Archive for the 'Hayek' Category

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.

Wherein Hayek Agrees with DeLong that Just Because You’re Rich, It Doesn’t Mean You Deserve to Be

Recently Brad DeLong expounded on the extent to which the earnings that accrue to individuals do not correspond to the contributions total output that can be ascribed to the personal efforts of those individuals or the contributions made by resources owned by thoe people. Here’s DeLong:

Pascal Lamy: “When the wise man points at the moon, the fool looks at the finger…”

Perhaps in the end the problem is that people want to pretend that they are filling a valuable role in the societal division of labor, and are receiving no more than they earn–than they contribute.

But that is not the case. The value–the societal dividend–is in the accumulated knowledge of humanity and in the painfully constructed networks that make up our value chains.

A “contribution” theory of what a proper distribution of income might be can only be made coherent if there are constant returns to scale in the scarce, priced, owned factors of production. Only then can you divide the pile of resources by giving to each the marginal societal product of their work and of the resources that they own.

That, however, is not the world we live in.

In a world–like the one we live in–of mammoth increasing returns to unowned knowledge and to networks, no individual and no community is especially valuable. Those who receive good livings are those who are lucky–as Carrier’s workers in Indiana have been lucky in living near Carrier’s initial location. It’s not that their contribution to society is large or that their luck is replicable: if it were, they would not care (much) about the departure of Carrier because there would be another productive network that they could fit into a slot in.

All of this “what you deserve” language is tied up with some vague idea that you deserve what you contribute–that what your work adds to the pool of society’s resources is what you deserve.

This illusion is punctured by any recognition that there is a large societal dividend to be distributed, and that the government can distribute it by supplementing (inadequate) market wages determined by your (low) societal marginal product, or by explicitly providing income support or services unconnected with work via social insurance. Instead, the government is supposed to, somehow, via clever redistribution, rearrange the pattern of market power in the economy so that the increasing-returns knowledge- and network-based societal dividend is predistributed in a relatively egalitarian way so that everybody can pretend that their income is just “to each according to his work”, and that they are not heirs and heiresses coupon clipping off of the societal capital of our predecessors’ accumulated knowledge and networks.

On top of this we add: Polanyian disruption of patterns of life–local communities, income levels, industrial specialization–that you believed you had a right to obtain or maintain, and a right to believe that you deserve. But in a market capitalist society, nobody has a right to the preservation of their local communities, to their income levels, or to an occupation in their industrial specialization. In a market capitalist society, those survive only if they pass a market profitability test. And so the only rights that matter are those property rights that at the moment carry with them market power–the combination of the (almost inevitably low) marginal societal products of your skills and the resources you own, plus the (sometimes high) market power that those resources grant to you.

This wish to believe that you are not a moocher is what keeps people from seeing issues of distribution and allocation clearly–and generates hostility to social insurance and to wage supplement policies, for they rip the veil off of the idea that you deserve to be highly paid because you are worth it. You aren’t.

And this ties itself up with regional issues: regional decline can come very quickly whenever a region finds that its key industries have, for whatever reason, lost the market power that diverted its previously substantial share of the knowledge- and network-based societal dividend into the coffers of its firms. The resources cannot be simply redeployed in other industries unless those two have market power to control the direction of a share of the knowledge- and network-based societal dividend. And so communities decline and die. And the social contract–which was supposed to have given you a right to a healthy community–is broken.

As I have said before, humans are, at a very deep and basic level, gift-exchange animals. We create and reinforce our social bonds by establishing patterns of “owing” other people and by “being owed”. We want to enter into reciprocal gift-exchange relationships. We create and reinforce social bonds by giving each other presents. We like to give. We like to receive. We like neither to feel like cheaters nor to feel cheated. We like, instead, to feel embedded in networks of mutual reciprocal obligation. We don’t like being too much on the downside of the gift exchange: to have received much more than we have given in return makes us feel very small. We don’t like being too much on the upside of the gift exchange either: to give and give and give and never receive makes us feel like suckers.

We want to be neither cheaters nor saps.

It is, psychologically, very hard for most of us to feel like we are being takers: that we are consuming more than we are contributing, and are in some way dependent on and recipients of the charity of others. It is also, psychologically, very hard for most of us to feel like we are being saps: that others are laughing at us as they toil not yet consume what we have produced.

And it is on top of this evopsych propensity to be gift-exchange animals–what Adam Smith called our “natural propensity to truck, barter, and exchange”–we have built our complex economic division of labor. We construct property and market exchange–what Adam Smith called our natural propensity “to truck, barter, and exchange” to set and regulate expectations of what the fair, non-cheater non-sap terms of gift-exchange over time are.

We devise money as an institution as a substitute for the trust needed in a gift-exchange relationship, and we thus construct a largely-peaceful global 7.4B-strong highly-productive societal division of labor, built on:

  • assigning things to owners—who thus have both the responsibility for stewardship and the incentive to be good stewards…
  • very large-scale webs of win-win exchange… mediated and regulated by market prices…

There are enormous benefits to arranging things this way. As soon as we enter into a gift-exchange relationship with someone or something we will see again–perhaps often–it will automatically shade over into the friend zone. This is just who we are. And as soon as we think about entering into a gift-exchange relationship with someone, we think better of them. Thus a large and extended division of labor mediated by the market version of gift-exchange is a ver powerful creator of social harmony.

