The Explanatory Gap and Mengerian Subjectivism

My last several posts have been focused on Marshall and Walras and the relationships and differences between the partial equilibrium approach of Marshall and the general-equilibrium approach of Walras and how that current state of neoclassical economics is divided between the more practical applied approach of Marshallian partial-equilibrium analysis and the more theoretical general-equilibrium approach of Walras. The divide is particularly important for the history of macroeconomics, because many of the macroeconomic controversies in the decades since Keynes have also involved differences between Marshallians and Walrasians. I’m not happy with either the Marshallian or Walrasian approach, and I have been trying to articulate my unhappiness with both branches of current neoclassical thinking by going back to the work of the forgotten marginal revolutionary, Carl Menger. I’ve been writing a paper for a conference later this month celebrating the 150th anniversary of Menger’s great work which draws on some of my recent musings, because I think it offers at least some hints at how to go about developing an improved neoclassical theory. Here’s a further sampling of my thinking which is drawn from one of the sections of my work in progress.

Both the Marshallian and the Walrasian versions of equilibrium analysis have failed to bridge an explanatory gap between the equilibrium state, whose existence is crucial for such empirical content as can be claimed on behalf of those versions of neoclassical theory, and such an equilibrium state could ever be attained. The gap was identified by one of the chief architects of modern neoclassical theory, Kenneth Arrow, in his 1958 paper “Toward a Theory of Price Adjustment.”

The equilibrium is defined in terms of a set of prices. In the Marshallian version, the equilibrium prices are assumed to have already been determined in all but a single market (or perhaps a subset of closely related markets), so that the Marshallian equilibrium simply represents how, in a single small or isolated market, an equilibrium price in that market is determined, under suitable ceteris-paribus conditions thereby leaving the equilibrium prices determined in other markets unaffected.

In the Walrasian version, all prices in all markets are determined simultaneously, but the method for determining those prices simultaneously was not spelled out by Walras other than by reference to the admittedly fictitious and purely heuristic tâtonnement process.

Both the Marshallian and Walrasian versions can show that equilibrium has optimal properties, but neither version can explain how the equilibrium is reached or how it can be discovered in practice. This is true even in the single-period context in which the Walrasian and Marshallian equilibrium analyses were originally carried out.

The single-period equilibrium has been extended, at least in a formal way, in the standard Arrow-Debreu-McKenzie (ADM) version of the Walrasian equilibrium, but this version is in important respects just an enhanced version of a single-period model inasmuch as all trades take place at time zero in a complete array of future state-contingent markets. So it is something of a stretch to consider the ADM model a truly intertemporal model in which the future can unfold in potentially surprising ways as opposed to just playing out a script already written in which agents go through the motions of executing a set of consistent plans to produce, purchase and sell in a sequence of predetermined actions.

Under less extreme assumptions than those of the ADM model, an intertemporal equilibrium involves both equilibrium current prices and equilibrium expected prices, and just as the equilibrium current prices are the same for all agents, equilibrium expected future prices must be equal for all agents. In his 1937 exposition of the concept of intertemporal equilibrium, Hayek explained the difference between what agents are assumed to know in a state of intertemporal equilibrium and what they are assumed to know in a single-period equilibrium.

If all agents share common knowledge, it may be plausible to assume that they will rationally arrive at similar expectations of the future prices. But if their stock of knowledge consists of both common knowledge and private knowledge, then it seems implausible to assume that the price expectations of different agents will always be in accord. Nevertheless, it is not necessarily inconceivable, though perhaps improbable, that agents will all arrive at the same expectations of future prices.

In the single-period equilibrium, all agents share common knowledge of equilibrium prices of all commodities. But in intertemporal equilibrium, agents lack knowledge of the future, but can only form expectations of future prices derived from their own, more or less accurate, stock of private knowledge. However, an equilibrium may still come about if, based on their private knowledge, they arrive at sufficiently similar expectations of future prices for their plans for their current and future purchases and sales to be mutually compatible.

Thus, just twenty years after Arrow called attention to the explanatory gap in neoclassical theory by observing that there is no neoclassical theory of how competitive prices can change, Milgrom and Stokey turned Arrow’s argument on its head by arguing that, under rational expectations, no trading would ever occur at prices other than equilibrium prices, so that it would be impossible for a trader with private information to take advantage of that information. This argument seems to suffer from a widely shared misunderstanding of what rational expectations signify.

Thus, in the Mengerian view articulated by Hayek, intertemporal equilibrium, given the diversity of private knowledge and expectations, is an unlikely, but not inconceivable, state of affairs, a view that stands in sharp contrast to the argument of Paul Milgrom and Nancy Stokey (1982), in which they argue that under a rational-expectations equilibrium there is no private knowledge, only common knowledge, and that it would be impossible for any trader to trade on private knowledge, because no other trader with rational expectations would be willing to trade with anyone at a price other than the equilibrium price.

