Archive for the 'Roy Radner' 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.

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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.

Roger Farmer’s Prosperity for All

I have just read a review copy of Roger Farmer’s new book Prosperity for All, which distills many of Roger’s very interesting ideas into a form which, though readable, is still challenging — at least, it was for me. There is a lot that I like and agree with in Roger’s book, and the fact that he is a UCLA economist, though he came to UCLA after my departure, is certainly a point in his favor. So I will begin by mentioning some of the things that I really liked about Roger’s book.

What I like most is that he recognizes that beliefs are fundamental, which is almost exactly what I meant when I wrote this post (“Expectations Are Fundamental”) five years ago. The point I wanted to make is that the idea that there is some fundamental existential reality that economic agents try — and, if they are rational, will — perceive is a gross and misleading oversimplification, because expectations themselves are part of reality. In a world in which expectations are fundamental, the Keynesian beauty-contest theory of expectations and stock prices (described in chapter 12 of The General Theory) is not absurd as it is widely considered to be believers in the efficient market hypothesis. The almost universal unprofitability of simple trading rules or algorithms is not inconsistent with a market process in which the causality between prices and expectations goes in both directions, in which case anticipating expectations is no less rational than anticipating future cash flows.

One of the treats of reading this book is Farmer’s recollections of his time as a graduate student at Penn in the early 1980s when David Cass, Karl Shell, and Costas Azariadis were developing their theory of sunspot equilibrium in which expectations are self-fulfilling, an idea skillfully deployed by Roger to revise the basic New Keynesian model and re-orient it along a very different path from the standard New Keynesian one. I am sympathetic to that reorientation, and the main reason for that re-orientation is that Roger rejects the idea that there is a unique equilibrium to which the economy automatically reverts, albeit somewhat more slowly than if speeded along by the appropriate monetary policy, on its own. The notion that there is a unique equilibrium to which the economy automatically reverts is an assumption with no basis in theory or experience. The most that the natural-rate hypothesis can tell us is that if an economy is operating at its natural rate of unemployment, monetary expansion cannot permanently reduce the rate of unemployment below that natural rate. Eventually — once economic agents come to expect that the monetary expansion and the correspondingly higher rate of inflation will be maintained indefinitely — the unemployment rate must revert to the natural rate. But the natural-rate hypothesis does not tell us that monetary expansion cannot reduce unemployment when the actual unemployment rate exceeds the natural rate, although it is often misinterpreted as making that assertion.

In his book, Roger takes the anti-natural-rate argument a step further, asserting that the natural rate of unemployment rate is not unique. There is actually a range of unemployment rates at which the economy can permanently remain; which of those alternative natural rates the economy winds up at depends on the expectations held by the public about nominal future income. The higher expected future income, the greater consumption spending and, consequently, the greater employment. Things are a bit more complicated than I have just described them, because Roger also believes that consumption depends not on current income but on wealth. However, in the very simplified model with which Roger operates, wealth depends on expectations about future income. The more optimistic people are about their income-earning opportunities, the higher asset values; the higher asset values, the wealthier the public, and the greater consumption spending. The relationship between current income and expected future income is what Roger calls the belief function.

Thus, Roger juxtaposes a simple New Keynesian model against his own monetary model. The New Keynesian model consists of 1) an investment equals saving equilibrium condition (IS curve) describing the optimal consumption/savings decision of the representative individual as a locus of combinations of expected real interest rates and real income, based on the assumed rate of time preference of the representative individual, expected future income, and expected future inflation; 2) a Taylor rule describing how the monetary authority sets its nominal interest rate as a function of inflation and the output gap and its target (natural) nominal interest rate; 3) a short-run Phillips Curve that expresses actual inflation as a function of expected future inflation and the output gap. The three basic equations allow three endogenous variables, inflation, real income and the nominal rate of interest to be determined. The IS curve represents equilibrium combinations of real income and real interest rates; the Taylor rule determines a nominal interest rate; given the nominal rate determined by the Taylor rule, the IS curve can be redrawn to represent equilibrium combinations of real income and inflation. The intersection of the redrawn IS curve with the Phillips curve determines the inflation rate and real income.