This is what the wise Albert Hirschman called the doux commerce thesis. People, as economists conceive them, are not “Hobbesians” focusing on their narrow personal self-interest, but rather “Lockeians”: believers in live-and-let live, respecting others and their spheres of autonomy, and eager to enter into reciprocal gift-exchange relationships—both one-offs mediated by cash alone and longer-run ones as well.

In an economist’s imagination, people do not enter a butcher’s shop only when armed cap-a-pie and only with armed guards. They do not fear that the butcher will knock him unconscious, take his money, slaughter him, smoke him, and sell him as long pig.

Rather, there is a presumed underlying order of property and ownership that is largely self-enforcing, that requires only a “night watchman” to keep it stable and secure.

Yet to keep the fiction that we are all fairly playing the reciprocal game of gift exchange in a 7.4 billion-strong social network–that we are neither cheaters nor saps–we need to ignore that we are coupon clippers living off of our societal inheritance.

And to do this, we need to do more than (a) set up a framework for the production of stuff, (b) set up a framework for the distribution of stuff, and so (c) create a very dense reciprocal network of interdependencies to create and reinforce our belief that we are all one society.

We need to do so in such a way that people do not see themselves, are not seen as saps–people who are systematically and persistently taken advantage of by others in their societal and market gift-exchange relationships. We need to do so in such a way that people do not see themselves, are not seen as, and are not moochers–people who systematically persistently take advantage of others in their societal and market gift-exchange relationships. We need to do this in the presence of a vast increasing-returns in the knowledge- and network-based societal dividend and in spite of the low societal marginal product of any one of us.

Thus we need to do this via clever redistribution rather than via explicit wage supplements or basic incomes or social insurance that robs people of the illusion that what they receive is what they have earned and what they are worth through their work.

Now I think it is an open question whether it is harder to do the job via predistribution, or to do the job via changing human perceptions to get everybody to understand that

  • no, none of us is worth what we are paid.
  • we are all living, to various extents, off of the dividends from our societal capital
  • those of us who are doing especially well are those of us who have managed to luck into situations in which we have market power–in which the resources we control are (a) scarce, (b) hard to replicate quickly, and (c) help produce things
  • that rich people have a serious jones for right now.

Compare with Hayek’s Law, Legislation and Liberty volume 2, pp. 73-74

It has been argued persuasively that people will tolerate major inequalities of the material positions only if they believe that the different individuals get on the whole what they deserve, that they did in fact support the market order only because (and so long as) they thought that the differences of remuneration corresponded roughly to differences of merit, and that in consequence the maintenance of a free society presupposes the belief that some sort of “social justice” is being done. The market order, however, does not in fact owe its origin to such beliefs, or was originally justified in this manner. This order could develop, after its earlier beginnings had decayed during the middle ages and to some extent been destroyed by the restrictions imposed by authority, when a thousand years of vain efforts to discover substantively just prices or wages were abandoned and the late schoolmen recognized them to be empty formulae and taught instead that the prices determined by just conduct of the parties in the market, i.e., the competitive prices arrived at without fraud, monopoly and violence, was all that justice required. It was from this tradition that John Locke and his contemporaries derived the classical liberal conception of justice for which, as has been rightly said, it was only ‘the way in which competition was carried on, not its results’, that could be just or unjust.

It is unquestionably true that, particularly among those who were very successful in the market order, a belief in a much stronger moral justification of individual success developed, and that, long after the basic principles of such an order had been fully elaborated and approved by catholic moral philosophers, it had in the Anglo-Saxon world received strong support from Calvinist teaching.It certainly is important in the market order (or free enterprise society, misleadingly called ‘capitalism’) that the individuals believe that their well-being depends primarily on their own efforts and decisions. Indeed, few circumstances will do more to make a person energetic and efficient than the belief that it depends chiefly on him whether he will reach the goals he has set himself. For this reason this belief is often encouraged by education and governing opinion — it seems to me, generally much to the benefit of most of the members of society in which it prevails, who will owe many important material and moral improvements to persons guided by it. But it leads not doubt also to an exaggerated confidence in the truth of this generalization which to those who regard themselves (and perhaps are) equally able but have failed must appear as a bitter irony and severe provocation.

It is probably a misfortune that, especially in the USA, popular writers like Samuel Smiles and Horatio Alger, and later the sociologist W. G. Sumner, have defended free enterprise on the ground that it regularly rewards the deserving, and it bodes ill for the future of the market order that this seems to have become the only defence of it which is understood by the general public. That it has largely become the basis of the self-esteem of the businessman often gives him an air of self-righteousness which does not make him more popular. [If only!]

It is therefore a real dilemma to what extent we ought to encourage in the young a belief that when they really try they will succeed, or should rather emphasize that inevitably some unworthy will succeed and some worthy fail — whenever we ought to allow the views of those groups to prevail with whom the over-confidence in the appropriate reward of the able and industrious is strong and who in consequence will do much that benefits the rest, and whether without such partly erroneous beliefs the large number will tolerate actual differences in rewards which will be based only partly on achievement and partly on mere chance.

