by No man is an island! Given how sweeping the changes wrought by SMD (Sonnenschein-Mantel-Debreu) 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. These views are widely shared … General equilibrium theory “poses some arduous challenges” as a “paradigm for organizing and synthesizing economic data” so that “a widely accepted empirical counterpart to general equilibrium theory remains to be developed” (Hansen and Heckman 1996). This seems to be the now-accepted view thirty years after the advent of SMD theory … S.
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No man is an island!
Given how sweeping the changes wrought by SMD (Sonnenschein-Mantel-Debreu) 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.
These views are widely shared … General equilibrium theory “poses some arduous challenges” as a “paradigm for organizing and synthesizing economic data” so that “a widely accepted empirical counterpart to general equilibrium theory remains to be developed” (Hansen and Heckman 1996). This seems to be the now-accepted view thirty years after the advent of SMD theory …
And so what? Why should we care about Sonnenschein-Mantel-Debreu?
Because Sonnenschein-Mantel-Debreu ultimately explains why New Classical, Real Business Cycles, Dynamic Stochastic General Equilibrium (DSGE) and “New Keynesian” 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.
In case you think this verdict is only a heterodox idiosyncrasy, here’s what one of the world’s leading microeconomists — Alan Kirman — writes in his thought provoking paper The intrinsic limits of modern economic theory:
If one maintains the fundamentally individualistic approach to constructing economic models no amount of attention to the walls will prevent the citadel from becoming empty. Empty in the sense that one cannot expect it to house the elements of a scientific theory, one capable of producing empirically falsifiable propositions …
Starting from ‘badly behaved’ individuals, we arrive at a situation in which not only is aggregate demand a nice function but, by a result of Debreu, equilibrium will be ‘locally unique. Whilst this means that at least there is some hope for local stability, the real question is, can we hope to proceed and obtain global uniqueness and stability?
The unfortunate answer is a categorical no! [The results of Sonnenchein (1972), Debreu (1974), Mantel (1976) and Mas Collel (1985)] shows clearly why any hope for uniqueness or stability must be unfounded … There is no hope that making the distribution of preferences or income ‘not to dispersed’ or ‘single peaked’ will help us to avoid the fundamental problem …
The problem seems to be embodied in what is an essential feature of a centuries-long tradition in economics, that of treating individuals as acting independently of each other …
To argue in this way suggests … that once the appropriate signals are given, individuals behave in isolation and the result of their behaviour may simply be added together …
The idea that we should start at the level of the isolated individual is one which we may well have to abandon … we should be honest from the outset and assert simply that by assumption we postulate that each sector of the economy behaves as one individual and not claim any spurious microjustification …
Economists therefore should not continue to make strong assertions about this behaviour based on so-called general equilibrium models which are, in reality, no more than special examples with no basis in economic theory as it stands.
Getting around Sonnenschein-Mantel-Debreu using representative agents may be — from a purely formalistic point of view — very expedient. But — from a scientific point of view — relevant and realistic? No way! Although garmented as representative agent, the emperor is still naked.
Treating people as if they live and act independently of each other takes us nowhere in understanding and explaining society.