Archive for the 'Walrasian equilibrium' Category

A New Version of my Paper “Between Walras and Marshall: Menger’s Third Way” Is Now Available on SSRN

Published January 29, 2023 Alfred Marshall , Carl Menger , coordination failure , Franklin Fisher , general equilibrium , partial equilibrium , stability of general equilibrium , Walrasian equilibrium Leave a Comment

Last week I reposted a revised version of a blogpost from last November, which was a revised section from my paper “Between Walras and Marshall: Menger’s Third Way.” That paper was presented at a conference in September 2021 marking the 100th anniversary of Menger’s death. I have now completed my revision of the entire paper, and the new version is now posted on SSRN.

Here is the link to the new version, and here is the abstract of the paper:

Neoclassical economics is bifurcated between Marshall’s partial-equilibrium and Walras’s general-equilibrium. Neoclassical theory having failed to explain the Great Depression, Keynes proposed a theory of involuntary unemployment, later subsumed under the neoclassical synthesis of Keynesian and Walrasian theories. Lacking suitable microfoundations, that synthesis collapsed. But Walrasian theory provides no account of how equilibrium is achieved. Marshallian partial-equilibrium analysis offered a more plausible account of how general equilibrium is reached. But presuming that all markets, but the one being analyzed, are already in equilibrium, Marshallian partial equilibrium, like Walrasian general equilibrium, begs the question of how equilibrium is attained. A Mengerian approach to circumvent this conceptual impasse, relying in part on a critique of Franklin Fisher’s analysis of the stability of general equilibrium, is proposed.

Commnets, criticisms and suggestions are welcomed and encouraged.

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 Rises and Falls of Keynesianism and Monetarism

Published January 9, 2022 Alfred Marshall , Arrow-Debrew-McKenzie model , Carl Menger , common knowledge , comparative statics , Erik Lindahl , general equilibrium , Great Depression , Keynes , Leon Walras , macroeconomics , Milton Friedman , Monetarism , partial equilibrium , sticky prices , sticky wages , supply-demand analysis , tatonnement , W. S. Jevons , Walrasian equilibrium 16 Comments

The following is extracted from a paper on the history of macroeconomics that I’m now writing. I don’t know yet where or when it will be published and there may or may not be further installments, but I would be interested in any comments or suggestions that readers might have. Regular readers, if there are any, will probably recognize some familiar themes that I’ve been writing about in a number of my posts over the past several months. So despite the diminished frequency of my posting, I haven’t been entirely idle.

Recognizing the cognitive dissonance between the vision of the optimal equilibrium of a competitive market economy described by Marshallian economic theory and the massive unemployment of the Great Depression, Keynes offered an alternative, and, in his view, more general, theory, the optimal neoclassical equilibrium being a special case.[1] The explanatory barrier that Keynes struggled, not quite successfully, to overcome in the dire circumstances of the 1930s, was why market-price adjustments do not have the equilibrating tendencies attributed to them by Marshallian theory. The power of Keynes’s analysis, enhanced by his rhetorical gifts, enabled him to persuade much of the economics profession, especially many of the most gifted younger economists at the time, that he was right. But his argument, failing to expose the key weakness in the neoclassical orthodoxy, was incomplete.

The full title of Keynes’s book, The General Theory of Employment, Interest and Money identifies the key elements of his revision of neoclassical theory. First, contrary to a simplistic application of Marshallian theory, the mass unemployment of the Great Depression would not be substantially reduced by cutting wages to “clear” the labor market. The reason, according to Keynes, is that the levels of output and unemployment depend not on money wages, but on planned total spending (aggregate demand). Mass unemployment is the result of too little spending not excessive wages. Reducing wages would simply cause a corresponding decline in total spending, without increasing output or employment.

If wage cuts do not increase output and employment, the ensuing high unemployment, Keynes argued, is involuntary, not the outcome of optimizing choices made by workers and employers. Ever since, the notion that unemployment can be involuntary has remained a contested issue between Keynesians and neoclassicists, a contest requiring resolution in favor of one or the other theory or some reconciliation of the two.

Besides rejecting the neoclassical theory of employment, Keynes also famously disputed the neoclassical theory of interest by arguing that the rate of interest is not, as in the neoclassical theory, a reward for saving, but a reward for sacrificing liquidity. In Keynes’s view, rather than equilibrate savings and investment, interest equilibrates the demand to hold the money issued by the monetary authority with the amount issued by the monetary authority. Under the neoclassical theory, it is the price level that adjusts to equilibrate the demand for money with the quantity issued.

Had Keynes been more attuned to the Walrasian paradigm, he might have recast his argument that cutting wages would not eliminate unemployment by noting the inapplicability of a Marshallian supply-demand analysis of the labor market (accounting for over 50 percent of national income), because wage cuts would shift demand and supply curves in almost every other input and output market, grossly violating the ceteris-paribus assumption underlying Marshallian supply-demand paradigm. When every change in the wage shifts supply and demand curves in all markets for good and services, which in turn causes the labor-demand and labor-supply curves to shift, a supply-demand analysis of aggregate unemployment becomes a futile exercise.

Keynes’s work had two immediate effects on economics and economists. First, it immediately opened up a new field of research – macroeconomics – based on his theory that total output and employment are determined by aggregate demand. Representing only one element of Keynes’s argument, the simplified Keynesian model, on which macroeconomic theory was founded, seemed disconnected from either the Marshallian or Walrasian versions of neoclassical theory.

Second, the apparent disconnect between the simple Keynesian macro-model and neoclassical theory provoked an ongoing debate about the extent to which Keynesian theory could be deduced, or even reconciled, with the premises of neoclassical theory. Initial steps toward a reconciliation were provided when a model incorporating the quantity of money and the interest rate into the Keynesian analysis was introduced, soon becoming the canonical macroeconomic model of undergraduate and graduate textbooks.

Critics of Keynesian theory, usually those opposed to its support for deficit spending as a tool of aggregate demand management, its supposed inflationary bias, and its encouragement or toleration of government intervention in the free-market economy, tried to debunk Keynesianism by pointing out its inconsistencies with the neoclassical doctrine of a self-regulating market economy. But proponents of Keynesian precepts were also trying to reconcile Keynesian analysis with neoclassical theory. Future Nobel Prize winners like J. R. Hicks, J. E. Meade, Paul Samuelson, Franco Modigliani, James Tobin, and Lawrence Klein all derived various Keynesian propositions from neoclassical assumptions, usually by resorting to the un-Keynesian assumption of rigid or sticky prices and wages.

What both Keynesian and neoclassical economists failed to see is that, notwithstanding the optimality of an economy with equilibrium market prices, in either the Walrasian or the Marshallian versions, cannot explain either how that set of equilibrium prices is, or can be, found, or how it results automatically from the routine operation of free markets.

The assumption made implicitly by both Keynesians and neoclassicals was that, in an ideal perfectly competitive free-market economy, prices would adjust, if not instantaneously, at least eventually, to their equilibrium, market-clearing, levels so that the economy would achieve an equilibrium state. Not all Keynesians, of course, agreed that a perfectly competitive economy would reach that outcome, even in the long-run. But, according to neoclassical theory, equilibrium is the state toward which a competitive economy is drawn.

Keynesian policy could therefore be rationalized as an instrument for reversing departures from equilibrium and ensuring that such departures are relatively small and transitory. Notwithstanding Keynes’s explicit argument that wage cuts cannot eliminate involuntary unemployment, the sticky-prices-and-wages story was too convenient not to be adopted as a rationalization of Keynesian policy while also reconciling that policy with the neoclassical orthodoxy associated with the postwar ascendancy of the Walrasian paradigm.

The Walrasian ascendancy in neoclassical theory was the culmination of a silent revolution beginning in the late 1920s when the work of Walras and his successors was taken up by a younger generation of mathematically trained economists. The revolution proceeded along many fronts, of which the most important was proving the existence of a solution of the system of equations describing a general equilibrium for a competitive economy — a proof that Walras himself had not provided. The sophisticated mathematics used to describe the relevant general-equilibrium models and derive mathematically rigorous proofs encouraged the process of rapid development, adoption and application of mathematical techniques by subsequent generations of economists.

Despite the early success of the Walrasian paradigm, Kenneth Arrow, perhaps the most important Walrasian theorist of the second half of the twentieth century, drew attention to the explanatory gap within the paradigm: how the adjustment of disequilibrium prices is possible in a model of perfect competition in which every transactor takes market price as given. The Walrasian theory shows that a competitive equilibrium ensuring the consistency of agents’ plans to buy and sell results from an equilibrium set of prices for all goods and services. But the theory is silent about how those equilibrium prices are found and communicated to the agents of the model, the Walrasian tâtonnement process being an empirically empty heuristic artifact.

In fact, the explanatory gap identified by Arrow was even wider than he had suggested or realized, for another aspect of the Walrasian revolution of the late 1920s and 1930s was the extension of the equilibrium concept from a single-period equilibrium to an intertemporal equilibrium. Although earlier works by Irving Fisher and Frank Knight laid a foundation for this extension, the explicit articulation of intertemporal-equilibrium analysis was the nearly simultaneous contribution of three young economists, two Swedes (Myrdal and Lindahl) and an Austrian (Hayek) whose significance, despite being partially incorporated into the canonical Arrow-Debreu-McKenzie version of the Walrasian model, remains insufficiently recognized.

