend of yours—and that I hold you personally responsible for my anguish.

Therefore, I am taking this occasion to sever all relationships with you and yours; and I am instructing my wife and family to the most distant connection, to do the same. In the future if we should meet and there is no one, present, I shall, of course, not speak to you; and I shall expect you to return the courtesy. However, should it become necessary, in connection with my departmental duties, to have deal­ings with you, I shall submit with as good grace as I can muster; but that is my limit.³⁴

There was, of course, no rupture, even if Samuelson had thought that Davis had taken too much of his time.