Why Hayek Was not a Conservative

At the end of his classic treatise The Constitution of Liberty, F. A. Hayek added a postscript entitled “Why I am not a Conservative.” Like everything he wrote, what Hayek has to say about the weaknesses of conservatism can be read with profit even by those who disagree with his arguments. The following passage, for a number of reasons, seems especially apt and relevant now, some 55 years after it was written.

Conservatives feel instinctively that it is new ideas more than anything else that cause change. But, from its point of view rightly, conservatism fears new ideas because it has no distinctive principles of  its own to oppose them; and, by its distrust of theory and its lack of imagination concerning anything except that which experience has already proved, it deprives itself of the weapons needed in the struggle of ideas. Unlike liberalism, with its fundamental belief in the long-range power of ideas, conservatism is bound by the stock of ideas inherited at a given time. And since it does not really believe in the power of argument, its last resort is generally a claim to superior wisdom, based on some self-arrogated superior quality. The difference shows itself most clearly in the different attitudes of the two traditions to the advance of knowledge. Though the liberal certainly does not regard all change as progress, he does regard the advance of knowledge as one of the chief aims of human effort and expects from it the gradual solution of such problems and difficulties as we can hope to solve. Without preferring the new merely because it is new, the liberal is aware that it is of the essence of human achievement that it produces something new; and he is prepared to come to terms with new knowledge, whether he likes its immediate effects or not.

Personally, I find that the most objectionable feature of the conservative attitude is its propensity to reject well-substantiated new knowledge because it dislikes some of the consequences which seem to follow from it – or, to put it bluntly, its obscurantism. I will not deny that scientists as much as others are given to fads and fashions and that we have much reason to be cautious in accepting the conclusions that they draw from their latest theories. But the reasons for our reluctance must themselves be rational and must be kept separate from our regret that the new theories upset our cherished beliefs. I can have little patience with those who oppose, for instance, the theory of evolution or what are called “mechanistic” explanations of the phenomena of life because of certain moral
consequences which at first seem to follow from these theories, and still less with those who regard it as irrelevant or impious to ask certain questions at all. By refusing to face the facts, the conservative only weakens his own position. Frequently the conclusions which rationalist presumption draws from new scientific insights do not at all follow from them. But only by actively taking part in the elaboration of the consequences of new discoveries do we learn whether or not they fit into our world picture and, if so, how. Should our moral beliefs really prove to be dependent on factual assumptions shown to be incorrect, it would hardly be moral to defend them by refusing to acknowledge facts.

Connected with the conservative distrust if the new and the strange is its hostility to internationalism and its proneness to a strident nationalism. Here is another source of its weakness in the struggle of ideas. It cannot alter the fact that the ideas which are changing our civilization respect no boundaries. But refusal to acquaint one’s self with new ideas merely deprives one of the power of effectively countering them when necessary. The growth of ideas is an international process, and only those who fully take part in the discussion will be able to exercise a significant influence. It is no real argument to say that an idea is un-American, or un-German, nor is a mistaken or vicious ideal better for having been conceived by one of our compatriots.

A great deal more might be said about the close connection between conservatism and nationalism, but I shall not dwell on this point because it might be felt that my personal position makes me unable to sympathize with any form of nationalism. I will merely add that it is this nationalistic bias which frequently provides the bridge from conservatism to collectivism: to think in terms of “our” industry or resource is only a short step away from demanding that these national assets be directed in the national interest. But in this respect the Continental liberalism which derives from the French Revolution is little better than conservatism. I need hardly say that nationalism of this sort is something very different from patriotism and that an aversion to nationalism is fully compatible with a
deep attachment to national traditions. But the fact that I prefer and feel reverence for some of the traditions of my society need not be the cause of hostility to what is strange and different.

Only at first foes it seem paradoxical that the anti-internationalism of conservatism is so frequently associated with imperialism. But the more a person dislikes the strange and thinks his own ways superior, the more he tends to regard it as his mission to “civilize” others – not by the voluntary and unhampered intercourse which the liberal favors, but by bringing them the blessings of efficient government. It is significant that here again we frequently find the conservatives joining hands with the socialists against the liberals – not only in England, where the Webbs and their Fabians were outspoken imperialists, or in Germany, where state socialism and colonial expansionism went together and found the support of the same group of “socialists of the chair,” but also in the United States,
where even at the time of the first Roosevelt it could be observed: “the Jingoes and the Social Reformers have gotten together; and have formed a political party, which threatened to capture the Government and use it for their program of Caesaristic paternalism, a danger which now seems to have been averted only by the other parties having adopted their program in a somewhat milder degree and form.”

 

A Primer on Equilibrium

After my latest post about rational expectations, Henry from Australia, one of my most prolific commenters, has been engaging me in a conversation about what assumptions are made – or need to be made – for an economic model to have a solution and for that solution to be characterized as an equilibrium, and in particular, a general equilibrium. Equilibrium in economics is not always a clearly defined concept, and it can have a number of different meanings depending on the properties of a given model. But the usual understanding is that the agents in the model (as consumers or producers) are trying to do as well for themselves as they can, given the endowments of resources, skills and technology at their disposal and given their preferences. The conversation was triggered by my assertion that rational expectations must be “compatible with the equilibrium of the model in which those expectations are embedded.”

