PKT message, The Method Of Comparative Statics

This morning, it occurred to me that an overview of the reasons for my challenge back in the 1970s to key methodological pre-suppositions of the neo-classical tradition become those of mainstream/monetarist/PK economics might be helpful in clearing the ground for the advancement of better - Creditary - economics in the 21st century. For, as Einstein put it, "Science without epistemology is - insofar as it is thinkable at all - primitive and muddled."

The result follows.

In his biographical essay on Alfred Marshall, Keynes wrote (a) that his Sixth Form "mathematical master" judged Marshall to have "a genius for mathematics", and (b) that Marshall's "design to study physics was (in his own words) 'cut short by the sudden rise of a deep interest in the philosophical foundation of knowledge, especially in relation to theology'."

These twin strands of Marshall's intellectual endowment and interests were later reflected in his contention - noted and disputed by Schumpeter in History of Economic Analysis - to the effect that use of the differential calculus in economics was predicated on epistemological considerations analogous to those underlying its use in theoretical physics.

In Foundations of Economic Analysis, Paul Samuelson - "a genius for mathematics" - summarized the mathematical aspects of "the method of comparative statics" in theoretical economics, noting that it "is but one special application of the more general practice of scientific deduction in which the behavior of a system (possibly through time) is defined in terms of a given set of functional equations and initial conditions." (p. 8)

Curiously, Samuelson did not address directly associated epistemological issues which, as indicated by the conflicting views of Marshall and Schumpeter, are anything but transparent - indeed, as F. H. Hahn would later put it in response to my own views thereon, "epistemology is a very hard subject." Instead, in a famous passage, Samuelson invoked his own 'feelings' to launch an indirect attack on certain key methodological implications of Marshall's epistemological conclusions.

"I have come to feel," Samuelson wrote, "that Marshall's dictum that 'it seems doubtful whether any one spends his time well in reading lengthy translations of economic doctrines into mathematics, that have not been made by himself' should be exactly reversed. The laborious literary working over of essentially simple mathematical concepts such as is characteristic of much of modern economic theory is not only unrewarding from the standpoint of advancing the science, but involves as well mental gymnastics of a peculiarly depraved type." (p. 6)

A point well taken if "the method of comparative statics" is shown to be admissible on epistemological grounds in the first place. In the specific context of Samuelson's Foundations, the key point at issue reduces to the question whether "the method of comparative statics" can in principle serve as point of departure for specification of what Samuelson called "operationally meaningful theorems" and claimed to exist "in diverse fields of economic affairs." (pp. 4-5)

"By a meaningful theorem," he explained, "I mean simply a hypothesis about empirical data which could conceivably be refuted, if only under ideal conditions. A meaningful theorem may be false. It may be valid but of trivial importance. Its validity may be indeterminate, and practically difficult or impossible to determine. Thus, with existing data, it may be impossible to check upon the hypothesis that the demand for salt is of elasticity - 1.0. But it is meaningful because under ideal circumstances an experiment could be devised whereby one could hope to refute the hypothesis." (p. 4)

Such "hypotheses", Samuelson added, "are not deduced from thin air or from a priori propositions of universal truth and vacuous applicability. They proceed almost wholly from two types of very general hypotheses. The first is that the conditions of equilibrium are equivalent to the maximization (minimization) of some magnitude.

"However, when we leave single economic units, the determination of unknowns is found to be unrelated to an extremum position. In even the simplest business cycle theories there is lacking symmetry in the conditions of equilibrium so that there is no possibility of directly reducing the problem to that of a maximum or minimum. Instead the dynamical properties of the system are specified, and the hypothesis is made that the system is in "stable" equilibrium or motion. By means of what I have called the Correspondence Principle between comparative statics and dynamics, definite operationally meaningful theorems can be derived from so simple a hypothesis. One interested only in fruitful statics must study dynamics.

"The empirical validity or fruitfulness of the theorems, of course, cannot surpass that of the original hypothesis." (p. 5)

The question, then, is whether - in principle - the requisite "ideal circumstances" can exist within real-world economic systems of the kind described by Samuelson in the opening pages of Foundations of Economic Analysis.

"Within the framework of any [such] system," Samuelson explained in this respect, "the relationships between our variables are strictly those of mutual interdependence. It is sterile and misleading to speak of one variable as causing or determining another. Once the conditions of equilibrium are imposed, all variables are simultaneously determined. Indeed, from the standpoint of comparative statics equilibrium is not something which is attained; it is something which, if attained, displays certain properties.

"The only sense in which the use of the term causation is admissible is in respect to changes in external data or parameters. As a figure of speech, it may be said that changes in these cause changes in the variables of our system. An increase in demand, i.e., a shift in the demand function due to a change in the data, tastes, may be said to cause an increased output to be sold. Even here, when several parameters change simultaneously, it is impossible to speak of causation attributable to each except in respect to limiting rates of change (partial derivatives)." (pp. 9-10)

In the final analysis, therefore, the admissibility of "the method of comparative statics" is contingent on the admissibility in general equilibrium reasoning of "external data or parameters" in the first place. In the late 1970s, I suggested to Samuelson that the very concept of "external data or parameters" had no place in general equilibrium systems of the kind exemplified by Newtonian Mechancis as evidenced, inter alia, by the Laplacian construction thereof in the 19th century.

In his reply, Samuelson did not address the point at issue directly - instead, he noted that "there are few expert in both economics and physics" and professed to be "confident that any such would not agree that you have isolated a contradiction in my Foundations." Later, he declined to respond to my challenge on grounds of advancing age, pressure of other research, and his decision, in principle, not to respond to comments, "favorable or unfavorable", on his Foundations.

And how might all this relate to Marshall's epistemological views noted above?

Briefly, his proposition "to the effect that use of the differential calculus in economics was predicated on epistemological considerations analogous to those underlying its use in theoretical physics" reflects a view of the relationship between "theory" and "reality" shared by Isaac Newton, David Hume, and Albert Einstein, namely, that "theory" is an acausal or purely descriptive model of empirical data within its domain, be it that of theoretical physics or economics.

That is, "theory" is to "reality" as "map" is to "territory" - a mental or pictorial representation of its domain. Whence it follows that the fit between prediction and outcome is the sole criterion for judging the merits of any theory in either physics or economics - the subject of Marshall's 'dictum' that "it seems doubtful whether any one spends his time well in reading lengthy translations of economic doctrines into mathematics, that have not been made by himself."

Indeed, there is nothing "doubtful" about it!

For, insofar as "economic doctrines" predicated on "the method of comparative statics" are concerned, the epistemological considerations outlined above reveal their substantive - or would-be scientific - worth to be precisely nil.

Gunnar