Hayek and Intertemporal Equilibrium

I am starting to write a paper on Hayek and intertemporal equilibrium, and as I write it over the next couple of weeks, I am going to post sections of it on this blog. Comments from readers will be even more welcome than usual, and I will do my utmost to reply to comments, a goal that, I am sorry to say, I have not been living up to in my recent posts.

The idea of equilibrium is an essential concept in economics. It is an essential concept in other sciences as well, its meaning in economics is not the same as in other disciplines. The concept having originally been borrowed from physics, the meaning originally attached to it by economists corresponded to the notion of a system at rest, and it took a long time for economists to see that viewing an economy as a system at rest was not the only, or even the most useful, way of applying the equilibrium concept to economic phenomena.

What would it mean for an economic system to be at rest? The obvious answer was to say that prices and quantities would not change. If supply equals demand in every market, and if there no exogenous change introduced into the system, e.g., in population, technology, tastes, etc., it would seem that would be no reason for the prices paid and quantities produced to change in that system. But that view of an economic system was a very restrictive one, because such a large share of economic activity – savings and investment — is predicated on the assumption and expectation of change.

The model of a stationary economy at rest in which all economic activity simply repeats what has already happened before did not seem very satisfying or informative, but that was the view of equilibrium that originally took hold in economics. The idea of a stationary timeless equilibrium can be traced back to the classical economists, especially Ricardo and Mill who wrote about the long-run tendency of an economic system toward a stationary state. But it was the introduction by Jevons, Menger, Walras and their followers of the idea of optimizing decisions by rational consumers and producers that provided the key insight for a more robust and fruitful version of the equilibrium concept.

If each economic agent (household or business firm) is viewed as making optimal choices based on some scale of preferences subject to limitations or constraints imposed by their capacities, endowments, technology and the legal system, then the equilibrium of an economy must describe a state in which each agent, given his own subjective ranking of the feasible alternatives, is making a optimal decision, and those optimal decisions are consistent with those of all other agents. The optimal decisions of each agent must simultaneously be optimal from the point of view of that agent while also being consistent, or compatible, with the optimal decisions of every other agent. In other words, the decisions of all buyers of how much to purchase must be consistent with the decisions of all sellers of how much to sell.

The idea of an equilibrium as a set of independently conceived, mutually consistent optimal plans was latent in the earlier notions of equilibrium, but it could not be articulated until a concept of optimality had been defined. That concept was utility maximization and it was further extended to include the ideas of cost minimization and profit maximization. Once the idea of an optimal plan was worked out, the necessary conditions for the mutual consistency of optimal plans could be articulated as the necessary conditions for a general economic equilibrium. Once equilibrium was defined as the consistency of optimal plans, the path was clear to define an intertemporal equilibrium as the consistency of optimal plans extending over time. Because current goods and services and otherwise identical goods and services in the future could be treated as economically distinct goods and services, defining the conditions for an intertemporal equilibrium was formally almost equivalent to defining the conditions for a static, stationary equilibrium. Just as the conditions for a static equilibrium could be stated in terms of equalities between marginal rates of substitution of goods in consumption and in production to their corresponding price ratios, an intertemporal equilibrium could be stated in terms of equalities between the marginal rates of intertemporal substitution in consumption and in production and their corresponding intertemporal price ratios.

The only formal adjustment required in the necessary conditions for static equilibrium to be extended to intertemporal equilibrium was to recognize that, inasmuch as future prices (typically) are unobservable, and hence unknown to economic agents, the intertemporal price ratios cannot be ratios between actual current prices and actual future prices, but, instead, ratios between current prices and expected future prices. From this it followed that for optimal plans to be mutually consistent, all economic agents must have the same expectations of the future prices in terms of which their plans were optimized.

