Archive for the 'intertemporal equilibrium' Category

The 2017 History of Economics Society Conference in Toronto

I arrived in Toronto last Thursday for the History of Economics Society Meeting at the University of Toronto (Trinity College to be exact) to give talks on Friday about two papers, one of which (“Hayek and Three Equilibrium Concepts: Sequential, Temporary and Rational Expectations”) I have been posting over the past few weeks on this blog (here, here, here, here, and here). I want to thank those of you who have posted your comments, which have been very helpful, and apologize for not responding to the more recent comments. The other paper about which I gave a talk was based on a post from three of years ago (“Real and Pseudo Gold Standards: Did Friedman Know the Difference?”) on which one of the sections of that paper was based.

Here I am talking about Friedman.

Here are the abstracts of the two papers:

“Hayek and Three Equilibrium Concepts: Sequential, Temporary, and Rational Expectations”

Almost 40 years ago, Murray Milgate (1979) drew attention to the neglected contribution of F. A. Hayek to the concept of intertemporal equilibrium, which had previously been associated with Erik Lindahl and J. R. Hicks. Milgate showed that although Lindahl had developed the concept of intertemporal equilibrium independently, Hayek’s original 1928 contribution was published before Lindahl’s and that, curiously, Hicks in Value and Capital had credited Lindahl with having developed the concept despite having been Hayek’s colleague at LSE in the early 1930s and having previously credited Hayek for the idea of intertemporal equilibrium. Aside from Milgate’s contribution, few developments of the idea of intertemporal equilibrium have adequately credited Hayek’s contribution. This paper attempts to compare three important subsequent developments of that idea with Hayek’s 1937 refinement of the key idea of his 1928 paper. In non-chronological order, the three developments of interest are: 1) Radner’s model of sequential equilibrium with incomplete markets as an alternative to the Arrow-Debreu-McKenzie model of full equilibrium with complete markets; 2) Hicks’s temporary equilibrium model, and 3) the Muth-Lucas rational expectations model. While Hayek’s 1937 treatment most closely resembles Radner’s sequential equilibrium model, which Radner, echoing Hayek, describes as an equilibrium of plans, prices, and price expectations, Hicks’s temporary equilibrium model seems to be the natural development of Hayek’s approach. The Muth-Lucas rational-expectations model, however, develops the concept of intertemporal equilibrium in a way that runs counter to the fundamental Hayekian insight about the nature of intertemporal equilibrium

“Milton Friedman and the Gold Standard”

Milton Friedman discussed the gold standard in a number of works. His two main discussions of the gold standard appear in a 1951 paper on commodity-reserve currencies and in a 1961 paper on real and pseudo gold standards. In the 1951 paper, he distinguished between a gold standard in which only gold or warehouse certificates to equivalent amounts of gold circulated as a medium of exchange and one in which mere fiduciary claims to gold also circulated as media of exchange. Friedman called the former a strict gold standard and the latter as a partial gold standard. In the later paper, he distinguished between a gold standard in which gold is used as money, and a gold standard in which the government merely fixes the price of gold, dismissing the latter as a “pseudo” gold standard. In this paper, I first discuss the origin for the real/partial distinction, an analytical error, derived from David Hume via the nineteenth-century Currency School, about the incentives of banks to overissue convertible claims to base money, which inspired the Chicago plan for 100-percent reserve banking. I then discuss the real/pseudo distinction and argue that it was primarily motivated by the ideological objective of persuading libertarian and classical-liberal supporters of the gold standard to support a fiat standard supplemented by the k-percent quantity rule that Friedman was about to propose.

And here is my concluding section from the Friedman paper:

Milton Friedman’s view of the gold standard was derived from his mentors at the University Chicago, an inheritance that, in a different context, he misleadingly described as the Chicago oral tradition. The Chicago view of the gold standard was, in turn, derived from the English Currency School of the mid-nineteenth century, which successfully promoted the enactment of the Bank Charter Act of 1844, imposing a 100-percent marginal reserve requirement on the banknotes issued by the Bank of England, and served as a model for the Chicago Plan for 100-percent-reserve banking. The Currency School, in turn, based its proposals for reform on the price-specie-flow analysis of David Hume (1742).

The pure quantity-theoretic lineage of Friedman’s views of the gold standard and the intellectual debt that he owed to the Currency School and the Bank Charter Act disposed him to view the gold standard as nothing more than a mechanism for limiting the quantity of money. If the really compelling purpose and justification of the gold standard was to provide a limitation on the capacity of a government or a monetary authority to increase the quantity of money, then there was nothing special or exceptional about the gold standard.

I have no interest in exploring the reasons why supporters of, and true believers in, the gold standard feel a strong ideological or emotional attachment to that institution, and even if I had such an interest, this would not be the place to enter into such an exploration, but I conjecture that the sources of that attachment to the gold standard go deeper than merely to provide a constraint on the power of the government to increase the quantity of money.

But from Friedman’s quantity-theoretical perspective, if the primary virtue of the gold standard was that it served to limit the ability of the government to increase the quantity of money, if another institution could perform that service, it would serve just as well as the gold standard. The lesson that Friedman took from the efforts of the Currency School to enact the Bank Charter Act was that the gold standard, on its own, did not provide a sufficient constraint on the ability of private banks to increase the quantity of money. Otherwise, the 100-percent marginal reserve requirement of the Bank Charter Act would have been unnecessary.

Now if the gold standard could not function well without additional constraints on the quantity of money, then obviously the constraint on the quantity of money that really matters is not the gold standard itself, but the 100-percent marginal reserve requirement imposed on the banking system. But if the relevant constraint on the quantity of money is the 100 percent marginal reserve requirement, then the gold standard is really just excess baggage.

That was the view of Henry Simons and the other authors of the Chicago Plan. For a long time, Friedman accepted the Chicago Plan as the best prescription for monetary stability, but at about the time that he was writing his paper on real and pseudo gold standards, Friedman was frcoming to position that a k-percent rule would be a superior alternative to the old Chicago Plan. His paper on Pseudo gold standards for the Mont Pelerin Society was his initial attempt to persuade his libertarian and classical-liberal friends and colleagues to reconsider their support for the gold standard and prepare the ground for the k-percent rule that he was about to offer. But in his ideological enthusiasm he, in effect, denied the reality of the historical gold standard.

