Stiglitz and the full force of Sonnenschein-Mantel-Debreu

16 September, 2017 at 15:43 | Posted in Economics | 1 Comment

In his recent article on Where Modern Macroeconomics Went Wrong, Joseph Stiglitz acknowledges that his approach “and that of DSGE models begins with the same starting point: the competitive equilibrium model of Arrow and Debreu.”

This is probably also the reason why Stiglitz’ critique doesn’t go far enough.

It’s strange that mainstream macroeconomists still stick to a general equilibrium paradigm more than forty years after the Sonnenschein-Mantel-Debreu theorem — SMD — devastatingly showed that it  is an absolute non-starter for building realist and relevant macroeconomics:

SMD theory means that assumptions guaranteeing good behavior at the microeconomic level do not carry over to the aggregate level or to qualitative features of the equilibrium …

24958274Given how sweeping the changes wrought by SMD theory seem to be, it is understandable that some very broad statements about the character of general equilibrium theory were made. Fifteen years after General Competitive Analysis, Arrow (1986) stated that the hypothesis of rationality had few implications at the aggregate level. Kirman (1989) held that general equilibrium theory could not generate falsifiable propositions, given that almost any set of data seemed consistent with the theory …

S. Abu Turab Rizvi

New Classical-Real Business Cycles-DSGE-New Keynesian microfounded macromodels 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 SMD unequivocally showed that there did not exist any condition by which assumptions on individuals would guarantee either stability or uniqueness of the equilibrium solution.

Opting for cloned representative agents that are all identical is of course not a real solution to the fallacy of composition that SMD 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.

Of course, most macroeconomists know that to use a representative agent is a flagrantly illegitimate method of ignoring real aggregation issues. They keep on with their business, nevertheless, just because it significantly simplifies what they are doing. It reminds — not so little — of the drunkard who has lost his keys in some dark place and deliberately chooses to look for them under a neighbouring street light just because it is easier to see there.

Frank-Ackerman_0General equilibrium is fundamental to economics on a more normative level as well. A story about Adam Smith, the invisible hand, and the merits of markets pervades introductory textbooks, classroom teaching, and contemporary political discourse. The intellectual foundation of this story rests on general equilibrium, not on the latest mathematical excursions. If the foundation of everyone’s favourite economics story is now known to be unsound — and according to some, uninteresting as well — then the profession owes the world a bit of an explanation.

Frank Ackerman

Almost a century and a half after Léon Walras founded general equilibrium theory, economists still have not been able to show that markets lead economies to equilibria. We do know that — under very restrictive assumptions — equilibria do exist, are unique and are Pareto-efficient. But — what good does that do? As long as we cannot show that there are convincing reasons to suppose there are forces which lead economies to equilibria — the value of general equilibrium theory is nil. 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.

Continuing to model 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.

 kirman

The full force of the Sonnenschein, Mantel, and Debreu (SMD) result is often not appreciated. Without stability or uniqueness, the intrinsic interest of economic analysis based on the general equilibrium model is extremely limited …

The usual way out of this problem is to assume a “representative agent,” and this obviously generates a unique equilibrium. However, the assumption of such an individual is open to familiar criticisms (Kirman 1992; Stoker 1995), and recourse to this creature raises one of the basic problems encountered on the route to the place where general equilibrium has found itself: the problem of aggregation. In fact, we know that, in general, there is no simple relation between individual and aggregate behavior, and to assume that behavior at one level can be assimilated to that at the other is simply erroneous …

The very fact that we observe, in reality, increasing amounts of resources being devoted to informational acquisition and processing implies that the standard general equilibrium model and the standard models of financial markets are failing to capture important aspects of reality.

Alan Kirman

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1 Comment

  1. “Santa Claus is for kids.”

    For me, the great promise of technology is that we can create anything we imagine, nondestructively, in virtual settings at least. We can program Santa Claus.

    “a gross misallocation of intellectual resources and time.”

    I would say, let modelers program their models and live in them. I’ll program my model, populate it as needed with voluntary participants and/or holograms. Live and let live (but if you want to kill you can do that in your VR …).


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