Archive for the 'Oskar Morgensterm' Category

Correct Foresight, Perfect Foresight, and Intertemporal Equilibrium

In my previous post, I discussed Hayek’s path-breaking insight into the meaning of intertemporal equilibrium. His breakthrough was to see that an equilibrium can be understood not as a stationary state in which nothing changes, but as a state in which decentralized plans are both optimal from the point of view of the individuals formulating the plans and mutually consistent, so that the individually optimal plans, at least potentially, could be simultaneously executed. In the simple one-period model, the plans of individuals extending over a single-period time horizon are constrained by the necessary equality for each agent between the value of all planned purchases and the value of all planned sales in that period. A single-period or stationary equilibrium, if it exists, is characterized by a set of prices such that the optimal plans corresponding to that set of prices such that total amount demanded for each product equals the total amount supplied for each product. Thus, an equilibrium price vector has the property that every individual is choosing optimally based on the choice criteria and the constraints governing the decisions for each individual and that those individually optimal choices are mutually consistent, that mutual consistency being manifested in the equality of the total amount demanded and the total amount supplied of each product in that single period.

The problem posed by the concept of intertemporal equilibrium is how to generalize the single-period notion of an equilibrium as a vector of all the observed prices of goods and services actually traded in that single period into a multi-period concept in which the prices on which optimal choices depend include both the actual prices of goods traded in the current period as well as the prices of goods and services that agents plan to buy or sell only in some future time period. In an intertemporal context, the prices on the basis of which optimal plans are chosen cannot be just those prices at which transactions are being executed in the current period; the relevant set of prices must also include those prices at which transactions already being planned in the current period will be executed. Because even choices about transactions today may depend on the prices at which future transactions will take place, future prices can affect not only future demands and supplies they can also affect current demands and supplies.

But because prices in future periods are typically not observable by individuals in the present, it is not observed — but expected — future prices on the basis of which individual agents are making the optimal choices reflected in their intertemporal plans. And insofar as optimal plans depend on expected future prices, those optimal plans can be mutually consistent only if they are based on the same expected future prices, because if their choices are based on different expected future prices, then it is not possible that all expectations are realized. If the expectations of at least one agent, and probably of many agents, will be disappointed, implying that the plans of at least one and probably of many agents will not be optimized and will have to be revised.

The recognition that the mutual consistency of optimal plans requires individuals to accurately foresee the future prices upon which their optimal choices are based suggested that individual agents must be endowed with remarkable capacities to foresee the future. To assume that all individual agents would be endowed with the extraordinary ability to foresee correctly all the future prices relevant to their optimal choices about their intertemporal plans seemed an exceedingly unrealistic assumption on which to premise an economic model.

This dismissive attitude toward the concept of intertemporal equilibrium and the seemingly related assumption of “perfect foresight” necessary for an intertemporal equilibrium to exist was stridently expressed by Oskar Morgenstern in his famous 1935 article “Perfect Foresight and Economic Equilibrium.”

The impossibly high claims which are attributed to the intellectual efficiency of the economic subject immediately indicate that there are included in this equilibrium system not ordinary men, but rather, at least to one another, exactly equal demi-gods, in case the claim of complete foresight is fulfilled. If this is the case, there is, of course, nothing more to be done. If “full” or “perfect” foresight is to provide the basis of the theory of equilibrium in the strictly specified sense, and in the meaning obviously intended by the economic authors, then, a completely meaningless assumption is being considered. If limitations are introduced in such a way that the perfection of foresight is not reached, then these limitations are to be stated very precisely. They would have to be so narrowly drawn that the fundamental aim of producing ostensibly full rationality of the system by means of high, de facto unlimited, foresight, would be lost. For the theoretical economist, there is no way out of this dilemma. ln this discussion, “full” and “perfect” foresight are not only used synonymously, but both are employed, moreover, in the essentialIy more exact sense of limitlessness. This expression would have to be preferred because with the words “perfect” or “imperfect”, there arise superficial valuations which play no role here at all.

Morgenstern then went on to make an even more powerful attack on the idea of perfect foresight: that the idea is itself self-contradictory. Interestingly, he did so by positing an example that would figure in Morgenstern’s later development of game theory with his collaborator John von Neumann (and, as we now know, with his research assistant who in fact was his mathematical guide and mentor, Abraham Wald, fcredited as a co-author of The Theory of Games and Economic Behavior).