That was the key insight of John Muth in his paper introducing the rational-expectations assumption into economic modelling. So in any model in which the current and future actions of individuals depend on their expectations of the future, the model cannot arrive at an equilibrium unless those expectations are consistent with the equilibrium of the model. If the expectations of agents are incompatible or inconsistent with the equilibrium of the model, then, since the actions taken or plans made by agents are based on those expectations, the model cannot have an equilibrium solution.

Now Henry thinks that this reasoning is circular. My argument would be circular if I defined an equilibrium to be the same thing as correct expectations. But I am not so defining an equilibrium. I am saying that the correctness of expectations by all agents implies 1) that their expectations are mutually consistent, and 2) that, having made plans, based on their expectations, which, by assumption, agents felt were the best set of choices available to them given those expectations, if the expectations of the agents are realized, then they would not regret the decisions and the choices that they made. Each agent would be as well off as he could have made himself, given his perceived opportunities when the decision were made. That the correctness of expectations implies equilibrium is the consequence of assuming that agents are trying to optimize their decision-making process, given their available and expected opportunities. If all expected opportunities are correctly foreseen, then all decisions will have been the optimal decisions under the circumstances. But nothing has been said that requires all expectations to be correct, or even that it is possible for all expectations to be correct. If an equilibrium does not exist, and just because you can write down an economic model, it does not mean that a solution to the model exists, then the sweet spot where all expectations are consistent and compatible is just a blissful fantasy. So a logical precondition to showing that rational expectations are even possible is to prove that an equilibrium exists. There is nothing circular about the argument.

Now the key to proving the existence of a general equilibrium is to show that the general equilibrium model implies the existence of what mathematicians call a fixed point. A fixed point is said to exist when there is a mapping – a rule or a function – that takes every point in a convex compact set of points and assigns that point to another point in the same set. A convex, compact set has two important properties: 1) the line connecting any two points in the set is entirely contained within the boundaries of the set, and 2) there are no gaps between any two points in set. The set of points in a circle or a rectangle is a convex compact set; the set of points contained in the Star of David is not a convex set. Any two points in the circle will be connected by a line that lies completely within the circle; the points at adjacent edges of a Star of David will be connected by a line that lies entirely outside the Star of David.

If you think of the set of all possible price vectors for an economy, those vectors – each containing a price for each good or service in the economy – could be mapped onto itself in the following way. Given all the equations describing the behavior of each agent in the economy, the quantity demanded and supplied of each good could be calculated, giving us the excess demand (the difference between amount demand and supplied) for each good. Then the price of every good in excess demand would be raised, the price of every good in negative excess demand would be reduced, and the price of every good with zero excess demand would be held constant. To ensure that the mapping was taking a point from a given convex set onto itself, all prices could be normalized so that they would have the property that the sum of all the individual prices would always equal 1. The fixed point theorem ensures that for a mapping from one convex compact set onto itself there must be at least one fixed point, i.e., at least one point in the set that gets mapped onto itself. The price vector corresponding to that point is an equilibrium, because, given how our mapping rule was defined, a point would be mapped onto itself if and only if all excess demands are zero, so that no prices changed. Every fixed point – and there may be one or more fixed points – corresponds to an equilibrium price vector and every equilibrium price vector is associated with a fixed point.

Before going on, I ought to make an important observation that is often ignored. The mathematical proof of the existence of an equilibrium doesn’t prove that the economy operates at an equilibrium, or even that the equilibrium could be identified under the mapping rule described (which is a kind of formalization of the Walrasian tatonnement process). The mapping rule doesn’t guarantee that you would ever discover a fixed point in any finite amount of iterations. Walras thought the price adjustment rule of raising the prices of goods in excess demand and reducing prices of goods in excess supply would converge on the equilibrium price vector. But the conditions under which you can prove that the naïve price-adjustment rule converges to an equilibrium price vector turn out to be very restrictive, so even though we can prove that the competitive model has an equilibrium solution – in other words the behavioral, structural and technological assumptions of the model are coherent, meaning that the model has a solution, the model has no assumptions about how prices are actually determined that would prove that the equilibrium is ever reached. In fact, the problem is even more daunting than the previous sentence suggest, because even Walrasian tatonnement imposes an incredibly powerful restriction, namely that no trading is allowed at non-equilibrium prices. In practice there are almost never recontracting provisions allowing traders to revise the terms of their trades once it becomes clear that the prices at which trades were made were not equilibrium prices.

I now want to show how price expectations fit into all of this, because the original general equilibrium models were either one-period models or formal intertemporal models that were reduced to single-period models by assuming that all trading for future delivery was undertaken in the first period by long-lived agents who would eventually carry out the transactions that were contracted in period 1 for subsequent consumption and production. Time was preserved in a purely formal, technical way, but all economic decision-making was actually concluded in the first period. But even though the early general-equilibrium models did not encompass expectations, one of the extraordinary precursors of modern economics, Augustin Cournot, who was way too advanced for his contemporaries even to comprehend, much less make any use of, what he was saying, had incorporated the idea of expectations into the solution of his famous economic model of oligopolistic price setting.

