Archive for the 'C. J. Bliss' Category

Keynes and the Fisher Equation

Published June 5, 2018 C. J. Bliss , Fisher effect , Jack Hirshleifer , Keynes 8 Comments

The history of economics society is holding its annual meeting in Chicago from Friday June 15 to Sunday June 17. Bringing together material from a number of posts over the past five years or so about Keynes and the Fisher equation and Fisher effect, I will be presenting a new paper called “Keynes and the Fisher Equation.” Here is the abstract of my paper.

One of the most puzzling passages in the General Theory is the attack (GT p. 142) on Fisher’s distinction between the money rate of interest and the real rate of interest “where the latter is equal to the former after correction for changes in the value of money.” Keynes’s attack on the real/nominal distinction is puzzling on its own terms, inasmuch as the distinction is a straightforward and widely accepted distinction that was hardly unique to Fisher, and was advanced as a fairly obvious proposition by many earlier economists including Marshall. What makes Keynes’s criticism even more problematic is that Keynes’s own celebrated theorem in the Tract on Monetary Reform about covered interest arbitrage is merely an application of Fisher’s reasoning in Appreciation and Interest. Moreover, Keynes endorsed Fisher’s distinction in the Treatise on Money. But even more puzzling is that Keynes’s analysis in Chapter 17 demonstrates that in equilibrium the return on alternative assets must reflect their differences in their expected rates of appreciation. Thus Keynes, himself, in the General Theory endorsed the essential reasoning underlying the distinction between real and the money rates of interest. The solution to the puzzle lies in understanding the distinction between the relationships between the real and nominal rates of interest at a moment in time and the effects of a change in expected rates of appreciation that displaces an existing equilibrium and leads to a new equilibrium. Keynes’s criticism of the Fisher effect must be understood in the context of his criticism of the idea of a unique natural rate of interest implicitly identifying the Fisherian real rate with a unique natural rate.

And here is the concluding section of my paper.

Keynes’s criticisms of the Fisher effect, especially the facile assumption that changes in inflation expectations are reflected mostly, if not entirely, in nominal interest rates – an assumption for which neither Fisher himself nor subsequent researchers have found much empirical support – were grounded in well-founded skepticism that changes in expected inflation do not affect the real interest rate. A Fisherian analysis of an increase in expected deflation at the zero lower bound shows that the burden of the adjustment must be borne by an increase in the real interest rate. Of course, such a scenario might be dismissed as a special case, which it certainly is, but I very much doubt that it is the only assumptions leading to the conclusion that a change in expected inflation or deflation affects the real as well as the nominal interest rate.

Although Keynes’s criticism of the Fisher equation (or more precisely against the conventional simplistic interpretation) was not well argued, his intuition was sound. And in his contribution to the Fisher festschrift, Keynes (1937b) correctly identified the two key assumptions leading to the conclusion that changes in inflation expectations are reflected entirely in nominal interest rates: (1) a unique real equilibrium and (2) the neutrality (actually superneutrality) of money. Keynes’s intuition was confirmed by Hirshleifer (1970, 135-38) who derived the Fisher equation as a theorem by performing a comparative-statics exercise in a two-period general-equilibrium model with money balances, when the money stock in the second period was increased by an exogenous shift factor k. The price level in the second period increases by a factor of k and the nominal interest rate increases as well by a factor of k, with no change in the real interest rate.

But typical Keynesian and New Keynesian macromodels based on the assumption of no capital or a single capital good drastically oversimplify the analysis, because those highly aggregated models assume that the determination of the real interest rate takes place in a single market. The market-clearing assumption invites the conclusion that the rate of interest, like any other price, is determined by the equality of supply and demand – both of which are functions of that price — in  that market.

The equilibrium rate of interest, as C. J. Bliss (1975) explains in the context of an intertemporal general-equilibrium analysis, is not a price; it is an intertemporal rate of exchange characterizing the relationships between all equilibrium prices and expected equilibrium prices in the current and future time periods. To say that the interest rate is determined in any single market, e.g., a market for loanable funds or a market for cash balances, is, at best, a gross oversimplification, verging on fallaciousness. The interest rate or term structure of interest rates is a reflection of the entire intertemporal structure of prices, so a market for something like loanable funds cannot set the rate of interest at a level inconsistent with that intertemporal structure of prices without disrupting and misaligning that structure of intertemporal price relationships. The interest rates quoted in the market for loanable funds are determined and constrained by those intertemporal price relationships, not the other way around.