These three economists transformed the concept of equilibrium from an unchanging static economic system at rest to a dynamic system changing from period to period. While Walras and Marshall had conceived of a single-period equilibrium with no tendency to change barring an exogenous change in underlying conditions, Myrdal, Lindahl and Hayek conceived of an equilibrium unfolding through time, defined by the mutual consistency of the optimal plans of disparate agents to buy and sell in the present and in the future.

In formulating optimal plans that extend through time, agents consider both the current prices at which they can buy and sell, and the prices at which they will (or expect to) be able to buy and sell in the future. Although it may sometimes be possible to buy or sell forward at a currently quoted price for future delivery, agents planning to buy and sell goods or services rely, for the most part, on their expectations of future prices. Those expectations, of course, need not always turn out to have been accurate.

The dynamic equilibrium described by Myrdal, Lindahl and Hayek is a contingent event in which all agents have correctly anticipated the future prices on which they have based their plans. In the event that some, if not all, agents have incorrectly anticipated future prices, those agents whose plans were based on incorrect expectations may have to revise their plans or be unable to execute them. But unless all agents share the same expectations of future prices, their expectations cannot all be correct, and some of those plans may not be realized.

The impossibility of an intertemporal equilibrium of optimal plans if agents do not share the same expectations of future prices implies that the adjustment of perfectly flexible market prices is not sufficient an optimal equilibrium to be achieved. I shall have more to say about this point below, but for now I want to note that the growing interest in the quiet Walrasian revolution in neoclassical theory that occurred almost simultaneously with the Keynesian revolution made it inevitable that Keynesian models would be recast in explicitly Walrasian terms.

What emerged from the Walrasian reformulation of Keynesian analysis was the neoclassical synthesis that became the textbook version of macroeconomics in the 1960s and 1970s. But the seemingly anomalous conjunction of both inflation and unemployment during the 1970s led to a reconsideration and widespread rejection of the Keynesian proposition that output and employment are directly related to aggregate demand.

Indeed, supporters of the Monetarist views of Milton Friedman argued that the high inflation and unemployment of the 1970s amounted to an empirical refutation of the Keynesian system. But Friedman’s political conservatism, free-market ideology, and his acerbic criticism of Keynesian policies obscured the extent to which his largely atheoretical monetary thinking was influenced by Keynesian and Marshallian concepts that rendered his version of Monetarism an unattractive alternative for younger monetary theorists, schooled in the Walrasian version of neoclassicism, who were seeking a clear theoretical contrast with the Keynesian macro model.

The brief Monetarist ascendancy following 1970s inflation conveniently collapsed in the early 1980s, after Friedman’s Monetarist policy advice for controlling the quantity of money proved unworkable, when central banks, foolishly trying to implement the advice, prolonged a needlessly deep recession while central banks consistently overshot their monetary targets, thereby provoking a long series of embarrassing warnings from Friedman about the imminent return of double-digit inflation.

[1] Hayek, both a friend and a foe of Keynes, would chide Keynes decades after Keynes’s death for calling his theory a general theory when, in Hayek’s view, it was a special theory relevant only in periods of substantially less than full employment when increasing aggregate demand could increase total output. But in making this criticism, Hayek, himself, implicitly assumed that which he had himself admitted in his theory of intertemporal equilibrium that there is no automatic equilibration mechanism that ensures that general equilibrium obtains.

General Equilibrium, Partial Equilibrium and Costs

Published August 4, 2021 Alfred Marshall , comparative statics , general equilibrium , Irving Fisher , Kenneth Arrow , Keynes , Leon Walras , macroeconomics , microfoundations , partial equilibrium , supply-demand analysis , Walrasian equilibrium 27 Comments

Neoclassical economics is now bifurcated between Marshallian partial-equilibrium and Walrasian general-equilibrium analyses. With the apparent inability of neoclassical theory to explain the coordination failure of the Great Depression, J. M. Keynes proposed an alternative paradigm to explain the involuntary unemployment of the 1930s. But within two decades, Keynes’s contribution was subsumed under what became known as the neoclassical synthesis of the Keynesian and Walrasian theories (about which I have written frequently, e.g., here and here). Lacking microfoundations that could be reconciled with the assumptions of Walrasian general-equilibrium theory, the neoclassical synthesis collapsed, owing to the supposedly inadequate microfoundations of Keynesian theory.

But Walrasian general-equilibrium theory provides no plausible, much less axiomatic, account of how general equilibrium is, or could be, achieved. Even the imaginary tatonnement process lacks an algorithm that guarantees that a general-equilibrium solution, if it exists, would be found. Whatever plausibility is attributed to the assumption that price flexibility leads to equilibrium derives from Marshallian partial-equilibrium analysis, with market prices adjusting to equilibrate supply and demand.

Yet modern macroeconomics, despite its explicit Walrasian assumptions, implicitly relies on the Marshallian intuition that the fundamentals of general-equilibrium, prices and costs are known to agents who, except for random disturbances, continuously form rational expectations of market-clearing equilibrium prices in all markets.

I’ve written many earlier posts (e.g., here and here) contesting, in one way or another, the notion that all macroeconomic theories must be founded on first principles (i.e., microeconomic axioms about optimizing individuals). Any macroeconomic theory not appropriately founded on the axioms of individual optimization by consumers and producers is now dismissed as scientifically defective and unworthy of attention by serious scientific practitioners of macroeconomics.

When contesting the presumed necessity for macroeconomics to be microeconomically founded, I’ve often used Marshall’s partial-equilibrium method as a point of reference. Though derived from underlying preference functions that are independent of prices, the demand curves of partial-equilibrium analysis presume that all product prices, except the price of the product under analysis, are held constant. Similarly, the supply curves are derived from individual firm marginal-cost curves whose geometric position or algebraic description depends critically on the prices of raw materials and factors of production used in the production process. But neither the prices of alternative products to be purchased by consumers nor the prices of raw materials and factors of production are given independently of the general-equilibrium solution of the whole system.

Thus, partial-equilibrium analysis, to be analytically defensible, requires a ceteris-paribus proviso. But to be analytically tenable, that proviso must posit an initial position of general equilibrium. Unless the analysis starts from a state of general equilibrium, the assumption that all prices but one remain constant can’t be maintained, the constancy of disequilibrium prices being a nonsensical assumption.

The ceteris-paribus proviso also entails an assumption about the market under analysis; either the market itself, or the disturbance to which it’s subject, must be so small that any change in the equilibrium price of the product in question has de minimus repercussions on the prices of every other product and of every input and factor of production used in producing that product. Thus, the validity of partial-equilibrium analysis depends on the presumption that the unique and locally stable general-equilibrium is approximately undisturbed by whatever changes result from by the posited change in the single market being analyzed. But that presumption is not so self-evidently plausible that our reliance on it to make empirical predictions is always, or even usually, justified.

Perhaps the best argument for taking partial-equilibrium analysis seriously is that the analysis identifies certain deep structural tendencies that, at least under “normal” conditions of moderate macroeconomic stability (i.e., moderate unemployment and reasonable price stability), will usually be observable despite the disturbing influences that are subsumed under the ceteris-paribus proviso. That assumption — an assumption of relative ignorance about the nature of the disturbances that are assumed to be constant — posits that those disturbances are more or less random, and as likely to cause errors in one direction as another. Consequently, the predictions of partial-equilibrium analysis can be assumed to be statistically, though not invariably, correct.

Of course, the more interconnected a given market is with other markets in the economy, and the greater its size relative to the total economy, the less confidence we can have that the implications of partial-equilibrium analysis will be corroborated by empirical investigation.

Despite its frequent unsuitability, economists and commentators are often willing to deploy partial-equilibrium analysis in offering policy advice even when the necessary ceteris-paribus proviso of partial-equilibrium analysis cannot be plausibly upheld. For example, two of the leading theories of the determination of the rate of interest are the loanable-funds doctrine and the Keynesian liquidity-preference theory. Both these theories of the rate of interest suppose that the rate of interest is determined in a single market — either for loanable funds or for cash balances — and that the rate of interest adjusts to equilibrate one or the other of those two markets. But the rate of interest is an economy-wide price whose determination is an intertemporal-general-equilibrium phenomenon that cannot be reduced, as the loanable-funds and liquidity preference theories try to do, to the analysis of a single market.

Similarly partial-equilibrium analysis of the supply of, and the demand for, labor has been used of late to predict changes in wages from immigration and to advocate for changes in immigration policy, while, in an earlier era, it was used to recommend wage reductions as a remedy for persistently high aggregate unemployment. In the General Theory, Keynes correctly criticized those using a naïve version of the partial-equilibrium method to recommend curing high unemployment by cutting wage rates, correctly observing that the conditions for full employment required the satisfaction of certain macroeconomic conditions for equilibrium that would not necessarily be satisfied by cutting wages.

