Archive for the 'rational expectations equilibrium' Category

Although RATEX Must Be a Contingent Property of any Economic Model, RATEX Is an Unlikely Property of Reality

Published July 29, 2022 No-trade theorem , rational expectations equilibrium , Uncategorized 2 Comments

Without searching through my old posts, I’m confident that I’ve already made this point many times in passing, but I just want to restate this point up front — highlighted and underscored. Any economic model must satisfy the following rational-expectations condition:

If the agents in the model expect the equilibrium outcome of the model (or, if there are multiple equilibrium outcomes, they all expect the same one of those equilibrium outcomes), that expected equilibrium outcome will be realized.

When the agents in an economic model all expect the equilibrium outcome of the model, the agents may be said to have rational expectations, and those rational expectations are self-fulfilling. Any economic model that lacks this contingent RATEX property is incoherent. But unless an economic model provides a theory of expectation formation whereby the agents all form correct expectations of the equilibrium outcome of the model, RATEX is a merely contingent, not an essential, property of the model.

Although an actual expectation-formation theory of rational expectations has never, to my knowledge, been derived from plausible assumptions, the RATEX assumption is disingenuously insisted upon as a property of rational decision-making implied by neoclassical theory. Such tyrannizing methodological intimidation is groundless and entails the reductio ad absurdum of the Milgrom and Stokey No-Trade Theorem.

Axel Leijonhufvud and Modern Macroeconomics

Published June 20, 2022 Alchian , Axel Leijonfuvud , common knowledge , coordination failure , Earl Thompson , Hayek , IS-LM , J. R. Hicks , Keynes , microfoundations , Milton Friedman , neoclassical synthesis , New Classical macroeconomics , New Keynesians , rational expectations , rational expectations equilibrium , Robert Clower , Robert Lucas , search theories , sticky prices , sticky wages , tatonnement , temporary equilibrium , Thomas Sargent , Walrasian equilibrium 10 Comments

For many baby boomers like me growing up in Los Angeles, UCLA was an almost inevitable choice for college. As an incoming freshman, I was undecided whether to major in political science or economics. PoliSci 1 didn’t impress me, but Econ 1 did. More than my Econ 1 professor, it was the assigned textbook, University Economics, 1st edition, by Alchian and Allen that impressed me. That’s how my career in economics started.

After taking introductory micro and macro as a freshman, I started the intermediate theory sequence of micro (utility and cost theory, econ 101a), (general equilibrium theory, 101b), and (macro theory, 102) as a sophomore. It was in the winter 1968 quarter that I encountered Axel Leijonhufvud. This was about a year before his famous book – his doctoral dissertation – Keynesian Economics and the Economics of Keynes was published in the fall of 1968 to instant acclaim. Although it must have been known in the department that the book, which he’d been working on for several years, would soon appear, I doubt that its remarkable impact on the economics profession could have been anticipated, turning Axel almost overnight from an obscure untenured assistant professor into a tenured professor at one of the top economics departments in the world and a kind of academic rock star widely sought after to lecture and appear at conferences around the globe. I offer the following scattered recollections of him, drawn from memories at least a half-century old, to those interested in his writings, and some reflections on his rise to the top of the profession, followed by a gradual loss of influence as theoretical marcroeconomics, fell under the influence of Robert Lucas and the rational-expectations movement in its various forms (New Classical, Real Business-Cycle, New-Keynesian).

Axel, then in his early to mid-thirties, was an imposing figure, very tall and gaunt with a short beard and a shock of wavy blondish hair, but his attire reflecting the lowly position he then occupied in the academic hierarchy. He spoke perfect English with a distinct Swedish lilt, frequently leavening his lectures and responses to students’ questions with wry and witty comments and asides.  

Axel’s presentation of general-equilibrium theory was, as then still the norm, at least at UCLA, mostly graphical, supplemented occasionally by some algebra and elementary calculus. The Edgeworth box was his principal technique for analyzing both bilateral trade and production in the simple two-output, two-input case, and he used it to elucidate concepts like Pareto optimality, general-equilibrium prices, and the two welfare theorems, an exposition which I, at least, found deeply satisfying. The assigned readings were the classic paper by F. M. Bator, “The Simple Analytics of Welfare-Maximization,” which I relied on heavily to gain a working grasp of the basics of general-equilibrium theory, and as a supplementary text, Peter Newman’s The Theory of Exchange, much of which was too advanced for me to comprehend more than superficially. Axel also introduced us to the concept of tâtonnement and highlighting its importance as an explanation of sorts of how the equilibrium price vector might, at least in theory, be found, an issue whose profound significance I then only vaguely comprehended, if at all. Another assigned text was Modern Capital Theory by Donald Dewey, providing an introduction to the role of capital, time, and the rate of interest in monetary and macroeconomic theory and a bridge to the intermediate macro course that he would teach the following quarter.

A highlight of Axel’s general-equilibrium course was the guest lecture by Bob Clower, then visiting UCLA from Northwestern, with whom Axel became friendly only after leaving Northwestern, and two of whose papers (“A Reconsideration of the Microfoundations of Monetary Theory,” and “The Keynesian Counterrevolution: A Theoretical Appraisal”) were discussed at length in his forthcoming book. (The collaboration between Clower and Leijonhufvud and their early Northwestern connection has led to the mistaken idea that Clower had been Axel’s thesis advisor. Axel’s dissertation was actually written under Meyer Burstein.) Clower himself came to UCLA economics a few years later when I was already a third-year graduate student, and my contact with him was confined to seeing him at seminars and workshops. I still have a vivid memory of Bob in his lecture explaining, with the aid of chalk and a blackboard, how ballistic theory was developed into an orbital theory by way of a conceptual experiment imagining that the distance travelled by a projectile launched from a fixed position being progressively lengthened until the projectile’s trajectory transitioned into an orbit around the earth.

Axel devoted the first part of his macro course to extending the Keynesian-cross diagram we had been taught in introductory macro into the Hicksian IS-LM model by making investment a negative function of the rate of interest and adding a money market with a fixed money stock and a demand for money that’s a negative function of the interest rate. Depending on the assumptions about elasticities, IS-LM could be an analytical vehicle that could accommodate either the extreme Keynesian-cross case, in which fiscal policy is all-powerful and monetary policy is ineffective, or the Monetarist (classical) case, in which fiscal policy is ineffective and monetary policy all-powerful, which was how macroeconomics was often framed as a debate about the elasticity of the demand for money curve with respect to interest rate. Friedman himself, in his not very successful attempt to articulate his own framework for monetary analysis, accepted that framing, one of the few rhetorical and polemical misfires of his career.

In his intermediate macro course, Axel presented the standard macro model, and I don’t remember his weighing in that much with his own criticism; he didn’t teach from a standard intermediate macro textbook, standard textbook versions of the dominant Keynesian model not being at all to his liking. Instead, he assigned early sources of what became Keynesian economics like Hicks’s 1937 exposition of the IS-LM model and Alvin Hansen’s A Guide to Keynes (1953), with Friedman’s 1956 restatement of the quantity theory serving as a counterpoint, and further developments of Keynesian thought like Patinkin’s 1948 paper on price flexibility and full employment, A. W. Phillips original derivation of the Phillips Curve, Harry Johnson on the General Theory after 25 years, and his own preview “Keynes and the Keynesians: A Suggested Interpretation” of his forthcoming book, and probably others that I’m not now remembering. Presenting the material piecemeal from original sources allowed him to underscore the weaknesses and questionable assumptions latent in the standard Keynesian model.

Of course, for most of us, it was a challenge just to reproduce the standard model and apply it to some specific problems, but we at least we got the sense that there was more going on under the hood of the model than we would have imagined had we learned its structure from a standard macro text. I have the melancholy feeling that the passage of years has dimmed my memory of his teaching too much to adequately describe how stimulating, amusing and enjoyable his lectures were to those of us just starting our journey into economic theory.

The following quarter, in the fall 1968 quarter, when his book had just appeared in print, Axel created a new advanced course called macrodynamics. He talked a lot about Wicksell and Keynes, of course, but he was then also fascinated by the work of Norbert Wiener on cybernetics, assigning Wiener’s book Cybernetics as a primary text and a key to understanding what Keynes was really trying to do. He introduced us to concepts like positive and negative feedback, servo mechanisms, stable and unstable dynamic systems and related those concepts to economic concepts like the price mechanism, stable and unstable equilibria, and to business cycles. Here’s how a put it in On Keynesian Economics and the Economics of Keynes:

Cybernetics as a formal theory, of course, began to develop only during the was and it was only with the appearance of . . . Weiner’s book in 1948 that the first results of serious work on a general theory of dynamic systems – and the term itself – reached a wider public. Even then, research in this field seemed remote from economic problems, and it is thus not surprising that the first decade or more of the Keynesian debate did not go in this direction. But it is surprising that so few monetary economists have caught on to developments in this field in the last ten or twelve years, and that the work of those who have has not triggered a more dramatic chain reaction. This, I believe, is the Keynesian Revolution that did not come off.

In conveying the essential departure of cybernetics from traditional physics, Wiener once noted:

Here there emerges a very interesting distinction between the physics of our grandfathers and that of the present day. In nineteenth-century physics, it seemed to cost nothing to get information.