Aside from the getting to talk about my papers, the other highlights of the HES meeting for me included the opportunity to renew a very old acquaintance with the eminent Samuel Hollander whom I met about 35 years ago at the first History of Economics Society meeting that I ever attended and making the acquaintance for the first time with the eminent Deidre McCloskey who was at both of my sessions and with the eminent E. Roy Weintraub who has been doing important research on my illustrious cousin Abraham Wald, the first one to prove the existence of a competitive equilibrium almost 20 years before Arrow, Debreu and McKenzie came up with their proofs. Doing impressive and painstaking historical research Weintraub found a paper, long thought to have been lost in which Wald, using the fixed-point theorem that Arrow, Debreu and McKenzie had independently used in their proofs, gave a more general existence proof than he had provided in his published existence proofs, clearly establishing Wald’s priority over Arrow, Debreu and McKenzie in proving the existence of general equilibrium.

HT: Rebeca Betancourt

 

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Hayek and Rational Expectations

In this, my final, installment on Hayek and intertemporal equilibrium, I want to focus on a particular kind of intertemporal equilibrium: rational-expectations equilibrium. In his discussions of intertemporal equilibrium, Roy Radner assigns a meaning to the term “rational-expectations equilibrium” very different from the meaning normally associated with that term. Radner describes a rational-expectations equilibrium as the equilibrium that results when some agents are able to make inferences about the beliefs held by other agents when observed prices differ from what they had expected prices to be. Agents attribute the differences between observed and expected prices to information held by agents better informed than themselves, and revise their own expectations accordingly in light of the information that would have justified the observed prices.

In the early 1950s, one very rational agent, Armen Alchian, was able to figure out what chemicals were being used in making the newly developed hydrogen bomb by identifying companies whose stock prices had risen too rapidly to be explained otherwise. Alchian, who spent almost his entire career at UCLA while also moonlighting at the nearby Rand Corporation, wrote a paper for Rand in which he listed the chemicals used in making the hydrogen bomb. When people at the Defense Department heard about the paper – the Rand Corporation was started as a think tank largely funded by the Department of Defense to do research that the Defense Department was interested in – they went to Alchian, confiscated and destroyed the paper. Joseph Newhard recently wrote a paper about this episode in the Journal of Corporate Finance. Here’s the abstract:

At RAND in 1954, Armen A. Alchian conducted the world’s first event study to infer the fuel material used in the manufacturing of the newly-developed hydrogen bomb. Successfully identifying lithium as the fusion fuel using only publicly available financial data, the paper was seen as a threat to national security and was immediately confiscated and destroyed. The bomb’s construction being secret at the time but having since been partially declassified, the nuclear tests of the early 1950s provide an opportunity to observe market efficiency through the dissemination of private information as it becomes public. I replicate Alchian’s event study of capital market reactions to the Operation Castle series of nuclear detonations in the Marshall Islands, beginning with the Bravo shot on March 1, 1954 at Bikini Atoll which remains the largest nuclear detonation in US history, confirming Alchian’s results. The Operation Castle tests pioneered the use of lithium deuteride dry fuel which paved the way for the development of high yield nuclear weapons deliverable by aircraft. I find significant upward movement in the price of Lithium Corp. relative to the other corporations and to DJIA in March 1954; within three weeks of Castle Bravo the stock was up 48% before settling down to a monthly return of 28% despite secrecy, scientific uncertainty, and public confusion surrounding the test; the company saw a return of 461% for the year.

Radner also showed that the ability of some agents to infer the information on which other agents are causing prices to differ from the prices that had been expected does not necessarily lead to an equilibrium. The process of revising expectations in light of observed prices may not converge on a shared set of expectations of the future based on commonly shared knowledge.

So rather than pursue Radner’s conception of rational expectations, I will focus here on the conventional understanding of “rational expectations” in modern macroeconomics, which is that the price expectations formed by the agents in a model should be consistent with what the model itself predicts that those future prices will be. In this very restricted sense, I believe rational expectations is a very important property that any model ought to have. It simply says that a model ought to have the property that if one assumes that the agents in a model expect the equilibrium predicted by the model, then, given those expectations, the solution of the model will turn out to be the equilibrium of the model. This property is a consistency and coherence property that any model, regardless of its substantive predictions, ought to have. If a model lacks this property, there is something wrong with the model.

But there is a huge difference between saying that a model should have the property that correct expectations are self-fulfilling and saying that agents are in fact capable of predicting the equilibrium of the model. Assuming the former does not entail the latter. What kind of crazy model would have the property that correct expectations are not self-fulfilling? I mean think about: a model in which correct expectations are not self-fulfilling is a nonsense model.

But demanding that a model not spout out jibberish is very different from insisting that the agents in the model necessarily have the capacity to predict what the equilibrium of the model will be. Rational expectations in the first sense is a minimal consistency property of an economic model; rational expectations in the latter sense is an empirical assertion about the real world. You can make such an assumption if you want, but you can’t claim that it is a property of the real world. Whether it is a property of the real world is a matter of fact, not a matter of methodological fiat. But methodological fiat is what rational expectations has become in macroeconomics.

In his 1937 paper on intertemporal equilibrium, Hayek was very clear that correct expectations are logically implied by the concept of an equilibrium of plans extending through time. But correct expectations are not a necessary, or even descriptively valid, characteristic of reality. Hayek also conceded that we don’t even have an explanation in theory of how correct expectations come into existence. He merely alluded to the empirical observation – perhaps not the most accurate description of empirical reality in 1937 – that there is an observed general tendency for markets to move toward equilibrium, implying that over time expectations do tend to become more accurate.

It is worth pointing out that when the idea of rational expectations was introduced by John Muth in the early 1960s, he did so in the context of partial-equilibrium models in which the rational expectation in the model was the rational expectation of the equilibrium price in a paraticular market. The motivation for Muth to introduce the idea of a rational expectation was idea of a cobweb cycle in which producers simply assume that the current price will remain at whatever level currently prevails. If there is a time lag between production, as in agricultural markets between the initial application of inputs and the final yield of output, it is easy to generate an alternating sequence of boom and bust, with current high prices inducing increased output in the following period, driving prices down, thereby inducing low output and high prices in the next period and so on.

Muth argued that rational producers would not respond to price signals in a way that led to consistently mistaken expectations, but would base their price expectations on more realistic expectations of what future prices would turn out to be. In his microeconomic work on rational expectations, Muth showed that the rational-expectation assumption was a better predictor of observed prices than the assumption of static expectations underlying the traditional cobweb-cycle model. So Muth’s rational-expectations assumption was based on a realistic conjecture of how real-world agents would actually form expectations. In that sense, Muth’s assumption was consistent with Hayek’s conjecture that there is an empirical tendency for markets to move toward equilibrium.