The concept of an intertemporal equilibrium was first presented in English by F. A. Hayek in his 1937 article “Economics and Knowledge.” But it was through J. R. Hicks’s Value and Capital published two years later in 1939 that the concept became more widely known and understood. In explaining and applying the concept of intertemporal equilibrium and introducing the derivative concept of a temporary equilibrium in which current markets clear, but individual expectations of future prices are not the same, Hicks did not claim originality, but instead of crediting Hayek for the concept, or even mentioning Hayek’s 1937 paper, Hicks credited the Swedish economist Erik Lindahl, who had published articles in the early 1930s in which he had articulated the concept. But although Lindahl had published his important work on intertemporal equilibrium before Hayek’s 1937 article, Hayek had already explained the concept in a 1928 article “Das intertemporale Gleichgewichtasystem der Priese und die Bewegungen des ‘Geltwertes.'” (English translation: “Intertemporal price equilibrium and movements in the value of money.“)

Having been a junior colleague of Hayek’s in the early 1930s when Hayek arrived at the London School of Economics, and having come very much under Hayek’s influence for a few years before moving in a different theoretical direction in the mid-1930s, Hicks was certainly aware of Hayek’s work on intertemporal equilibrium, so it has long been a puzzle to me why Hicks did not credit Hayek along with Lindahl for having developed the concept of intertemporal equilibrium. It might be worth pursuing that question, but I mention it now only as an aside, in the hope that someone else might find it interesting and worthwhile to try to find a solution to that puzzle. As a further aside, I will mention that Murray Milgate in a 1979 article “On the Origin of the Notion of ‘Intertemporal Equilibrium’” has previously tried to redress the failure to credit Hayek’s role in introducing the concept of intertemporal equilibrium into economic theory.

What I am going to discuss in here and in future posts are three distinct ways in which the concept of intertemporal equilibrium has been developed since Hayek’s early work – his 1928 and 1937 articles but also his 1941 discussion of intertemporal equilibrium in The Pure Theory of Capital. Of course, the best known development of the concept of intertemporal equilibrium is the Arrow-Debreu-McKenzie (ADM) general-equilibrium model. But although it can be thought of as a model of intertemporal equilibrium, the ADM model is set up in such a way that all economic decisions are taken before the clock even starts ticking; the transactions that are executed once the clock does start simply follow a pre-determined script. In the ADM model, the passage of time is a triviality, merely a way of recording the sequential order of the predetermined production and consumption activities. This feat is accomplished by assuming that all agents are present at time zero with their property endowments in hand and capable of transacting – but conditional on the determination of an equilibrium price vector that allows all optimal plans to be simultaneously executed over the entire duration of the model — in a complete set of markets (including state-contingent markets covering the entire range of contingent events that will unfold in the course of time whose outcomes could affect the wealth or well-being of any agent with the probabilities associated with every contingent event known in advance).

Just as identical goods in different physical locations or different time periods can be distinguished as different commodities that cn be purchased at different prices for delivery at specific times and places, identical goods can be distinguished under different states of the world (ice cream on July 4, 2017 in Washington DC at 2pm only if the temperature is greater than 90 degrees). Given the complete set of state-contingent markets and the known probabilities of the contingent events, an equilibrium price vector for the complete set of markets would give rise to optimal trades reallocating the risks associated with future contingent events and to an optimal allocation of resources over time. Although the ADM model is an intertemporal model only in a limited sense, it does provide an ideal benchmark describing the characteristics of a set of mutually consistent optimal plans.

The seminal work of Roy Radner in relaxing some of the extreme assumptions of the ADM model puts Hayek’s contribution to the understanding of the necessary conditions for an intertemporal equilibrium into proper perspective. At an informal level, Hayek was addressing the same kinds of problems that Radner analyzed with far more powerful analytical tools than were available to Hayek. But the were both concerned with a common problem: under what conditions could an economy with an incomplete set of markets be said to be in a state of intertemporal equilibrium? In an economy lacking the full set of forward and state contingent markets describing the ADM model, intertemporal equilibrium cannot predetermined before trading even begins, but must, if such an equilibrium obtains, unfold through the passage of time. Outcomes might be expected, but they would not be predetermined in advance. Echoing Hayek, though to my knowledge he does not refer to Hayek in his work, Radner describes his intertemporal equilibrium under uncertainty as an equilibrium of plans, prices, and price expectations. Even if it exists, the Radner equilibrium is not the same as the ADM equilibrium, because without a full set of markets, agents can’t fully hedge against, or insure, all the risks to which they are exposed. The distinction between ex ante and ex post is not eliminated in the Radner equilibrium, though it is eliminated in the ADM equilibrium.