In the real world, in which current prices, future prices and expected future prices are not and almost certainly never are in an equilibrium relationship with each other, there is always some scope for second-order variations in the interest rates transacted in markets for loanable funds, but those variations are still tightly constrained by the existing intertemporal relationships between current, future and expected future prices. Because the conditions under which Hirshleifer derived his theorem demonstrating that changes in expected inflation are fully reflected in nominal interest rates are not satisfied, there is no basis for assuming that a change in expected inflation affect only nominal interest rates with no effect on real rates.

There are probably a huge range of possible scenarios of how changes in expected inflation could affect nominal and real interest rates. One should not disregard the Fisher equation as one possibility, it seems completely unwarranted to assume that it is the most plausible scenario in any actual situation. If we read Keynes at the end of his marvelous Chapter 17 in the General Theory in which he remarks that he has abandoned the belief he had once held in the existence of a unique natural rate of interest, and has come to believe that there are really different natural rates corresponding to different levels of unemployment, we see that he was indeed, notwithstanding his detour toward a pure liquidity preference theory of interest, groping his way toward a proper understanding of the Fisher equation.

In my Treatise on Money I defined what purported to be a unique rate of interest, which I called the natural rate of interest – namely, the rate of interest which, in the terminology of my Treatise, preserved equality between the rate of saving (as there defined) and the rate of investment. I believed this to be a development and clarification of of Wicksell’s “natural rate of interest,” which was, according to him, the rate which would preserve the stability of some, not quite clearly specified, price-level.

I had, however, overlooked the fact that in any given society there is, on this definition, a different natural rate for each hypothetical level of employment. And, similarly, for every rate of interest there is a level of employment for which that rate is the “natural” rate, in the sense that the system will be in equilibrium with that rate of interest and that level of employment. Thus, it was a mistake to speak of the natural rate of interest or to suggest that the above definition would yield a unique value for the rate of interest irrespective of the level of employment. . . .

If there is any such rate of interest, which is unique and significant, it must be the rate which we might term the neutral rate of interest, namely, the natural rate in the above sense which is consistent with full employment, given the other parameters of the system; though this rate might be better described, perhaps, as the optimum rate. (pp. 242-43)

Because Keynes believed that an increased in the expected future price level implies an increase in the marginal efficiency of capital, it follows that an increase in expected inflation under conditions of less than full employment would increase investment spending and employment, thereby raising the real rate of interest as well the nominal rate. Cottrell (1994) has attempted to make an argument along such lines within a traditional IS-LM framework. I believe that, in a Fisherian framework, my argument points in a similar direction.

 

Hayek and Temporary Equilibrium

Published June 11, 2017 Axel Leijonfuvud , C. J. Bliss , expectations , general equilibrium , Hayek , incomplete markets , intertemporal equilibrium , J. R. Hicks , temporary equilibrium , Uncategorized 8 Comments

In my three previous posts (here, here, and here) about intertemporal equilibrium, I have been emphasizing that the defining characteristic of an intertemporal equilibrium is that agents all share the same expectations of future prices – or at least the same expectations of those future prices on which they are basing their optimizing plans – over their planning horizons. At a given moment at which agents share the same expectations of future prices, the optimizing plans of the agents are consistent, because none of the agents would have any reason to change his optimal plan as long as price expectations do not change, or are not disappointed as a result of prices turning out to be different from what they had been expected to be.

The failure of expected prices to be fulfilled would therefore signify that the information available to agents in forming their expectations and choosing optimal plans conditional on their expectations had been superseded by newly obtained information. The arrival of new information can thus be viewed as a cause of disequilibrium as can any difference in information among agents. The relationship between information and equilibrium can be expressed as follows: differences in information or differences in how agents interpret information leads to disequilibrium, because those differences lead agents to form differing expectations of future prices.