In context, the reference was to Maxwell’s Demon. In its economic reincarnation as Walras’ auctioneer, the demon has not yet been exorcised. But this certainly must be what Keynes tried to do. If a single distinction is to be drawn between the Economics of Keynes and the economics of our grandfathers, this is it. It is only on this basis that Keynes’ claim to have essayed a more “general theory” can be maintained. If this distinction is not recognized as both valid and important, I believe we must conclude that Keynes’ contribution to pure theory is nil.

Axel’s hopes that cybernetics could provide an analytical tool with which to bring Keynes’s insights into informational scarcity on macroeconomic analysis were never fulfilled. A glance at the index to Axel’s excellent collection of essays written from the late 1960s and the late 1970s Information and Coordination reveals not a single reference either to cybernetics or to Wiener. Instead, to his chagrin and disappointment, macroeconomics took a completely different path following the path blazed by Robert Lucas and his followers of insisting on a nearly continuous state of rational-expectations equilibrium and implicitly denying that there is an intertemporal coordination problem for macroeconomics to analyze, much less to solve.

After getting my BA in economics at UCLA, I stayed put and began my graduate studies there in the next academic year, taking the graduate micro sequence given that year by Jack Hirshleifer, the graduate macro sequence with Axel and the graduate monetary theory sequence with Ben Klein, who started his career as a monetary economist before devoting himself a few years later entirely to IO and antitrust.

Not surprisingly, Axel’s macro course drew heavily on his book, which meant it drew heavily on the history of macroeconomics including, of course, Keynes himself, but also his Cambridge predecessors and collaborators, his friendly, and not so friendly, adversaries, and the Keynesians that followed him. His main point was that if you take Keynes seriously, you can’t argue, as the standard 1960s neoclassical synthesis did, that the main lesson taught by Keynes was that if the real wage in an economy is somehow stuck above the market-clearing wage, an increase in aggregate demand is necessary to allow the labor market to clear at the prevailing market wage by raising the price level to reduce the real wage down to the market-clearing level.

This interpretation of Keynes, Axel argued, trivialized Keynes by implying that he didn’t say anything that had not been said previously by his predecessors who had also blamed high unemployment on wages being kept above market-clearing levels by minimum-wage legislation or the anticompetitive conduct of trade-union monopolies.

Axel sought to reinterpret Keynes as an early precursor of search theories of unemployment subsequently developed by Armen Alchian and Edward Phelps who would soon be followed by others including Robert Lucas. Because negative shocks to aggregate demand are rarely anticipated, the immediate wage and price adjustments to a new post-shock equilibrium price vector that would maintain full employment would occur only under the imaginary tâtonnement system naively taken as the paradigm for price adjustment under competitive market conditions, Keynes believed that a deliberate countercyclical policy response was needed to avoid a potentially long-lasting or permanent decline in output and employment. The issue is not price flexibility per se, but finding the equilibrium price vector consistent with intertemporal coordination. Price flexibility that doesn’t arrive quickly (immediately?) at the equilibrium price vector achieves nothing. Trading at disequilibrium prices leads inevitably to a contraction of output and income. In an inspired turn of phrase, Axel called this cumulative process of aggregate demand shrinkage Say’s Principle, which years later led me to write my paper “Say’s Law and the Classical Theory of Depressions” included as Chapter 9 of my recent book Studies in the History of Monetary Theory.

Attention to the implications of the lack of an actual coordinating mechanism simply assumed (either in the form of Walrasian tâtonnement or the implicit Marshallian ceteris paribus assumption) by neoclassical economic theory was, in Axel’s view, the great contribution of Keynes. Axel deplored the neoclassical synthesis, because its rote acceptance of the neoclassical equilibrium paradigm trivialized Keynes’s contribution, treating unemployment as a phenomenon attributable to sticky or rigid wages without inquiring whether alternative informational assumptions could explain unemployment even with flexible wages.

The new literature on search theories of unemployment advanced by Alchian, Phelps, et al. and the success of his book gave Axel hope that a deepened version of neoclassical economic theory that paid attention to its underlying informational assumptions could lead to a meaningful reconciliation of the economics of Keynes with neoclassical theory and replace the superficial neoclassical synthesis of the 1960s. That quest for an alternative version of neoclassical economic theory was for a while subsumed under the trite heading of finding microfoundations for macroeconomics, by which was meant finding a way to explain Keynesian (involuntary) unemployment caused by deficient aggregate demand without invoking special ad hoc assumptions like rigid or sticky wages and prices. The objective was to analyze the optimizing behavior of individual agents given limitations in or imperfections of the information available to them and to identify and provide remedies for the disequilibrium conditions that characterize coordination failures.

For a short time, perhaps from the early 1970s until the early 1980s, a number of seemingly promising attempts to develop a disequilibrium theory of macroeconomics appeared, most notably by Robert Barro and Herschel Grossman in the US, and by and J. P. Benassy, J. M. Grandmont, and Edmond Malinvaud in France. Axel and Clower were largely critical of these efforts, regarding them as defective and even misguided in many respects.

But at about the same time, another, very different, approach to microfoundations was emerging, inspired by the work of Robert Lucas and Thomas Sargent and their followers, who were introducing the concept of rational expectations into macroeconomics. Axel and Clower had focused their dissatisfaction with neoclassical economics on the rise of the Walrasian paradigm which used the obviously fantastical invention of a tâtonnement process to account for the attainment of an equilibrium price vector perfectly coordinating all economic activity. They argued for an interpretation of Keynes’s contribution as an attempt to steer economics away from an untenable theoretical and analytical paradigm rather than, as the neoclassical synthesis had done, to make peace with it through the adoption of ad hoc assumptions about price and wage rigidity, thereby draining Keynes’s contribution of novelty and significance.

And then Lucas came along to dispense with the auctioneer, eliminate tâtonnement, while achieving the same result by way of a methodological stratagem in three parts: a) insisting that all agents be treated as equilibrium optimizers, and b) who therefore form identical rational expectations of all future prices using the same common knowledge, so that c) they all correctly anticipate the equilibrium price vector that earlier economists had assumed could be found only through the intervention of an imaginary auctioneer conducting a fantastical tâtonnement process.

This methodological imperatives laid down by Lucas were enforced with a rigorous discipline more befitting a religious order than an academic research community. The discipline of equilibrium reasoning, it was decreed by methodological fiat, imposed a question-begging research strategy on researchers in which correct knowledge of future prices became part of the endowment of all optimizing agents.

While microfoundations for Axel, Clower, Alchian, Phelps and their collaborators and followers had meant relaxing the informational assumptions of the standard neoclassical model, for Lucas and his followers microfoundations came to mean that each and every individual agent must be assumed to have all the knowledge that exists in the model. Otherwise the rational-expectations assumption required by the model could not be justified.

The early Lucasian models did assume a certain kind of informational imperfection or ambiguity about whether observed price changes were relative changes or absolute changes, which would be resolved only after a one-period time lag. However, the observed serial correlation in aggregate time series could not be rationalized by an informational ambiguity resolved after just one period. This deficiency in the original Lucasian model led to the development of real-business-cycle models that attribute business cycles to real-productivity shocks that dispense with Lucasian informational ambiguity in accounting for observed aggregate time-series fluctuations. So-called New Keynesian economists chimed in with ad hoc assumptions about wage and price stickiness to create a new neoclassical synthesis to replace the old synthesis but with little claim to any actual analytical insight.

The success of the Lucasian paradigm was disheartening to Axel, and his research agenda gradually shifted from macroeconomic theory to applied policy, especially inflation control in developing countries. Although my own interest in macroeconomics was largely inspired by Axel, my approach to macroeconomics and monetary theory eventually diverged from Axel’s, when, in my last couple of years of graduate work at UCLA, I became close to Earl Thompson whose courses I had not taken as an undergraduate or a graduate student. I had read some of Earl’s monetary theory papers when preparing for my preliminary exams; I found them interesting but quirky and difficult to understand. After I had already started writing my dissertation, under Harold Demsetz on an IO topic, I decided — I think at the urging of my friend and eventual co-author, Ron Batchelder — to sit in on Earl’s graduate macro sequence, which he would sometimes offer as an alternative to Axel’s more popular graduate macro sequence. It was a relatively small group — probably not more than 25 or so attended – that met one evening a week for three hours. Each session – and sometimes more than one session — was devoted to discussing one of Earl’s published or unpublished macroeconomic or monetary theory papers. Hearing Earl explain his papers and respond to questions and criticisms brought them alive to me in a way that just reading them had never done, and I gradually realized that his arguments, which I had previously dismissed or misunderstood, were actually profoundly insightful and theoretically compelling.

For me at least, Earl provided a more systematic way of thinking about macroeconomics and a more systematic critique of standard macro than I could piece together from Axel’s writings and lectures. But one of the lessons that I had learned from Axel was the seminal importance of two Hayek essays: “The Use of Knowledge in Society,” and, especially “Economics and Knowledge.” The former essay is the easier to understand, and I got the gist of it on my first reading; the latter essay is more subtle and harder to follow, and it took years and a number of readings before I could really follow it. I’m not sure when I began to really understand it, but it might have been when I heard Earl expound on the importance of Hicks’s temporary-equilibrium method first introduced in Value and Capital.