So while Muth’s introduction of the rational-expectations hypothesis was an empirically progressive theoretical innovation, extending rational-expectations into the domain of macroeconomics has not been empirically progressive, rational expectations models having consistently failed to generate better predictions than macro-models using other expectational assumptions. Instead, a rational-expectations axiom has been imposed as part of a spurious methodological demand that all macroeconomic models be “micro-founded.” But the deeper point – a point that Hayek understood better than perhaps anyone else — is that there is a huge difference in kind between forming rational expectations about a single market price and forming rational expectations about the vector of n prices on the basis of which agents are choosing or revising their optimal intertemporal consumption and production plans.

It is one thing to assume that agents have some expert knowledge about the course of future prices in the particular markets in which they participate regularly; it is another thing entirely to assume that they have knowledge sufficient to forecast the course of all future prices and in particular to understand the subtle interactions between prices in one market and the apparently unrelated prices in another market. The former kind of knowledge is knowledge that expert traders might be expected to have; the latter kind of knowledge is knowledge that would be possessed by no one but a nearly omniscient central planner, whose existence was shown by Hayek to be a practical impossibility.

Standard macroeconomic models are typically so highly aggregated that the extreme nature of the rational-expectations assumption is effectively suppressed. To treat all output as a single good (which involves treating the single output as both a consumption good and a productive asset generating a flow of productive services) effectively imposes the assumption that the only relative price that can ever change is the wage, so that all but one future relative prices are known in advance. That assumption effectively assumes away the problem of incorrect expectations except for two variables: the future price level and the future productivity of labor (owing to the productivity shocks so beloved of Real Business Cycle theorists). Having eliminated all complexity from their models, modern macroeconomists, purporting to solve micro-founded macromodels, simply assume that there is but one or at most two variables about which agents have to form their rational expectations.

Four score years since Hayek explained how challenging the notion of intertemporal equilibrium really is and the difficulties inherent in explaining any empirical tendency toward intertempral equilibrium, modern macroeconomics has succeeded in assuming all those difficulties out of existence. Many macroeconomists feel rather proud of what modern macroeconomics has achieved. I am not quite as impressed as they are.

Hayek and Temporary Equilibrium

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.

Roy Radner and the Equilibrium of Plans, Prices and Price Expectations

In this post I want to discuss Roy Radner’s treatment of an equilibrium of plans, prices, and price expectations (EPPPE) and its relationship to Hayek’s conception of intertemporal equilibrium, of which Radner’s treatment is a technically more sophisticated version. Although I seen no evidence that Radner was directly influenced by Hayek’s work, I consider Radner’s conception of EPPPE to be a version of Hayek’s conception of intertemporal equilibrium, because it captures essential properties of Hayek’s conception of intertemporal equilibrium as a situation in which agents independently formulate their own optimizing plans based on the prices that they actually observe – their common knowledge – and on the future prices that they expect to observe over the course of their planning horizons. While currently observed prices are common knowledge – not necessarily a factual description of economic reality but not an entirely unreasonable simplifying assumption – the prices that individual agents expect to observe in the future are subjective knowledge based on whatever common or private knowledge individuals may have and whatever methods they may be using to form their expectations of the prices that will be observed in the future. An intertemporal equilibrium refers to a set of decentralized plans that are both a) optimal from the standpoint of every agent’s own objectives given their common knowledge of current prices and their subjective expectations of future prices and b) mutually consistent.

If an agent has chosen an optimal plan given current and expected future prices, that plan will not be changed unless the agent acquires new information that renders the existing plan sub-optimal relative to the new information. Otherwise, there would be no reason for the agent to deviate from an optimal plan. The new information that could cause an agent to change a formerly optimal plan would either affect the preferences of the agent, the technology available to the agent, or would somehow be reflected in current prices or in expected future prices. But it seems improbable that there could be a change in preferences or technology would not also be reflected in current or expected future prices. So absent a change in current or expected future prices, there would seem to be almost no likelihood that an agent would deviate from a plan that was optimal given current prices and the future prices expected by the agent.

The mutual consistency of the optimizing plans of independent agents therefore turns out to be equivalent to the condition that all agents observe the same current prices – their common knowledge – and have exactly the same forecasts of the future prices upon which they have relied in choosing their optimal plans. Even should their forecasts of future prices turn out to be wrong, at the moment before their forecasts of future prices were changed or disproved by observation, their plans were still mutually consistent relative to the information on which their plans had been chosen. The failure of the equilibrium to be maintained could be attributed to a change in information that meant that the formerly optimal plans were no longer optimal given the newly acquired information. But until the new information became available, the mutual consistency of optimal plans at that (fleeting) moment signified an equilibrium state. Thus, the defining characteristic of an intertemporal equilibrium in which current prices are common knowledge is that all agents share the same expectations of the future prices on which their optimal plans have been based.

There are fundamental differences between the Arrow-Debreu-McKenzie (ADM) equilibrium and the EPPPE. One difference worth mentioning is that, under the standard assumptions of the ADM model, the equilibrium is Pareto-optimal, and any Pareto-optimum allocation, by a suitable redistribution of initial endowments, could be achieved as a general equilibrium (two welfare theorems). These results do not generally hold for EPPPE, because, in contrast to the ADM model, it is possible for agents in EPPPE to acquire additional information over time, not only passively, but by investing resources in the production of information. Investing resources in the production of information can cause inefficiency in two ways: first, by creating non-convexities (owing to start-up costs in information gathering activities) that are inconsistent with the uniform competitive prices characteristic of the ADM equilibrium, and second, by creating incentives to devote resources to produce information whose value is derived from profits in trading with less well-informed agents. The latter source of inefficiency was discovered by Jack Hirshleifer in his classic 1971 paper, which I have written about in several previous posts (here, here, here, and here).

But the important feature of Radner’s EPPPE that I want to emphasize here — and what radically distinguishes it from the ADM equilibrium — is its fragility. Unlike the ADM equilibrium which is established once and forever at time zero of a model in which all production and consumption starts in period one, the EPPPE, even if it ever exists, is momentary, and is subject to unraveling whenever there is a change in the underlying information upon which current prices and expected future prices depend, and upon which agents, in choosing their optimal plans, rely. Time is not just, as it is in the ADM model, an appendage to the EPPPE, and, as a result, EPPPE can account for many phenomena, practices, and institutions that are left out of the ADM model.

