Home > Uncategorized > Sonnenschein-Mantel-Debreu at fifty

Sonnenschein-Mantel-Debreu at fifty

from Lars Syll

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. It has been difficult to make progress on the elaborations of general equilibrium theory that were put forth in Arrow and Hahn 1971 …

24958274Fifteen 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. Bliss (1993, 227) wrote that the “near emptiness of general equilibrium theory is a theorem of the theory.” Mas-Colell, Michael Whinston, and Jerry Green (1995) titled a section of their graduate microeconomics textbook “Anything Goes: The Sonnenschein-Mantel-Debreu Theorem.”

S. Abu Turab Rizvi

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 equilibrium​ solution. A century and a half after Léon Walras founded neoclassical general equilibrium theory, modern mainstream economics hasn’t been able to show that markets move economies to equilibria. This if anything shows that the whole Bourbaki-Debreu project of axiomatizing​ economics was nothing but a delusion.

You enquire whether or not Walras was supposing that exchanges actually take place at the prices originally proposed when the prices are not equilibrium prices. The footnote which you quote convinces me that he assuredly supposed that they did not take place except at the equilibrium prices … All the same, I shall hope to convince you some day that Walras’ theory and all the others along those lines are little better than nonsense!

Letter from J. M. Keynes to N. Georgescu-Roegen, December 9, 1934

Opting for cloned representative agents that are all identical is of course not a real solutionto the fallacy of composition that the Sonnenschein-Mantel-Debreu theorem points to. Representative agent models are — as I have argued at length in my On the use and misuse of theories and models in mainstream economics — 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 …

  1. Robert Locke
    May 26, 2019 at 7:55 am

    Sorry Lars, you are wasting our time with this constant rehash of the work of economists. I’ve known since I ran into the stuff fifty years ago, the limits of their theory (see Locke 1984, End of the Practical Man), and so should you, because it has been reshashed so often before (. e. g. Fullbrook on the shortcomings of arrow debrew in a 2006 paper, Amadae and de Mesquita, in one in 1999). If the theory you rehash is of so little value when dealing with current economic problems, what should you discuss that is relevant. I tried to point the way in the conclusion of the 1984 book, “Space,Time, and Uncertainty.”

  2. Rob
    May 27, 2019 at 12:29 am

    S. Abu Turab Rizvi is a dead-end link.

  3. Helen Sakho
    May 27, 2019 at 12:35 am

    Same old, same old…
    Is there any point in time soon when the rise of fascism and its confirmation (please observe the EU elections, the situation in the US and almost everywhere else) going to be discussed and the implications of the disastrous state of affairs worldwide?

    Some of us appear to just post and observe (if that); others appear (rightly, thank you Rob) fed up; and yet others are tempted to give it up once and for all. I am beginning to lean towards the last group, I am afraid.

  4. Rob
    May 27, 2019 at 10:07 am

    I don’t think we can reasonably expect that this blog (or economics for that matter) can alone address the civilizational crisis we are swiftly entering. I have read almost the entire WEA library, learned much from the posts by the various authors on RWER, and learned a great deal from some of the posters. Lars has taught me much (including his book) and has given me invaluable recommendations for reading resources. He cannot be expected to do all the lifting let alone provide the solution. Wouldn’t that be asking to much of one person?

    Robert Locke’s Confronting Managerialism (CM) has in my estimation proven its weight in gold from where I am sitting. JC Spender made a valuable point about the need for intellectuals to break complex problems down into bite sized chunks so we can understand and communicate them. Robert’s CM has done this in spades.

    The Nobel Factor has also been very valuable in putting the history of economics in context (thanks Lars, for recommending it).

    I have come to the conclusion that RWER is NOT the place to hash out solutions. That is fine with me, for I am here to learn, primarily.

  5. Ken Zimmerman
    June 2, 2019 at 2:30 pm

    It is irritating for me that most who participate on this blog don’t really have any idea how to change economics. But then again, I don’t believe this was the intent of the blog. Nonetheless, considering the urgency many economics students placed on changing economics to make it “more relevant” to conditions on the ground, I have to wonder where all that urgency has gone. At this point it seems more soul searching on the part of the rebels is called for.

    Anthropologists don’t have that sort of urgency about changing economics either. Most consider economics somewhere between irrelevant and a discipline attached at the hip to tyrants and capitalist greed machines. But there are Economic Anthropologists examining the discipline. Their research results are both fascinating and contradictory of almost every aspect of the primary tenets of what predominates today as economics. I’ve described some of that research here. I hope it is helpful.

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