Now the natural way to generalize the intertemporal equilibrium model is to allow for agents to have different expectations of future prices reflecting their differences in how they acquire, or in how they process, information. But if agents have different information, so that their expectations of future prices are not the same, the plans on which agents construct their subjectively optimal plans will be inconsistent and incapable of implementation without at least some revisions. But this generalization seems incompatible with the equilibrium of optimal plans, prices and price expectations described by Roy Radner, which I have identified as an updated version of Hayek’s concept of intertemporal equilibrium.

The question that I want to explore in this post is how to reconcile the absence of equilibrium of optimal plans, prices, and price expectations, with the intuitive notion of market clearing that we use to analyze asset markets and markets for current delivery. If markets for current delivery and for existing assets are in equilibrium in the sense that prices are adjusting in those markets to equate demand and supply in those markets, how can we understand the idea that  the optimizing plans that agents are seeking to implement are mutually inconsistent?

The classic attempt to explain this intermediate situation which partially is and partially is not an equilibrium, was made by J. R. Hicks in 1939 in Value and Capital when he coined the term “temporary equilibrium” to describe a situation in which current prices are adjusting to equilibrate supply and demand in current markets even though agents are basing their choices of optimal plans to implement over time on different expectations of what prices will be in the future. The divergence of the price expectations on the basis of which agents choose their optimal plans makes it inevitable that some or all of those expectations won’t be realized, and that some, or all, of those agents won’t be able to implement the optimal plans that they have chosen, without at least some revisions.

In Hayek’s early works on business-cycle theory, he argued that the correct approach to the analysis of business cycles must be analyzed as a deviation by the economy from its equilibrium path. The problem that he acknowledged with this approach was that the tools of equilibrium analysis could be used to analyze the nature of the equilibrium path of an economy, but could not easily be deployed to analyze how an economy performs once it deviates from its equilibrium path. Moreover, cyclical deviations from an equilibrium path tend not to be immediately self-correcting, but rather seem to be cumulative. Hayek attributed the tendency toward cumulative deviations from equilibrium to the lagged effects of monetary expansion which cause cumulative distortions in the capital structure of the economy that lead at first to an investment-driven expansion of output, income and employment and then later to cumulative contractions in output, income, and employment. But Hayek’s monetary analysis was never really integrated with the equilibrium analysis that he regarded as the essential foundation for a theory of business cycles, so the monetary analysis of the cycle remained largely distinct from, if not inconsistent with, the equilibrium analysis.

I would suggest that for Hayek the Hicksian temporary-equilibrium construct would have been the appropriate theoretical framework within which to formulate a monetary analysis consistent with equilibrium analysis. Although there are hints in the last part of The Pure Theory of Capital that Hayek was thinking along these lines, I don’t believe that he got very far, and he certainly gave no indication that he saw in the Hicksian method the analytical tool with which to weave the two threads of his analysis.

I will now try to explain how the temporary-equilibrium method makes it possible to understand  the conditions for a cumulative monetary disequilibrium. I make no attempt to outline a specifically Austrian or Hayekian theory of monetary disequilibrium, but perhaps others will find it worthwhile to do so.

As I mentioned in my previous post, agents understand that their price expectations may not be realized, and that their plans may have to be revised. Agents also recognize that, given the uncertainty underlying all expectations and plans, not all debt instruments (IOUs) are equally reliable. The general understanding that debt – promises to make future payments — must be evaluated and assessed makes it profitable for some agents to specialize in in debt assessment. Such specialists are known as financial intermediaries. And, as I also mentioned previously, the existence of financial intermediaries cannot be rationalized in the ADM model, because, all contracts being made in period zero, there can be no doubt that the equilibrium exchanges planned in period zero will be executed whenever and exactly as scheduled, so that everyone’s promise to pay in time zero is equally good and reliable.

For our purposes, a particular kind of financial intermediary — banks — are of primary interest. The role of a bank is to assess the quality of the IOUs offered by non-banks, and select from the IOUs offered to them those that are sufficiently reliable to be accepted by the bank. Once a prospective borrower’s IOU is accepted, the bank exchanges its own IOU for the non-bank’s IOU. No non-bank would accept a non-bank’s IOU, at least not on terms as favorable as those on which the bank offers in accepting an IOU. In return for the non-bank IOU, the bank credits the borrower with a corresponding amount of its own IOUs, which, because the bank promises to redeem its IOUs for the numeraire commodity on demand, is generally accepted at face value.