Roger doesn’t like the New Keynesian model because he rejects the notion of a unique equilibrium with a unique natural rate of unemployment, a notion that I have argued is theoretically unfounded. Roger dismisses the natural-rate hypothesis on empirical grounds, the frequent observations of persistently high rates of unemployment being inconsistent with the idea that there are economic forces causing unemployment to revert back to the natural rate. Two responses to this empirical anomaly are possible: 1) the natural rate of unemployment is unstable, so that the observed persistence of high unemployment reflect increases in the underlying but unobservable natural rate of unemployment; 2) the adverse economic shocks that produce high unemployment are persistent, with unemployment returning to a natural level only after the adverse shocks have ceased. In the absence of independent empirical tests of the hypothesis that the natural rate of unemployment has changed, or of the hypothesis that adverse shocks causing unemployment to rise above the natural rate are persistent, neither of these responses is plausible, much less persuasive.

So Roger recasts the basic New Keynesian model in a very different form. While maintaining the Taylor Rule, he rewrites the IS curve so that it describes a relationship between the nominal interest rate and the expected growth of nominal income given the assumed rate of time preference, and in place of the Phillips Curve, he substitutes his belief function, which says that the expected growth of nominal income in the next period equals the current rate of growth. The IS curve and the Taylor Rule provide two steady state equations in three variables, nominal income growth, nominal interest rate and inflation, so that the rate of inflation is left undetermined. Once the belief function specifies the expected rate of growth of nominal income, the nominal interest rate consistent with expected nominal-income growth is determined. Since the belief function tells us only that the expected nominal-income growth equals the current rate of nominal-income growth, any change in nominal-income growth persists into the next period.

At any rate, Roger’s policy proposal is not to change the interest-rate rule followed by the monetary authority, but to propose a rule whereby the monetary authority influences the public’s expectations of nominal-income growth. The greater expected nominal-income growth, the greater wealth, and the greater consumption expenditures. The greater consumption expenditures, the greater income and employment. Expectations are self-fulfilling. Roger therefore advocates a policy by which the government buys and sells a stock-market index fund in order to keep overall wealth at a level that will generate enough consumption expenditures to support maximum sustainable employment.

This is a quick summary of some of the main substantive arguments that Roger makes in his book, and I hope that I have not misrepresented them too badly. As I have already said, I very much sympathize with his criticism of the New Keynesian model, and I agree with nearly all of his criticisms. I also agree wholeheartedly with his emphasis on the importance of expectations and on self-fulfilling character of expectations. Nevertheless, I have to admit that I have trouble taking Roger’s own monetary model and his policy proposal for stabilizing a broad index of equity prices over time seriously. And the reason I am so skeptical about Roger’s model and his policy recommendation is that his model, which does after all bear at least a family resemblance to the simple New Keynesian model, strikes me as being far too simplified to be credible as a representation of a real-world economy. His model, like the New Keynesian model, is an intertemporal model with neither money nor real capital, and the idea that there is an interest rate in such model is, though theoretically defensible, not very plausible. There may be a sequence of periods in such a model in which some form of intertemporal exchange takes place, but without explicitly introducing at least one good that is carried over from period to period, the extent of intertemporal trading is limited and devoid of the arbitrage constraints inherent in a system in which real assets are held from one period to the next.

So I am very skeptical about any macroeconomic model with no market for real assets so that the interest rate interacts with asset values and expected future prices in such a way that the existing stock of durable assets is willingly held over time. The simple New Keynesian model in which there is no money and no durable assets, but simply bonds whose existence is difficult to rationalize in the absence of money or durable assets, does not strike me as a sound foundation for making macroeconomic policy. An interest rate may exist in such a model, but such a model strikes me as woefully inadequate for macroeconomic policy analysis. And although Roger has certainly offered some interesting improvements on the simple New Keynesian model, I would not be willing to rely on Roger’s monetary model for the sweeping policy and institutional recommendations that he proposes, especially his proposal for stabilizing the long-run growth path of a broad index of stock prices.