However, in the very same volume, Keynes argued that the rate of interest is determined exclusively by the relationship between the quantity of money and the demand to hold money, ignoring that the rate of interest is an intertemporal relationship between current and expected future prices, an insight earlier explained by Irving Fisher that Keynes himself had expertly deployed in his Tract on Monetary Reform and elsewhere (Chapter 17) in the General Theory itself.

Evidently, the allure of supply-demand analysis can sometimes be too powerful for well-trained economists to resist even when they actually know better themselves that it ought to be resisted.

A further point also requires attention: the conditions necessary for partial-equilibrium analysis to be valid are never really satisfied; firms don’t know the costs that determine the optimal rate of production when they actually must settle on a plan of how much to produce, how much raw materials to buy, and how much labor and other factors of production to employ. Marshall, the originator of partial-equilibrium analysis, analogized supply and demand to the blades of a scissor acting jointly to achieve a intended result.

But Marshall erred in thinking that supply (i.e., cost) is an independent determinant of price, because the equality of costs and prices is a characteristic of general equilibrium. It can be applied to partial-equilibrium analysis only under the ceteris-paribus proviso that situates partial-equilibrium analysis in a pre-existing general equilibrium of the entire economy. It is only in general-equilibrium state, that the cost incurred by a firm in producing its output represents the value of the foregone output that could have been produced had the firm’s output been reduced. Only if the analyzed market is so small that changes in how much firms in that market produce do not affect the prices of the inputs used in to produce that output can definite marginal-cost curves be drawn or algebraically specified.

Unless general equilibrium obtains, prices need not equal costs, as measured by the quantities and prices of inputs used by firms to produce any product. Partial equilibrium analysis is possible only if carried out in the context of general equilibrium. Cost cannot be an independent determinant of prices, because cost is itself determined simultaneously along with all other prices.

But even aside from the reasons why partial-equilibrium analysis presumes that all prices, but the price in the single market being analyzed, are general-equilibrium prices, there’s another, even more problematic, assumption underlying partial-equilibrium analysis: that producers actually know the prices that they will pay for the inputs and resources to be used in producing their outputs. The cost curves of the standard economic analysis of the firm from which the supply curves of partial-equilibrium analysis are derived, presume that the prices of all inputs and factors of production correspond to those that are consistent with general equilibrium. But general-equilibrium prices are never known by anyone except the hypothetical agents in a general-equilibrium model with complete markets, or by agents endowed with perfect foresight (aka rational expectations in the strict sense of that misunderstood term).

At bottom, Marshallian partial-equilibrium analysis is comparative statics: a comparison of two alternative (hypothetical) equilibria distinguished by some difference in the parameters characterizing the two equilibria. By comparing the equilibria corresponding to the different parameter values, the analyst can infer the effect (at least directionally) of a parameter change.

But comparative-statics analysis is subject to a serious limitation: comparing two alternative hypothetical equilibria is very different from making empirical predictions about the effects of an actual parameter change in real time.

Comparing two alternative equilibria corresponding to different values of a parameter may be suggestive of what could happen after a policy decision to change that parameter, but there are many reasons why the change implied by the comparative-statics exercise might not match or even approximate the actual change.

First, the initial state was almost certainly not an equilibrium state, so systemic changes will be difficult, if not impossible, to disentangle from the effect of parameter change implied by the comparative-statics exercise.

Second, even if the initial state was an equilibrium, the transition to a new equilibrium is never instantaneous. The transitional period therefore leads to changes that in turn induce further systemic changes that cause the new equilibrium toward which the system gravitates to differ from the final equilibrium of the comparative-statics exercise.

Third, each successive change in the final equilibrium toward which the system is gravitating leads to further changes that in turn keep changing the final equilibrium. There is no reason why the successive changes lead to convergence on any final equilibrium end state. Nor is there any theoretical proof that the adjustment path leading from one equilibrium to another ever reaches an equilibrium end state. The gap between the comparative-statics exercise and the theory of adjustment in real time remains unbridged and may, even in principle, be unbridgeable.

Finally, without a complete system of forward and state-contingent markets, equilibrium requires not just that current prices converge to equilibrium prices; it requires that expectations of all agents about future prices converge to equilibrium expectations of future prices. Unless, agents’ expectations of future prices converge to their equilibrium values, an equilibrium many not even exist, let alone be approached or attained.

So the Marshallian assumption that producers know their costs of production and make production and pricing decisions based on that knowledge is both factually wrong and logically untenable. Nor do producers know what the demand curves for their products really looks like, except in the extreme case in which suppliers take market prices to be parametrically determined. But even then, they make decisions not on known prices, but on expected prices. Their expectations are constantly being tested against market information about actual prices, information that causes decision makers to affirm or revise their expectations in light of the constant flow of new information about prices and market conditions.

I don’t reject partial-equilibrium analysis, but I do call attention to its limitations, and to its unsuitability as a supposedly essential foundation for macroeconomic analysis, especially inasmuch as microeconomic analysis, AKA partial-equilibrium analysis, is utterly dependent on the uneasy macrofoundation of general-equilibrium theory. The intuition of Marshallian partial equilibrium cannot fil the gap, long ago noted by Kenneth Arrow, in the neoclassical theory of equilibrium price adjustment.

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
Tags: , , ,

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.

A Tale of Two Syntheses

Published May 8, 2020 Arrow-Debrew-McKenzie model , Axel Leijonfuvud , comparative statics , coordination failure , Don Patinkin , DSGE models , Franklin Fisher , general equilibrium , Hawtrey , Hayek , intertemporal equilibrium , Kenneth Arrow , macroeconomics , microfoundations , neoclassical synthesis , New Classical macroeconomics , New Keynesians , Oskar Morgensterm , Robert Lucas , Roy Radner , Samuelson , stability of general equilibrium , temporary equilibrium , Thomas Schelling , Walrasian equilibrium 13 Comments
Tags: , , , , , , ,

I recently finished reading a slender, but weighty, collection of essays, Microfoundtions Reconsidered: The Relationship of Micro and Macroeconomics in Historical Perspective, edited by Pedro Duarte and Gilberto Lima; it contains in addition to a brief introductory essay by the editors, and contributions by Kevin Hoover, Robert Leonard, Wade Hands, Phil Mirowski, Michel De Vroey, and Pedro Duarte. The volume is both informative and stimulating, helping me to crystalize ideas about which I have been ruminating and writing for a long time, but especially in some of my more recent posts (e.g., here, here, and here) and my recent paper “Hayek, Hicks, Radner and Four Equilibrium Concepts.”

Hoover’s essay provides a historical account of the microfoundations, making clear that the search for microfoundations long preceded the Lucasian microfoundations movement of the 1970s and 1980s that would revolutionize macroeconomics in the late 1980s and early 1990s. I have been writing about the differences between varieties of microfoundations for quite a while (here and here), and Hoover provides valuable detail about early discussions of microfoundations and about their relationship to the now regnant Lucasian microfoundations dogma. But for my purposes here, Hoover’s key contribution is his deconstruction of the concept of microfoundations, showing that the idea of microfoundations depends crucially on the notion that agents in a macroeconomic model be explicit optimizers, meaning that they maximize an explicit function subject to explicit constraints.

What Hoover clarifies is vacuity of the Lucasian optimization dogma. Until Lucas, optimization by agents had been merely a necessary condition for a model to be microfounded. But there was also another condition: that the optimizing choices of agents be mutually consistent. Establishing that the optimizing choices of agents are mutually consistent is not necessarily easy or even possible, so often the consistency of optimizing plans can only be suggested by some sort of heuristic argument. But Lucas and his cohorts, followed by their acolytes, unable to explain, even informally or heuristically, how the optimizing choices of individual agents are rendered mutually consistent, instead resorted to question-begging and question-dodging techniques to avoid addressing the consistency issue, of which one — the most egregious, but not the only — is the representative agent. In so doing, Lucas et al. transformed the optimization problem from the coordination of multiple independent choices into the optimal plan of a single decision maker. Heckuva job!

The second essay by Robert Leonard, though not directly addressing the question of microfoundations, helps clarify and underscore the misrepresentation perpetrated by the Lucasian microfoundational dogma in disregarding and evading the need to describe a mechanism whereby the optimal choices of individual agents are, or could be, reconciled. Leonard focuses on a particular economist, Oskar Morgenstern, who began his career in Vienna as a not untypical adherent of the Austrian school of economics, a member of the Mises seminar and successor of F. A. Hayek as director of the Austrian Institute for Business Cycle Research upon Hayek’s 1931 departure to take a position at the London School of Economics. However, Morgenstern soon began to question the economic orthodoxy of neoclassical economic theory and its emphasis on the tendency of economic forces to reach a state of equilibrium.

In his famous early critique of the foundations of equilibrium theory, Morgenstern tried to show that the concept of perfect foresight, upon which, he alleged, the concept of equilibrium rests, is incoherent. To do so, Morgenstern used the example of the Holmes-Moriarity interaction in which Holmes and Moriarty are caught in a dilemma in which neither can predict whether the other will get off or stay on the train on which they are both passengers, because the optimal choice of each depends on the choice of the other. The unresolvable conflict between Holmes and Moriarty, in Morgenstern’s view, showed that the incoherence of the idea of perfect foresight.

