A visiting Federal Reserve scholar attempts to explicate the difference between Hayek’s explanatory universe and the Arrow-Debreu explanatory universe using the conceptual language / conceptual straight jacket of . . . Arrow and Debreu:

Arrow and Debreu showed that allocations will be Pareto efficient even in economies in which time and uncertainty are explicitly represented. They showed that, in any economy, there is an irreducible minimum level of risk that somebody has to bear. In a competitive economy with well-functioning financial markets, this risk will be borne by those who are most risk tolerant and who therefore require the least compensation in terms of higher expected return for bearing the risk.  This is exactly as one would expect—risk-tolerant participants use financial markets to insure the risk averse. These aspects of equilibrium are discussed in standard texts on financial economics (such as LeRoy and Werner 2001).

However, demonstrating these results mathematically depends on assuming symmetric information — that is, assuming that everyone has unrestricted access to the same information. Such an assumption is less unrealistic than excluding uncertainty altogether, but it is still a strong restriction. The advent of game theory in recent decades has made it possible to relax the unattractive assumption of symmetric information. But Pareto efficiency often does not survive in settings that allow for asymmetric information.  Based on mathematical economic theory, then, it appears that the argument that private markets produce good economic outcomes is open to serious question ..

Nonmathematical economists such as Friedrich Hayek proposed an argument for the superiority of market systems that did not depend on Pareto efficiency. In fact, Hayek’s argument was the exact opposite of that of Arrow and Debreu. For him, it was the existence of asymmetric information that provided the strongest rationale in favor of market-based economic systems. Hayek emphasized that prices incorporate valuable information about desirability and scarcity, and the profit motive induces producers and consumers to respond to this information by economizing on expensive goods. He expressed the view that economies in which prices are not used to communicate information — planned economies, such as that of the Soviet Union — could not possibly induce suppliers to produce efficiently …

Note to Stephen LeRoy:  the notion of “information” as used in economics is a model builder’s makeshift — but failed — attempt to capture in “given bits” what in the real world are rival understandings of the world, with a place in unique, non-univocal individual networks of valuational relations.  These imaginary bits of “information” within an economist’s toy economy have an existence as univocal “givens” only within the reality of an economist’s math construct, and it is only this math construct and its elements which can be “given” to a single mind playing with the economic math construct.  These elements can never be found in the real world as given “information” univocal shared between real world human beings uniquely navigating the real world economy.

In the real world folks don’t have “given” information, they have rival ways of understanding the world, which are not univocal “bits” of objectively given “information”.  And these rival ways of understanding the world find there place within uniquely individual networks of valuational relations, which are never isomorphically shared between different individuals.  This is the marginalist real world economics of Carl Menger and Friedrich Hayek — essentially unknown to the math economists of today.

What Hayek in his work is talking about is “asymetrical” rivalrous understandings of the world, understandings which necessarily are both imperfect, non-univocal, and continually adapting to changing local conditions and relative prices.  None of this can be fully capture in a univocal mathematical construction — not the imperfect, non-univocal, rivalrous understandings and not the learning, correcting, and adapting process.

The central failure of the mathematical economists attempting the understand Hayek — and the market economy — is the signal failure to understand this central fact of economic science.

We know that much of Hick’s work was inspired by Hayek:

“I can date my own personal ‘revolution’ rather exactly to May or June 1933. It was like this. It began . . with Hayek. His Prices and Production is one of the influences that can be detected in The Theory of Wages; it could not have been otherwise, for 1931 was a Prices and Production year at the London School of Economics . . I did not in fact find it all easy to fit in with my own ideas. What started me off in 1933 was an earlier work of Hayek’s, his paper on ‘Intertemporal Equilibrium’, an idea which I found easier to reduce to my preferred (Paretian or Wicksellian) pattern.” (John Hicks, The Theory of Wages, 2nd Edition,1963, p. 307)

“.. it was from Hayek that I began [the breakthrough essay "Equilibrium and the Cycle" (1933), the original beginnings of Hick's influential work on the topics of intertemporal equilibrium, monetary theory, and trade cycle phenomena] “. (John Hicks, Money, Interest and Wages, Cambridge: Harvard U. Press, 1982, p. 28).

“There were four years, 1931-1935, when I was myself a member of [Hayek's] seminar in London; it has left a deep mark on my thinking.” (John Hicks, Classics and Moderns, New York: Basil Blackwell, 1983, p. 97).

B. Ingrao & G. Israel, “Hicks elaborated the concept of temporary equilibrium, perhaps the most original contribution of Value and Capital, following the path laid down by Hayek and the Swedish school.” (B. Ingrao & G. Israel, 1990, p. 239)

“Hayek was making us think of the productive process as a process in time, inputs coming before outputs ..”. (John Hicks, Classics and Moderns, New York: Basil Blackwell, 1983, p. 359).

“I did not begin from Keynes: I began from Pareto, and Hayek (footnote 10: There is evidence for this, in the paper ‘Equilibrium and the Cycle’) ..”. (John Hicks, Classics and Moderns, New York: Basil Blackwell, 1983, p. 359).

Much of Hicks can be understood as an attempt to cram the insights of the Menger-Bohm-Bawerk-Weiser-Hayek research program in capital production/equilibrium theory into a British/Marshallian reconception of Walras/Pareto.  It didn’t really work.  But it was enormously influential.  Kenneth Arrow was among those inspired by Hicks (note well that, contra Arrow, Hicks is not an adequate lens for reading Hayek — it’s easy to guess that Arrow as a grad student wasn’t competent to understand Hayek because Arrow really had no background in the work of Menger, Bohm-Bawerk or Wieser.):

When I enrolled as a student in the Economics Department at Columbia (1941), I was assigned a desk in the library stacks near the economics book collection. As is my wont when placed in the neighborhood of books, I immediately started browsing and ran across a work by an economist whose name I had never heard mentioned, J.R. Hicks’s Value and Capital (1939). As apparently happened to other like-minded economics students (e.g., my good friend, Frank H. Hahn) at that time, it gave me a powerful orientation to economic analysis. It showed how the techniques of static analysis (already familiar to me from Hotelling’s course but expressed with more verve and style) could be applied to events unfolding in time. Savings and investment could be analyzed using the same tools. If the reader thinks this is obvious, I recommend that he read the controversies over capital theory, as exemplified by the papers of Frank Knight (1936) and Friedrich von Hayek’s book (1941) and try to find out, as I tried then, what in the world were the questions being debated. Hicks had a simple approach: Decisions on commodity consumption and production today are made jointly with consumption and production in the future. Therefore, simply put a time subscript on commodities; use the static formalism with the enlarged commodity space. (To be fair, after reading Hicks, one can understand that Hayek was saying much the same, but I defy anyone to learn that from reading Hayek alone.)

Of course, Hicks’s s reformulation did not end the difficulties in theories of savings and investment; rather, it enabled one to understand what they were. In brief, as Hicks explained, the problem was the nonexistence of a full set of futures markets. There were a few commodity futures markets, and, more importantly, there were markets for credit. As Hicks emphasized, the nonexistent futures markets were replaced in the calculations of firms and households by expectations, and the resulting supply and demand behavior determined “temporary” equilibrium prices and allocations on the current and existing futures markets. As Hicks showed, one consistent set of expectations was the equilibrium set that would have been obtained if all markets existed (what later became known as “rational expectations”) …

Read the whole thing (pdf).