Thus, bank debt functions as a medium of exchange even as it enables non-bank agents to make current expenditures they could not have made otherwise if they can demonstrate to the bank that they are sufficiently likely to repay the loan in the future at agreed upon terms. Such borrowing and repayments are presumably similar to the borrowing and repayments that would occur in the ADM model unmediated by any financial intermediary. In assessing whether a prospective borrower will repay a loan, the bank makes two kinds of assessments. First, does the borrower have sufficient income-earning capacity to generate enough future income to make the promised repayments that the borrower would be committing himself to make? Second, should the borrower’s future income, for whatever reason, turn out to be insufficient to finance the promised repayments, does the borrower have collateral that would allow the bank to secure repayment from the collateral offered as security? In making both kinds of assessments the bank has to form an expectation about the future — the future income of the borrower and the future value of the collateral.

In a temporary-equilibrium context, the expectations of future prices held by agents are not the same, so the expectations of future prices of at least some agents will not be accurate, and some agents won’tbe able to execute their plans as intended. Agents that can’t execute their plans as intended are vulnerable if they have incurred future obligations based on their expectations of future prices that exceed their repayment capacity given the future prices that are actually realized. If they have sufficient wealth — i.e., if they have asset holdings of sufficient value — they may still be able to repay their obligations. However, in the process they may have to sell assets or reduce their own purchases, thereby reducing the income earned by other agents. Selling assets under pressure of obligations coming due is almost always associated with selling those assets at a significant loss, which is precisely why it usually preferable to finance current expenditure by borrowing funds and making repayments on a fixed schedule than to finance the expenditure by the sale of assets.

Now, in adjusting their plans when they observe that their price expectations are disappointed, agents may respond in two different ways. One type of adjustment is to increase sales or decrease purchases of particular goods and services that they had previously been planning to purchase or sell; such marginal adjustments do not fundamentally alter what agents are doing and are unlikely to seriously affect other agents. But it is also possible that disappointed expectations will cause some agents to conclude that their previous plans are no longer sustainable under the conditions in which they unexpectedly find themselves, so that they must scrap their old plans replacing them with completely new plans instead. In the latter case, the abandonment of plans that are no longer viable given disappointed expectations may cause other agents to conclude that the plans that they had expected to implement are no longer profitable and must be scrapped.

When agents whose price expectations have been disappointed respond with marginal adjustments in their existing plans rather than scrapping them and replacing them with new ones, a temporary equilibrium with disappointed expectations may still exist and that equilibrium may be reached through appropriate price adjustments in the markets for current delivery despite the divergent expectations of future prices held by agents. Operation of the price mechanism may still be able to achieve a reconciliation of revised but sub-optimal plans. The sub-optimal temporary equilibrium will be inferior to the allocation that would have resulted had agents all held correct expectations of future prices. Nevertheless, given a history of incorrect price expectations and misallocations of capital assets, labor, and other factors of production, a sub-optimal temporary equilibrium may be the best feasible outcome.

But here’s the problem. There is no guarantee that, when prices turn out to be very different from what they were expected to be, the excess demands of agents will adjust smoothly to changes in current prices. A plan that was optimal based on the expectation that the price of widgets would be $500 a unit may well be untenable at a price of $120 a unit. When realized prices are very different from what they had been expected to be, those price changes can lead to discontinuous adjustments, violating a basic assumption — the continuity of excess demand functions — necessary to prove the existence of an equilibrium. Once output prices reach some minimum threshold, the best response for some firms may be to shut down, the excess demand for the product produced by the firm becoming discontinuous at the that threshold price. The firms shutting down operations may be unable to repay loans they had obligated themselves to repay based on their disappointed price expectations. If ownership shares in firms forced to cease production are held by households that have predicated their consumption plans on prior borrowing and current repayment obligations, the ability of those households to fulfill their obligations may be compromised once those firms stop paying out the expected profit streams. Banks holding debts incurred by firms or households that borrowers cannot service may find that their own net worth is reduced sufficiently to make the banks’ own debt unreliable, potentially causing a breakdown in the payment system. Such effects are entirely consistent with a temporary-equilibrium model if actual prices turn out to be very different from what agents had expected and upon which they had constructed their future consumption and production plans.