As his disillusionment with orthodox economic theory deepened, Morgenstern became increasingly interested in the potential of mathematics to serve as a tool of economic analysis. Through his acquaintance with the mathematician Karl Menger, the son of Carl Menger, founder of the Austrian School of economics. Morgenstern became close to Menger’s student, Abraham Wald, a pure mathematician of exceptional ability, who, to support himself, was working on statistical and mathematical problems for the Austrian Institute for Business Cycle Resarch, and tutoring Morgenstern in mathematics and its applications to economic theory. Wald, himself, went on to make seminal contributions to mathematical economics and statistical analysis.

Moregenstern also became acquainted with another student of Menger, John von Neumnn, with an interest in applying advanced mathematics to economic theory. Von Neumann and Morgenstern would later collaborate in writing The Theory of Games and Economic Behavior, as a result of which Morgenstern came to reconsider his early view of the Holmes-Moriarty paradox inasmuch as it could be shown that an equilibrium solution of their interaction could be found if payoffs to their joint choices were specified, thereby enabling Holmes and Moriarty to choose optimal probablistic strategies.

I don’t think that the game-theoretic solution to the Holmes Moriarty game is as straightforward as Morgenstern eventually agreed, but the critical point in the microfoundations discussion is that the mathematical solution to the Holmes-Moriarty paradox acknowledges the necessity for the choices made by two or more agents in an economic or game-theoretic equilibrium to be reconciled – i.e., rendered mutually consistent — in equilibrium. Under Lucasian microfoundations dogma, the problem is either annihilated by positing an optimizing representative agent having no need to coordinate his decision with other agents (I leave the question who, in the Holmes-Moriarty interaction, is the representative agent as an exercise for the reader) or it is assumed away by positing the existence of a magical equilibrium with no explanation of how the mutually consistent choices are arrived at.

The third essay (“The Rise and Fall of Walrasian Economics: The Keynes Effect”) by Wade Hands considers the first of the two syntheses – the neoclassical synthesis — that are alluded to in the title of this post. Hands gives a learned account of the mutually reinforcing co-development of Walrasian general equilibrium theory and Keynesian economics in the 25 years or so following World War II. Although Hands agrees that there is no necessary connection between Walrasian GE theory and Keynesian theory, he argues that there was enough common ground between Keynesians and Walrasians, as famously explained by Hicks in summarizing Keynesian theory by way of his IS-LM model, to allow the two disparate research programs to nourish each other in a kind of symbiotic relationship as the two research programs came to dominate postwar economics.

The task for Keynesian macroeconomists following the lead of Samuelson, Solow and Modigliani at MIT, Alvin Hansen at Harvard and James Tobin at Yale was to elaborate the Hicksian IS-LM approach by embedding it in a more general Walrasian framework. In so doing, they helped to shape a research agenda for Walrasian general-equilibrium theorists working out the details of the newly developed Arrow-Debreu model, deriving conditions for the uniqueness and stability of the equilibrium of that model. The neoclassical synthesis followed from those efforts, achieving an uneasy reconciliation between Walrasian general equilibrium theory and Keynesian theory. It received its most complete articulation in the impressive treatise of Don Patinkin which attempted to derive or at least evaluate key Keyensian propositions in the context of a full general equilibrium model. At an even higher level of theoretical sophistication, the 1971 summation of general equilibrium theory by Arrow and Hahn, gave disproportionate attention to Keynesian ideas which were presented and analyzed using the tools of state-of-the art Walrasian analysis.

Hands sums up the coexistence of Walrasian and Keynesian ideas in the Arrow-Hahn volume as follows:

Arrow and Hahn’s General Competitive Analysis – the canonical summary of the literature – dedicated far more pages to stability than to any other topic. The book had fourteen chapters (and a number of mathematical appendices); there was one chapter on consumer choice, one chapter on production theory, and one chapter on existence [of equilibrium], but there were three chapters on stability analysis, (two on the traditional tatonnement and one on alternative ways of modeling general equilibrium dynamics). Add to this the fact that there was an important chapter on “The Keynesian Model’; and it becomes clear how important stability analysis and its connection to Keynesian economics was for Walrasian microeconomics during this period. The purpose of this section has been to show that that would not have been the case if the Walrasian economics of the day had not been a product of co-evolution with Keynesian economic theory. (p. 108)

What seems most unfortunate about the neoclassical synthesis is that it elevated and reinforced the least relevant and least fruitful features of both the Walrasian and the Keynesian research programs. The Hicksian IS-LM setup abstracted from the dynamic and forward-looking aspects of Keynesian theory, modeling a static one-period model, not easily deployed as a tool of dynamic analysis. Walrasian GE analysis, which, following the pathbreaking GE existence proofs of Arrow and Debreu, then proceeded to a disappointing search for the conditions for a unique and stable general equilibrium.

It was Paul Samuelson who, building on Hicks’s pioneering foray into stability analysis, argued that the stability question could be answered by investigating whether a system of Lyapounov differential equations could describe market price adjustments as functions of market excess demands that would converge on an equilibrium price vector. But Samuelson’s approach to establishing stability required the mechanism of a fictional tatonnement process. Even with that unsatisfactory assumption, the stability results were disappointing.

Although for Walrasian theorists the results hardly repaid the effort expended, for those Keynesians who interpreted Keynes as an instability theorist, the weak Walrasian stability results might have been viewed as encouraging. But that was not any easy route to take either, because Keynes had also argued that a persistent unemployment equilibrium might be the norm.

It’s also hard to understand how the stability of equilibrium in an imaginary tatonnement process could ever have been considered relevant to the operation of an actual economy in real time – a leap of faith almost as extraordinary as imagining an economy represented by a single agent. Any conventional comparative-statics exercise – the bread and butter of microeconomic analysis – involves comparing two equilibria, corresponding to a specified parametric change in the conditions of the economy. The comparison presumes that, starting from an equilibrium position, the parametric change leads from an initial to a new equilibrium. If the economy isn’t stable, a disturbance causing an economy to depart from an initial equilibrium need not result in an adjustment to a new equilibrium comparable to the old one.

If conventional comparative statics hinges on an implicit stability assumption, it’s hard to see how a stability analysis of tatonnement has any bearing on the comparative-statics routinely relied upon by economists. No actual economy ever adjusts to a parametric change by way of tatonnement. Whether a parametric change displacing an economy from its equilibrium time path would lead the economy toward another equilibrium time path is another interesting and relevant question, but it’s difficult to see what insight would be gained by proving the stability of equilibrium under a tatonnement process.

Moreover, there is a distinct question about the endogenous stability of an economy: are there endogenous tendencies within an economy that lead it away from its equilibrium time path. But questions of endogenous stability can only be posed in a dynamic, rather than a static, model. While extending the Walrasian model to include an infinity of time periods, Arrow and Debreu telescoped determination of the intertemporal-equilibrium price vector into a preliminary time period before time, production, exchange and consumption begin. So, even in the formally intertemporal Arrow-Debreu model, the equilibrium price vector, once determined, is fixed and not subject to revision. Standard stability analysis was concerned with the response over time to changing circumstances only insofar as changes are foreseen at time zero, before time begins, so that they can be and are taken fully into account when the equilibrium price vector is determined.

Though not entirely uninteresting, the intertemporal analysis had little relevance to the stability of an actual economy operating in real time. Thus, neither the standard Keyensian (IS-LM) model nor the standard Walrasian Arrow-Debreu model provided an intertemporal framework within which to address the dynamic stability that Keynes (and contemporaries like Hayek, Myrdal, Lindahl and Hicks) had developed in the 1930s. In particular, Hicks’s analytical device of temporary equilibrium might have facilitated such an analysis. But, having introduced his IS-LM model two years before publishing his temporary equilibrium analysis in Value and Capital, Hicks concentrated his attention primarily on Keynesian analysis and did not return to the temporary equilibrium model until 1965 in Capital and Growth. And it was IS-LM that became, for a generation or two, the preferred analytical framework for macroeconomic analysis, while temproary equilibrium remained overlooked until the 1970s just as the neoclassical synthesis started coming apart.

The fourth essay by Phil Mirowski investigates the role of the Cowles Commission, based at the University of Chicago from 1939 to 1955, in undermining Keynesian macroeconomics. While Hands argues that Walrasians and Keynesians came together in a non-hostile spirit of tacit cooperation, Mirowski believes that owing to their Walrasian sympathies, the Cowles Committee had an implicit anti-Keynesian orientation and was therefore at best unsympathetic if not overtly hostile to Keynesian theorizing, which was incompatible the Walrasian optimization paradigm endorsed by the Cowles economists. (Another layer of unexplored complexity is the tension between the Walrasianism of the Cowles economists and the Marshallianism of the Chicago School economists, especially Knight and Friedman, which made Chicago an inhospitable home for the Cowles Commission and led to its eventual departure to Yale.)

Whatever differences, both the Mirowski and the Hands essays support the conclusion that the uneasy relationship between Walrasianism and Keynesianism was inherently problematic and unltimately unsustainable. But to me the tragedy is that before the fall, in the 1950s and 1960s, when the neoclassical synthesis bestrode economics like a colossus, the static orientation of both the Walrasian and the Keynesian research programs combined to distract economists from a more promising research program. Such a program, instead of treating expectations either as parametric constants or as merely adaptive, based on an assumed distributed lag function, might have considered whether expectations could perform a potentially equilibrating role in a general equilibrium model.