In working out the temporary equilibrium method, Hicks relied on the work of Myrdal, Lindahl and Hayek, and Earl’s explanation of the temporary-equilibrium method based on the assumption that markets for current delivery clear, but those market-clearing prices are different from the prices that agents had expected when formulating their optimal intertemporal plans, causing agents to revise their plans and their expectations of future prices. That seemed to be the proper way to think about the intertemporal-coordination failures that Axel was so concerned about, but somehow he never made the connection between Hayek’s work, which he greatly admired, and the Hicksian temporary-equilibrium method which I never heard him refer to, even though he also greatly admired Hicks.

It always seemed to me that a collaboration between Earl and Axel could have been really productive and might even have led to an alternative to the Lucasian reign over macroeconomics. But for some reason, no such collaboration ever took place, and macroeconomics was impoverished as a result. They are both gone, but we still benefit from having Duncan Foley still with us, still active, and still making important contributions to our understanding, And we should be grateful.

Robert Lucas and the Pretense of Science

Published March 9, 2022 Abraham Wald , Alfred Marshall , Arrow-Debrew-McKenzie model , common knowledge , expectations , general equilibrium , Hayek , intertemporal equilibrium , Kenneth Arrow , Leon Walras , Lucas Critique , macroeconomics , microfoundations , New Classical macroeconomics , partial equilibrium , rational expectations , rational expectations equilibrium , representative agent , Uncategorized , Walrasian equilibrium 21 Comments

F. A. Hayek entitled his 1974 Nobel Lecture whose principal theme was to attack the simple notion that the long-observed correlation between aggregate demand and employment was a reliable basis for conducting macroeconomic policy, “The Pretence of Knowledge.” Reiterating an argument that he had made over 40 years earlier about the transitory stimulus provided to profits and production by monetary expansion, Hayek was informally anticipating the argument that Robert Lucas famously repackaged two years later in his famous critique of econometric policy evaluation. Hayek’s argument hinged on a distinction between “phenomena of unorganized complexity” and phenomena of organized complexity.” Statistical relationships or correlations between phenomena of disorganized complexity may be relied upon to persist, but observed statistical correlations displayed by phenomena of organized complexity cannot be relied upon without detailed knowledge of the individual elements that constitute the system. It was the facile assumption that observed statistical correlations in systems of organized complexity can be uncritically relied upon in making policy decisions that Hayek dismissed as merely the pretense of knowledge.

Adopting many of Hayek’s complaints about macroeconomic theory, Lucas founded his New Classical approach to macroeconomics on a methodological principle that all macroeconomic models be grounded in the axioms of neoclassical economic theory as articulated in the canonical Arrow-Debreu-McKenzie models of general equilibrium models. Without such grounding in neoclassical axioms and explicit formal derivations of theorems from those axioms, Lucas maintained that macroeconomics could not be considered truly scientific. Forty years of Keynesian macroeconomics were, in Lucas’s view, largely pre-scientific or pseudo-scientific, because they lacked satisfactory microfoundations.

Lucas’s methodological program for macroeconomics was thus based on two basic principles: reductionism and formalism. First, all macroeconomic models not only had to be consistent with rational individual decisions, they had to be reduced to those choices. Second, all the propositions of macroeconomic models had to be explicitly derived from the formal definitions and axioms of neoclassical theory. Lucas demanded nothing less than the explicit assumption individual rationality in every macroeconomic model and that all decisions by agents in a macroeconomic model be individually rational.

In practice, implementing Lucasian methodological principles required that in any macroeconomic model all agents’ decisions be derived within an explicit optimization problem. However, as Hayek had himself shown in his early studies of business cycles and intertemporal equilibrium, individual optimization in the standard Walrasian framework, within which Lucas wished to embed macroeconomic theory, is possible only if all agents are optimizing simultaneously, all individual decisions being conditional on the decisions of other agents. Individual optimization can only be solved simultaneously for all agents, not individually in isolation.

The difficulty of solving a macroeconomic equilibrium model for the simultaneous optimal decisions of all the agents in the model led Lucas and his associates and followers to a strategic simplification: reducing the entire model to a representative agent. The optimal choices of a single agent would then embody the consumption and production decisions of all agents in the model.

The staggering simplification involved in reducing a purported macroeconomic model to a representative agent is obvious on its face, but the sleight of hand being performed deserves explicit attention. The existence of an equilibrium solution to the neoclassical system of equations was assumed, based on faulty reasoning by Walras, Fisher and Pareto who simply counted equations and unknowns. A rigorous proof of existence was only provided by Abraham Wald in 1936 and subsequently in more general form by Arrow, Debreu and McKenzie, working independently, in the 1950s. But proving the existence of a solution to the system of equations does not establish that an actual neoclassical economy would, in fact, converge on such an equilibrium.

Neoclassical theory was and remains silent about the process whereby equilibrium is, or could be, reached. The Marshallian branch of neoclassical theory, focusing on equilibrium in individual markets rather than the systemic equilibrium, is often thought to provide an account of how equilibrium is arrived at, but the Marshallian partial-equilibrium analysis presumes that all markets and prices except the price in the single market under analysis, are in a state of equilibrium. So the Marshallian approach provides no more explanation of a process by which a set of equilibrium prices for an entire economy is, or could be, reached than the Walrasian approach.

Lucasian methodology has thus led to substituting a single-agent model for an actual macroeconomic model. It does so on the premise that an economic system operates as if it were in a state of general equilibrium. The factual basis for this premise apparently that it is possible, using versions of a suitable model with calibrated coefficients, to account for observed aggregate time series of consumption, investment, national income, and employment. But the time series derived from these models are derived by attributing all observed variations in national income to unexplained shocks in productivity, so that the explanation provided is in fact an ex-post rationalization of the observed variations not an explanation of those variations.

Nor did Lucasian methodology have a theoretical basis in received neoclassical theory. In a famous 1960 paper “Towards a Theory of Price Adjustment,” Kenneth Arrow identified the explanatory gap in neoclassical theory: the absence of a theory of price change in competitive markets in which every agent is a price taker. The existence of an equilibrium does not entail that the equilibrium will be, or is even likely to be, found. The notion that price flexibility is somehow a guarantee that market adjustments reliably lead to an equilibrium outcome is a presumption or a preconception, not the result of rigorous analysis.

However, Lucas used the concept of rational expectations, which originally meant no more than that agents try to use all available information to anticipate future prices, to make the concept of equilibrium, notwithstanding its inherent implausibility, a methodological necessity. A rational-expectations equilibrium was methodologically necessary and ruthlessly enforced on researchers, because it was presumed to be entailed by the neoclassical assumption of rationality. Lucasian methodology transformed rational expectations into the proposition that all agents form identical, and correct, expectations of future prices based on the same available information (common knowledge). Because all agents reach the same, correct expectations of future prices, general equilibrium is continuously achieved, except at intermittent moments when new information arrives and is used by agents to revise their expectations.

In his Nobel Lecture, Hayek decried a pretense of knowledge about correlations between macroeconomic time series that lack a foundation in the deeper structural relationships between those related time series. Without an understanding of the deeper structural relationships between those time series, observed correlations cannot be relied on when formulating economic policies. Lucas’s own famous critique echoed the message of Hayek’s lecture.

The search for microfoundations was always a natural and commendable endeavor. Scientists naturally try to reduce higher-level theories to deeper and more fundamental principles. But the endeavor ought to be conducted as a theoretical and empirical endeavor. If successful, the reduction of the higher-level theory to a deeper theory will provide insight and disclose new empirical implications to both the higher-level and the deeper theories. But reduction by methodological fiat accomplishes neither and discourages the research that might actually achieve a theoretical reduction of a higher-level theory to a deeper one. Similarly, formalism can provide important insights into the structure of theories and disclose gaps or mistakes the reasoning underlying the theories. But most important theories, even in pure mathematics, start out as informal theories that only gradually become axiomatized as logical gaps and ambiguities in the theories are discovered and filled or refined.

The resort to the reductionist and formalist methodological imperatives with which Lucas and his followers have justified their pretentions to scientific prestige and authority, and have used that authority to compel compliance with those imperatives, only belie their pretensions.

The Explanatory Gap and Mengerian Subjectivism

Published November 7, 2021 Alfred Marshall , Arrow-Debrew-McKenzie model , Carl Menger , common knowledge , general equilibrium , Hayek , Kenneth Arrow , Leon Walras , Nancy Stokey , partial equilibrium , Paul Milgrom , private knowledge , rational expectations equilibrium 8 Comments

My last several posts have been focused on Marshall and Walras and the relationships and differences between the partial equilibrium approach of Marshall and the general-equilibrium approach of Walras and how that current state of neoclassical economics is divided between the more practical applied approach of Marshallian partial-equilibrium analysis and the more theoretical general-equilibrium approach of Walras. The divide is particularly important for the history of macroeconomics, because many of the macroeconomic controversies in the decades since Keynes have also involved differences between Marshallians and Walrasians. I’m not happy with either the Marshallian or Walrasian approach, and I have been trying to articulate my unhappiness with both branches of current neoclassical thinking by going back to the work of the forgotten marginal revolutionary, Carl Menger. I’ve been writing a paper for a conference later this month celebrating the 150th anniversary of Menger’s great work which draws on some of my recent musings, because I think it offers at least some hints at how to go about developing an improved neoclassical theory. Here’s a further sampling of my thinking which is drawn from one of the sections of my work in progress.