Additionally, because all trades in the ADM model have been executed before “time” begins, it seems impossible to rationalize holding any asset whose only use is to serve as a medium of exchange. In his early writings on business cycles, e.g., Monetary Theory and the Trade Cycle, Hayek questioned whether it would be possible to rationalize the holding of money in the context of a model of full equilibrium, suggesting that monetary exchange, by severing the link between aggregate supply and aggregate demand characteristic of a barter economy as described by Say’s Law, was the source of systematic deviations from the intertemporal equilibrium corresponding to the solution of a system of Walrasian equations. Hayek suggested that progress in analyzing economic fluctuations would be possible only if the Walrasian equilibrium method could be somehow be extended to accommodate the existence of money, uncertainty, and other characteristics of the real world while maintaining the analytical discipline imposed by the equilibrium method and the optimization principle. It proved to be a task requiring resources that were beyond those at Hayek’s, or probably anyone else’s, disposal at the time. But it would be wrong to fault Hayek for having had to insight to perceive and frame a problem that was beyond his capacity to solve. What he may be criticized for is mistakenly believing that he he had in fact grasped the general outlines of a solution when in fact he had only perceived some aspects of the solution and offering seriously inappropriate policy recommendations based on that seriously incomplete understanding.

In Value and Capital, Hicks also expressed doubts whether it would be possible to analyze the economic fluctuations characterizing the business cycle using a model of pure intertemporal equilibrium. He proposed an alternative approach for analyzing fluctuations which he called the method of temporary equilibrium. The essence of the temporary-equilibrium method is to analyze the behavior of an economy under the assumption that all markets for current delivery clear (in some not entirely clear sense of the term “clear”) while understanding that demand and supply in current markets depend not only on current prices but also upon expected future prices, and that the failure of current prices to equal what they had been expected to be is a potential cause for the plans that economic agents are trying to execute to be modified and possibly abandoned. In the Pure Theory of Capital, Hayek discussed Hicks’s temporary-equilibrium method a possible method of achieving the modification in the Walrasian method that he himself had proposed in Monetary Theory and the Trade Cycle. But after a brief critical discussion of the method, he dismissed it for reasons that remain obscure. Hayek’s rejection of the temporary-equilibrium method seems in retrospect to have been one of Hayek’s worst theoretical — or perhaps, meta-theoretical — blunders.

Decades later, C. J. Bliss developed the concept of temporary equilibrium to show that temporary equilibrium method can rationalize both holding an asset purely for its services as a medium of exchange and the existence of financial intermediaries (private banks) that supply financial assets held exclusively to serve as a medium of exchange. In such a temporary-equilibrium model with financial intermediaries, it seems possible to model not only the existence of private suppliers of a medium of exchange, but also the conditions – in a very general sense — under which the system of financial intermediaries breaks down. The key variable of course is vectors of expected prices subject to which the plans of individual households, business firms, and financial intermediaries are optimized. The critical point that emerges from Bliss’s analysis is that there are sets of expected prices, which if held by agents, are inconsistent with the existence of even a temporary equilibrium. Thus price flexibility in current market cannot, in principle, result in even a temporary equilibrium, because there is no price vector of current price in markets for present delivery that solves the temporary-equilibrium system. Even perfect price flexibility doesn’t lead to equilibrium if the equilibrium does not exist. And the equilibrium cannot exist if price expectations are in some sense “too far out of whack.”

Expected prices are thus, necessarily, equilibrating variables. But there is no economic mechanism that tends to cause the adjustment of expected prices so that they are consistent with the existence of even a temporary equilibrium, much less a full equilibrium.