The equilibrating role of expectations, though implicit in various contributions by Hayek, Myrdal, Lindahl, Irving Fisher, and even Keynes, is contingent so that equilibrium is not inevitable, only a possibility. Instead, the introduction of expectations as an equilibrating variable did not occur until the mid-1970s when Robert Lucas, Tom Sargent and Neil Wallace, borrowing from John Muth’s work in applied microeconomics, introduced the idea of rational expectations into macroeconomics. But in introducing rational expectations, Lucas et al. made rational expectations not the condition of a contingent equilibrium but an indisputable postulate guaranteeing the realization of equilibrium without offering any theoretical account of a mechanism whereby the rationality of expectations is achieved.

The fifth essay by Michel DeVroey (“Microfoundations: a decisive dividing line between Keynesian and new classical macroeconomics?”) is a philosophically sophisticated analysis of Lucasian microfoundations methodological principles. DeVroey begins by crediting Lucas with the revolution in macroeconomics that displaced a Keynesian orthodoxy already discredited in the eyes of many economists after its failure to account for simultaneously rising inflation and unemployment.

The apparent theoretical disorder characterizing the Keynesian orthodoxy and its Monetarist opposition left a void for Lucas to fill by providing a seemingly rigorous microfounded alternative to the confused state of macroeconomics. And microfoundations became the methodological weapon by which Lucas and his associates and followers imposed an iron discipline on the unruly community of macroeconomists. “In Lucas’s eyes,” DeVroey aptly writes,“ the mere intention to produce a theory of involuntary unemployment constitutes an infringement of the equilibrium discipline.” Showing that his description of Lucas is hardly overstated, DeVroey quotes from the famous 1978 joint declaration of war issued by Lucas and Sargent against Keynesian macroeconomics:

After freeing himself of the straightjacket (or discipline) imposed by the classical postulates, Keynes described a model in which rules of thumb, such as the consumption function and liquidity preference schedule, took the place of decision functions that a classical economist would insist be derived from the theory of choice. And rather than require that wages and prices be determined by the postulate that markets clear – which for the labor market seemed patently contradicted by the severity of business depressions – Keynes took as an unexamined postulate that money wages are sticky, meaning that they are set at a level or by a process that could be taken as uninfluenced by the macroeconomic forces he proposed to analyze.

Echoing Keynes’s famous description of the sway of Ricardian doctrines over England in the nineteenth century, DeVroey remarks that the microfoundations requirement “conquered macroeconomics as quickly and thoroughly as the Holy Inquisition conquered Spain,” noting, even more tellingly, that the conquest was achieved without providing any justification. Ricardo had, at least, provided a substantive analysis that could be debated; Lucas offered only an undisputable methodological imperative about the sole acceptable mode of macroeconomic reasoning. Just as optimization is a necessary component of the equilibrium discipline that had to be ruthlessly imposed on pain of excommunication from the macroeconomic community, so, too, did the correlate principle of market-clearing. To deviate from the market-clearing postulate was ipso facto evidence of an impure and heretical state of mind. DeVroey further quotes from the war declaration of Lucas and Sargent.

Cleared markets is simply a principle, not verifiable by direct observation, which may or may not be useful in constructing successful hypotheses about the behavior of these [time] series.

What was only implicit in the war declaration became evident later after right-thinking was enforced, and woe unto him that dared deviate from the right way of thinking.

But, as DeVroey skillfully shows, what is most remarkable is that, having declared market clearing an indisputable methodological principle, Lucas, contrary to his own demand for theoretical discipline, used the market-clearing postulate to free himself from the very equilibrium discipline he claimed to be imposing. How did the market-clearing postulate liberate Lucas from equilibrium discipline? To show how the sleight-of-hand was accomplished, DeVroey, in an argument parallel to that of Hoover in chapter one and that suggested by Leonard in chapter two, contrasts Lucas’s conception of microfoundations with a different microfoundations conception espoused by Hayek and Patinkin. Unlike Lucas, Hayek and Patinkin recognized that the optimization of individual economic agents is conditional on the optimization of other agents. Lucas assumes that if all agents optimize, then their individual optimization ensures that a social optimum is achieved, the whole being the sum of its parts. But that assumption ignores that the choices made interacting agents are themelves interdependent.

To capture the distinction between independent and interdependent optimization, DeVroey distinguishes between optimal plans and optimal behavior. Behavior is optimal only if an optimal plan can be executed. All agents can optimize individually in making their plans, but the optimality of their behavior depends on their capacity to carry those plans out. And the capacity of each to carry out his plan is contingent on the optimal choices of all other agents.

Optimizing plans refers to agents’ intentions before the opening of trading, the solution to the choice-theoretical problem with which they are faced. Optimizing behavior refers to what is observable after trading has started. Thus optimal behavior implies that the optimal plan has been realized. . . . [O]ptmizing plans and optimizing behavior need to be logically separated – there is a difference between finding a solution to a choice problem and implementing the solution. In contrast, whenever optimizing behavior is the sole concept used, the possibility of there being a difference between them is discarded by definition. This is the standpoint takenby Lucas and Sargent. Once it is adopted, it becomes misleading to claim . . .that the microfoundations requirement is based on two criteria, optimizing behavior and market clearing. A single criterion is needed, and it is irrelevant whether this is called generalized optimizing behavior or market clearing. (De Vroey, p. 176)

Each agent is free to optimize his plan, but no agent can execute his optimal plan unless the plan coincides with the complementary plans of other agents. So, the execution of an optimal plan is not within the unilateral control of an agent formulating his own plan. One can readily assume that agents optimize their plans, but one cannot just assume that those plans can be executed as planned. The optimality of interdependent plans is not self-evident; it is a proposition that must be demonstrated. Assuming that agents optimize, Lucas simply asserts that, because agents optimize, markets must clear.

That is a remarkable non-sequitur. And from that non-sequitur, Lucas jumps to a further non-sequitur: that an optimizing representative agent is all that’s required for a macroeconomic model. The logical straightjacket (or discipline) of demonstrating that interdependent optimal plans are consistent is thus discarded (or trampled upon). Lucas’s insistence on a market-clearing principle turns out to be subterfuge by which the pretense of its upholding conceals its violation in practice.

My own view is that the assumption that agents formulate optimizing plans cannot be maintained without further analysis unless the agents are operating in isolation. If the agents interacting with each other, the assumption that they optimize requires a theory of their interaction. If the focus is on equilibrium interactions, then one can have a theory of equilibrium, but then the possibility of non-equilibrium states must also be acknowledged.

That is what John Nash did in developing his equilibrium theory of positive-sum games. He defined conditions for the existence of equilibrium, but he offered no theory of how equilibrium is achieved. Lacking such a theory, he acknowledged that non-equilibrium solutions might occur, e.g., in some variant of the Holmes-Moriarty game. To simply assert that because interdependent agents try to optimize, they must, as a matter of principle, succeed in optimizing is to engage in question-begging on a truly grand scale. To insist, as a matter of methodological principle, that everyone else must also engage in question-begging on equally grand scale is what I have previously called methodological arrogance, though an even harsher description might be appropriate.

In the sixth essay (“Not Going Away: Microfoundations in the making of a new consensus in macroeconomics”), Pedro Duarte considers the current state of apparent macroeconomic consensus in the wake of the sweeping triumph of the Lucasian micorfoundtions methodological imperative. In its current state, mainstream macroeconomists from a variety of backgrounds have reconciled themselves and adjusted to the methodological absolutism Lucas and his associates and followers have imposed on macroeconomic theorizing. Leading proponents of the current consensus are pleased to announce, in unseemly self-satisfaction, that macroeconomics is now – but presumably not previously – “firmly grounded in the principles of economic [presumably neoclassical] theory.” But the underlying conception of neoclassical economic theory motivating such a statement is almost laughably narrow, and, as I have just shown, strictly false even if, for argument’s sake, that narrow conception is accepted.

Duarte provides an informative historical account of the process whereby most mainstream Keynesians and former old-line Monetarists, who had, in fact, adopted much of the underlying Keynesian theoretical framework themselves, became reconciled to the non-negotiable methodological microfoundational demands upon which Lucas and his New Classical followers and Real-Business-Cycle fellow-travelers insisted. While Lucas was willing to tolerate differences of opinion about the importance of monetary factors in accounting for business-cycle fluctuations in real output and employment, and even willing to countenance a role for countercyclical monetary policy, such differences of opinion could be tolerated only if they could be derived from an acceptable microfounded model in which the agent(s) form rational expectations. If New Keynesians were able to produce results rationalizing countercyclical policies in such microfounded models with rational expectations, Lucas was satisfied. Presumably, Lucas felt the price of conceding the theoretical legitimacy of countercyclical policy was worth paying in order to achieve methodological hegemony over macroeconomic theory.

And no doubt, for Lucas, the price was worth paying, because it led to what Marvin Goodfriend and Robert King called the New Neoclassical Synthesis in their 1997 article ushering in the new era of good feelings, a synthesis based on “the systematic application of intertemporal optimization and rational expectations” while embodying “the insights of monetarists . . . regarding the theory and practice of monetary policy.”

