Mathiness is Next to Growthiness

What should worry economists is the pattern, not any one of these papers. And our response. Why do we seem resigned to tolerating papers like this? What cumulative harm are they doing? -- Paul Romer

It is bracing to see the intense (dare I call it petulant?) indignation expressed by Paul Romer toward papers by McGrattan and Prescott, Lucas and Moll, and Boldrin and Levine. He goes so far as to confess "embarrassment" that his suggestions as discussant were acknowledged by McGrattan and Prescott in an earlier version of their paper. He complains of "a lemons equilibrium in the market for mathematical theory" and laments "years of being bullied by bad theory."

Economists detained after theory rumble between "Freshwater" and "Saltwater" gangs

Superficially, Romer's diatribe against mathiness may recall Nicolas Georgescu-Roegen's principled objection to unhinged "arithmomorphism." But any perceived resemblance is purely coincidental.

Georgescu-Roegen was described in a critical note as "the methodological conscience of the profession for over a decade" whose mathematical renown rendered "his closely argued objections to the domination by mathematical methods... all the more welcome." In "Methods in Economic Science" (1979), Georgescu-Roegen wrote:

"According to the temper that has prevailed for some time now in the social sciences, but especially in economics, the contributions that deserve the highest praise are those using a heavy mathematical armamentarium; the heavier and the more esoteric, the more worthy of praise. Protests against this situation have not failed to be made sufficiently often to have deserved attention. What is more, protests of this kind were made not only by "verbal" economists, such as Thorstein Veblen and Frank H. Knight, but also by some who were well familiar with the mathematical tool, for example, Alfred Marshall, Knut Wicksell, and Lord Keynes. Knight lamented that there are many members of the economic profession who are "mathematicians first and economists afterwards." The situation since Knight’s time has become much worse. There are endeavors that now pass for the most desirable kind of economic contributions although they are just plain mathematical exercises, not only without any economic substance but also without mathematical value. Their authors are not something first and something else afterwards; they are neither mathematicians nor economists. How dangerous is the infatuation with pure mathematical symbolism is proved by the fact that voices from the circle of natural scientists have also often denounced it. ...

The fundamental reason why we cannot do without dialectical concepts is that actuality, at least as seen by the human mind, continuously changes qualitatively. … 

The most we can expect from an arithmomorphic model is to depict pure growth, or rather pure quantitative variations of qualitatively different but self-identical elements. 

In a 1981 commentary on Georgescu-Roegen's paper, Salim Rashid defended economists' persistence in undialectical methods as lying "not in their failure to appreciate the importance of dialectical logic, but in the institutional structure within which they live and work." To illustrate the utility of mathiness to career survival "at any reasonably good university," Rashid offered what he described as a "somewhat exaggerated" account of the "inimitable merits of mathematics" for facilitating "the process of grinding out articles." Furthermore, he maintained,

"...it is not the good mathematical economists or econometricians who insist upon the value of mathematical methods... The best users of mathematics can always move to a related field and do their research; it is the hordes of practitioners with lesser abilities who feel it essential to insist upon the value of mathematical methods."

By this account, then, the value of excessive mathiness was that it enabled mediocre junior faculty to survive and gain promotion in "any reasonably good university." In his reply to Rashid's commentary, Georgescu-Roegen asked, "Since publish or perish applies to all academe, why is it that economists alone can subsist by automatically grinding out empty exercises from the mathematical mechanism?" His answer was that "the American economics profession is dominated by a powerful and well-entrenched establishment determined to defend at all cost the type of economics by which virtually all its members climbed to the summit."

Romer lionizes Robert Solow and Gary Becker in contrast to Prescott, et al. In my opinion, Romer vastly overstates the cogency of Becker's contribution. As for Solow's growth theory, Georgescu-Roegen had a few things to say about that, too. In "Dynamic Models and Economic Growth" (1975), Georgescu-Roegen characterized Solow's model as one of "the most pertinent examples of the shortcomings of the mechanico-descriptive approach":