Sherlock Holmes, pursued by his opponent, Moriarity, leaves London for Dover. The train stops at a station on the way, and he alights there rather than traveling on to Dover. He has seen Moriarity at the railway station, recognizes that he is very clever and expects that Moriarity will take a faster special train in order to catch him in Dover. Holmes’ anticipation turns out to be correct. But what if Moriarity had been still more clever, had estimated Holmes’ mental abilities better and had foreseen his actions accordingly? Then, obviously, he would have traveled to the intermediate station. Holmes, again, would have had to calculate that, and he himself would have decided to go on to Dover. Whereupon, Moriarity would again have “reacted” differently. Because of so much thinking they might not have been able to act at all or the intellectually weaker of the two would have surrendered to the other in the Victoria Station, since the whole flight would have become unnecessary. Examples of this kind can be drawn from everywhere. However, chess, strategy, etc. presuppose expert knowledge, which encumbers the example unnecessarily.

One may be easily convinced that here lies an insoluble paradox. And the situation is not improved, but, rather, greatly aggravated if we assume that more than two individuals-as, for example, is the case with exchange-are brought together into a position, which would correspond to the one brought forward here. Always, there is exhibited an endless chain of reciprocally conjectural reactions and counter-reactions. This chain can never be broken by an act of knowledge but always only through an arbitrary act-a resolution. This resolution, again, would have to be foreseen by the two or more persons concerned. The paradox still remains no matter how one attempts to twist or turn things around. Unlimited foresight and economic equilibrium are thus irreconcilable with one another. But can equilibrium really take place with a faulty, heterogeneous foresight, however, it may be disposed? This is the question which arises at once when an answer is sought. One can even say this: has foresight been truly introduced at all into the consideration of equilibrium, or, rather, does not the theorem of equilibrium generally stand in no proven connection with the assumptions about foresight, so that a false assumption is being considered?

As Carlo Zappia has shown, it was probably Morgenstern’s attack on the notion of intertemporal equilibrium and perfect foresight that led Hayek to his classic restatement of the idea in his 1937 paper “Economics and Knowledge.” The point that Hayek clarified in his 1937 version, but had not been clear in his earlier expositions of the concept, is that correct foresight is not an assumption from which the existence of an intertemporal equilibrium can be causally deduced; there is no assertion that a state of equilibrium is the result of correct foresight. Rather, correct foresight is the characteristic that defines what is meant when the term “intertemporal equilibrium” is used in economic theory. Morgenstern’s conceptual error was to mistake a tautological statement about what would have to be true if an intertemporal equilibrium were to obtain for a causal statement about what conditions would bring an intertemporal equilibrium into existence.

The idea of correct foresight does not attribute any special powers to the economic agents who might under hypothetical circumstances possess correct expectations of future prices. The term is not meant to be a description of an actual state of affairs, but a description of what would have to be true for a state of affairs to be an equilibrium state of affairs.

As an aside, I would simply mention that many years ago when I met Hayek and had the opportunity to ask him about his 1937 paper and his role in developing the concept of intertemporal equilibrium, he brought my attention to his 1928 paper in which he first described an intertemporal equilibrium as state of affairs in which agents had correct expectations about future prices. My recollection of that conversation is unfortunately rather vague, but I do remember that he expressed some regret for not having had the paper translated into English, which would have established his priority in articulating the intertemporal equilibrium concept. My recollection is that the reason he gave for not having had the paper translated into English was that there was something about the paper about which he felt dissatisfied, but I can no longer remember what it was that he said he was dissatisfied with. However, I would now be inclined to conjecture that he was dissatisfied with not having disambiguated, as he did in the 1937 paper, between correct foresight as a defining characteristic of what intertemporal equilibrium means versus perfect foresight as the cause that brings intertemporal equilibruim into existence.

It is also interesting to note that the subsequent development of game theory in which Morgenstern played a not insubstantial role, shows that under a probabilistic interpretation of the interaction between Holmes and Moriarity, there could be an optimal mixed strategy that would provide an equilibrium solution of repeated Holmes-Moriarity interactions. But if the interaction is treated as a single non-repeatable event with no mixed strategy available to either party, the correct interpretation of the interaction is certainly that there is no equilibrium solution to the interaction. If there is no equilibrium solution, then it is precisely the absence of an equilibrium solution that implies the impossibility of correct foresight, correct foresight and the existence of an equilibrium being logically equivalent concepts.

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.

Enter your email address to follow this blog and receive notifications of new posts by email.

Join 1,389 other followers

Follow Uneasy Money on