The two differences that are most relevant in this context are the existence of stock markets in which shares of firms are traded based on expectations of the future net income streams associated with those firms, and the existence of a medium of exchange supplied by private financial intermediaries known as banks. In the ADM model in which all transactions are executed in time zero, in advance of all the actual consumption and production activities determined by those transactions, there would be no reason to hold, or to supply, a medium of exchange. The ADM equilibrium allows for agents to borrow or lend at equilibrium interest rates to optimize the time profiles of their consumption relative to their endowments and the time profiles of their earnings. Since all such transactions are consummated in time zero, and since, through some undefined process, the complete solvency and the integrity of all parties to all transactions is ascertained in time zero, the probability of a default on any loan contracted at time zero is zero. As a result, each agent faces a single intertemporal budget constraint at time zero over all periods from 1 to n. Walras’s Law therefore holds across all time periods for this intertemporal budget constraint, each agent transacting at the same prices in each period as every other agent does.

Once an equilibrium price vector is established in time zero, each agent knows that his optimal plan based on that price vector (which is the common knowledge of all agents) will be executed over time exactly as determined in time zero. There is no reason for any exchange of ownership shares in firms, the future income streams from each firm being known in advance.

The ADM equilibrium is a model of an economic process very different from Radner’s EPPPE, because in EPPPE, agents have no reason to assume that their current plans, even if they are momentarily both optimal and mutually consistent with the plans of all other agents, will remain optimal and consistent with the plans of all other agents. New information can arrive or be produced that will necessitate a revision in plans. Because even equilibrium plans are subject to revision, agents must take into account the solvency and credit worthiness of counterparties with whom they enter into transactions. The potentially imperfect credit-worthiness of at least some agents enables certain financial intermediaries (aka banks) to provide a service by offering to exchange their debt, which is widely considered to be more credit-worthy than the debt of ordinary agents, to agents seeking to borrow to finance purchases of either consumption or investment goods. Many agents seeking to borrow therefore prefer exchanging their debt for bank debt, bank debt being acceptable by other agents at face value. In addition, because the acquisition of new information is possible, there is a reason for agents to engage in speculative trades of commodities or assets. Such assets include ownership shares of firms, and agents may revise their valuations of those firms as they revise their expectations about future prices and their expectations about the revised plans of those firms in response to newly acquired information.

I will discuss the special role of banks at greater length in my next post on temporary equilibrium. But for now, I just want to underscore a key point: in the EPPE, unless all agents have the same expectations of future prices, Walras’s Law need not hold. The proof that Walras’s holds depends on the assumption that individual plans to buy and sell are based on the assumption that every agent buys or sells each commodity at the same price that every other transactor buys  or sells that commodity. But in the intertemporal context, in which only current, not future prices, are observed, plans for current and future prices are made based on expectations about future prices. If agents don’t share the same expectations about future prices, agents making plans for future purchases based on overly optimistic expectations about the prices at which they will be able to sell, may make commitments to buy in the future (or commitment to repay loans to finance purchases in the present) that they will be unable to discharge. Reneging on commitments to buy in the future or to repay obligations incurred in the present may rule out the existence of even a temporary equilibrium in the future.

Finally, let me add a word about Radner’s terminology. In his 1987 entry on “Uncertainty and General Equilibrium” for the New Palgrave Dictionary of Economics, (Here is a link to the revised version on line), Radner writes:

A trader’s expectations concern both future environmental events and future prices. Regarding expectations about future environmental events, there is no conceptual problem. According to the Expected Utility Hypothesis, each trader is characterized by a subjective probability measure on the set of complete histories of the environment. Since, by definition, the evolution of the environment is exogenous, a trader’s conditional probability of a future event, given the information to date, is well defined.

It is not so obvious how to proceed with regard to trader’s expectations about future prices. I shall contrast two possible approaches. In the first, which I shall call the perfect foresight approach, let us assume that the behaviour of traders is such as to determine, for each complete history of the environment, a unique corresponding sequence of price system[s]. . .

Thus, the perfect foresight approach implies that, in equilibrium, traders have common price expectation functions. These price expectation functions indicate, for each date-event pair, what the equilibrium price system would be in the corresponding market at that date event pair. . . . [I]t follows that, in equilibrium the traders would have strategies (plans) such that if these strategies were carried out, the markets would be cleared at each date-event pair. Call such plans consistent. A set of common price expectations and corresponding consistent plans is called an equilibrium of plans, prices, and price expectations.

My only problem with Radner’s formulation here is that he is defining his equilibrium concept in terms of the intrinsic capacity of the traders to predict prices rather the simple fact that traders form correct expectations. For purposes of the formal definition of EPPE, it is irrelevant whether traders predictions of future prices are correct because they are endowed with the correct model of the economy or because they are all lucky and randomly have happened simultaneously to form the same expectations of future prices. Radner also formulates an alternative version of his perfect-foresight approach in which agents don’t all share the same information. In such cases, it becomes possible for traders to make inferences about the environment by observing prices differ from what they had expected.

The situation in which traders enter the market with different non-price information presents an opportunity for agents to learn about the environment from prices, since current prices reflect, in a possibly complicated manner, the non-price information signals received by the various agents. To take an extreme example, the “inside information” of a trader in a securities market may lead him to bid up the price to a level higher than it otherwise would have been. . . . [A]n astute market observer might be able to infer that an insider has obtained some favourable information, just by careful observation of the price movement.

The ability to infer non-price information from otherwise inexplicable movements in prices leads Radner to define a concept of rational expectations equilibrium.

[E]conomic agents have the opportunity to revise their individual models in the light of observations and published data. Hence, there is a feedback from the true relationship to the individual models. An equilibrium of this system, in which the individual models are identical with the true model, is called a rational expectations equilibrium. This concept of equilibrium is more subtle, of course, that the ordinary concept of equilibrium of supply and demand. In a rational expectations equilibrium, not only are prices determined so as to equate supply and demand, but individual economic agents correctly perceive the true relationship between the non-price information received by the market participants and the resulting equilibrium market prices.

Though this discussion is very interesting from several theoretical angles, as an explanation of what is entailed by an economic equilibrium, it misses the key point, which is the one that Hayek identified in his 1928 and (especially) 1937 articles mentioned in my previous posts. An equilibrium corresponds to a situation in which all agents have identical expectations of the future prices upon which they are making optimal plans given the commonly observed current prices and the expected future prices. If all agents are indeed formulating optimal plans based on the information that they have at that moment, their plans will be mutually consistent and will be executable simultaneously without revision as long as the state of their knowledge at that instant does not change. How it happened that they arrived at identical expectations — by luck chance or supernatural powers of foresight — is irrelevant to that definition of equilibrium. Radner does acknowledge that, under the perfect-foresight approach, he is endowing economic agents with a wildly unrealistic powers of imagination and computational capacity, but from his exposition, I am unable to decide whether he grasped the subtle but crucial point about the irrelevance of an assumption about the capacities of agents to the definition of EPPPE.

