Krugman on math and models in economics
from Lars Syll
Paul Krugman had a post up on his blog a while ago where he argued that “Keynesian” macroeconomics more than anything else “made economics the model-oriented field it has become.” In Krugman’s eyes, Keynes was a “pretty klutzy modeler,” and it was only thanks to Samuelson’s famous 45-degree diagram and Hicks’s IS-LM that things got into place. Although admitting that economists have a tendency to use ”excessive math” and “equate hard math with quality” he still vehemently defends — and always have — the mathematization of economics:
I’ve seen quite a lot of what economics without math and models looks like — and it’s not good.
Sure, “New Keynesian” economists like Krugman — and their forerunners, “Keynesian” economists like Paul Samuelson and the young John Hicks — certainly have contributed to making economics more mathematical and “model-oriented.”
But if these math-is-the-message-modelers aren’t able to show that the mechanisms or causes that they isolate and handle in their mathematically formalized macromodels are stable in the sense that they do not change when we “export” them to our “target systems,” these mathematical models do only hold under ceteris paribus conditions and are consequently of limited value to our understandings, explanations or predictions of real economic systems. Or as the eminently quotable Keynes wrote already in Treatise on Probability (1921):
The kind of fundamental assumption about the character of material laws, on which scientists appear commonly to act, seems to me to be [that] the system of the material universe must consist of bodies … such that each of them exercises its own separate, independent, and invariable effect, a change of the total state being compounded of a number of separate changes each of which is solely due to a separate portion of the preceding state … Yet there might well be quite different laws for wholes of different degrees of complexity, and laws of connection between complexes which could not be stated in terms of laws connecting individual parts … If different wholes were subject to different laws qua wholes and not simply on account of and in proportion to the differences of their parts, knowledge of a part could not lead, it would seem, even to presumptive or probable knowledge as to its association with other parts … These considerations do not show us a way by which we can justify induction … /427 No one supposes that a good induction can be arrived at merely by counting cases. The business of strengthening the argument chiefly consists in determining whether the alleged association is stable, when accompanying conditions are varied … /468 In my judgment, the practical usefulness of those modes of inference … on which the boasted knowledge of modern science depends, can only exist … if the universe of phenomena does in fact present those peculiar characteristics of atomism and limited variety which appears more and more clearly as the ultimate result to which material science is tending.
According to Keynes, science should help us penetrate to “the true process of causation lying behind current events” and disclose “the causal forces behind the apparent facts.” We should look out for causal relations. But models — mathematical, econometric, or what have you — can never be more than a starting point in that endeavour. There is always the possibility that there are other (non-quantifiable) variables – of vital importance and although perhaps unobservable and non-additive not necessarily epistemologically inaccessible – that were not considered for the formalized mathematical model.
These fundamental and radical problems are akin to those Keynes talked about when he launched his critique against the “atomistic fallacy” already in the 1920s:
The atomic hypothesis which has worked so splendidly in Physics breaks down in Psychics. We are faced at every turn with the problems of Organic Unity, of Discreteness, of Discontinuity – the whole is not equal to the sum of the parts, comparisons of quantity fails us, small changes produce large effects, the assumptions of a uniform and homogeneous continuum are not satisfied. Thus the results of Mathematical Psychics turn out to be derivative, not fundamental, indexes, not measurements, first approximations at the best; and fallible indexes, dubious approximations at that, with much doubt added as to what, if anything, they are indexes or approximations of.
The kinds of laws and relations that “modern” economics has established, are laws and relations about mathematically formalized entities in models that presuppose causal mechanisms being atomistic and additive. When causal mechanisms operate in real world social target systems they only do it in ever-changing and unstable combinations where the whole is more than a mechanical sum of parts. If economic regularities obtain they do it (as a rule) only because we engineered them for that purpose. Outside man-made mathematical-statistical “nomological machines” they are rare, or even non-existant. Unfortunately that also makes most of contemporary mainstream neoclassical endeavours of mathematical economic modeling rather useless. And that also goes for Krugman and the rest of the “New Keynesian” family.