Both the Marshallian and the Walrasian versions of equilibrium analysis have failed to bridge an explanatory gap between the equilibrium state, whose existence is crucial for such empirical content as can be claimed on behalf of those versions of neoclassical theory, and such an equilibrium state could ever be attained. The gap was identified by one of the chief architects of modern neoclassical theory, Kenneth Arrow, in his 1958 paper “Toward a Theory of Price Adjustment.”

The equilibrium is defined in terms of a set of prices. In the Marshallian version, the equilibrium prices are assumed to have already been determined in all but a single market (or perhaps a subset of closely related markets), so that the Marshallian equilibrium simply represents how, in a single small or isolated market, an equilibrium price in that market is determined, under suitable ceteris-paribus conditions thereby leaving the equilibrium prices determined in other markets unaffected.

In the Walrasian version, all prices in all markets are determined simultaneously, but the method for determining those prices simultaneously was not spelled out by Walras other than by reference to the admittedly fictitious and purely heuristic tâtonnement process.

Both the Marshallian and Walrasian versions can show that equilibrium has optimal properties, but neither version can explain how the equilibrium is reached or how it can be discovered in practice. This is true even in the single-period context in which the Walrasian and Marshallian equilibrium analyses were originally carried out.

The single-period equilibrium has been extended, at least in a formal way, in the standard Arrow-Debreu-McKenzie (ADM) version of the Walrasian equilibrium, but this version is in important respects just an enhanced version of a single-period model inasmuch as all trades take place at time zero in a complete array of future state-contingent markets. So it is something of a stretch to consider the ADM model a truly intertemporal model in which the future can unfold in potentially surprising ways as opposed to just playing out a script already written in which agents go through the motions of executing a set of consistent plans to produce, purchase and sell in a sequence of predetermined actions.

Under less extreme assumptions than those of the ADM model, an intertemporal equilibrium involves both equilibrium current prices and equilibrium expected prices, and just as the equilibrium current prices are the same for all agents, equilibrium expected future prices must be equal for all agents. In his 1937 exposition of the concept of intertemporal equilibrium, Hayek explained the difference between what agents are assumed to know in a state of intertemporal equilibrium and what they are assumed to know in a single-period equilibrium.

If all agents share common knowledge, it may be plausible to assume that they will rationally arrive at similar expectations of the future prices. But if their stock of knowledge consists of both common knowledge and private knowledge, then it seems implausible to assume that the price expectations of different agents will always be in accord. Nevertheless, it is not necessarily inconceivable, though perhaps improbable, that agents will all arrive at the same expectations of future prices.

In the single-period equilibrium, all agents share common knowledge of equilibrium prices of all commodities. But in intertemporal equilibrium, agents lack knowledge of the future, but can only form expectations of future prices derived from their own, more or less accurate, stock of private knowledge. However, an equilibrium may still come about if, based on their private knowledge, they arrive at sufficiently similar expectations of future prices for their plans for their current and future purchases and sales to be mutually compatible.

Thus, just twenty years after Arrow called attention to the explanatory gap in neoclassical theory by observing that there is no neoclassical theory of how competitive prices can change, Milgrom and Stokey turned Arrow’s argument on its head by arguing that, under rational expectations, no trading would ever occur at prices other than equilibrium prices, so that it would be impossible for a trader with private information to take advantage of that information. This argument seems to suffer from a widely shared misunderstanding of what rational expectations signify.

Thus, in the Mengerian view articulated by Hayek, intertemporal equilibrium, given the diversity of private knowledge and expectations, is an unlikely, but not inconceivable, state of affairs, a view that stands in sharp contrast to the argument of Paul Milgrom and Nancy Stokey (1982), in which they argue that under a rational-expectations equilibrium there is no private knowledge, only common knowledge, and that it would be impossible for any trader to trade on private knowledge, because no other trader with rational expectations would be willing to trade with anyone at a price other than the equilibrium price.

Rational expectations is not a property of individual agents making rational and efficient use of the information from whatever source it is acquired. As I have previously explained here (and a revised version here) rational expectations is a property of intertemporal equilibrium; it is not an intrinsic property that agents have by virtue of being rational, just as the fact that the three angles in a triangle sum to 180 degrees is not a property of the angles qua angles, but a property of the triangle. When the expectations that agents hold about future prices are identical, their expectations are equilibrium expectations and they are rational. That the agents hold rational expectations in equilibrium, does not mean that the agents are possessed of the power to calculate equilibrium prices or even to know if their expectations of future prices are equilibrium expectations. Equilibrium is the cause of rational expectations; rational expectations do not exist if the conditions for equilibrium aren’t satisfied. See Blume, Curry and Easley (2006).

The assumption, now routinely regarded as axiomatic, that rational expectations is sufficient to ensure that equilibrium is automatic achieved, and that agents’ price expectations necessarily correspond to equilibrium price expectations is a form of question begging disguised as a methodological imperative that requires all macroeconomic models to be properly microfounded. The newly published volume edited by Arnon, Young and van der Beek Expectations: Theory and Applications from Historical Perspectives contains a wonderful essay by Duncan Foley that elucidates these issues.

In his centenary retrospective on Menger’s contribution, Hayek (1970), commenting on the inexactness of Menger’s account of economic theory, focused on Menger’s reluctance to embrace mathematics as an expository medium with which to articulate economic-theoretical concepts. While this may have been an aspect of Menger’s skepticism about mathematical reasoning, his recognition that expectations of the future are inherently inexact and conjectural and more akin to a range of potential outcomes of different probability may have been an even more significant factor in how Menger chose to articulate his theoretical vision.

But it is noteworthy that Hayek (1937) explicitly recognized that there is no theoretical explanation that accounts for any tendency toward intertemporal equilibrium, and instead merely (and in 1937!) relied an empirical tendency of economies to move in the direction of equilibrium as a justification for considering economic theory to have any practical relevance.

An Austrian Tragedy

Published May 24, 2020 Alfred Marshall , Carl Menger , E. v. Bohm-Bawerk , expectations , general equilibrium , Great Depression , Hayek , Irving Fisher , IS-LM , Israel Kirzner , Joseph Schumpeter , Keynes , Leon Walras , Ludwig Lachmann , Ludwig von Mises , macroeconomics , neoclassical synthesis , New Classical macroeconomics , New Keynesians , Old Keynesians , Oskar Morgensterm , rational expectations , rational expectations equilibrium , representative agent , Walrasian equilibrium 32 Comments
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It was hardly predictable that the New York Review of Books would take notice of Marginal Revolutionaries by Janek Wasserman, marking the susquicentenial of the publication of Carl Menger’s Grundsätze (Principles of Economics) which, along with Jevons’s Principles of Political Economy and Walras’s Elements of Pure Economics ushered in the marginal revolution upon which all of modern economics, for better or for worse, is based. The differences among the three founding fathers of modern economic theory were not insubstantial, and the Jevonian version was largely superseded by the work of his younger contemporary Alfred Marshall, so that modern neoclassical economics is built on the work of only one of the original founders, Leon Walras, Jevons’s work having left little impression on the future course of economics.

Menger’s work, however, though largely, but not totally, eclipsed by that of Marshall and Walras, did leave a more enduring imprint and a more complicated legacy than Jevons’s — not only for economics, but for political theory and philosophy, more generally. Judging from Edward Chancellor’s largely favorable review of Wasserman’s volume, one might even hope that a start might be made in reassessing that legacy, a process that could provide an opportunity for mutually beneficial interaction between long-estranged schools of thought — one dominant and one marginal — that are struggling to overcome various conceptual, analytical and philosophical problems for which no obvious solutions seem available.

In view of the failure of modern economists to anticipate the Great Recession of 2008, the worst financial shock since the 1930s, it was perhaps inevitable that the Austrian School, a once favored branch of economics that had made a specialty of booms and busts, would enjoy a revival of public interest.

The theme of Austrians as outsiders runs through Janek Wasserman’s The Marginal Revolutionaries: How Austrian Economists Fought the War of Ideas, a general history of the Austrian School from its beginnings to the present day. The title refers both to the later marginalization of the Austrian economists and to the original insight of its founding father, Carl Menger, who introduced the notion of marginal utility—namely, that economic value does not derive from the cost of inputs such as raw material or labor, as David Ricardo and later Karl Marx suggested, but from the utility an individual derives from consuming an additional amount of any good or service. Water, for instance, may be indispensable to humans, but when it is abundant, the marginal value of an extra glass of the stuff is close to zero. Diamonds are less useful than water, but a great deal rarer, and hence command a high market price. If diamonds were as common as dewdrops, however, they would be worthless.