Unfortunately, modern macroeconomics continues to neglect the temporary-equilibrium method; instead macroeconomists have for the most part insisted on the adoption of the rational-expectations hypothesis, a hypothesis that elevates question-begging to the status of a fundamental axiom of rationality. The crucial error in the rational-expectations hypothesis was to misunderstand the role of the comparative-statics method developed by Samuelson in The Foundations of Economic Analysis. The role of the comparative-statics method is to isolate the pure theoretical effect of a parameter change under a ceteris-paribus assumption. Such an effect could be derived only by comparing two equilibria under the assumption of a locally unique and stable equilibrium before and after the parameter change. But the method of comparative statics is completely inappropriate to most macroeconomic problems which are precisely concerned with the failure of the economy to achieve, or even to approximate, the unique and stable equilibrium state posited by the comparative-statics method.

Moreover, the original empirical application of the rational-expectations hypothesis by Muth was in the context of the behavior of a single market in which the market was dominated by well-informed specialists who could be presumed to have well-founded expectations of future prices conditional on a relatively stable economic environment. Under conditions of macroeconomic instability, there is good reason to doubt that the accumulated knowledge and experience of market participants would enable agents to form accurate expectations of the future course of prices even in those markets about which they expert knowledge. Insofar as the rational expectations hypothesis has any claim to empirical relevance it is only in the context of stable market situations that can be assumed to be already operating in the neighborhood of an equilibrium. For the kinds of problems that macroeconomists are really trying to answer that assumption is neither relevant nor appropriate.

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14 Responses to “Hayek and Intertemporal Equilibrium”


  1. 1 Adrien May 22, 2017 at 12:27 am

    Very interesting (I did not read all, but keep it in mind for later). I am particularly interested in Hicks point of view, since I am working now on the Traverse. It is difficult to assess if it is precisely the temporal equilibrium concept he had in mind also.

    From what I’ve understood, the traverse model describes an economy with full employment of factors (L & K), but which dynamics (given by one variable describing the spreading of workers in two sectors) moves toward or away from an equilibrium position. There are prices too, that are all the time “equilibrium prices” (those are given by simple linear constrains). Therefore, I tend to tell a story where there is a sequence of equilibria (factors, prices) which are simple solutions to a linear system (I call it static viability), and a meta-equilibrium, that is structural and very long term. The formers go to or depart from the latter, depending on structural interesting conditions.

    I know that, away from classical concept of equilibrium, J. Robinson interacted with Hicks about this concept of an economy moving “towad” an equilibrium, which itself moves according to economic foundations, so that it is never (in practice) reached in short term.

  2. 2 JKH May 22, 2017 at 5:52 am

    Very interesting and well explained.

    First principles question:

    ” The idea of equilibrium is an essential concept in economics. ”

    Why ?

    To what end ?

    Does the end justify the means ?

  3. 3 Adrien May 22, 2017 at 6:49 am

    I have found this article http://www.persee.fr/doc/reco_0035-2764_1999_num_50_2_410075 which is in French; If that bothers you, I can translate some paragraphs if you need.

    regards,

  4. 4 JF May 22, 2017 at 7:32 am

    1. I am concerned too that the equilibrium perspective invites a look at flow, or change, or differential.

    This may ignore Net Wealth too much and invite the sophist’s trick of running the math so the concentrating accumulation of net wealth is simply not included in the views.

    So how is Wealth/stock used in the models (and right to note about the need to have models explain the stock creating effects; i.e. credit and money, of financing agents)?

    2. I am also concerned that lazy presumptions about Price can be used, indeed may be demanded to make the math-models work, and undermining their credibility. The business literature, as I know it, and most business people’s experience in setting prices on real goods and services tells us that price is a greatly emotional thing influenced by the offering agents control over pricing as a mechanism. It is laziness to reflect current or expected prices as having too much dependency on production factors and these model linkages need to be questioned greatly (unless the model somehow builds around the idea that prices are marketing and selling and positioning, all attributes of the offeror and in their control substantially).

    Very much enjoyed the read. Well done, and appreciated.

    JF

  5. 5 JM May 22, 2017 at 10:36 am

    Nice post!

    I would however echo JKH here: what makes equilibrium essential in economics?