Although it is capable of describing a richer set of institutions and behavior than is the Arrow-Debreu model, the perfect-foresight approach is contrary to the spirit of much of competitive market theory in that it postulates that individual traders must be able to forecast, in some sense, the equilibrium prices that will prevail in the future under all alternative states of the environment. . . .[T]his approach . . . seems to require of the traders a capacity for imagination and computation far beyond what is realistic. . . .

These last considerations lead us in a different direction, which I shall call the bounded rationality approach. . . . An example of the bounded-rationality approach is the theory of temporary equilibrium.

By eschewing any claims about the rationality of the agents or their computational powers, one can simply talk about whether agents do or do not have identical expectations of future prices and what the implications of those assumptions are. When expectations do agree, there is at least a momentary equilibrium of plans, prices and price expectations. When they don’t agree, the question becomes whether even a temporary equilibrium exists and what kind of dynamic process is implied by the divergence of expectations. That it seems to me would be a fruitful way forward for macroeconomics to follow. In my next post, I will discuss some of the characteristics and implications of a temporary-equilibrium approach to macroeconomics.

 

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.

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.

Rational Expectations, or, The Road to Incoherence

J. W. Mason left a very nice comment on my recent post about Paul Romer’s now-famous essay on macroeconomics, a comment now embedded in his interesting and insightful blog post on the Romer essay. As a wrote in my reply to Mason’s comment, I really liked the way he framed his point about rational expectations and intertemporal equilibrium. Sometimes when you see a familiar idea expressed in a particular way, the novelty of the expression, even though it’s not substantively different from other ways of expressing the idea, triggers a new insight. And that’s what I think happened in my own mind as I read Mason’s comment. Here’s what he wrote:

David Glasner’s interesting comment on Romer makes in passing a point that’s bugged me for years — that you can’t talk about transitions from one intertemporal equilibrium to another, there’s only the one. Or equivalently, you can’t have a model with rational expectations and then talk about what happens if there’s a “shock.” To say there is a shock in one period, is just to say that expectations in the previous period were wrong. Glasner:

the Lucas Critique applies even to micro-founded models, those models being strictly valid only in equilibrium settings and being unable to predict the adjustment of economies in the transition between equilibrium states. All models are subject to the Lucas Critique.

So the further point that I would make, after reading Mason’s comment, is just this. For an intertemporal equilibrium to exist, there must be a complete set of markets for all future periods and contingent states of the world, or, alternatively, there must be correct expectations shared by all agents about all future prices and the probability that each contingent future state of the world will be realized. By the way, If you think about it for a moment, the notion that probabilities can be assigned to every contingent future state of the world is mind-bogglingly unrealistic, because the number of contingent states must rapidly become uncountable, because every single contingency itself gives rise to further potential contingencies, and so on and on and on. But forget about that little complication. What intertemporal equilibrium requires is that all expectations of all individuals be in agreement – or at least not be inconsistent, some agents possibly having an incomplete set of expectations about future prices and future states of the world. If individuals differ in their expectations, so that their planned future purchases and sales are based on what they expect future prices to be when the time comes for those transactions to be carried out, then individuals will not be able to execute their plans as intended when at least one of them finds that actual prices are different from what they had been expected to be.

What this means is that expectations can be rational only when everyone has identical expectations. If people have divergent expectations, then the expectations of at least some people will necessarily be disappointed — the expectations of both people with differing expectations cannot be simultaneously realized — and those individuals whose expectations have been disappointed will have to revise their plans. But that means that the expectations of those people who were correct were also not rational, because the prices that they expected were not equilibrium prices. So unless all agents have the same expectations about the future, the expectations of no one are rational. Rational expectations are a fixed point, and that fixed point cannot be attained unless everyone shares those expectations.

Beyond that little problem, Mason raises the further problem that, in a rational-expectations equilibrium, it makes no sense to speak of a shock, because the only possible meaning of “shock” in the context of a full intertemporal (aka rational-expectations) equilibrium is a failure of expectations to be realized. But if expectations are not realized, expectations were not rational. So the whole New Classical modeling strategy of identifying shocks  to a system in rational-expectations equilibrium, and “predicting” the responses to these shocks as if they had been anticipated is self-contradictory and incoherent.

Representative Agents, Homunculi and Faith-Based Macroeconomics

After my previous post comparing the neoclassical synthesis in its various versions to the mind-body problem, there was an interesting Twitter exchange between Steve Randy Waldman and David Andolfatto in which Andolfatto queried whether Waldman and I are aware that there are representative-agent models in which the equilibrium is not Pareto-optimal. Andalfatto raised an interesting point, but what I found interesting about it might be different from what Andalfatto was trying to show, which, I am guessing, was that a representative-agent modeling strategy doesn’t necessarily commit the theorist to the conclusion that the world is optimal and that the solutions of the model can never be improved upon by a monetary/fiscal-policy intervention. I concede the point. It is well-known I think that, given the appropriate assumptions, a general-equilibrium model can have a sub-optimal solution. Given those assumptions, the corresponding representative-agent will also choose a sub-optimal solution. So I think I get that, but perhaps there’s a more subtle point  that I’m missing. If so, please set me straight.

But what I was trying to argue was not that representative-agent models are necessarily optimal, but that representative-agent models suffer from an inherent, and, in my view, fatal, flaw: they can’t explain any real macroeconomic phenomenon, because a macroeconomic phenomenon has to encompass something more than the decision of a single agent, even an omniscient central planner. At best, the representative agent is just a device for solving an otherwise intractable general-equilibrium model, which is how I think Lucas originally justified the assumption.

Yet just because a general-equilibrium model can be formulated so that it can be solved as the solution of an optimizing agent does not explain the economic mechanism or process that generates the solution. The mathematical solution of a model does not necessarily provide any insight into the adjustment process or mechanism by which the solution actually is, or could be, achieved in the real world. Your ability to find a solution for a mathematical problem does not mean that you understand the real-world mechanism to which the solution of your model corresponds. The correspondence between your model may be a strictly mathematical correspondence which may not really be in any way descriptive of how any real-world mechanism or process actually operates.