This is an important point, so I will try to restate it within a wider context. Modern macroeconomics, of which Roger’s model is one of the more interesting examples, flatters itself by claiming to be grounded in the secure microfoundations of the Arrow-Debreu-McKenzie general equilibrium model. But the great achievement of the ADM model was to show the logical possibility of an equilibrium of the independently formulated, optimizing plans of an unlimited number of economic agents producing and trading an unlimited number of commodities over an unlimited number of time periods.

To prove the mutual consistency of such a decentralized decision-making process coordinated by a system of equilibrium prices was a remarkable intellectual achievement. Modern macroeconomics deceptively trades on the prestige of this achievement in claiming to be founded on the ADM general-equilibrium model; the claim is at best misleading, because modern macroeconomics collapses the multiplicity of goods, services, and assets into a single non-durable commodity, so that the only relevant plan the agents in the modern macromodel are called upon to make is a decision about how much to spend in the current period given a shared utility function and a shared production technology for the single output. In the process, all the hard work performed by the ADM general-equilibrium model in explaining how a system of competitive prices could achieve an equilibrium of the complex independent — but interdependent — intertemporal plans of a multitude of decision-makers is effectively discarded and disregarded.

This approach to macroeconomics is not microfounded, but its opposite. The approach relies on the assumption that all but a very small set of microeconomic issues are irrelevant to macroeconomics. Now it is legitimate for macroeconomics to disregard many microeconomic issues, but the assumption that there is continuous microeconomic coordination, apart from the handful of potential imperfections on which modern macroeconomics chooses to focus is not legitimate. In particular, to collapse the entire economy into a single output, implies that all the separate markets encompassed by an actual economy are in equilibrium and that the equilibrium is maintained over time. For that equilibrium to be maintained over time, agents must formulate correct expectations of all the individual relative prices that prevail in those markets over time. The ADM model sidestepped that expectational problem by assuming that a full set of current and forward markets exists in the initial period and that all the agents participating in the economy are present and endowed with wealth enabling them to trade in the initial period. Under those rather demanding assumptions, if an equilibrium price vector covering all current and future markets is arrived at, the optimizing agents will formulate a set of mutually consistent optimal plans conditional on that vector of equilibrium prices so that all the optimal plans can and will be carried out as time happily unfolds for as long as the agents continue in their blissful existence.

However, without a complete set of current and forward markets, achieving the full equilibrium of the ADM model requires that agents formulate consistent expectations of the future prices that will be realized only over the course of time not in the initial period. Roy Radner, who extended the ADM model to accommodate the case of incomplete markets, called such a sequential equilibrium, an equilibrium of plans, prices and expectations. The sequential equilibrium described by Radner has the property that expectations are rational, but the assumption of rational expectations for all future prices over a sequence of future time periods is so unbelievably outlandish as an approximation to reality — sort of like the assumption that it could be 76 degrees fahrenheit in Washington DC in February — that to build that assumption into a macroeconomic model is an absurdity of mind-boggling proportions. But that is precisely what modern macroeconomics, in both its Real Business Cycle and New Keynesian incarnations, has done.

If instead of the sequential equilibrium of plans, prices and expectations, one tries to model an economy in which the price expectations of agents can be inconsistent, while prices adjust within any period to clear markets – the method of temporary equilibrium first described by Hicks in Value and Capital – one can begin to develop a richer conception of how a macroeconomic system can be subject to the financial disturbances, and financial crises to which modern macroeconomies are occasionally, if not routinely, vulnerable. But that would require a reorientation, if not a repudiation, of the path on which macroeconomics has been resolutely marching for nigh on forty years. In his 1984 paper “Consistent Temporary Equilibrium,” published in a volume edited by J. P. Fitoussi, C. J. Bliss made a start on developing such a macroeconomic theory.

There are few economists better equipped than Roger Farmer to lead macroeconomics onto a new and more productive path. He has not done so in this book, but I am hoping that, in his next one, he will.


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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