    It’s a notion pertaining to a way of modelling and somewhat interesting from that point of view. However, it’s not clear why it should be regarded as essential from a scientific and empirical point of view.

  6. 6 Henry May 22, 2017 at 3:03 pm

    Very interesting post.

    My question is: what has neoclassical equilibrium have to do with macroeconomics?

  7. 7 Blissex May 23, 2017 at 5:31 am

    The interesting post is a good explanation of various issues with Arrow-Debreu-Lucas, but is sort of futile.

    The reason is that in Economics models and approaches must be validated by supporting JB Clark’s three “fables”, in particular the one that factor income distribution is, absent government distortion, exactly the same as, and uniquely determined by, the marginal productivity distribution, and is Pareto-optimal. The three “fables” are the core “verities” of Economics.

    Unfortunately in the case of “temporary equilibrium” the three “fables”, in particular the one about distribution of income, cannot be supported by “temporary equilibrium” approaches in general; the three fables are only compatible with a very narrow set of assumptions, of which Arrow-Debreu-Lucas and comparative statics is probably the most sophisticated.

    Therefore other approaches are outside Economics, and only acceptable to practitioners of political economy studies, which is a nearly dead topic, and pursuing them results in nearly dead careers.

    «there is good reason to doubt that the accumulated knowledge and experience of market participants would enable agents to form accurate expectations of the future course of prices even in those markets about which they expert knowledge.»

    That would be relevant only if that was compatible with the three “fables”, but obviously that is not the case: that gives rise to multiple potential equilibriums, path dependency including of income distribution, potential for factor mispricing and factor involuntary unemployment.

    The issue is the old one of “internal consistency” (with the three “fables” in particular) and “external consistency” (with mere accidental facts) and in Economics “internal consistency” is always preferred.

  8. 8 Val Popov May 24, 2017 at 5:06 am

    Fascinating post! You reveal the inconvenient truth that Walrasian equilibrium is nothing but a model of a barter economy as it has no place for money and banks. I will be interested to get your thoughts on how Frank Hahn fits in this conversation as I believe the issue of money and equilibrium is commonly referred to as Hahn’s Problem.

    In my view, the introduction of money changes the notion of equilibrium in three material respects. First, money is a credit arrangement between a borrower and a bank that can be created and redeemed upon demand. Second, in a barter economy, people produce first and only then engage in trade. In a monetary economy, people go to the bank first to create money and only then do they engage in production and trade. That’s a fancy way of saying that people borrow prior to receipt of incomes but in anticipation of such incomes. What this means is that in a monetary economy, Say’s Law is reversed: money-financed demand creates its own nominal supply. Last but not least, private banks interface independently with borrowers and savers and as such, have infinite capacity to create and destroy money. This means that private banks are agents with infinite strategies. Nash equilibrium (and ADM by extension) requires agents with finite strategies, hence it does not apply to a monetary economy.

    Based on these three points, it can be shown that a system of excess demand equations, describing equilibrium in a monetary economy, has an infinite number solutions, each capable of satisfying agents’ utility optimization and budget constraints. This exposes the notion of equilibrium as a tautology. In a monetary economy, money-financed demand always creates its own nominal supply with prices, output and employment in the present as well as money persisting into the future being the unknown residuals. I’ve done quite a bit of work along these lines, which I believe solves Hahn’s Problem. I would be glad to share and would appreciate some comments/feedback. Let me know if you are interested and how best to correspond…

  9. 9 JKH May 25, 2017 at 5:19 am

    Another first principles question:

    Why should so-called temporary equilibrium be immune to the uncertainties of intertemporal equilibrium ?

    It’s only a matter of the choice of time units.

    The claim of conceptual distinction seems like nonsense to me.

    As it does for the distinction between so-called short run and long run.