Here’s an example of what I am talking about. Consider a traffic-flow model explaining how congestion affects vehicle speed and the flow of traffic. It seems obvious that traffic congestion is caused by interactions between the different vehicles traversing a thoroughfare, just as it seems obvious that market exchange arises as the result of interactions between the different agents seeking to advance their own interests. OK, can you imagine building a useful traffic-flow model based on solving for the optimal plan of a representative vehicle?

I don’t think so. Once you frame the model in terms of a representative vehicle, you have abstracted from the phenomenon to be explained. The entire exercise would be pointless – unless, that is, you assumed that interactions between vehicles are so minimal that they can be ignored. But then why would you be interested in congestion effects? If you want to claim that your model has any relevance to the effect of congestion on traffic flow, you can’t base the claim on an assumption that there is no congestion.

Or to take another example, suppose you want to explain the phenomenon that, at sporting events, all, or almost all, the spectators sit in their seats but occasionally get up simultaneously from their seats to watch the play on the field or court. Would anyone ever think that an explanation in terms of a representative spectator could explain that phenomenon?

In just the same way, a representative-agent macroeconomic model necessarily abstracts from the interactions between actual agents. Obviously, by abstracting from the interactions, the model can’t demonstrate that there are no interactions between agents in the real world or that their interactions are too insignificant to matter. I would be shocked if anyone really believed that the interactions between agents are unimportant, much less, negligible; nor have I seen an argument that interactions between agents are unimportant, the concept of network effects, to give just one example, being an important topic in microeconomics.

It’s no answer to say that all the interactions are accounted for within the general-equilibrium model. That is just a form of question-begging. The representative agent is being assumed because without him the problem of finding a general-equilibrium solution of the model is very difficult or intractable. Taking into account interactions makes the model too complicated to work with analytically, so it is much easier — but still hard enough to allow the theorist to perform some fancy mathematical techniques — to ignore those pesky interactions. On top of that, the process by which the real world arrives at outcomes to which a general-equilibrium model supposedly bears at least some vague resemblance can’t even be described by conventional modeling techniques.

The modeling approach seems like that of a neuroscientist saying that, because he could simulate the functions, electrical impulses, chemical reactions, and neural connections in the brain – which he can’t do and isn’t even close to doing, even though a neuroscientist’s understanding of the brain far surpasses any economist’s understanding of the economy – he can explain consciousness. Simulating the operation of a brain would not explain consciousness, because the computer on which the neuroscientist performed the simulation would not become conscious in the course of the simulation.

Many neuroscientists and other materialists like to claim that consciousness is not real, that it’s just an epiphenomenon. But we all have the subjective experience of consciousness, so whatever it is that someone wants to call it, consciousness — indeed the entire world of mental phenomena denoted by that term — remains an unexplained phenomenon, a phenomenon that can only be dismissed as unreal on the basis of a metaphysical dogma that denies the existence of anything that can’t be explained as the result of material and physical causes.

I call that metaphysical belief a dogma not because it’s false — I have no way of proving that it’s false — but because materialism is just as much a metaphysical belief as deism or monotheism. It graduates from belief to dogma when people assert not only that the belief is true but that there’s something wrong with you if you are unwilling to believe it as well. The most that I would say against the belief in materialism is that I can’t understand how it could possibly be true. But I admit that there are a lot of things that I just don’t understand, and I will even admit to believing in some of those things.

New Classical macroeconomists, like, say, Robert Lucas and, perhaps, Thomas Sargent, like to claim that unless a macroeconomic model is microfounded — by which they mean derived from an explicit intertemporal optimization exercise typically involving a representative agent or possibly a small number of different representative agents — it’s not an economic model, because the model, being vulnerable to the Lucas critique, is theoretically superficial and vacuous. But only models of intertemporal equilibrium — a set of one or more mutually consistent optimal plans — are immune to the Lucas critique, so insisting on immunity to the Lucas critique as a prerequisite for a macroeconomic model is a guarantee of failure if your aim to explain anything other than an intertemporal equilibrium.

Unless, that is, you believe that real world is in fact the realization of a general equilibrium model, which is what real-business-cycle theorists, like Edward Prescott, at least claim to believe. Like materialist believers that all mental states are epiphenomenous, and that consciousness is an (unexplained) illusion, real-business-cycle theorists purport to deny that there is such a thing as a disequilibrium phenomenon, the so-called business cycle, in their view, being nothing but a manifestation of the intertemporal-equilibrium adjustment of an economy to random (unexplained) productivity shocks. According to real-business-cycle theorists, such characteristic phenomena of business cycles as surprise, regret, disappointed expectations, abandoned and failed plans, the inability to find work at wages comparable to wages that other similar workers are being paid are not real phenomena; they are (unexplained) illusions and misnomers. The real-business-cycle theorists don’t just fail to construct macroeconomic models; they deny the very existence of macroeconomics, just as strict materialists deny the existence of consciousness.

What is so preposterous about the New-Classical/real-business-cycle methodological position is not the belief that the business cycle can somehow be modeled as a purely equilibrium phenomenon, implausible as that idea seems, but the insistence that only micro-founded business-cycle models are methodologically acceptable. It is one thing to believe that ultimately macroeconomics and business-cycle theory will be reduced to the analysis of individual agents and their interactions. But current micro-founded models can’t provide explanations for what many of us think are basic features of macroeconomic and business-cycle phenomena. If non-micro-founded models can provide explanations for those phenomena, even if those explanations are not fully satisfactory, what basis is there for rejecting them just because of a methodological precept that disqualifies all non-micro-founded models?

According to Kevin Hoover, the basis for insisting that only micro-founded macroeconomic models are acceptable, even if the microfoundation consists in a single representative agent optimizing for an entire economy, is eschatological. In other words, because of a belief that economics will eventually develop analytical or computational techniques sufficiently advanced to model an entire economy in terms of individual interacting agents, an analysis based on a single representative agent, as the first step on this theoretical odyssey, is somehow methodologically privileged over alternative models that do not share that destiny. Hoover properly rejects the presumptuous notion that an avowed, but unrealized, theoretical destiny, can provide a privileged methodological status to an explanatory strategy. The reductionist microfoundationalism of New-Classical macroeconomics and real-business-cycle theory, with which New Keynesian economists have formed an alliance of convenience, is truly a faith-based macroeconomics.

