Krugman on math and models in economics

19 Nov, 2013 at 23:03 | Posted in Economics | 4 Comments

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.