  10. 10 PrestoPundit May 25, 2017 at 10:06 am

    “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)

  11. 11 David Glasner May 30, 2017 at 9:35 am

    Adrien, Thanks for your query. I am afraid that I have never studied Hicks’s idea of the Traverse, so I can’t really help you out with it. My recollection is that he discussed the Traverse in his later work, long after he had developed the idea of temporary equilibrium, but I agree it would be interesting to study whether the two ideas are related in a fundamental way. Presumably, there must be some assumption about what expectations are held by agents over the course of the Traverse, but I don’t know what Hick’s assumption was. That would be where I would start.

    JKH, Thank you. The existence of equilibrium shows that the basic explanatory tools of neoclassical economic theory are, in a certain sense, coherent. If there were no equilibrium, then the whole analytical structure of economic theory would collapse. Coherence is not an end in itself, but if economic theory were not coherent, there would certainly not be much point in studying it. We also want economic theory to provide some insight into how the world actually works, so we either want to say that the world corresponds to (or approximates) something resembling an equilibrium, or we want to be able to identify where the world is inconsistent with or departs form the characteristics of an equilibrium and, if possible, ascertain what causes those departures from equilibrium.

    Adrien, Thanks for the link. Unfortunately, my French is now so rusty that reading almost anything in French is difficult and time-consuming for me. So if you would like me to comment on something, I am afraid you will need to translate for me.

    JF, Thanks. Any intertemporal model must include both stocks and flows.

    JM, Thanks. In addition to my reply to JKH, see my reply to Henry below.

    Henry, Equilibrium corresponds to a state in which individuals are optimizing subject to the constrains of other individuals also optimizing and the constraints imposed by nature, technology (the state of knowledge) and the legal system. A coherent system of mutually consistent individually optimizing choices would presumably have some desirable properties like maximum feasible output and full employment of available productive resources. If macroeconomics is concerned with whether and why such a desirable state of affairs – full employment and maximum output – is not attained by a free market economy, presumably one would want to be able to specify the ways in which actual economies differ from equilibrium states of affairs and how such undesirable departures form full employment and maximum output could be minimized or at least mitigated.

    Blissex, I agree that too much of macroeconomists’ attention has been placed on internal consistency and not enough on external consistency.

    Val, I will try to address the issue of money in the Walrasian general equilibrium economy in a future post. There are transactions costs associated with barter that can be reduced by using a common medium of exchange. A common medium of exchange emerges through the operation of a credit system and a credit system would only become necessary in the context of an intertemporal system with incomplete markets that unfolds through time. The question of what happens first is not always a helpful question to try to resolve because it is usually a chicken-egg problem that can’t be addressed analytically.
    JKH, Temporary equilibrium is not immune to the uncertainties of intertemporal equilibrium, it faces up to them. Temporary equilibrium allows for an analysis of how an incomplete system of markets operates when individual expectations of future prices are not correct, which is the case that is macroeconomically relevant and interesting than the case in which expectations are correct. I will write about this more in an upcoming post.

    PrestoPundit, Many thanks for this quotations and reference.

  12. 12 Henry May 30, 2017 at 8:31 pm

    ” Equilibrium corresponds to a state in which individuals are optimizing subject to the constrains of…..”

    David,

    Macroeconomics is about understanding the circumstances under which societal goals of the level of output, unemployment and general prices are satisfied. Neoclassical equilibrium theory is about finding those conditions whereby some optimal level of output and employment is met. It is about the deployment of a given bundle of resources to optimal uses. It addresses these questions through the discovery of equilibrium relative prices. When an economy is operating below optimum output etc. there are no constraints hence relative prices do not come into play. What must come into play is the level of spending (i.e. income) necessary to lift output to optimum levels. The pure theory of neoclassical equilibrium assumes a level of income, so it cannot address the question of the level of income necessary to raise output to the optimum. Neoclassical theory also neglects the fact that in aggregate, demand and supply functions are interrelated. In aggregate, one man’s expense is another’s income, inherently binding supply and demand functions to each other. Neoclassical theory has them be independent.


  1. 1 Correct Foresight, Perfect Foresight, and Intertemporal Equilibrium | Uneasy Money Trackback on May 28, 2017 at 8:18 pm
  2. 2 Hayek and Temporary Equilibrium | Uneasy Money Trackback on June 11, 2017 at 7:43 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.

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