The remarkable similarity between the reductionist microfoundational methodology of New-Classical macroeconomics and the reductionist materialist approach to the concept of mind suggests to me that there is also a close analogy between the representative agent and what philosophers of mind call a homunculus. The Cartesian materialist theory of mind maintains that, at some place or places inside the brain, there resides information corresponding to our conscious experience. The question then arises: how does our conscious experience access the latent information inside the brain? And the answer is that there is a homunculus (or little man) that processes the information for us so that we can perceive it through him. For example, the homunculus (see the attached picture of the little guy) views the image cast by light on the retina as if he were watching a movie projected onto a screen.

homunculus

But there is an obvious fallacy, because the follow-up question is: how does our little friend see anything? Well, the answer must be that there’s another, smaller, homunculus inside his brain. You can probably already tell that this argument is going to take us on an infinite regress. So what purports to be an explanation turns out to be just a form of question-begging. Sound familiar? The only difference between the representative agent and the homunculus is that the representative agent begs the question immediately without having to go on an infinite regress.

PS I have been sidetracked by other responsibilities, so I have not been blogging much, if at all, for the last few weeks. I hope to post more frequently, but I am afraid that my posting and replies to comments are likely to remain infrequent for the next couple of months.

Forget the Monetary Base and Just Pay Attention to the Price Level

Kudos to David Beckworth for eliciting a welcome concession or clarification from Paul Krugman that monetary policy is not necessarily ineffectual at the zero lower bound. The clarification is welcome because Krugman and Simon Wren Lewis seemed to be making a big deal about insisting that monetary policy at the zero lower bound is useless if it affects only the current, but not the future, money supply, and touting the discovery as if it were a point that was not already well understood.

Now it’s true that Krugman is entitled to take credit for having come up with an elegant way of showing the difference between a permanent and a temporary increase in the monetary base, but it’s a point that, WADR, was understood even before Krugman. See, for example, the discussion in chapter 5 of Jack Hirshleifer’s textbook on capital theory (published in 1970), Investment, Interest and Capital, showing that the Fisher equation follows straightforwardly in an intertemporal equilibrium model, so that the nominal interest rate can be decomposed into a real component and an expected-inflation component. If holding money is costless, then the nominal rate of interest cannot be negative, and expected deflation cannot exceed the equilibrium real rate of interest. This implies that, at the zero lower bound, the current price level cannot be raised without raising the future price level proportionately. That is all Krugman was saying in asserting that monetary policy is ineffective at the zero lower bound, even though he couched the analysis in terms of the current and future money supplies rather than in terms of the current and future price levels. But the entire argument is implicit in the Fisher equation. And contrary to Krugman, the IS-LM model (with which I am certainly willing to coexist) offers no unique insight into this proposition; it would be remarkable if it did, because the IS-LM model in essence is a static model that has to be re-engineered to be used in an intertemporal setting.

Here is how Hirshleifer concludes his discussion:

The simple two-period model of choice between dated consumptive goods and dated real liquidities has been shown to be sufficiently comprehensive as to display both the quantity theorists’ and the Keynesian theorists’ predicted results consequent upon “changes in the money supply.” The seeming contradiction is resolved by noting that one result or the other follows, or possibly some mixture of the two, depending upon the precise meaning of the phrase “changes in the quantity of money.” More exactly, the result follows from the assumption made about changes in the time-distributed endowments of money and consumption goods.  pp. 150-51

Another passage from Hirshleifer is also worth quoting:

Imagine a financial “panic.” Current money is very scarce relative to future money – and so monetary interest rates are very high. The monetary authorities might then provide an increment [to the money stock] while announcing that an equal aggregate amount of money would be retired at some date thereafter. Such a change making current money relatively more plentiful (or less scarce) than before in comparison with future money, would clearly tend to reduce the monetary rate of interest. (p. 149)

In this passage Hirshleifer accurately describes the objective of Fed policy since the crisis: provide as much liquidity as needed to prevent a panic, but without even trying to generate a substantial increase in aggregate demand by increasing inflation or expected inflation. The refusal to increase aggregate demand was implicit in the Fed’s refusal to increase its inflation target.

However, I do want to make explicit a point of disagreement between me and Hirshleifer, Krugman and Beckworth. The point is more conceptual than analytical, by which I mean that although the analysis of monetary policy can formally be carried out either in terms of current and future money supplies, as Hirshleifer, Krugman and Beckworth do, or in terms of price levels, as I prefer to do so in terms of price levels. For one thing, reasoning in terms of price levels immediately puts you in the framework of the Fisher equation, while thinking in terms of current and future money supplies puts you in the framework of the quantity theory, which I always prefer to avoid.

The problem with the quantity theory framework is that it assumes that quantity of money is a policy variable over which a monetary authority can exercise effective control, a mistake — imprinted in our economic intuition by two or three centuries of quantity-theorizing, regrettably reinforced in the second-half of the twentieth century by the preposterous theoretical detour of monomaniacal Friedmanian Monetarism, as if there were no such thing as an identification problem. Thus, to analyze monetary policy by doing thought experiments that change the quantity of money is likely to mislead or confuse.

I can’t think of an effective monetary policy that was ever implemented by targeting a monetary aggregate. The optimal time path of a monetary aggregate can never be specified in advance, so that trying to target any monetary aggregate will inevitably fail, thereby undermining the credibility of the monetary authority. Effective monetary policies have instead tried to target some nominal price while allowing monetary aggregates to adjust automatically given that price. Sometimes the price being targeted has been the conversion price of money into a real asset, as was the case under the gold standard, or an exchange rate between one currency and another, as the Swiss National Bank is now doing with the franc/euro exchange rate. Monetary policies aimed at stabilizing a single price are easy to implement and can therefore be highly credible, but they are vulnerable to sudden changes with highly deflationary or inflationary implications. Nineteenth century bimetallism was an attempt to avoid or at least mitigate such risks. We now prefer inflation targeting, but we have learned (or at least we should have) from the Fed’s focus on inflation in 2008 that inflation targeting can also lead to disastrous consequences.

I emphasize the distinction between targeting monetary aggregates and targeting the price level, because David Beckworth in his post is so focused on showing 1) that the expansion of the Fed’s balance sheet under QE has been temoprary and 2) that to have been effective in raising aggregate demand at the zero lower bound, the increase in the monetary base needed to be permanent. And I say: both of the facts cited by David are implied by the fact that the Fed did not raise its inflation target or, preferably, replace its inflation target with a sufficiently high price-level target. With a higher inflation target or a suitable price-level target, the monetary base would have taken care of itself.

PS If your name is Scott Sumner, you have my permission to insert “NGDP” wherever “price level” appears in this post.