Menger was not the first economist to ponder . . . the “paradox of value” (why useless things are worth more than essentials)—the Italian Ferdinando Galiani had gotten there more than a century earlier. His central idea of marginal utility was simultaneously developed in England by W. S. Jevons and on the Continent by Léon Walras. Menger’s originality lay in applying his theory to the entire production process, showing how the value of capital goods like factory equipment derived from the marginal value of the goods they produced. As a result, Austrian economics developed a keen interest in the allocation of capital. Furthermore, Menger and his disciples emphasized that value was inherently subjective, since it depends on what consumers are willing to pay for something; this imbued the Austrian school from the outset with a fiercely individualistic and anti-statist aspect.

Menger’s unique contribution is indeed worthy of special emphasis. He was more explicit than Jevons or Walras, and certainly more than Marshall, in explaining that the value of factors of production is derived entirely from the value of the incremental output that could be attributed (or imputed) to their services. This insight implies that cost is not an independent determinant of value, as Marshall, despite accepting the principle of marginal utility, continued to insist – famously referring to demand and supply as the two blades of the analytical scissors that determine value. The cost of production therefore turns out to be nothing but the value the output foregone when factors are used to produce one output instead of the next most highly valued alternative. Cost therefore does not determine, but is determined by, equilibrium price, which means that, in practice, costs are always subjective and conjectural. (I have made this point in an earlier post in a different context.) I will have more to say below about the importance of Menger’s specific contribution and its lasting imprint on the Austrian school.

Menger’s Principles of Economics, published in 1871, established the study of economics in Vienna—before then, no economic journals were published in Austria, and courses in economics were taught in law schools. . . .

The Austrian School was also bound together through family and social ties: [his two leading disciples, [Eugen von] Böhm-Bawerk and Friedrich von Wieser [were brothers-in-law]. [Wieser was] a close friend of the statistician Franz von Juraschek, Friedrich Hayek’s maternal grandfather. Young Austrian economists bonded on Alpine excursions and met in Böhm-Bawerk’s famous seminars (also attended by the Bolshevik Nikolai Bukharin and the German Marxist Rudolf Hilferding). Ludwig von Mises continued this tradition, holding private seminars in Vienna in the 1920s and later in New York. As Wasserman notes, the Austrian School was “a social network first and last.”

After World War I, the Habsburg Empire was dismantled by the victorious Allies. The Austrian bureaucracy shrank, and university placements became scarce. Menger, the last surviving member of the first generation of Austrian economists, died in 1921. The economic school he founded, with its emphasis on individualism and free markets, might have disappeared under the socialism of “Red Vienna.” Instead, a new generation of brilliant young economists emerged: Schumpeter, Hayek, and Mises—all of whom published best-selling works in English and remain familiar names today—along with a number of less well known but influential economists, including Oskar Morgenstern, Fritz Machlup, Alexander Gerschenkron, and Gottfried Haberler.

Two factual corrections are in order. Menger outlived Böhm-Bawerk, but not his other chief disciple von Wieser, who died in 1926, not long after supervising Hayek’s doctoral dissertation, later published in 1927, and, in 1933, translated into English and published as Monetary Theory and the Trade Cycle. Moreover, a 16-year gap separated Mises and Schumpeter, who were exact contemporaries, from Hayek (born in 1899) who was a few years older than Gerschenkron, Haberler, Machlup and Morgenstern.

All the surviving members or associates of the Austrian school wound up either in the US or Britain after World War II, and Hayek, who had taken a position in London in 1931, moved to the US in 1950, taking a position in the Committee on Social Thought at the University of Chicago after having been refused a position in the economics department. Through the intervention of wealthy sponsors, Mises obtained an academic appointment of sorts at the NYU economics department, where he succeeded in training two noteworthy disciples who wrote dissertations under his tutelage, Murray Rothbard and Israel Kirzner. (Kirzner wrote his dissertation under Mises at NYU, but Rothbard did his graduate work at Colulmbia.) Schumpeter, Haberler and Gerschenkron eventually took positions at Harvard, while Machlup (with some stops along the way) and Morgenstern made their way to Princeton. However, Hayek’s interests shifted from pure economic theory to deep philosophical questions. While Machlup and Haberler continued to work on economic theory, the Austrian influence on their work after World War II was barely recognizable. Morgenstern and Schumpeter made major contributions to economics, but did not hide their alienation from the doctrines of the Austrian School.

So there was little reason to expect that the Austrian School would survive its dispersal when the Nazis marched unopposed into Vienna in 1938. That it did survive is in no small measure due to its ideological usefulness to anti-socialist supporters who provided financial support to Hayek, enabling his appointment to the Committee on Social Thought at the University of Chicago, and Mises’s appointment at NYU, and other forms of research support to Hayek, Mises and other like-minded scholars, as well as funding the Mont Pelerin Society, an early venture in globalist networking, started by Hayek in 1947. Such support does not discredit the research to which it gave rise. That the survival of the Austrian School would probably not have been possible without the support of wealthy benefactors who anticipated that the Austrians would advance their political and economic interests does not invalidate the research thereby enabled. (In the interest of transparency, I acknowledge that I received support from such sources for two books that I wrote.)

Because Austrian School survivors other than Mises and Hayek either adapted themselves to mainstream thinking without renouncing their earlier beliefs (Haberler and Machlup) or took an entirely different direction (Morgenstern), and because the economic mainstream shifted in two directions that were most uncongenial to the Austrians: Walrasian general-equilibrium theory and Keynesian macroeconomics, the Austrian remnant, initially centered on Mises at NYU, adopted a sharply adversarial attitude toward mainstream economic doctrines.

Despite its minute numbers, the lonely remnant became a house divided against itself, Mises’s two outstanding NYU disciples, Murray Rothbard and Israel Kirzner, holding radically different conceptions of how to carry on the Austrian tradition. An extroverted radical activist, Rothbard was not content just to lead a school of economic thought, he aspired to become the leader of a fantastical anarchistic revolutionary movement to replace all established governments under a reign of private-enterprise anarcho-capitalism. Rothbard’s political radicalism, which, despite his Jewish ancestry, even included dabbling in Holocaust denialism, so alienated his mentor, that Mises terminated all contact with Rothbard for many years before his death. Kirzner, self-effacing, personally conservative, with no political or personal agenda other than the advancement of his own and his students’ scholarship, published hundreds of articles and several books filling 10 thick volumes of his collected works published by the Liberty Fund, while establishing a robust Austrian program at NYU, training many excellent scholars who found positions in respected academic and research institutions. Similar Austrian programs, established under the guidance of Kirzner’s students, were started at other institutions, most notably at George Mason University.

One of the founders of the Cato Institute, which for nearly half a century has been the leading avowedly libertarian think tank in the US, Rothbard was eventually ousted by Cato, and proceeded to set up a rival think tank, the Ludwig von Mises Institute, at Auburn University, which has turned into a focal point for extreme libertarians and white nationalists to congregate, get acquainted, and strategize together.

Isolation and marginalization tend to cause a subspecies either to degenerate toward extinction, to somehow blend in with the members of the larger species, thereby losing its distinctive characteristics, or to accentuate its unique traits, enabling it to find some niche within which to survive as a distinct sub-species. Insofar as they have engaged in economic analysis rather than in various forms of political agitation and propaganda, the Rothbardian Austrians have focused on anarcho-capitalist theory and the uniquely perverse evils of fractional-reserve banking.

Rejecting the political extremism of the Rothbardians, Kirznerian Austrians differentiate themselves by analyzing what they call market processes and emphasizing the limitations on the knowledge and information possessed by actual decision-makers. They attribute this misplaced focus on equilibrium to the extravagantly unrealistic and patently false assumptions of mainstream models on the knowledge possessed by economic agents, which effectively make equilibrium the inevitable — and trivial — conclusion entailed by those extreme assumptions. In their view, the focus of mainstream models on equilibrium states with unrealistic assumptions results from a preoccupation with mathematical formalism in which mathematical tractability rather than sound economics dictates the choice of modeling assumptions.

Skepticism of the extreme assumptions about the informational endowments of agents covers a range of now routine assumptions in mainstream models, e.g., the ability of agents to form precise mathematical estimates of the probability distributions of future states of the world, implying that agents never confront decisions about which they are genuinely uncertain. Austrians also object to the routine assumption that all the information needed to determine the solution of a model is the common knowledge of the agents in the model, so that an existing equilibrium cannot be disrupted unless new information randomly and unpredictably arrives. Each agent in the model having been endowed with the capacity of a semi-omniscient central planner, solving the model for its equilibrium state becomes a trivial exercise in which the optimal choices of a single agent are taken as representative of the choices made by all of the model’s other, semi-omnicient, agents.

Although shreds of subjectivism — i.e., agents make choices based own preference orderings — are shared by all neoclassical economists, Austrian criticisms of mainstream neoclassical models are aimed at what Austrians consider to be their insufficient subjectivism. It is this fierce commitment to a robust conception of subjectivism, in which an equilibrium state of shared expectations by economic agents must be explained, not just assumed, that Chancellor properly identifies as a distinguishing feature of the Austrian School.