The key to oligopolistic pricing is that each oligopolist must take into account not just consumer demand for his product, and his own production costs; he must consider as well what actions will be taken by his rivals. This is not a problem for a competitive producer (a price-taker) or a pure monopolist. The price-taker simply compares the price at which he can sell as much as he wants with his production costs and decides how much it is worthwhile to produce by comparing his marginal cost to price ,and increases output until the marginal cost rises to match the price at which he can sell. The pure monopolist, if he knows, as is assumed in such exercises, or thinks he knows the shape of the customer demand curve, selects the price and quantity combination on the demand curve that maximizes total profit (corresponding to the equality of marginal revenue and marginal cost). In oligopolistic situations, each producer must take into account how much his rivals will sell, or what prices they will set.

It was by positing such a situation and finding an analytic solution, that Cournot made a stunning intellectual breakthrough. In the simple duopoly case, Cournot posited that if the duopolists had identical costs, then each could find his optimal price conditional on the output chosen by the other. This is a simple profit-maximization problem for each duopolist, given a demand curve for the combined output of both (assumed to be identical, so that a single price must obtain for the output of both) a cost curve and the output of the other duopolist. Thus, for each duopolist there is a reaction curve showing his optimal output given the output of the other. See the accompanying figure.cournot

If one duopolist produces zero, the optimal output for the other is the monopoly output. Depending on what the level of marginal cost is, there is some output by either of the duopolists that is sufficient to make it unprofitable for the other duopolist to produce anything. That level of output corresponds to the competitive output where price just equals marginal cost. So the slope of the two reaction functions corresponds to the ratio of the monopoly output to the competitive output, which, with constant marginal cost is 2:1. Given identical costs, the two reaction curves are symmetric and the optimal output for each, given the expected output of the other, corresponds to the intersection of the two reaction curves, at which both duopolists produce the same quantity. The combined output of the two duopolists will be greater than the monopoly output, but less than the competitive output at which price equals marginal cost. With constant marginal cost, it turns out that each duopolist produces one-third of the competitive output. In the general case with n oligoplists, the ratio of the combined output of all n firms to the competitive output equals n/(n+1).

Cournot’s solution corresponds to a fixed point where the equilibrium of the model implies that both duopolists have correct expectations of the output of the other. Given the assumptions of the model, if the duopolists both expect the other to produce an output equal to one-third of the competitive output, their expectations will be consistent and will be realized. If either one expects the other to produce a different output, the outcome will not be an equilibrium, and each duopolist will regret his output decision, because the price at which he can sell his output will differ from the price that he had expected. In the Cournot case, you could define a mapping of a vector of the quantities that each duopolist had expected the other to produce and the corresponding planned output of each duopolist. An equilibrium corresponds to a case in which both duopolists expected the output planned by the other. If either duopolist expected a different output from what the other planned, the outcome would not be an equilibrium.

We can now recognize that Cournot’s solution anticipated John Nash’s concept of an equilibrium strategy in which player chooses a strategy that is optimal given his expectation of what the other player’s strategy will be. A Nash equilibrium corresponds to a fixed point in which each player chooses an optimal strategy based on the correct expectation of what the other player’s strategy will be. There may be more than one Nash equilibrium in many games. For example, rather than base their decisions on an expectation of the quantity choice of the other duopolist, the two duopolists could base their decisions on an expectation of what price the other duopolist would set. In the constant-cost case, this choice of strategies would lead to the competitive output because both duopolists would conclude that the optimal strategy of the other duopolist would be to charge a price just sufficient to cover his marginal cost. This was the alternative oligopoly model suggested by another French economist J. L. F. Bertrand. Of course there is a lot more to be said about how oligopolists strategize than just these two models, and the conditions under which one or the other model is the more appropriate. I just want to observe that assumptions about expectations are crucial to how we analyze market equilibrium, and that the importance of these assumptions for understanding market behavior has been recognized for a very long time.

But from a macroeconomic perspective, the important point is that expected prices become the critical equilibrating variable in the theory of general equilibrium and in macroeconomics in general. Single-period models of equilibrium, including general-equilibrium models that are formally intertemporal, but in which all trades are executed in the initial period at known prices in a complete array of markets determining all future economic activity, are completely sterile and useless for macroeconomics except as a stepping stone to analyzing the implications of imperfect forecasts of future prices. If we want to think about general equilibrium in a useful macroeconomic context, we have to think about a general-equilibrium system in which agents make plans about consumption and production over time based on only the vaguest conjectures about what future conditions will be like when the various interconnected stages of their plans will be executed.

Unlike the full Arrow-Debreu system of complete markets, a general-equilibrium system with incomplete markets cannot be equilibrated, even in principle, by price adjustments in the incomplete set of present markets. Equilibration depends on the consistency of expected prices with equilibrium. If equilibrium is characterized by a fixed point, the fixed point must be mapping of a set of vectors of current prices and expected prices on to itself. That means that expected future prices are as much equilibrating variables as current market prices. But expected future prices exist only in the minds of the agents, they are not directly subject to change by market forces in the way that prices in actual markets are. If the equilibrating tendencies of market prices in a system of complete markets are very far from completely effective, the equilibrating tendencies of expected future prices may not only be non-existent, but may even be potentially disequilibrating rather than equilibrating.