Hicks on IS-LM and Temporary Equilibrium

Jan, commenting on my recent post about Krugman, Minsky and IS-LM, quoted the penultimate paragraph of J. R. Hicks’s 1980 paper on IS-LM in the Journal of Post-Keynesian Economics, a brand of economics not particularly sympathetic to Hicks’s invention. Hicks explained that in the mid-1930s he had been thinking along lines similar to Keynes’s even before the General Theory was published, and had the basic idea of IS-LM in his mind even before he had read the General Theory, while also acknowledging that his enthusiasm for the IS-LM construct had waned considerably over the years.

Hicks discussed both the similarities and the differences between his model and IS-LM. But as the discussion proceeds, it becomes clear that what he is thinking of as his model is what became his model of temporary equilibrium in Value and Capital. So it really is important to understand what Hicks felt were the similarities as well as the key differences between the temporary- equilibrium model, and the IS-LM model. Here is how Hicks put it:

I recognized immediately, as soon as I read The General Theory, that my model and Keynes’ had some things in common. Both of us fixed our attention on the behavior of an economy during a period—a period that had a past, which nothing that was done during the period could alter, and a future, which during the period was unknown. Expectations of the future would nevertheless affect what happened during the period. Neither of us made any assumption about “rational expectations” ; expectations, in our models, were strictly exogenous.3 (Keynes made much more fuss over that than I did, but there is the same implication in my model also.) Subject to these data— the given equipment carried over from the past, the production possibilities within the period, the preference schedules, and the given expectations— the actual performance of the economy within the period was supposed to be determined, or determinable. It would be determined as an equilibrium performance, with respect to these data.

There was all this in common between my model and Keynes’; it was enough to make me recognize, as soon as I saw The General Theory, that his model was a relation of mine and, as such, one which I could warmly welcome. There were, however, two differences, on which (as we shall see) much depends. The more obvious difference was that mine was a flexprice model, a perfect competition model, in which all prices were flexible, while in Keynes’ the level of money wages (at least) was exogenously determined. So Keynes’ was a model that was consistent with unemployment, while mine, in his terms, was a full employment model. I shall have much to say about this difference, but I may as well note, at the start, that I do not think it matters much. I did not think, even in 1936, that it mattered much. IS-LM was in fact a translation of Keynes’ nonflexprice model into my terms. It seemed to me already that that could be done; but how it is done requires explanation.

The other difference is more fundamental; it concerns the length of the period. Keynes’ (he said) was a “short-period,” a term with connotations derived from Marshall; we shall not go far wrong if we think of it as a year. Mine was an “ultra-short-period” ; I called it a week. Much more can happen in a year than in a week; Keynes has to allow for quite a lot of things to happen. I wanted to avoid so much happening, so that my (flexprice) markets could reflect propensities (and expectations) as they are at a moment. So it was that I made my markets open only on a Monday; what actually happened during the ensuing week was not to affect them. This was a very artificial device, not (I would think now) much to be recommended. But the point of it was to exclude the things which might happen, and must disturb the markets, during a period of finite length; and this, as we shall see, is a very real trouble in Keynes. (pp. 139-40)

Hicks then explained how the specific idea of the IS-LM model came to him as a result of working on a three-good Walrasian system in which the solution could be described in terms of equilibrium in two markets, the third market necessarily being in equilibrium if the other two were in equilibrium. That’s an interesting historical tidbit, but the point that I want to discuss is what I think is Hicks’s failure to fully understand the significance of his own model, whose importance, regrettably, he consistently underestimated in later work (e.g., in Capital and Growth and in this paper).

The point that I want to focus on is in the second paragraph quoted above where Hicks says “mine [i.e. temporary equilibrium] was a flexprice model, a perfect competition model, in which all prices were flexible, while in Keynes’ the level of money wages (at least) was exogenously determined. So Keynes’ was a model that was consistent with unemployment, while mine, in his terms, was a full employment model.” This, it seems to me, is all wrong, because Hicks, is taking a very naïve and misguided view of what perfect competition and flexible prices mean. Those terms are often mistakenly assumed to meant that if prices are simply allowed to adjust freely, all  markets will clear and all resources will be utilized.

I think that is a total misconception, and the significance of the temporary-equilibrium construct is in helping us understand why an economy can operate sub-optimally with idle resources even when there is perfect competition and markets “clear.” What prevents optimality and allows resources to remain idle despite freely adjustming prices and perfect competition is that the expectations held by agents are not consistent. If expectations are not consistent, the plans based on those expectations are not consistent. If plans are not consistent, then how can one expect resources to be used optimally or even at all? Thus, for Hicks to assert, casually without explicit qualification, that his temporary-equilibrium model was a full-employment model, indicates to me that Hicks was unaware of the deeper significance of his own model.

If we take a full equilibrium as our benchmark, and look at how one of the markets in that full equilibrium clears, we can imagine the equilibrium as the intersection of a supply curve and a demand curve, whose positions in the standard price/quantity space depend on the price expectations of suppliers and of demanders. Different, i.e, inconsistent, price expectations would imply shifts in both the demand and supply curves from those corresponding to full intertemporal equilibrium. Overall, the price expectations consistent with a full intertemporal equilibrium will in some sense maximize total output and employment, so when price expectations are inconsistent with full intertemporal equilibrium, the shifts of the demand and supply curves will be such that they will intersect at points corresponding to less output and less employment than would have been the case in full intertemporal equilibrium. In fact, it is possible to imagine that expectations on the supply side and the demand side are so inconsistent that the point of intersection between the demand and supply curves corresponds to an output (and hence employment) that is way less than it would have been in full intertemporal equilibrium. The problem is not that the price in the market doesn’t allow the market to clear. Rather, given the positions of the demand and supply curves, their point of intersection implies a low output, because inconsistent price expectations are such that potentially advantageous trading opportunities are not being recognized.

So for Hicks to assert that his flexprice temporary-equilibrium model was (in Keynes’s terms) a full-employment model without noting the possibility of a significant contraction of output (and employment) in a perfectly competitive flexprice temporary-equilibrium model when there are significant inconsistencies in expectations suggests strongly that Hicks somehow did not fully comprehend what his own creation was all about. His failure to comprehend his own model also explains why he felt the need to abandon the flexprice temporary-equilibrium model in his later work for a fixprice model.

There is, of course, a lot more to be said about all this, and Hicks’s comments concerning the choice of a length of the period are also of interest, but the clear (or so it seems to me) misunderstanding by Hicks of what is entailed by a flexprice temporary equilibrium is an important point to recognize in evaluating both Hicks’s work and his commentary on that work and its relation to Keynes.


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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