Menger’s original idea of marginal utility was posited on the subjective preferences of consumers. This subjectivist position was retained by subsequent generations of the school. It inspired a tradition of radical individualism, which in time made the Austrians the favorite economists of American libertarians. Subjectivism was at the heart of the Austrians’ polemical rejection of Marxism. Not only did they dismiss Marx’s labor theory of value, they argued that socialism couldn’t possibly work since it would lack the means to allocate resources efficiently.

The problem with central planning, according to Hayek, is that so much of the knowledge that people act upon is specific knowledge that individuals acquire in the course of their daily activities and life experience, knowledge that is often difficult to articulate – mere intuition and guesswork, yet more reliable than not when acted upon by people whose livelihoods depend on being able to do the right thing at the right time – much less communicate to a central planner.

Chancellor attributes Austrian mistrust of statistical aggregates or indices, like GDP and price levels, to Austrian subjectivism, which regards such magnitudes as abstractions irrelevant to the decisions of private decision-makers, except perhaps in forming expectations about the actions of government policy makers. (Of course, this exception potentially provides full subjectivist license and legitimacy for macroeconomic theorizing despite Austrian misgivings.) Observed statistical correlations between aggregate variables identified by macroeconomists are dismissed as irrelevant unless grounded in, and implied by, the purposeful choices of economic agents.

But such scruples about the use of macroeconomic aggregates and inferring causal relationships from observed correlations are hardly unique to the Austrian school. One of the most important contributions of the 20th century to the methodology of economics was an article by T. C. Koopmans, “Measurement Without Theory,” which argued that measured correlations between macroeconomic variables provide a reliable basis for business-cycle research and policy advice only if the correlations can be explained in terms of deeper theoretical or structural relationships. The Nobel Prize Committee, in awarding the 1975 Prize to Koopmans, specifically mentioned this paper in describing Koopmans’s contributions. Austrians may be more fastidious than their mainstream counterparts in rejecting macroeconomic relationships not based on microeconomic principles, but they aren’t the only ones mistrustful of mere correlations.

Chancellor cites mistrust about the use of statistical aggregates and price indices as a factor in Hayek’s disastrous policy advice warning against anti-deflationary or reflationary measures during the Great Depression.

Their distrust of price indexes brought Austrian economists into conflict with mainstream economic opinion during the 1920s. At the time, there was a general consensus among leading economists, ranging from Irving Fisher at Yale to Keynes at Cambridge, that monetary policy should aim at delivering a stable price level, and in particular seek to prevent any decline in prices (deflation). Hayek, who earlier in the decade had spent time at New York University studying monetary policy and in 1927 became the first director of the Austrian Institute for Business Cycle Research, argued that the policy of price stabilization was misguided. It was only natural, Hayek wrote, that improvements in productivity should lead to lower prices and that any resistance to this movement (sometimes described as “good deflation”) would have damaging economic consequences.

The argument that deflation stemming from economic expansion and increasing productivity is normal and desirable isn’t what led Hayek and the Austrians astray in the Great Depression; it was their failure to realize the deflation that triggered the Great Depression was a monetary phenomenon caused by a malfunctioning international gold standard. Moreover, Hayek’s own business-cycle theory explicitly stated that a neutral (stable) monetary policy ought to aim at keeping the flow of total spending and income constant in nominal terms while his policy advice of welcoming deflation meant a rapidly falling rate of total spending. Hayek’s policy advice was an inexcusable error of judgment, which, to his credit, he did acknowledge after the fact, though many, perhaps most, Austrians have refused to follow him even that far.

Considered from the vantage point of almost a century, the collapse of the Austrian School seems to have been inevitable. Hayek’s long-shot bid to establish his business-cycle theory as the dominant explanation of the Great Depression was doomed from the start by the inadequacies of the very specific version of his basic model and his disregard of the obvious implication of that model: prevent total spending from contracting. The promising young students and colleagues who had briefly gathered round him upon his arrival in England, mostly attached themselves to other mentors, leaving Hayek with only one or two immediate disciples to carry on his research program. The collapse of his research program, which he himself abandoned after completing his final work in economic theory, marked a research hiatus of almost a quarter century, with the notable exception of publications by his student, Ludwig Lachmann who, having decamped in far-away South Africa, labored in relative obscurity for most of his career.

The early clash between Keynes and Hayek, so important in the eyes of Chancellor and others, is actually overrated. Chancellor, quoting Lachmann and Nicholas Wapshott, describes it as a clash of two irreconcilable views of the economic world, and the clash that defined modern economics. In later years, Lachmann actually sought to effect a kind of reconciliation between their views. It was not a conflict of visions that undid Hayek in 1931-32, it was his misapplication of a narrowly constructed model to a problem for which it was irrelevant.

Although the marginalization of the Austrian School, after its misguided policy advice in the Great Depression and its dispersal during and after World War II, is hardly surprising, the unwillingness of mainstream economists to sort out what was useful and relevant in the teachings of the Austrian School from what is not was unfortunate not only for the Austrians. Modern economics was itself impoverished by its disregard for the complexity and interconnectedness of economic phenomena. It’s precisely the Austrian attentiveness to the complexity of economic activity — the necessity for complementary goods and factors of production to be deployed over time to satisfy individual wants – that is missing from standard economic models.

That Austrian attentiveness, pioneered by Menger himself, to the complementarity of inputs applied over the course of time undoubtedly informed Hayek’s seminal contribution to economic thought: his articulation of the idea of intertemporal equilibrium that comprehends the interdependence of the plans of independent agents and the need for them to all fit together over the course of time for equilibrium to obtain. Hayek’s articulation represented a conceptual advance over earlier versions of equilibrium analysis stemming from Walras and Pareto, and even from Irving Fisher who did pay explicit attention to intertemporal equilibrium. But in Fisher’s articulation, intertemporal consistency was described in terms of aggregate production and income, leaving unexplained the mechanisms whereby the individual plans to produce and consume particular goods over time are reconciled. Hayek’s granular exposition enabled him to attend to, and articulate, necessary but previously unspecified relationships between the current prices and expected future prices.

Moreover, neither mainstream nor Austrian economists have ever explained how prices are adjust in non-equilibrium settings. The focus of mainstream analysis has always been the determination of equilibrium prices, with the implicit understanding that “market forces” move the price toward its equilibrium value. The explanatory gap has been filled by the mainstream New Classical School which simply posits the existence of an equilibrium price vector, and, to replace an empirically untenable tâtonnement process for determining prices, posits an equally untenable rational-expectations postulate to assert that market economies typically perform as if they are in, or near the neighborhood of, equilibrium, so that apparent fluctuations in real output are viewed as optimal adjustments to unexplained random productivity shocks.

Alternatively, in New Keynesian mainstream versions, constraints on price changes prevent immediate adjustments to rationally expected equilibrium prices, leading instead to persistent reductions in output and employment following demand or supply shocks. (I note parenthetically that the assumption of rational expectations is not, as often suggested, an assumption distinct from market-clearing, because the rational expectation of all agents of a market-clearing price vector necessarily implies that the markets clear unless one posits a constraint, e.g., a binding price floor or ceiling, that prevents all mutually beneficial trades from being executed.)

Similarly, the Austrian school offers no explanation of how unconstrained price adjustments by market participants is a sufficient basis for a systemic tendency toward equilibrium. Without such an explanation, their belief that market economies have strong self-correcting properties is unfounded, because, as Hayek demonstrated in his 1937 paper, “Economics and Knowledge,” price adjustments in current markets don’t, by themselves, ensure a systemic tendency toward equilibrium values that coordinate the plans of independent economic agents unless agents’ expectations of future prices are sufficiently coincident. To take only one passage of many discussing the difficulty of explaining or accounting for a process that leads individuals toward a state of equilibrium, I offer the following as an example:

All that this condition amounts to, then, is that there must be some discernible regularity in the world which makes it possible to predict events correctly. But, while this is clearly not sufficient to prove that people will learn to foresee events correctly, the same is true to a hardly less degree even about constancy of data in an absolute sense. For any one individual, constancy of the data does in no way mean constancy of all the facts independent of himself, since, of course, only the tastes and not the actions of the other people can in this sense be assumed to be constant. As all those other people will change their decisions as they gain experience about the external facts and about other people’s actions, there is no reason why these processes of successive changes should ever come to an end. These difficulties are well known, and I mention them here only to remind you how little we actually know about the conditions under which an equilibrium will ever be reached.

In this theoretical muddle, Keynesian economics and the neoclassical synthesis were abandoned, because the key proposition of Keynesian economics was supposedly the tendency of a modern economy toward an equilibrium with involuntary unemployment while the neoclassical synthesis rejected that proposition, so that the supposed synthesis was no more than an agreement to disagree. That divided house could not stand. The inability of Keynesian economists such as Hicks, Modigliani, Samuelson and Patinkin to find a satisfactory (at least in terms of a preferred Walrasian general-equilibrium model) rationalization for Keynes’s conclusion that an economy would likely become stuck in an equilibrium with involuntary unemployment led to the breakdown of the neoclassical synthesis and the displacement of Keynesianism as the dominant macroeconomic paradigm.