The economic literature of the last hundred years abounds in examples of this [mechanico-descriptive] category. The situation is the inevitable consequence of the mechanistic epistemology of our Neoclassical forefathers, who succeeded in convincing almost every subsequent economist that, if economics is to be a science at all, it must be set up as 'the mechanics of utility and self-interest'. We may mention, first of all, the picture of the economic process as  a self-sustained circular movement between production and consumption (indifferently, between consumption and production) which adorns the most respected manuals. Perfect reversibility is present everywhere. It constitutes the main pillar of the theory of market equilibrium. According to the ultra-familiar picture, if demand shifts from D to D ', the market moves from E to E'; and should, later, the factor responsible for the shift disappear, the market would return to E, in a manner perfectly similar to that of a mechanical pendulum which can swing back and forth with equal ease. True, no economist has even suggested that a process of production may be reversed so as to convert pieces of furniture back into trees. However, the classical theory of business cycles -- as this traditional name indicates -- rests on the idea that the entire economic process may come back to any previous position by following the same path in reverse. We should also note that the entire theory of production is still based on the simple formula known as the production function, which is not a satisfactory description even of the reproducible process of production, i.e., of the simplest possible arrangement. But the most pertinent examples of the shortcomings of the mechanico-descriptive approach are the standard dynamic models beginning with that of Harrod and Domar and ending with those of Solow and Leontief. ...

…no analysis which, instead of assuming away the qualitative change associated with an actual process, focuses on that very change can attain its aim through an arithmomorphic model alone. The reason is that there is an irreducible incompatibility between qualitative change, i.e., between essential novelty, and arithmomorphic structures. It is this last point that shatters the generally accepted validity of the standard dynamic models as adequate representations of actual processes.  

…mere growth -- i.e., change confined to quantity -- cannot exist in actuality continuously. The same is true even for the so-called stationary state.  Briefly, continuous existence in a finite environment necessarily requires qualitative change. And it is this qualitative change that accounts for the irreversibility of the economic process, of any actual process for that matter.   

Irreversibility and reversibility are the very properties that distinguish actual processes (which all are evolutionary in some sense or another) from those governed only by the laws of mechanics. We may therefore define a purely dynamic system as a system capable of returning to any of its previous positions. Certainly, all dynamic economic systems fulfil this condition: the fundamental notion behind dynamic economics is that investing and disinvesting, growth and contraction, are absolutely symmetrical operations.

Note that Georgescu-Roegen didn't exclude the "stationary state" from his critique. In a footnote, he singled out the fallacy of the Limits to Growth prescription: "Incidentally, this conclusion exposes the fallacy of those topical programmes which see the ecological salvation of mankind in a stationary state -- as the Club of Rome, for instance, does. See Donella Meadows et al." In "Energy and Economic Myths" (1975), however, Georgescu-Roegen noted the irony that Limits to Growth caused such consternation among economists -- "criticism of the report has come mainly from economists" (including Solow) -- apparently because it "employed analytical models of the kind used in econometrics and simulation works." What irked economists, in Georgescu-Roegen's view, was the intrusion on what they regarded as their turf:

Let us begin by recalling, first, that economists, especially during the last thirty years, have preached right and left that only mathematical models can serve the highest aims of their science. With the advent of the computer, the use of econometric models and simulation became a widespread routine. The fallacy of relying on arithmomorphic models to predict the march of history has been denounced occasionally with technical arguments. But all was in vain. Now, however, economists fault The Limits to Growth for that very sin and for seeking "an aura of scientific authority" through the use of the computer; some have gone so far as to impugn the use of mathematics. Let us observe, secondly, that aggregation has always been regarded as a mutilating yet inevitable procedure in macroeconomics, which thus greatly ignores structure. Nevertheless, economists now denounce the report for using an aggregative model. Thirdly, one common article of economic faith, known as the acceleration principle, is that output is proportional to capital stock. Yet some economists again have indicted the authors of The Limits for assuming (implicitly) that the same proportionality prevails for pollution — which is an output, too! Fourthly, the price complex has not prevented economists from developing and using models whose blueprints contain no prices explicitly — the static and dynamic Leontief models, the Harrod-Domar model, the Solow model, to cite some of the most famous ones. In spite of this, some critics (including Solow himself) have decried the value of The Limits on the sole ground that its model does not involve prices.  

The final and most important point concerns the indisputable fact that, except for some isolated voices in the last few years, economists have always suffered from growthmania. Economic systems as well as economic plans have always been evaluated only in relation to their ability to sustain a great rate of economic growth. Economic plans, without a single exception, have been aimed at the highest possible rate of economic growth. The very theory of economic development is anchored solidly in exponential growth models. But when the authors of The Limits also used the assumption of exponential growth, the chorus of economists cried "foul!" This is all the more curious since some of the same critics concomitantly maintained that technology grows exponentially. Some, while admitting at long last that economic growth cannot continue forever at the present rate, suggested, however, that it could go on at some lower rates.

As these observations from Georgescu-Roegen testify, mathiness has always been deeply implicated in growth theory from the earliest days. This analysis continues in the follow-up post, Denial, Then and Now: "Is the End of the World at Hand?" "Is the Economic System Self-Adjusting?"