Related Articles:
The Debunking of Economics https://sttpml.org/the-debunking-of-economics-a-review-of-the-work-of-steve-keen-et-al/
Some Lectures and Papers Presented in China https://sttpml.org/some-lectures-and-papers-presented-in-china/
Plutonomy on Steroids https://sttpml.org/plutonomy-on-steroids/
Paul Romer and Paul Krugman’s Dangerous Idea https://sttpml.org/paul-romers-and-paul-krugmans-dangerous-idea/
Malinvaud on how USA economists increasingly dismissed measurement
One of the problems of the economics curriculum is that very little attention is paid to measurement. And indeed, academic economists generally know little about this as most measurement is carried out by specialized statistical institutes. What about the history of this regrettable situation? The French economist Malinvaud (and long time head of the French statistical institute INSEE) has a nice metric on how USA economists increasingly dismissed empirical economics (let alone actual measurement) and turned to a-empirical ´high theory´ littered will ill-defined variables instead:
Econometric Methodology
at the Cowles Commission: Rise and MaturityEdmond Malinvaud
Abstracted from the Cowles Fiftieth Anniversary Volume
Considering the contribution of the Cowles research institute to the development of econometrics, one has little choice but to focus on one major achievement, the building of the simultaneous-equation methodology. It is not necessary to demonstrate the indisputable fact that this methodology was conceived and elaborated at the Cowles Commission in the forties. Neither does one need to insist on the long-standing significance of this achievement nor on its central place in any education or reflection concerning statistical inference about economic phenomena. More interesting is the question of how research at Cowles during the first 15 years of its existence led to this result and how further econometric research here during the last 30 years relates to the simultaneous-equation achievement.
For 20 years, the motto of the Cowles Commission, printed on its monographs and reports, was Lord Kelvin’s sentence, “Science is measurement.” This might suggest that the main emphasis was then given to econometrics and that, from the beginning, research was devoted to the subject that matured in the forties.
The facts are not so simple. In the first place, during the first years a good deal of attention was devoted to direct measurement, as distinct from inference based on available statistical measures. Cowles Commission Monograph No. 3, written by A. Cowles and associates, first published in 1938, was the outcome of the first research project selected in 1932 and was entirely devoted to working out monthly indexes of stock prices and annual indexes of stock yields. During the six Cowles Commission summer conferences held from 1935 to 1940, which then played a great role in the Commission’s activities, the progress of official statistics was occasionally discussed, in particular in papers that dealt with such subjects as population censuses.
During those first years, the research program at Cowles may be characterized as a combination of direct measurement, econometrics, and nonformalized study of economic evolution. Particularly typical of the last component was Cowles Commission Monograph No. 4, Silver Money, written by D.H. Leavens and published in 1939.
What about pure economic theory, which later took the predominant place in the Cowles Foundation activities? But it was not the direct subject of substantial research before September 1939 when O. Lange and I. Mosak simultaneously joined the staff Their Cowles Commission Monographs, respectively Nos. 8 and 7, both published in 1944, Price Flexibility and Employment, and General-Equilibrium Theory in International Trade, were the first ones to deal with formalized economic theory …
The next step occurred in 1942–1943 when L. Hurwicz, I. Marschak, and T. Haavelmo successively joined the Commission and when the series of the Cowles Commission Papers was started, to be later called the Cowles Foundation Paper Series. Glancing through the titles of the papers contained in this series, one may note that a sharp turn took place in 1950; indeed, economic theory was the subject of about one-third of the papers up to 1950, but of roughly two-thirds in the following years. By 1952 the role of theory had become so important that the motto “Science is measurement” no longer seemed to be appropriate. When C. Hildreth proposed to change it to “Theory and measurement,” the suggestion was immediately accepted. I do not know exactly when and why the motto was dropped; but I note that it still appears on the report for the two years 1952–54 but no longer on the 1954–56 Report of Research Activity.
…
Looking at the Cowles Foundation Papers published since then, I estimate that roughly one-fourth of them were devoted to such applications, the proportion being definitely higher during the late fifties. From the point of view of this paper, the important observation is, however, that research in econometric methodology did not regain, for three decades, the predominance it had had in the forties: only some 35 Cowles Foundation Papers out of more than 460 published between 1956 and 1982 clearly concerned this subject.