Rational expectations is not a property of individual agents making rational and efficient use of the information from whatever source it is acquired. As I have previously explained here (and a revised version here) rational expectations is a property of intertemporal equilibrium; it is not an intrinsic property that agents have by virtue of being rational, just as the fact that the three angles in a triangle sum to 180 degrees is not a property of the angles qua angles, but a property of the triangle. When the expectations that agents hold about future prices are identical, their expectations are equilibrium expectations and they are rational. That the agents hold rational expectations in equilibrium, does not mean that the agents are possessed of the power to calculate equilibrium prices or even to know if their expectations of future prices are equilibrium expectations. Equilibrium is the cause of rational expectations; rational expectations do not exist if the conditions for equilibrium aren’t satisfied. See Blume, Curry and Easley (2006).

The assumption, now routinely regarded as axiomatic, that rational expectations is sufficient to ensure that equilibrium is automatic achieved, and that agents’ price expectations necessarily correspond to equilibrium price expectations is a form of question begging disguised as a methodological imperative that requires all macroeconomic models to be properly microfounded. The newly published volume edited by Arnon, Young and van der Beek Expectations: Theory and Applications from Historical Perspectives contains a wonderful essay by Duncan Foley that elucidates these issues.

In his centenary retrospective on Menger’s contribution, Hayek (1970), commenting on the inexactness of Menger’s account of economic theory, focused on Menger’s reluctance to embrace mathematics as an expository medium with which to articulate economic-theoretical concepts. While this may have been an aspect of Menger’s skepticism about mathematical reasoning, his recognition that expectations of the future are inherently inexact and conjectural and more akin to a range of potential outcomes of different probability may have been an even more significant factor in how Menger chose to articulate his theoretical vision.

But it is noteworthy that Hayek (1937) explicitly recognized that there is no theoretical explanation that accounts for any tendency toward intertemporal equilibrium, and instead merely (and in 1937!) relied an empirical tendency of economies to move in the direction of equilibrium as a justification for considering economic theory to have any practical relevance.

8 Responses to “The Explanatory Gap and Mengerian Subjectivism”


  1. 1 Henry Rech November 8, 2021 at 1:45 am

    David,

    I am ever fascinated by your fascination with the notion of finding a way to render neoclassical economics as useful theory.

    Neoclassical theory is based on a bunch of fanciful and impossible assumptions, whether it includes rational expectations or not.

    As microeconomic theory, it bears no relation to the real world so is practically useless.

    Two of it’s assumption, full employment and fixed income, render it useless as macroeconomic theory because it assumes away the fundamental macroeconomic problem leaving only changes in relative prices to effect macro equilibrium, no satisfactory theory for which, as far as I know, has been formulated. If you have one I would very much appreciate seeing it.

  2. 2 David Glasner November 8, 2021 at 8:54 am

    Thanks so much, Henry, for your fascination. We keep arguing and neither of us appears ready to budge. Maybe if you read my book cover to cover, you’ll change your mind about me and about what neoclassical theory is and isn’t. But I’m not gonna bet on it. Anyway, thanks for sticking with me all these years.

  3. 3 Henry Rech November 8, 2021 at 12:33 pm

    David,

    “But I’m not gonna bet on it. ”

    Well, you never know.

    I looked over the chapter abstracts the other day and they all looked very interesting.

    Your perspective on these things I find very stimulating even if sometimes challenging. 🙂

  4. 4 philipji November 8, 2021 at 8:58 pm

    1. The idea that Marshall’s demand-supply diagrams constitute a case of partial equilibrium is incorrect. Using simple school geometry it can be proved that you cannot have movements along a demand curve while simultaneously holding other prices constant. I could provide a link to a paper of mine showing this but your anti-spam software would block my post. There is no difference between Marshallian economics and “General Equilibrium Theory”. Neither is of course “general equilibrium”.

    2. The unstated assumption in this post is that quantities bought and quantities sold can be brought into equality only through a change of prices. Again, I could direct you to a post of mine that shows why it would profit a capitalist to sell higher quantities at the existing price or even at a lower price, even in the short run.

  5. 5 David Glasner November 9, 2021 at 7:00 am

    phillipji,

    My antispam software doesn’t block comments with links; it sends them into moderation. If you include a link, I’ll approve it once I see that it’s awaiting approval in moderation. I think it’s well known that the ceteris paribus assumptions of PE analysis are not exact, but only approximate. Applied theory is always inexact. The problem with PE is that people tend to ignore these rough edges.

  6. 6 philipji November 9, 2021 at 6:11 pm

    David,
    I wonder whether this recent post of mine would help illuminate the problem you are trying to address: http://www.philipji.com/item/2021-10-24/when-do-markets-fail-to-clear

    Chapter 2 of my recently published book has more on Marshallian economics (and why it is equivalent to General Equilibrium Theory) but Chapter 1 also addresses some of the problems and can be read for free at https://www.amazon.com/dp/B098PYL8ZW/

  7. 7 Henry Rech November 25, 2021 at 7:18 am

    Philipji,

    Is your book only published in Kindle?

    Any hardcopy versions?


  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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