The problem of price expectations in an intertemporal general-equilibrium system is central to the understanding of macroeconomics. Hayek, who was the father of intertemporal equilibrium theory, which he was the first to outline in a 1928 paper in German, and who explained the problem with unsurpassed clarity in his 1937 paper “Economics and Knowledge,” unfortunately did not seem to acknowledge its radical consequences for macroeconomic theory, and the potential ineffectiveness of self-equilibrating market forces. My quarrel with rational expectations as a strategy of macroeconomic analysis is its implicit assumption, lacking any analytical support, that prices and price expectations somehow always adjust to equilibrium values. In certain contexts, when there is no apparent basis to question whether a particular market is functioning efficiently, rational expectations may be a reasonable working assumption for modelling observed behavior. However, when there is reason to question whether a given market is operating efficiently or whether an entire economy is operating close to its potential, to insist on principle that the rational-expectations assumption must be made, to assume, in other words, that actual and expected prices adjust rapidly to their equilibrium values allowing an economy to operate at or near its optimal growth path, is simply, as I have often said, an exercise in circular reasoning and question begging.

Whither Conservatism?

I’m not sure why – well, maybe I can guess – but I have been thinking about an article (“Hayek and the Conservatives”) I wrote in 1992 for Commentary. I just reread it — probably for the first time this century — and although I can’t say that I agree with everything I wrote over 20 years ago, it somehow still seems relevant, perhaps even more so now than then. So I thought I would share it.

At the time of his death on March 23, 1992, less than two months before his ninety-third birthday, F.A. Hayek was widely if not universally acknowledged as this century’s preeminent intellectual advocate of the free market and one of its leading opponents of socialism. His death, coming so soon after the collapse of Communism in Eastern Europe and the abandonment of Marxism and socialism as intellectual ideals, occasioned understandable comment by his admirers about the vindication that Hayek, after years of vilification at the hands of critics, had received at the hands of history.

Though long in coming, however, Hayek’s vindication did not occur all at once. For his work had exerted a crucial, though basically indirect, influence over the renascent conservative and libertarian movements that had grown up after World War II in the United States and Great Britain. Indeed, the revival of those movements culminated in the rise to power of two politicians, Ronald Reagan in America and Margaret Thatcher in England, who were proud to list Hayek among their intellectual mentors. And his vindication had also been presaged, though in an oddly ambiguous way, when Hayek was named co-winner, with the Swedish socialist economist Gunnar Myrdal, of the 1974 Nobel prize in economics.

Still, most of Hayek’s career was spent in the relative obscurity befitting an expatriate Central European intellectual of reserve, urbanity, erudition—and unfashionable views. Hayek’s economic theories had apparently been superseded, first by those of John Maynard Keynes and then by the increasingly mathematical economic analysis of the postwar period, and his political philosophy was considered either a relic of an obsolete Victorian liberalism or, less charitably, an apology for the worst excesses of capitalist exploitation. Before winning the Nobel prize, Hayek, who never served either officially or unofficially as an adviser to any political figure and never sought a mass audience, only twice transcended the obscurity in which he labored for so long: first in the early 1930’s when, as a young man newly arrived in Great Britain, he was briefly considered the chief intellectual rival of Keynes, and a decade later in the mid-1940’s when, much to Hayek’s own surprise, his book, The Road to Serfdom, became a trans-Atlantic best-seller. . . .

Ironically, Hayek’s death occurred not only after his critique of socialism had just received decisive historical confirmation, but when the conservative movement in the United States, whose free-market and free-trade principles he, perhaps more than anyone else, had shaped, was undergoing a fundamental crisis. To understand the nature of the crisis, one must first understand how Hayek came to play such a crucial role in the development of conservatism.

Before World War II what passed for conservatism in the United States was an amalgam of views and prejudices which lacked sufficient coherence to be summarized by any clear set of principles. The chief characteristics of the Old Right were a fanatical opposition to . . . Roosevelt’s New Deal or indeed to any national measures aimed at improving the lot of the least well-off groups or individuals in the country; opposition to international alliances, coupled with decidedly nativist tendencies and a bias in favor of protectionist trade policies; a primitive bias against banks, speculation, high finance, and Wall Street; and complacent toleration of, or occasionally even active support for, racial and religious discrimination against blacks, Jews, and other minorities. . . .

Even more disastrously, American conservatives, mistrusting the federal government and its tendency to become involved in European conflicts, and viscerally hating Roosevelt, bitterly opposed any U.S. efforts to resist or contain the spread of European fascism. These attitudes gave birth to the America First movement of the 1930’s, whose often implicit and occasionally explicit anti-Semitic overtones can only be understood in the light of the broader set of fears, hatreds, and neuroses that animated the movement.

The onset of World War II, the attack on Pearl Harbor, and the subsequent horrific revelations about the Holocaust perpetrated by the Nazis (with whom the America Firsters had uniformly urged coexistence and for whom some of them had expressed sympathy) left American conservatism discredited both morally and intellectually, just as the Depression and a reflexive opposition to the New Deal had discredited conservatism programmatically.

Thus, when The Road to Serfdom was published in 1945, it filled a gaping moral and intellectual vacuum. For here was a book, written by an Austrian expatriate of impeccable anti-Nazi credentials, fundamentally opposed to the socialist ideas now guiding progressive thought everywhere. Moreover, in a profound and eloquent argument, The Road to Serfdom contended that the path the fascists had followed to absolute power had been prepared for them by the very instruments of central planning and the ideology of an all-powerful state which socialists had created before them. The Nazis, after all, had been National Socialists, and Mussolini had been a leader of the Italian Socialist party before starting the Fascist party. The common characteristic of all such movements was to subordinate the individual to the supposed interests of some abstract collective entity—class, nation, race, or simply society.