While the first synthesis brought about a convergence of sorts between the disparate Walrasian and Keynesian theoretical frameworks, the convergence proved unstable because the inherent theoretical weaknesses of both paradigms were unable to withstand criticisms of the theoretical apparatus and of the policy recommendations emerging from that synthesis, particularly an inability to provide a straightforward analysis of inflation when it became a serious policy problem in the late 1960s and 1970s. But neither the Keynesian nor the Walrasian paradigms were developing in a way that addressed the points of most serious weakness.

On the Keynesian side, the defects included the static nature of the workhorse IS-LM model, the absence of a market for real capital and of a market for endogenous money. On the Walrasian side, the defects were the lack of any theory of actual price determination or of dynamic adjustment. The Hicksian temporary equilibrium paradigm might have provided a viable way forward, and for a very different kind of synthesis, but not even Hicks himself realized the potential of his own creation.

While the first synthesis was a product of convenience and misplaced optimism, the second synthesis is a product of methodological hubris and misplaced complacency derived from an elementary misunderstanding of the distinction between optimization by a single agent and the simultaneous optimization of two or more independent, yet interdependent, agents. The equilibrium of each is the result of the equilibrium of all, and a theory of optimization involving two or more agents requires a theory of how two or more interdependent agents can optimize simultaneously. The New neoclassical synthesis rests on the demand for a macroeconomic theory of individual optimization that refuses even to ask, let along provide an answer to, the question whether the optimization that it demands is actually achieved in practice or what happens if it is not. This is not a synthesis that will last, or that deserves to. And the sooner it collapses, the better off macroeconomics will be.

What the answer is I don’t know, but if I had to offer a suggestion, the one offered by my teacher Axel Leijonhufvud towards the end of his great book, written more than half a century ago, strikes me as not bad at all:

One cannot assume that what went wrong was simply that Keynes slipped up here and there in his adaptation of standard tool, and that consequently, if we go back and tinker a little more with the Marshallian toolbox his purposes will be realized. What is required, I believe, is a systematic investigation, form the standpoint of the information problems stressed in this study, of what elements of the static theory of resource allocation can without further ado be utilized in the analysis of dynamic and historical systems. This, of course, would be merely a first-step: the gap yawns very wide between the systematic and rigorous modern analysis of the stability of “featureless,” pure exchange systems and Keynes’ inspired sketch of the income-constrained process in a monetary-exchange-cum-production system. But even for such a first step, the prescription cannot be to “go back to Keynes.” If one must retrace some steps of past developments in order to get on the right track—and that is probably advisable—my own preference is to go back to Hayek. Hayek’s Gestalt-conception of what happens during business cycles, it has been generally agreed, was much less sound than Keynes’. As an unhappy consequence, his far superior work on the fundamentals of the problem has not received the attention it deserves. (p. 401)

I agree with all that, but would also recommend Roy Radner’s development of an alternative to the Arrow-Debreu version of Walrasian general equilibrium theory that can accommodate Hicksian temporary equilibrium, and Hawtrey’s important contributions to our understanding of monetary theory and the role and potential instability of endogenous bank money. On top of that, Franklin Fisher in his important work, The Disequilibrium Foundations of Equilibrium Economics, has given us further valuable guidance in how to improve the current sorry state of macroeconomics.

 

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.

Jack Schwartz on the Weaknesses of the Mathematical Mind

Published October 4, 2019 general equilibrium , Jack Schwartz , Karl Popper , Keynes , partial equilibrium , Walrasian equilibrium 20 Comments
Tags: , ,

I was recently rereading an essay by Karl Popper, “A Realistic View of Logic, Physics, and History” published in his collection of essays, Objective Knowledge: An Evolutionary Approach, because it discusses the role of reductivism in science and philosophy, a topic about which I’ve written a number of previous posts discussing the microfoundations of macroeconomics.

Here is an important passage from Popper’s essay:

What I should wish to assert is (1) that criticism is a most important methodological device: and (2) that if you answer criticism by saying, “I do not like your logic: your logic may be all right for you, but I prefer a different logic, and according to my logic this criticism is not valid”, then you may undermine the method of critical discussion.

Now I should distinguish between two main uses of logic, namely (1) its use in the demonstrative sciences – that is to say, the mathematical sciences – and (2) its use in the empirical sciences.

In the demonstrative sciences logic is used in the main for proofs – for the transmission of truth – while in the empirical sciences it is almost exclusively used critically – for the retransmission of falsity. Of course, applied mathematics comes in too, which implicitly makes use of the proofs of pure mathematics, but the role of mathematics in the empirical sciences is somewhat dubious in several respects. (There exists a wonderful article by Schwartz to this effect.)

The article to which Popper refers appears by Jack Schwartz in a volume edited by Ernst Nagel, Patrick Suppes, and Alfred Tarski, Logic, Methodology and Philosophy of Science. The title of the essay, “The Pernicious Influence of Mathematics on Science” caught my eye, so I tried to track it down. Unavailable on the internet except behind a paywall, I bought a used copy for $6 including postage. The essay was well worth the $6 I paid to read it.

Before quoting from the essay, I would just note that Jacob T. (Jack) Schwartz was far from being innocent of mathematical and scientific knowledge. Here’s a snippet from the Wikipedia entry on Schwartz.

His research interests included the theory of linear operators, von Neumann algebras, quantum field theory, time-sharing, parallel computing, programming language design and implementation, robotics, set-theoretic approaches in computational logic, proof and program verification systems; multimedia authoring tools; experimental studies of visual perception; multimedia and other high-level software techniques for analysis and visualization of bioinformatic data.

He authored 18 books and more than 100 papers and technical reports.

He was also the inventor of the Artspeak programming language that historically ran on mainframes and produced graphical output using a single-color graphical plotter.[3]

He served as Chairman of the Computer Science Department (which he founded) at the Courant Institute of Mathematical Sciences, New York University, from 1969 to 1977. He also served as Chairman of the Computer Science Board of the National Research Council and was the former Chairman of the National Science Foundation Advisory Committee for Information, Robotics and Intelligent Systems. From 1986 to 1989, he was the Director of DARPA‘s Information Science and Technology Office (DARPA/ISTO) in Arlington, Virginia.

Here is a link to his obituary.

Though not trained as an economist, Schwartz, an autodidact, wrote two books on economic theory.

With that introduction, I quote from, and comment on, Schwartz’s essay.

Our announced subject today is the role of mathematics in the formulation of physical theories. I wish, however, to make use of the license permitted at philosophical congresses, in two regards: in the first place, to confine myself to the negative aspects of this role, leaving it to others to dwell on the amazing triumphs of the mathematical method; in the second place, to comment not only on physical science but also on social science, in which the characteristic inadequacies which I wish to discuss are more readily apparent.

Computer programmers often make a certain remark about computing machines, which may perhaps be taken as a complaint: that computing machines, with a perfect lack of discrimination, will do any foolish thing they are told to do. The reason for this lies of course in the narrow fixation of the computing machines “intelligence” upon the basely typographical details of its own perceptions – its inability to be guided by any large context. In a psychological description of the computer intelligence, three related adjectives push themselves forward: single-mindedness, literal-mindedness, simple-mindedness. Recognizing this, we should at the same time recognize that this single-mindedness, literal-mindedness, simple-mindedness also characterizes theoretical mathematics, though to a lesser extent.

It is a continual result of the fact that science tries to deal with reality that even the most precise sciences normally work with more or less ill-understood approximations toward which the scientist must maintain an appropriate skepticism. Thus, for instance, it may come as a shock to the mathematician to learn that the Schrodinger equation for the hydrogen atom, which he is able to solve only after a considerable effort of functional analysis and special function theory, is not a literally correct description of this atom, but only an approximation to a somewhat more correct equation taking account of spin, magnetic dipole, and relativistic effects; that this corrected equation is itself only an ill-understood approximation to an infinite set of quantum field-theoretic equations; and finally that the quantum field theory, besides diverging, neglects a myriad of strange-particle interactions whose strength and form are largely unknown. The physicist looking at the original Schrodinger equation, learns to sense in it the presence of many invisible terms, integral, intergrodifferential, perhaps even more complicated types of operators, in addition to the differential terms visible, and this sense inspires an entirely appropriate disregard for the purely technical features of the equation which he sees. This very healthy self-skepticism is foreign to the mathematical approach. . . .

Schwartz, in other words, is noting that the mathematical equations that physicists use in many contexts cannot be relied upon without qualification as accurate or exact representations of reality. The understanding that the mathematics that physicists and other physical scientists use to express their theories is often inexact or approximate inasmuch as reality is more complicated than our theories can capture mathematically. Part of what goes into the making of a good scientist is a kind of artistic feeling for how to adjust or interpret a mathematical model to take into account what the bare mathematics cannot describe in a manageable way.

