Finding equilibrium

5 Feb, 2015 at 12:32 | Posted in Economics | 5 Comments

Finding Equilibrium explores the post–World War II transformation of economics by constructing a history of the proof of its central dogma—that a competitive market economy may possess a set of equilibrium prices. The model economy for which the theorem could be proved was mapped out in 1954 by Kenneth Arrow and Gerard Debreu collaboratively, and by Lionel McKenzie separately, and would become widely known as the “Arrow-Debreu Model.” While Arrow and Debreu would later go on to win separate Nobel prizes in economics, McKenzie would never receive it. Till Düppe and E. Roy Weintraub explore the lives and work of these economists and the issues of scientific credit against the extraordinary backdrop of overlapping research communities and an economics discipline that was shifting dramatically to mathematical modes of expression.

Based on recently opened archives, Finding Equilibrium shows the complex interplay between each man’s personal life and work, and examines compelling ideas about scientific credit, publication, regard for different research institutions, and the awarding of Nobel prizes. Instead of asking whether recognition was rightly or wrongly given, and who were the heroes or villains, the book considers attitudes toward intellectual credit and strategies to gain it vis-à-vis the communities that grant it.

Telling the story behind the proof of the central theorem in economics, Finding Equilibrium sheds light on the changing nature of the scientific community and the critical connections between the personal and public rewards of scientific work.

Although I find Düppe’s and Weintraub’s book a well-researched and interesting reading , I still can’t get rid of the feeling that all these efforts at modeling a world full of agents behaving as economists — “often wrong, but never uncertain” — and still not being able to show that the system under reasonable assumptions converges to equilibrium (or simply assume the problem away), is a gross misallocation of intellectual resources and time.

Almost a century and a half after Léon Walras founded neoclassical general equilibrium theory, economists still have not been able to show that markets move economies to equilibria.

We do know that — under very restrictive assumptions — equilibria do exist, are unique and are Pareto-efficient. After reading Franklin M. Fisher’s masterly paper The stability of general equilibrium: results and problems one however has to ask oneself — what good does that do?

An extremely prominent economist [Milton Friedman – LPS] long ago remarked to me in passing that the study of stability is unimportant because it is obvious that the economy is stable and, if it isn’t, we are all wasting our time. I pass over the question of whether it really is obvious that the economy is stable and observe that the issue of time-wasting by economists is not one of whether the economy is stable but rather of whether the theory is. A principal reason for studying general equilibrium in the first place is to examine the consistency of partial equilibrium analyses. Having powerful theories of the firm, the household, and the market, may not be very useful if all those theories cannot be true at the same time.

Clearly, the heart of this important consistency question lies in the existence of general equilibrium, and existence theory, fortunately, is a subject which is in pretty satisfactory shape. Nevertheless, there is a sense in which the consistency question cannot be regarded as settled with- out a satisfactory analysis of stability. It is no use knowing that there exist points at which all partial equilibrium propositions can be jointly true, if such points are not attainable. Hence the question of the stability of general competitive equilibrium is a vital one for economic theorists, particularly if the economy is stable, but not only then. If general equilibrium turns out to be stable only under a very restrictive set of assumptions, then, indeed, we will all have been wasting our time, for there will be something wrong with the partial theory that we think we understand.

As long as we cannot show, except under exceedingly special assumptions, that there are convincing reasons to suppose there are forces which lead economies to equilibria — the value of general equilibrium theory is negligible. As long as we cannot really demonstrate that there are forces operating — under reasonable, relevant and at least mildly realistic conditions — at moving markets to equilibria, there cannot really be any sustainable reason for anyone to pay any interest or attention to this theory.

A stability that can only be proved by assuming “Santa Claus” conditions is of no avail. Most people do not believe in Santa Claus anymore. And for good reasons. Santa Claus is for kids, and general equilibrium economists ought to grow up.

And then, of course, there is Sonnenschein-Mantel-Debreu!

So what? Why should we care about Sonnenschein-Mantel-Debreu?

Because  Sonnenschein-Mantel-Debreu ultimately explains why “modern neoclassical economics” — New Classical, Real Business Cycles, Dynamic Stochastic General Equilibrium (DSGE) and “New Keynesian” — with its microfounded macromodels are such bad substitutes for real macroeconomic analysis!

These models try to describe and analyze complex and heterogeneous real economies with a single rational-expectations-robot-imitation-representative-agent. That is, with something that has absolutely nothing to do with reality. And — worse still — something that is not even amenable to the kind of general equilibrium analysis that they are thought to give a foundation for, since Hugo Sonnenschein (1972) , Rolf Mantel (1976) and Gerard Debreu (1974) unequivocally showed that there did not exist any condition by which assumptions on individuals would guarantee neither stability nor uniqueness of the equlibrium solution.

Opting for cloned representative agents that are all identical is of course not a real solution to the fallacy of composition that the Sonnenschein-Mantel-Debreu theorem points to. Representative agent models are — as I have argued at length here — rather an evasion whereby issues of distribution, coordination, heterogeneity — everything that really defines macroeconomics — are swept under the rug.

Instead of real maturity, we see that general equilibrium theory possesses only pseudo-maturity. For the description of the economic system, mathematical economics has succeeded in constructing a formalized theoretical structure, thus giving an impression of maturity, but one of the main criteria of maturity, namely, verification, has hardly been satisfied. In comparison to the amount of work devoted to the construction of the abstract theory, the amount of effort which has been applied, up to now, in checking the assumptions and statements seems inconsequential.