But perhaps the way out of the muddle is to abandon the idea that a systemic tendency toward equilibrium is a property of an economic system, and, instead, to recognize that equilibrium is, as Hayek suggested, a contingent, not a necessary, property of a complex economy. Ludwig Lachmann, cited by Chancellor for his remark that the early theoretical clash between Hayek and Keynes was a conflict of visions, eventually realized that in an important sense both Hayek and Keynes shared a similar subjectivist conception of the crucial role of individual expectations of the future in explaining the stability or instability of market economies. And despite the efforts of New Classical economists to establish rational expectations as an axiomatic equilibrating property of market economies, that notion rests on nothing more than arbitrary methodological fiat.

Chancellor concludes by suggesting that Wasserman’s characterization of the Austrians as marginalized is not entirely accurate inasmuch as “the Austrians’ view of the economy as a complex, evolving system continues to inspire new research.” Indeed, if economics is ever to find a way out of its current state of confusion, following Lachmann in his quest for a synthesis of sorts between Keynes and Hayek might just be a good place to start from.

Filling the Arrow Explanatory Gap

Published April 24, 2020 Arrow-Debrew-McKenzie model , comparative statics , expectations , general equilibrium , incomplete markets , intertemporal equilibrium , Kenneth Arrow , Keynes , macroeconomics , microfoundations , New Classical macroeconomics , New Keynesians , partial equilibrium , rational expectations , rational expectations equilibrium , Roy Radner , Samuelson , Sonnenschein-Mantel-Debreu theorem , temporary equilibrium , Walrasian equilibrium 42 Comments

The following (with some minor revisions) is a Twitter thread I posted yesterday. Unfortunately, because it was my first attempt at threading the thread wound up being split into three sub-threads and rather than try to reconnect them all, I will just post the complete thread here as a blogpost.

1. Here’s an outline of an unwritten paper developing some ideas from my paper “Hayek Hicks Radner and Four Equilibrium Concepts” (see here for an earlier ungated version) and some from previous blog posts, in particular Phillips Curve Musings. 

2. Standard supply-demand analysis is a form of partial-equilibrium (PE) analysis, which means that it is contingent on a ceteris paribus (CP) assumption, an assumption largely incompatible with realistic dynamic macroeconomic analysis.

3. Macroeconomic analysis is necessarily situated a in general-equilibrium (GE) context that precludes any CP assumption, because there are no variables that are held constant in GE analysis.

4. In the General Theory, Keynes criticized the argument based on supply-demand analysis that cutting nominal wages would cure unemployment. Instead, despite his Marshallian training (upbringing) in PE analysis, Keynes argued that PE (AKA supply-demand) analysis is unsuited for understanding the problem of aggregate (involuntary) unemployment.

5. The comparative-statics method described by Samuelson in the Foundations of Econ Analysis formalized PE analysis under the maintained assumption that a unique GE obtains and deriving a “meaningful theorem” from the 1st- and 2nd-order conditions for a local optimum.

6. PE analysis, as formalized by Samuelson, is conditioned on the assumption that GE obtains. It is focused on the effect of changing a single parameter in a single market small enough for the effects on other markets of the parameter change to be made negligible.

7. Thus, PE analysis, the essence of micro-economics is predicated on the macrofoundation that all, but one, markets are in equilibrium.

8. Samuelson’s meaningful theorems were a misnomer reflecting mid-20th-century operationalism. They can now be understood as empirically refutable propositions implied by theorems augmented with a CP assumption that interactions b/w markets are small enough to be neglected.

9. If a PE model is appropriately specified, and if the market under consideration is small or only minimally related to other markets, then differences between predictions and observations will be statistically insignificant.

10. So PE analysis uses comparative-statics to compare two alternative general equilibria that differ only in respect of a small parameter change.

11. The difference allows an inference about the causal effect of a small change in that parameter, but says nothing about how an economy would actually adjust to a parameter change.

12. PE analysis is conditioned on the CP assumption that the analyzed market and the parameter change are small enough to allow any interaction between the parameter change and markets other than the market under consideration to be disregarded.

13. However, the process whereby one equilibrium transitions to another is left undetermined; the difference between the two equilibria with and without the parameter change is computed but no account of an adjustment process leading from one equilibrium to the other is provided.

14. Hence, the term “comparative statics.”

15. The only suggestion of an adjustment process is an assumption that the price-adjustment in any market is an increasing function of excess demand in the market.

16. In his seminal account of GE, Walras posited the device of an auctioneer who announces prices–one for each market–computes desired purchases and sales at those prices, and sets, under an adjustment algorithm, new prices at which desired purchases and sales are recomputed.

17. The process continues until a set of equilibrium prices is found at which excess demands in all markets are zero. In Walras’s heuristic account of what he called the tatonnement process, trading is allowed only after the equilibrium price vector is found by the auctioneer.

18. Walras and his successors assumed, but did not prove, that, if an equilibrium price vector exists, the tatonnement process would eventually, through trial and error, converge on that price vector.

19. However, contributions by Sonnenschein, Mantel and Debreu (hereinafter referred to as the SMD Theorem) show that no price-adjustment rule necessarily converges on a unique equilibrium price vector even if one exists.

20. The possibility that there are multiple equilibria with distinct equilibrium price vectors may or may not be worth explicit attention, but for purposes of this discussion, I confine myself to the case in which a unique equilibrium exists.

21. The SMD Theorem underscores the lack of any explanatory account of a mechanism whereby changes in market prices, responding to excess demands or supplies, guide a decentralized system of competitive markets toward an equilibrium state, even if a unique equilibrium exists.

22. The Walrasian tatonnement process has been replaced by the Arrow-Debreu-McKenzie (ADM) model in an economy of infinite duration consisting of an infinite number of generations of agents with given resources and technology.

23. The equilibrium of the model involves all agents populating the economy over all time periods meeting before trading starts, and, based on initial endowments and common knowledge, making plans given an announced equilibrium price vector for all time in all markets.

24. Uncertainty is accommodated by the mechanism of contingent trading in alternative states of the world. Given assumptions about technology and preferences, the ADM equilibrium determines the set prices for all contingent states of the world in all time periods.

25. Given equilibrium prices, all agents enter into optimal transactions in advance, conditioned on those prices. Time unfolds according to the equilibrium set of plans and associated transactions agreed upon at the outset and executed without fail over the course of time.

26. At the ADM equilibrium price vector all agents can execute their chosen optimal transactions at those prices in all markets (certain or contingent) in all time periods. In other words, at that price vector, excess demands in all markets with positive prices are zero.

27. The ADM model makes no pretense of identifying a process that discovers the equilibrium price vector. All that can be said about that price vector is that if it exists and trading occurs at equilibrium prices, then excess demands will be zero if prices are positive.

28. Arrow himself drew attention to the gap in the ADM model, writing in 1959:

29. In addition to the explanatory gap identified by Arrow, another shortcoming of the ADM model was discussed by Radner: the dependence of the ADM model on a complete set of forward and state-contingent markets at time zero when equilibrium prices are determined.

30. Not only is the complete-market assumption a backdoor reintroduction of perfect foresight, it excludes many features of the greatest interest in modern market economies: the existence of money, stock markets, and money-crating commercial banks.

31. Radner showed that for full equilibrium to obtain, not only must excess demands in current markets be zero, but whenever current markets and current prices for future delivery are missing, agents must correctly expect those future prices.

32. But there is no plausible account of an equilibrating mechanism whereby price expectations become consistent with GE. Although PE analysis suggests that price adjustments do clear markets, no analogous analysis explains how future price expectations are equilibrated.

33. But if both price expectations and actual prices must be equilibrated for GE to obtain, the notion that “market-clearing” price adjustments are sufficient to achieve macroeconomic “equilibrium” is untenable.

34. Nevertheless, the idea that individual price expectations are rational (correct), so that, except for random shocks, continuous equilibrium is maintained, became the bedrock for New Classical macroeconomics and its New Keynesian and real-business cycle offshoots.

35. Macroeconomic theory has become a theory of dynamic intertemporal optimization subject to stochastic disturbances and market frictions that prevent or delay optimal adjustment to the disturbances, potentially allowing scope for countercyclical monetary or fiscal policies.