The literal-mindedness of mathematics . . . makes it essential, if mathematics is to be appropriately used in science, that the assumptions upon which mathematics is to elaborate be correctly chosen from a larger point of view, invisible to mathematics itself. The single-mindedness of mathematics reinforces this conclusion. Mathematics is able to deal successfully only with the simplest of situations, more precisely, with a complex situation only to the extent that rare good fortune makes this complex situation hinge upon a few dominant simple factors. Beyond the well-traversed path, mathematics loses its bearing in a jungle of unnamed special functions and impenetrable combinatorial particularities. Thus, mathematical technique can only reach far if it starts from a point close to the simple essentials of a problem which has simple essentials. That form of wisdom which is the opposite of single-mindedness, the ability to keep many threads in hand, to draw for an argument from many disparate sources, is quite foreign to mathematics. The inability accounts for much of the difficulty which mathematics experiences in attempting to penetrate the social sciences. We may perhaps attempt a mathematical economics – but how difficult would be a mathematical history! Mathematics adjusts only with reluctance to the external, and vitally necessary, approximating of the scientists, and shudders each time a batch of small terms is cavalierly erased. Only with difficulty does it find its way to the scientist’s ready grasp of the relative importance of many factors. Quite typically, science leaps ahead and mathematics plods behind.

Schwartz having referenced mathematical economics, let me try to restate his point more concretely than he did by referring to the Walrasian theory of general equilibrium. “Mathematics,” Schwartz writes, “adjusts only with reluctance to the external, and vitally necessary, approximating of the scientists, and shudders each time a batch of small terms is cavalierly erased.” The Walrasian theory is at once too general and too special to be relied on as an applied theory. It is too general because the functional forms of most of its reliant equations can’t be specified or even meaningfully restricted on very special simplifying assumptions; it is too special, because the simplifying assumptions about the agents and the technologies and the constraints and the price-setting mechanism are at best only approximations and, at worst, are entirely divorced from reality.

Related to this deficiency of mathematics, and perhaps more productive of rueful consequence, is the simple-mindedness of mathematics – its willingness, like that of a computing machine, to elaborate upon any idea, however absurd; to dress scientific brilliancies and scientific absurdities alike in the impressive uniform of formulae and theorems. Unfortunately however, an absurdity in uniform is far more persuasive than an absurdity unclad. The very fact that a theory appears in mathematical form, that, for instance, a theory has provided the occasion for the application of a fixed-point theorem, or of a result about difference equations, somehow makes us more ready to take it seriously. And the mathematical-intellectual effort of applying the theorem fixes in us the particular point of view of the theory with which we deal, making us blind to whatever appears neither as a dependent nor as an independent parameter in its mathematical formulation. The result, perhaps most common in the social sciences, is bad theory with a mathematical passport. The present point is best established by reference to a few horrible examples. . . . I confine myself . . . to the citation of a delightful passage from Keynes’ General Theory, in which the issues before us are discussed with a characteristic wisdom and wit:

“It is the great fault of symbolic pseudomathematical methods of formalizing a system of economic analysis . . . that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep ‘at the back of our heads’ the necessary reserves and qualifications and adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials ‘at the back’ of several pages of algebra which assume they all vanish. Too large a proportion of recent ‘mathematical’ economics are mere concoctions, as imprecise as the initial assumptions they reset on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentions and unhelpful symbols.”

Although it would have been helpful if Keynes had specifically identified the pseudomathematical methods that he had in mind, I am inclined to think that he was expressing his impatience with the Walrasian general-equilibrium approach that was characteristic of the Marshallian tradition that he carried forward even as he struggled to transcend it. Walrasian general equilibrium analysis, he seems to be suggesting, is too far removed from reality to provide any reliable guide to macroeconomic policy-making, because the necessary qualifications required to make general-equilibrium analysis practically relevant are simply unmanageable within the framework of general-equilibrium analysis. A different kind of analysis is required. As a Marshallian he was less skeptical of partial-equilibrium analysis than of general-equilibrium analysis. But he also recognized that partial-equilibrium analysis could not be usefully applied in situations, e.g., analysis of an overall “market” for labor, where the usual ceteris paribus assumptions underlying the use of stable demand and supply curves as analytical tools cannot be maintained. But for some reason that didn’t stop Keynes from trying to explain the nominal rate of interest by positing a demand curve to hold money and a fixed stock of money supplied by a central bank. But we all have our blind spots and miss obvious implications of familiar ideas that we have already encountered and, at least partially, understand.

Schwartz concludes his essay with an arresting thought that should give us pause about how we often uncritically accept probabilistic and statistical propositions as if we actually knew how they matched up with the stochastic phenomena that we are seeking to analyze. But although there is a lot to unpack in his conclusion, I am afraid someone more capable than I will have to do the unpacking.

[M]athematics, concentrating our attention, makes us blind to its own omissions – what I have already called the single-mindedness of mathematics. Typically, mathematics, knows better what to do than why to do it. Probability theory is a famous example. . . . Here also, the mathematical formalism may be hiding as much as it reveals.

Hayek and Intertemporal Equilibrium

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

I am starting to write a paper on Hayek and intertemporal equilibrium, and as I write it over the next couple of weeks, I am going to post sections of it on this blog. Comments from readers will be even more welcome than usual, and I will do my utmost to reply to comments, a goal that, I am sorry to say, I have not been living up to in my recent posts.

The idea of equilibrium is an essential concept in economics. It is an essential concept in other sciences as well, its meaning in economics is not the same as in other disciplines. The concept having originally been borrowed from physics, the meaning originally attached to it by economists corresponded to the notion of a system at rest, and it took a long time for economists to see that viewing an economy as a system at rest was not the only, or even the most useful, way of applying the equilibrium concept to economic phenomena.

What would it mean for an economic system to be at rest? The obvious answer was to say that prices and quantities would not change. If supply equals demand in every market, and if there no exogenous change introduced into the system, e.g., in population, technology, tastes, etc., it would seem that would be no reason for the prices paid and quantities produced to change in that system. But that view of an economic system was a very restrictive one, because such a large share of economic activity – savings and investment — is predicated on the assumption and expectation of change.

The model of a stationary economy at rest in which all economic activity simply repeats what has already happened before did not seem very satisfying or informative, but that was the view of equilibrium that originally took hold in economics. The idea of a stationary timeless equilibrium can be traced back to the classical economists, especially Ricardo and Mill who wrote about the long-run tendency of an economic system toward a stationary state. But it was the introduction by Jevons, Menger, Walras and their followers of the idea of optimizing decisions by rational consumers and producers that provided the key insight for a more robust and fruitful version of the equilibrium concept.

If each economic agent (household or business firm) is viewed as making optimal choices based on some scale of preferences subject to limitations or constraints imposed by their capacities, endowments, technology and the legal system, then the equilibrium of an economy must describe a state in which each agent, given his own subjective ranking of the feasible alternatives, is making a optimal decision, and those optimal decisions are consistent with those of all other agents. The optimal decisions of each agent must simultaneously be optimal from the point of view of that agent while also being consistent, or compatible, with the optimal decisions of every other agent. In other words, the decisions of all buyers of how much to purchase must be consistent with the decisions of all sellers of how much to sell.

The idea of an equilibrium as a set of independently conceived, mutually consistent optimal plans was latent in the earlier notions of equilibrium, but it could not be articulated until a concept of optimality had been defined. That concept was utility maximization and it was further extended to include the ideas of cost minimization and profit maximization. Once the idea of an optimal plan was worked out, the necessary conditions for the mutual consistency of optimal plans could be articulated as the necessary conditions for a general economic equilibrium. Once equilibrium was defined as the consistency of optimal plans, the path was clear to define an intertemporal equilibrium as the consistency of optimal plans extending over time. Because current goods and services and otherwise identical goods and services in the future could be treated as economically distinct goods and services, defining the conditions for an intertemporal equilibrium was formally almost equivalent to defining the conditions for a static, stationary equilibrium. Just as the conditions for a static equilibrium could be stated in terms of equalities between marginal rates of substitution of goods in consumption and in production to their corresponding price ratios, an intertemporal equilibrium could be stated in terms of equalities between the marginal rates of intertemporal substitution in consumption and in production and their corresponding intertemporal price ratios.

The only formal adjustment required in the necessary conditions for static equilibrium to be extended to intertemporal equilibrium was to recognize that, inasmuch as future prices (typically) are unobservable, and hence unknown to economic agents, the intertemporal price ratios cannot be ratios between actual current prices and actual future prices, but, instead, ratios between current prices and expected future prices. From this it followed that for optimal plans to be mutually consistent, all economic agents must have the same expectations of the future prices in terms of which their plans were optimized.

