More on Arrow’s Explanatory Gap and the Milgrom-Stokey Argument

In my post yesterday, I discussed what I call Kenneth Arrow’s explanatory gap: the absence of any account in neoclassical economic theory of how the equilibrium price vector is actually arrived at and how changes in that equilibrium price vector result when changes in underlying conditions imply changes in equilibrium prices. I post below some revisions to several paragraphs in yesterday’s post supplemented by a more detailed discussion of the Milgrom-Stokey “no-trade theorem” and its significance. The following is drawn from a work in progress to be presented later this month at a conference celebrating the 150th anniversary of the publication of the Carl Menger’s Grundsätze der Volkswirtschaftslehre.

Thus, just twenty years after Arrow called attention to the explanatory gap in neoclassical theory by observing that neoclassical theory provides no explanation of how competitive prices can change, Paul Milgrom and Nancy Stokey (1982) turned Arrow’s argument on its head by arguing that, under rational expectations, no trading would ever occur at disequilibrium prices, because every potential trader would realize that an offer to trade at disequilibrium prices would not be made unless the offer was based on private knowledge and would therefore lead to a wealth transfer to the trader relying on private knowledge. Because no traders with rational expectations would agree to a trade at a disequilibrium price, there would be no incentive to seek or exploit private information, and all trades would occur at equilibrium prices.

This would have been a profound and important argument had it been made as a reductio ad absurdum to show the untenability of the rational-expectations as a theory of expectation formation, inasmuch as it leads to the obviously false factual implication that private information is never valuable and that no profitable trades are made by those possessed of private information. In concluding their paper, Milgrom and Stokey (1982) acknowledge the troubling implication of their argument:

Our results concerning rational expectations market equilibria raise anew the disturbing questions expressed by Beja (1977), Grossman and Stiglitz (1980), and Tirole (1980): Why do traders bother to gather information if they cannot profit from it? How does information come to be reflected in prices if informed traders do not trade or if they ignore their private information in making inferences? These questions can be answered satisfactorily only in the context of models of the price formation process; and our central result, the no-trade theorem, applies to all such models when rational expectations are assumed. (p. 17)

What Milgrom and Stokey seem not to have grasped is that the rational-expectations assumption dispenses with the need for a theory of price formation, inasmuch as every agent is assumed to be able to calculate what the equilibrium price is. They attempt to mitigate the extreme nature of this assumption by arguing that by observing price changes, traders can infer what changes in common knowledge would have implied the observed changes. That argument seems insufficient because any given change in price could be caused by more than one potential cause. As Scott Sumner has often argued, one can’t reason from a price change. If one doesn’t have independent knowledge of the cause of the price change, one can’t use the price change as a basis for further inference.

3 Responses to “More on Arrow’s Explanatory Gap and the Milgrom-Stokey Argument”


  1. 1 Benjamin Cole November 8, 2021 at 8:11 pm

    Well, this is certainly rarified conversation, and probably over my head.

    I do think some trades, and many economic transactions occur, not because an economic actor thinks he has all the info needed, or that the other side has less info.

    Rather, many trades and transactions take place “because they have to.”

    I might be on the “losing end” of a transaction, but I need to eat.

  2. 2 Henry Rech November 18, 2021 at 3:40 pm

    David,

    I am always challenged and left confused by your discussions dealing with equilibrium and rational expectations. You seem to mix up the ideal with the real. There can be no comparison. One either accepts rational expectations or one does not.

    Is it not correct that rational expectations is an assumption about behaviour rather than an explanation of that behaviour. It is an idealized state of affairs which essentially says a market system will be in equilibrium? It doesn’t seek to explain how that equilibrium is attained.

    To me the conclusions of Milgrom’s and Stockey’s paper makes sense (not that I tackled the logical development presented in their paper). There can be no question of new information altering an equilibrium position under rational expectations.

    And just as rational expectations is assumed to apply to current markets, it is assumed to apply to future markets. It just a crazy fantastical assumption.

    In the real world however, private information has an impact on price setting. Whether it is optimal is another question. And how can it be decided whether it is optimal? Arguing about whether it is optimal or not seems pointless to me.

    I would say that in the real world,that if there is equilibrium in any sense of the word, it is a fluke and it cannot be proved to be an equilibrium. So any amount of sophistry about rational expectations and Hayek etc. is a waste of time. The cows will be well and truly home before any resolution is available.

    In the worlds of perfect foresight, rational expectations and Walrasian tatonnement, equilibrium is assumed to pertain. That’s it.

    In the real world, no amount of rationalization will reveal whether a price setting is in equilibrium.

    Your endless quest to salve neoclassical economics is in vain. 🙂


  1. 1 My Paper “Between Walras and Marshall: Menger’s Third Way” Is Now Posted on SSRN | Uneasy Money Trackback on November 18, 2021 at 8:15 pm

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey’s unduly neglected contributions to the attention of a wider audience.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

Follow me on Twitter @david_glasner

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