Sufficiently large differences between expected and actual prices in a given period may result in discontinuities in excess demand functions once prices reach critical thresholds, thereby violating the standard continuity assumptions on which the existence of general equilibrium depends under the fixed-point theorems that are the lynchpin of modern existence proofs. C. J. Bliss made such an argument in a 1983 paper (“Consistent Temporary Equilibrium” in the volume Modern Macroeconomic Theory edited by  J. P. Fitoussi) in which he also suggested, as I did above, that the divergence of individual expectations implies that agents will not typically regard the debt issued by other agents as homogeneous. Bliss therefore posited the existence of a “Financier” who would subject the borrowing plans of prospective borrowers to an evaluation process to determine if the plan underlying the prospective loan sought by a borrower was likely to generate sufficient cash flow to enable the borrower to repay the loan. The role of the Financier is to ensure that the plans that firms choose are based on roughly similar expectations of future prices so that firms will not wind up acting on price expectations that must inevitably be disappointed.

I am unsure how to understand the function that Bliss’s Financier is supposed to perform. Presumably the Financier is meant as a kind of idealized companion to the Walrasian auctioneer rather than as a representation of an actual institution, but the resemblance between what the Financier is supposed to do and what bankers actually do is close enough to make it unclear to me why Bliss chose an obviously fictitious character to weed out business plans based on implausible price expectations rather than have the role filled by more realistic characters that do what their real-world counterparts are supposed to do. Perhaps Bliss’s implicit assumption is that real-world bankers do not constrain the expectations of prospective borrowers sufficiently to suggest that their evaluation of borrowers would increase the likelihood that a temporary equilibrium actually exists so that only an idealized central authority could impose sufficient consistency on the price expectations to make the existence of a temporary equilibrium likely.

But from the perspective of positive macroeconomic and business-cycle theory, explicitly introducing banks that simultaneously provide an economy with a medium of exchange – either based on convertibility into a real commodity or into a fiat base money issued by the monetary authority – while intermediating between ultimate borrowers and ultimate lenders seems to be a promising way of modeling a dynamic economy that sometimes may — and sometimes may not — function at or near a temporary equilibrium.

We observe economies operating in the real world that sometimes appear to be functioning, from a macroeconomic perspective, reasonably well with reasonably high employment, increasing per capita output and income, and reasonable price stability. At other times, these economies do not function well at all, with high unemployment and negative growth, sometimes with high rates of inflation or with deflation. Sometimes, these economies are beset with financial crises in which there is a general crisis of solvency, and even apparently solvent firms are unable to borrow. A macroeconomic model should be able to account in some way for the diversity of observed macroeconomic experience. The temporary equilibrium paradigm seems to offer a theoretical framework capable of accounting for this diversity of experience and for explaining at least in a very general way what accounts for the difference in outcomes: the degree of congruence between the price expectations of agents. When expectations are reasonably consistent, the economy is able to function at or near a temporary equilibrium which is likely to exist. When expectations are highly divergent, a temporary equilibrium may not exist, and even if it does, the economy may not be able to find its way toward the equilibrium. Price adjustments in current markets may be incapable of restoring equilibrium inasmuch as expectations of future prices must also adjust to equilibrate the economy, there being no market mechanism by which equilibrium price expectations can be adjusted or restored.

This, I think, is the insight underlying Axel Leijonhufvud’s idea of a corridor within which an economy tends to stay close to an equilibrium path. However if the economy drifts or is shocked away from its equilibrium time path, the stabilizing forces that tend to keep an economy within the corridor cease to operate at all or operate only weakly, so that the tendency for the economy to revert back to its equilibrium time path is either absent or disappointingly weak.

The temporary-equilibrium method, it seems to me, might have been a path that Hayek could have successfully taken in pursuing the goal he had set for himself early in his career: to reconcile equilibrium-analysis with a theory of business cycles. Why he ultimately chose not to take this path is a question that, for now at least, I will leave to others to try to answer.

Hayek and Intertemporal Equilibrium

Published May 21, 2017 Arrow-Debrew-McKenzie model , C. J. Bliss , comparative statics , Erik Lindahl , general equilibrium , Hayek , intertemporal equilibrium , J. R. Hicks , John Muth , macroeconomics , Roy Radner , Samuelson , Say's Law , temporary equilibrium , Walrasian equilibrium 18 Comments
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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.

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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