The concept of an intertemporal equilibrium was first presented in English by F. A. Hayek in his 1937 article “Economics and Knowledge.” But it was through J. R. Hicks’s Value and Capital published two years later in 1939 that the concept became more widely known and understood. In explaining and applying the concept of intertemporal equilibrium and introducing the derivative concept of a temporary equilibrium in which current markets clear, but individual expectations of future prices are not the same, Hicks did not claim originality, but instead of crediting Hayek for the concept, or even mentioning Hayek’s 1937 paper, Hicks credited the Swedish economist Erik Lindahl, who had published articles in the early 1930s in which he had articulated the concept. But although Lindahl had published his important work on intertemporal equilibrium before Hayek’s 1937 article, Hayek had already explained the concept in a 1928 article “Das intertemporale Gleichgewichtasystem der Priese und die Bewegungen des ‘Geltwertes.'” (English translation: “Intertemporal price equilibrium and movements in the value of money.“)

Having been a junior colleague of Hayek’s in the early 1930s when Hayek arrived at the London School of Economics, and having come very much under Hayek’s influence for a few years before moving in a different theoretical direction in the mid-1930s, Hicks was certainly aware of Hayek’s work on intertemporal equilibrium, so it has long been a puzzle to me why Hicks did not credit Hayek along with Lindahl for having developed the concept of intertemporal equilibrium. It might be worth pursuing that question, but I mention it now only as an aside, in the hope that someone else might find it interesting and worthwhile to try to find a solution to that puzzle. As a further aside, I will mention that Murray Milgate in a 1979 article “On the Origin of the Notion of ‘Intertemporal Equilibrium’” has previously tried to redress the failure to credit Hayek’s role in introducing the concept of intertemporal equilibrium into economic theory.

What I am going to discuss in here and in future posts are three distinct ways in which the concept of intertemporal equilibrium has been developed since Hayek’s early work – his 1928 and 1937 articles but also his 1941 discussion of intertemporal equilibrium in The Pure Theory of Capital. Of course, the best known development of the concept of intertemporal equilibrium is the Arrow-Debreu-McKenzie (ADM) general-equilibrium model. But although it can be thought of as a model of intertemporal equilibrium, the ADM model is set up in such a way that all economic decisions are taken before the clock even starts ticking; the transactions that are executed once the clock does start simply follow a pre-determined script. In the ADM model, the passage of time is a triviality, merely a way of recording the sequential order of the predetermined production and consumption activities. This feat is accomplished by assuming that all agents are present at time zero with their property endowments in hand and capable of transacting – but conditional on the determination of an equilibrium price vector that allows all optimal plans to be simultaneously executed over the entire duration of the model — in a complete set of markets (including state-contingent markets covering the entire range of contingent events that will unfold in the course of time whose outcomes could affect the wealth or well-being of any agent with the probabilities associated with every contingent event known in advance).

Just as identical goods in different physical locations or different time periods can be distinguished as different commodities that cn be purchased at different prices for delivery at specific times and places, identical goods can be distinguished under different states of the world (ice cream on July 4, 2017 in Washington DC at 2pm only if the temperature is greater than 90 degrees). Given the complete set of state-contingent markets and the known probabilities of the contingent events, an equilibrium price vector for the complete set of markets would give rise to optimal trades reallocating the risks associated with future contingent events and to an optimal allocation of resources over time. Although the ADM model is an intertemporal model only in a limited sense, it does provide an ideal benchmark describing the characteristics of a set of mutually consistent optimal plans.

The seminal work of Roy Radner in relaxing some of the extreme assumptions of the ADM model puts Hayek’s contribution to the understanding of the necessary conditions for an intertemporal equilibrium into proper perspective. At an informal level, Hayek was addressing the same kinds of problems that Radner analyzed with far more powerful analytical tools than were available to Hayek. But the were both concerned with a common problem: under what conditions could an economy with an incomplete set of markets be said to be in a state of intertemporal equilibrium? In an economy lacking the full set of forward and state contingent markets describing the ADM model, intertemporal equilibrium cannot predetermined before trading even begins, but must, if such an equilibrium obtains, unfold through the passage of time. Outcomes might be expected, but they would not be predetermined in advance. Echoing Hayek, though to my knowledge he does not refer to Hayek in his work, Radner describes his intertemporal equilibrium under uncertainty as an equilibrium of plans, prices, and price expectations. Even if it exists, the Radner equilibrium is not the same as the ADM equilibrium, because without a full set of markets, agents can’t fully hedge against, or insure, all the risks to which they are exposed. The distinction between ex ante and ex post is not eliminated in the Radner equilibrium, though it is eliminated in the ADM equilibrium.

Additionally, because all trades in the ADM model have been executed before “time” begins, it seems impossible to rationalize holding any asset whose only use is to serve as a medium of exchange. In his early writings on business cycles, e.g., Monetary Theory and the Trade Cycle, Hayek questioned whether it would be possible to rationalize the holding of money in the context of a model of full equilibrium, suggesting that monetary exchange, by severing the link between aggregate supply and aggregate demand characteristic of a barter economy as described by Say’s Law, was the source of systematic deviations from the intertemporal equilibrium corresponding to the solution of a system of Walrasian equations. Hayek suggested that progress in analyzing economic fluctuations would be possible only if the Walrasian equilibrium method could be somehow be extended to accommodate the existence of money, uncertainty, and other characteristics of the real world while maintaining the analytical discipline imposed by the equilibrium method and the optimization principle. It proved to be a task requiring resources that were beyond those at Hayek’s, or probably anyone else’s, disposal at the time. But it would be wrong to fault Hayek for having had to insight to perceive and frame a problem that was beyond his capacity to solve. What he may be criticized for is mistakenly believing that he he had in fact grasped the general outlines of a solution when in fact he had only perceived some aspects of the solution and offering seriously inappropriate policy recommendations based on that seriously incomplete understanding.

In Value and Capital, Hicks also expressed doubts whether it would be possible to analyze the economic fluctuations characterizing the business cycle using a model of pure intertemporal equilibrium. He proposed an alternative approach for analyzing fluctuations which he called the method of temporary equilibrium. The essence of the temporary-equilibrium method is to analyze the behavior of an economy under the assumption that all markets for current delivery clear (in some not entirely clear sense of the term “clear”) while understanding that demand and supply in current markets depend not only on current prices but also upon expected future prices, and that the failure of current prices to equal what they had been expected to be is a potential cause for the plans that economic agents are trying to execute to be modified and possibly abandoned. In the Pure Theory of Capital, Hayek discussed Hicks’s temporary-equilibrium method a possible method of achieving the modification in the Walrasian method that he himself had proposed in Monetary Theory and the Trade Cycle. But after a brief critical discussion of the method, he dismissed it for reasons that remain obscure. Hayek’s rejection of the temporary-equilibrium method seems in retrospect to have been one of Hayek’s worst theoretical — or perhaps, meta-theoretical — blunders.

Decades later, C. J. Bliss developed the concept of temporary equilibrium to show that temporary equilibrium method can rationalize both holding an asset purely for its services as a medium of exchange and the existence of financial intermediaries (private banks) that supply financial assets held exclusively to serve as a medium of exchange. In such a temporary-equilibrium model with financial intermediaries, it seems possible to model not only the existence of private suppliers of a medium of exchange, but also the conditions – in a very general sense — under which the system of financial intermediaries breaks down. The key variable of course is vectors of expected prices subject to which the plans of individual households, business firms, and financial intermediaries are optimized. The critical point that emerges from Bliss’s analysis is that there are sets of expected prices, which if held by agents, are inconsistent with the existence of even a temporary equilibrium. Thus price flexibility in current market cannot, in principle, result in even a temporary equilibrium, because there is no price vector of current price in markets for present delivery that solves the temporary-equilibrium system. Even perfect price flexibility doesn’t lead to equilibrium if the equilibrium does not exist. And the equilibrium cannot exist if price expectations are in some sense “too far out of whack.”

Expected prices are thus, necessarily, equilibrating variables. But there is no economic mechanism that tends to cause the adjustment of expected prices so that they are consistent with the existence of even a temporary equilibrium, much less a full equilibrium.

Unfortunately, modern macroeconomics continues to neglect the temporary-equilibrium method; instead macroeconomists have for the most part insisted on the adoption of the rational-expectations hypothesis, a hypothesis that elevates question-begging to the status of a fundamental axiom of rationality. The crucial error in the rational-expectations hypothesis was to misunderstand the role of the comparative-statics method developed by Samuelson in The Foundations of Economic Analysis. The role of the comparative-statics method is to isolate the pure theoretical effect of a parameter change under a ceteris-paribus assumption. Such an effect could be derived only by comparing two equilibria under the assumption of a locally unique and stable equilibrium before and after the parameter change. But the method of comparative statics is completely inappropriate to most macroeconomic problems which are precisely concerned with the failure of the economy to achieve, or even to approximate, the unique and stable equilibrium state posited by the comparative-statics method.

Moreover, the original empirical application of the rational-expectations hypothesis by Muth was in the context of the behavior of a single market in which the market was dominated by well-informed specialists who could be presumed to have well-founded expectations of future prices conditional on a relatively stable economic environment. Under conditions of macroeconomic instability, there is good reason to doubt that the accumulated knowledge and experience of market participants would enable agents to form accurate expectations of the future course of prices even in those markets about which they expert knowledge. Insofar as the rational expectations hypothesis has any claim to empirical relevance it is only in the context of stable market situations that can be assumed to be already operating in the neighborhood of an equilibrium. For the kinds of problems that macroeconomists are really trying to answer that assumption is neither relevant nor appropriate.

About Me

David Glasner
Washington, DC

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

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

Follow me on Twitter @david_glasner

Archives

Enter your email address to follow this blog and receive notifications of new posts by email.

Join 3,272 other subscribers
Follow Uneasy Money on WordPress.com