36. Given incomplete markets, the assumption of nearly continuous intertemporal equilibrium implies that agents correctly foresee future prices except when random shocks occur, whereupon agents revise expectations in line with the new information communicated by the shocks.
37. Modern macroeconomics replaced the Walrasian auctioneer with agents able to forecast the time path of all prices indefinitely into the future, except for intermittent unforeseen shocks that require agents to optimally their revise previous forecasts.
38. When new information or random events, requiring revision of previous expectations, occur, the new information becomes common knowledge and is processed and interpreted in the same way by all agents. Agents with rational expectations always share the same expectations.
39. So in modern macro, Arrow’s explanatory gap is filled by assuming that all agents, given their common knowledge, correctly anticipate current and future equilibrium prices subject to unpredictable forecast errors that change their expectations of future prices to change.
40. Equilibrium prices aren’t determined by an economic process or idealized market interactions of Walrasian tatonnement. Equilibrium prices are anticipated by agents, except after random changes in common knowledge. Semi-omniscient agents replace the Walrasian auctioneer.
41. Modern macro assumes that agents’ common knowledge enables them to form expectations that, until superseded by new knowledge, will be validated. The assumption is wrong, and the mistake is deeper than just the unrealism of perfect competition singled out by Arrow.
42. Assuming perfect competition, like assuming zero friction in physics, may be a reasonable simplification for some problems in economics, because the simplification renders an otherwise intractable problem tractable.
43. But to assume that agents’ common knowledge enables them to forecast future prices correctly transforms a model of decentralized decision-making into a model of central planning with each agent possessing the knowledge only possessed by an omniscient central planner.
44. The rational-expectations assumption fills Arrow’s explanatory gap, but in a deeply unsatisfactory way. A better approach to filling the gap would be to acknowledge that agents have private knowledge (and theories) that they rely on in forming their expectations.
45. Agents’ expectations are – at least potentially, if not inevitably – inconsistent. Because expectations differ, it’s the expectations of market specialists, who are better-informed than non-specialists, that determine the prices at which most transactions occur.
46. Because price expectations differ even among specialists, prices, even in competitive markets, need not be uniform, so that observed price differences reflect expectational differences among specialists.
47. When market specialists have similar expectations about future prices, current prices will converge on the common expectation, with arbitrage tending to force transactions prices to converge toward notwithstanding the existence of expectational differences.
48. However, the knowledge advantage of market specialists over non-specialists is largely limited to their knowledge of the workings of, at most, a small number of related markets.
49. The perspective of specialists whose expectations govern the actual transactions prices in most markets is almost always a PE perspective from which potentially relevant developments in other markets and in macroeconomic conditions are largely excluded.
50. The interrelationships between markets that, according to the SMD theorem, preclude any price-adjustment algorithm, from converging on the equilibrium price vector may also preclude market specialists from converging, even roughly, on the equilibrium price vector.
51. A strict equilibrium approach to business cycles, either real-business cycle or New Keynesian, requires outlandish assumptions about agents’ common knowledge and their capacity to anticipate the future prices upon which optimal production and consumption plans are based.
52. It is hard to imagine how, without those outlandish assumptions, the theoretical superstructure of real-business cycle theory, New Keynesian theory, or any other version of New Classical economics founded on the rational-expectations postulate can be salvaged.
53. The dominance of an untenable macroeconomic paradigm has tragically led modern macroeconomics into a theoretical dead end.

On Equilibrium in Economic Theory

Published April 18, 2018 Arrow-Debrew-McKenzie model , Hayek , intertemporal equilibrium , J. R. Hicks , Radner model , rational expectations equilibrium , Roy Radner , temporary equilibrium 9 Comments
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Here is the introduction to a new version of my paper, “Hayek and Three Concepts of Intertemporal Equilibrium” which I presented last June at the History of Economics Society meeting in Toronto, and which I presented piecemeal in a series of posts last May and June. This post corresponds to the first part of this post from last May 21.

Equilibrium is an essential concept in economics. While equilibrium is an essential concept in other sciences as well, and was probably imported into economics from physics, its meaning in economics cannot be straightforwardly transferred from physics into economics. The dissonance between the physical meaning of equilibrium and its economic interpretation required a lengthy process of explication and clarification, before the concept and its essential, though limited, role in economic theory could be coherently explained.

The concept of equilibrium having originally been imported from physics at some point in the nineteenth century, economists probably thought it natural to think of an economic system in equilibrium as analogous to a physical system at rest, in the sense of a system in which there was no movement or in the sense of all movements being repetitive. But what would it mean for an economic system to be at rest? The obvious answer was to say that prices of goods and the quantities produced, exchanged and consumed would not change. If supply equals demand in every market, and if there no exogenous disturbance displaces the system, e.g., in population, technology, tastes, etc., then there would seem to be no reason for the prices paid and quantities produced to change in that system. But that conception of an economic system at rest was understood to be overly restrictive, given the large, and perhaps causally important, share of economic activity – savings and investment – that is predicated on the assumption and expectation that prices and quantities not remain constant.

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 to economists, but that view of equilibrium remained dominant in the nineteenth century and for perhaps the first quarter of the twentieth. Equilibrium was not an actual state that an economy could achieve, it was just an end state that economic processes would move toward if given sufficient time to play themselves out with no disturbing influences. This idea of a stationary timeless equilibrium is found in the writings of the classical economists, especially Ricardo and Mill who used the idea of a stationary state as the end-state towards which natural economic processes were driving an an economic system.

This, not very satisfactory, concept of equilibrium was undermined when Jevons, Menger, Walras, and their followers began to develop the idea of optimizing decisions by rational consumers and producers. The notion of optimality provided the key insight that made it possible to refashion the earlier classical equilibrium concept into a new, more fruitful and robust, version.

If each economic agent (household or business firm) is viewed as making optimal choices, based on some scale of preferences, and subject to limitations or constraints imposed by their capacities, endowments, technologies, and the legal system, then the equilibrium of an economy can be understood as a state in which each agent, given his subjective ranking of the feasible alternatives, is making an optimal decision, and each optimal decision is both consistent with, and contingent upon, those of all other agents. The optimal decisions of each agent must simultaneously be optimal from the point of view of that agent while 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. But every decision, just like every piece in a jig-saw puzzle, must fit perfectly with every other decision. If any decision is suboptimal, none of the other decisions contingent upon that decision can be optimal.

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 only be coherently articulated on the basis of a notion of optimality. Originally framed in terms of utility maximization, the notion was gradually extended to encompass the ideas of cost minimization and profit maximization. The general concept of an optimal plan having been grasped, it then became possible to formulate a generically economic idea of equilibrium, not in terms of a system at rest, but in terms of the mutual consistency of optimal plans. Once equilibrium was conceived as the mutual consistency of optimal plans, the needlessly restrictiveness of defining equilibrium as a system at rest became readily apparent, though it remained little noticed and its significance overlooked for quite some time.

Because the defining characteristics of economic equilibrium are optimality and mutual consistency, change, even non-repetitive change, is not logically excluded from the concept of equilibrium as it was from the idea of an equilibrium as a stationary state. An optimal plan may be carried out, not just at a single moment, but over a period of time. Indeed, the idea of an optimal plan is, at the very least, suggestive of a future that need not simply repeat the present. So, once the idea of equilibrium as a set of mutually consistent optimal plans was grasped, it was to be expected that the concept of equilibrium could be formulated in a manner that accommodates the existence of change and development over time.

But the manner in which change and development could be incorporated into an equilibrium framework of optimality was not entirely straightforward, and it required an extended process of further intellectual reflection to formulate the idea of equilibrium in a way that gives meaning and relevance to the processes of change and development that make the passage of time something more than merely a name assigned to one of the n dimensions in vector space.

This paper examines the slow process by which the concept of equilibrium was transformed from a timeless or static concept into an intertemporal one by focusing on the pathbreaking contribution of F. A. Hayek who first articulated the concept, and exploring the connection between his articulation and three noteworthy, but very different, versions of intertemporal equilibrium: (1) an equilibrium of plans, prices, and expectations, (2) temporary equilibrium, and (3) rational-expectations equilibrium.

But before discussing these three versions of intertemporal equilibrium, I summarize in section two Hayek’s seminal 1937 contribution clarifying the necessary conditions for the existence of an intertemporal equilibrium. Then, in section three, I elaborate on an important, and often neglected, distinction, first stated and clarified by Hayek in his 1937 paper, between perfect foresight and what I call contingently correct foresight. That distinction is essential for an understanding of the distinction between the canonical Arrow-Debreu-McKenzie (ADM) model of general equilibrium, and Roy Radner’s 1972 generalization of that model as an equilibrium of plans, prices and price expectations, which I describe in section four.

Radner’s important generalization of the ADM model captured the spirit and formalized Hayek’s insights about the nature and empirical relevance of intertemporal equilibrium. But to be able to prove the existence of an equilibrium of plans, prices and price expectations, Radner had to make assumptions about agents that Hayek, in his philosophically parsimonious view of human knowledge and reason, had been unwilling to accept. In section five, I explore how J. R. Hicks’s concept of temporary equilibrium, clearly inspired by Hayek, though credited by Hicks to Erik Lindahl, provides an important bridge connecting the pure hypothetical equilibrium of correct expectations and perfect consistency of plans with the messy real world in which expectations are inevitably disappointed and plans routinely – and sometimes radically – revised. The advantage of the temporary-equilibrium framework is to provide the conceptual tools with which to understand how financial crises can occur and how such crises can be propagated and transformed into economic depressions, thereby making possible the kind of business-cycle model that Hayek tried unsuccessfully to create. But just as Hicks unaccountably failed to credit Hayek for the insights that inspired his temporary-equilibrium approach, Hayek failed to see the potential of temporary equilibrium as a modeling strategy that combines the theoretical discipline of the equilibrium method with the reality of expectational inconsistency across individual agents.

In section six, I discuss the Lucasian idea of rational expectations in macroeconomic models, mainly to point out that, in many ways, it simply assumes away the problem of plan expectational consistency with which Hayek, Hicks and Radner and others who developed the idea of intertemporal equilibrium were so profoundly concerned.

About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey’s unduly neglected contributions to the attention of a wider audience.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

Follow me on Twitter @david_glasner

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