In a relatively brief span of time, Hayek’s version of free-market, free-trade liberalism (in the traditional European sense of the word), and political internationalism, which had never before taken root among either American conservatives or liberals, became the bedrock on which the generation of American conservatives who came of age after 1945 built a political movement. Liberated from nativist, protectionist, and isolationist tendencies, this generation could turn its energies to the struggle against Communism and other forms of collectivism, and to the promotion of a free-market economy.

Naturally the transformation of American conservatism was never complete. . . The lingering Old Right influence is today most noticeable in the conspiratorial cast of mind, the obsession with betrayal and disloyalty, the search for alien influences, the siege mentality, the anti-intellectualism, the chauvinism, and the free-floating anger that unfortunately still pervade parts of the conservative movement. It is just these qualities that Patrick J. Buchanan would restore if he should ever succeed in “taking back” the movement from those who, in his words, have hijacked it. . . .

The key distinction for Hayek was not big government versus small government, but between a government of laws in which all coercive action is constrained by general and impartial rules, and a government of men in which coercion may be arbitrarily exercised to achieve whatever ends the government, or even the majority on whose behalf it acts, wishes to accomplish. Though Hayek contemplated with little enthusiasm the absorption by the state of a third or more of national income, the amount and character of government spending were to him very much a secondary issue that directly involved no fundamental principle. . . .

Hayek’s point is that there is no deductive proof from self-evident axioms that will establish the case for liberty. Rather, he argues, liberty is a condition and a value that has evolved with society. If we value liberty, it is because Western civilization has evolved in such a way that liberty has become part of its tradition. That tradition, the provisional outcome of a contingent historical and evolutionary process, cannot be explained in purely rational terms.

This approach to social theory, the product of a thoroughgoing philosophical skepticism, is decidedly incompatible with the religious beliefs to which a large segment of the conservative movement subscribes, and equally unattractive to those, conservative or libertarian, who ground their political beliefs in natural law or in any other set of self-evident truths. This no doubt explains the regrettably limited influence that Hayek’s later work has exerted on American conservatives—particularly unfortunate because his rich contributions to legal and constitutional theory have much to offer both conservatives and liberals struggling to formulate a coherent philosophy of adjudication.

That apart, however, it remains undeniable that the primary goals of American conservatism in the postwar era evolved steadily from an Old Right toward a Hayekian agenda: from isolationism to containing the military expansion of Communism and other aggressive totalitarian movements; from protectionism to reducing the extent of government interference with and disruption of the free-market economy both domestically and internationally; from wholesale opposition to the New Deal to reforming and rationalizing its social-insurance measures along more market-oriented lines, and focusing government efforts on helping the least well-off rather than redistributing income generally.

Given the conflicting pressures under which policies are made, this agenda has been far from perfectly implemented even under conservative administrations. Yet it was only by embracing such an agenda that conservatism attracted not just new intellectual supporters—the neoconservatives—but, at least in presidential elections, a majority of votes. A retreat to the Old Right stance advocated by Patrick J. Buchanan and his supporters would mean not just throwing overboard the neoconservative “parvenus,” it would mean eradicating root and branch the fundamental consensus that enabled American conservatism to grow and to thrive in the postwar era.

What’s Wrong with Monetarism?

UPDATE: (05/06): In an email Richard Lipsey has chided me for seeming to endorse the notion that 1970s stagflation refuted Keynesian economics. Lipsey rightly points out that by introducing inflation expectations into the Phillips Curve or the Aggregate Supply Curve, a standard Keynesian model is perfectly capable of explaining stagflation, so that it is simply wrong to suggest that 1970s stagflation constituted an empirical refutation of Keynesian theory. So my statement in the penultimate paragraph that the k-percent rule

was empirically demolished in the 1980s in a failure even more embarrassing than the stagflation failure of Keynesian economics.

should be amended to read “the supposed stagflation failure of Keynesian economics.”

Brad DeLong recently did a post (“The Disappearance of Monetarism”) referencing an old (apparently unpublished) paper of his following up his 2000 article (“The Triumph of Monetarism”) in the Journal of Economic Perspectives. Paul Krugman added his own gloss on DeLong on Friedman in a post called “Why Monetarism Failed.” In the JEP paper, DeLong argued that the New Keynesian policy consensus of the 1990s was built on the foundation of what DeLong called “classic monetarism,” the analytical core of the doctrine developed by Friedman in the 1950s and 1960s, a core that survived the demise of what he called “political monetarism,” the set of factual assumptions and policy preferences required to justify Friedman’s k-percent rule as the holy grail of monetary policy.

In his follow-up paper, DeLong balanced his enthusiasm for Friedman with a bow toward Keynes, noting the influence of Keynes on both classic and political monetarism, arguing that, unlike earlier adherents of the quantity theory, Friedman believed that a passive monetary policy was not the appropriate policy stance during the Great Depression; Friedman famously held the Fed responsible for the depth and duration of what he called the Great Contraction, because it had allowed the US money supply to drop by a third between 1929 and 1933. This was in sharp contrast to hard-core laissez-faire opponents of Fed policy, who regarded even the mild and largely ineffectual steps taken by the Fed – increasing the monetary base by 15% – as illegitimate interventionism to obstruct the salutary liquidation of bad investments, thereby postponing the necessary reallocation of real resources to more valuable uses. So, according to DeLong, Friedman, no less than Keynes, was battling against the hard-core laissez-faire opponents of any positive action to speed recovery from the Depression. While Keynes believed that in a deep depression only fiscal policy would be effective, Friedman believed that, even in a deep depression, monetary policy would be effective. But both agreed that there was no structural reason why stimulus would necessarily counterproductive; both rejected the idea that only if the increased output generated during the recovery was of a particular composition would recovery be sustainable.

Indeed, that’s why Friedman has always been regarded with suspicion by laissez-faire dogmatists who correctly judged him to be soft in his criticism of Keynesian doctrines, never having disputed the possibility that “artificially” increasing demand – either by government spending or by money creation — in a deep depression could lead to sustainable economic growth. From the point of view of laissez-faire dogmatists that concession to Keynesianism constituted a total sellout of fundamental free-market principles.

Friedman parried such attacks on the purity of his free-market dogmatism with a counterattack against his free-market dogmatist opponents, arguing that the gold standard to which they were attached so fervently was itself inconsistent with free-market principles, because, in virtually all historical instances of the gold standard, the monetary authorities charged with overseeing or administering the gold standard retained discretionary authority allowing them to set interest rates and exercise control over the quantity of money. Because monetary authorities retained substantial discretionary latitude under the gold standard, Friedman argued that a gold standard was institutionally inadequate and incapable of constraining the behavior of the monetary authorities responsible for its operation.

The point of a gold standard, in Friedman’s view, was that it makes it costly to increase the quantity of money. That might once have been true, but advances in banking technology eventually made it easy for banks to increase the quantity of money without any increase in the quantity of gold, making inflation possible even under a gold standard. True, eventually the inflation would have to be reversed to maintain the gold standard, but that simply made alternative periods of boom and bust inevitable. Thus, the gold standard, i.e., a mere obligation to convert banknotes or deposits into gold, was an inadequate constraint on the quantity of money, and an inadequate systemic assurance of stability.

In other words, if the point of a gold standard is to prevent the quantity of money from growing excessively, then, why not just eliminate the middleman, and simply establish a monetary rule constraining the growth in the quantity of money. That was why Friedman believed that his k-percent rule – please pardon the expression – trumped the gold standard, accomplishing directly what the gold standard could not accomplish, even indirectly: a gradual steady increase in the quantity of money that would prevent monetary-induced booms and busts.

Moreover, the k-percent rule made the monetary authority responsible for one thing, and one thing alone, imposing a rule on the monetary authority prescribing the time path of a targeted instrument – the quantity of money – over which the monetary authority has direct control: the quantity of money. The belief that the monetary authority in a modern banking system has direct control over the quantity of money was, of course, an obvious mistake. That the mistake could have persisted as long as it did was the result of the analytical distraction of the money multiplier: one of the leading fallacies of twentieth-century monetary thought, a fallacy that introductory textbooks unfortunately continue even now to foist upon unsuspecting students.

The money multiplier is not a structural supply-side variable, it is a reduced-form variable incorporating both supply-side and demand-side parameters, but Friedman and other Monetarists insisted on treating it as if it were a structural — and a deep structural variable at that – supply variable, so that it no less vulnerable to the Lucas Critique than, say, the Phillips Curve. Nevertheless, for at least a decade and a half after his refutation of the structural Phillips Curve, demonstrating its dangers as a guide to policy making, Friedman continued treating the money multiplier as if it were a deep structural variable, leading to the Monetarist forecasting debacle of the 1980s when Friedman and his acolytes were confidently predicting – over and over again — the return of double-digit inflation because the quantity of money was increasing for most of the 1980s at double-digit rates.

So once the k-percent rule collapsed under an avalanche of contradictory evidence, the Monetarist alternative to the gold standard that Friedman had persuasively, though fallaciously, argued was, on strictly libertarian grounds, preferable to the gold standard, the gold standard once again became the default position of laissez-faire dogmatists. There was to be sure some consideration given to free banking as an alternative to the gold standard. In his old age, after winning the Nobel Prize, F. A. Hayek introduced a proposal for direct currency competition — the elimination of legal tender laws and the like – which he later developed into a proposal for the denationalization of money. Hayek’s proposals suggested that convertibility into a real commodity was not necessary for a non-legal tender currency to have value – a proposition which I have argued is fallacious. So Hayek can be regarded as the grandfather of crypto currencies like the bitcoin. On the other hand, advocates of free banking, with a few exceptions like Earl Thompson and me, have generally gravitated back to the gold standard.

So while I agree with DeLong and Krugman (and for that matter with his many laissez-faire dogmatist critics) that Friedman had Keynesian inclinations which, depending on his audience, he sometimes emphasized, and sometimes suppressed, the most important reason that he was unable to retain his hold on right-wing monetary-economics thinking is that his key monetary-policy proposal – the k-percent rule – was empirically demolished in a failure even more embarrassing than the stagflation failure of Keynesian economics. With the k-percent rule no longer available as an alternative, what’s a right-wing ideologue to do?

Anyone for nominal gross domestic product level targeting (or NGDPLT for short)?


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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