Archive for the 'temporary equilibrium' Category

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.

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
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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.

My Paper “Hayek, Hicks, Radner and Four Equilibrium Concepts” Is Now Available Online.

Published January 30, 2020 Hayek , intertemporal equilibrium , J. R. Hicks , Robert Lucas , Roy Radner , temporary equilibrium , Uncategorized 1 Comment

The paper, forthcoming in The Review of Austrian Economics, can be read online.

Here is the abstract:

Hayek was among the first to realize that for intertemporal equilibrium to obtain all agents must have correct expectations of future prices. Before comparing four categories of intertemporal, the paper explains Hayek’s distinction between correct expectations and perfect foresight. The four equilibrium concepts considered are: (1) Perfect foresight equilibrium of which the Arrow-Debreu-McKenzie (ADM) model of equilibrium with complete markets is an alternative version, (2) Radner’s sequential equilibrium with incomplete markets, (3) Hicks’s temporary equilibrium, as extended by Bliss; (4) the Muth rational-expectations equilibrium as extended by Lucas into macroeconomics. While Hayek’s understanding closely resembles Radner’s sequential equilibrium, described by Radner as an equilibrium of plans, prices, and price expectations, Hicks’s temporary equilibrium seems to have been the natural extension of Hayek’s approach. The now dominant Lucas rational-expectations equilibrium misconceives intertemporal equilibrium, suppressing Hayek’s insights thereby retreating to a sterile perfect-foresight equilibrium.

And here is my concluding paragraph:

Four score and three years after Hayek explained how challenging the subtleties of the notion of intertemporal equilibrium and the elusiveness of any theoretical account of an empirical tendency toward intertemporal equilibrium, modern macroeconomics has now built a formidable theoretical apparatus founded on a methodological principle that rejects all the concerns that Hayek found so vexing denies that all those difficulties even exist. Many macroeconomists feel proud of what modern macroeconomics has achieved, but there is reason to think that the path trod by Hayek, Hicks and Radner could have led macroeconomics in a more fruitful direction than the one on which it has been led by Lucas and his associates.

Say’s (and Walras’s) Law Revisited

Published June 6, 2019 Axel Leijonfuvud , Robert Clower , Say's Law , temporary equilibrium , W. H. Hutt , Walras's Law 12 Comments

Update (6/18/2019): The current draft of my paper is now available on SSRN. Here is a link.

The annual meeting of the History of Economics Society is coming up in two weeks. It will be held at Columbia University at New York, and I will be presenting an unpublished paper of mine “Say’s Law and the Classical Theory of Depressions.” I began writing this paper about 20 years ago, but never finished it. My thinking about Say’s Law goes back to my first paper on classical monetary theory, and I have previously written blog-posts about Say’s Law (here and here). And more recently I realized that in a temporary-equilibrium framework, both Say’s Law and Walras’s Law, however understood, may be violated.

Here’s the abstract from my paper:

Say’s Law occupies a prominent, but equivocal, position in the history of economics, having been the object of repeated controversies about its meaning and significance since it was first propounded early in the nineteenth century. It has been variously defined, and arguments about its meaning and validity have not reached consensus about what was being attacked or defended. This paper proposes a unifying interpretation of Say’s Law based on the idea that the monetary sector of an economy with a competitively supplied money involves at least two distinct markets not just one. Thus, contrary to the Lange-Patinkin interpretation of Say’s Law, an excess supply or demand for money does not necessarily imply an excess supply or demand for goods in a Walrasian GE model. Beyond modifying the standard interpretation of the inconsistency between Say’s Law and a monetary economy, the paper challenges another standard interpretation of Say’s Law as being empirically refuted by the existence of lapses from full employment and economic depressions. Under the alternative interpretation, originally suggested by Clower and Leijonhufvud and by Hutt, Say’s Law provides a theory whereby disequilibrium in one market, causing the amount actually supplied to fall short of what had been planned to be supplied, reduces demand in other markets, initiating a cumulative process of shrinking demand and supply. This cumulative process of contracting supply is analogous to the Keynesian multiplier whereby a reduction in demand initiates a cumulative process of declining demand. Finally, it is shown that in a temporary-equilibrium context, Walras’s Law (and a fortiori Say’ Law) may be violated.

Here is the Introduction of my paper.

I. Introduction

Say’s Law occupies a prominent, but uncertain, position in the history of economics, having been the object of repeated controversies since the early nineteenth century. Despite a formidable secondary literature, the recurring controversies still demand a clear resolution. Say’s Law has been variously defined, and arguments about its meaning and validity have failed to achieve any clear consensus about just what is being defended or attacked. So, I propose in this paper to reconsider Say’s Law in a way that is faithful in spirit to how it was understood by its principal architects, J. B. Say, James Mill, and David Ricardo as well as their contemporary critics, and to provide a conceptual framework within which to assess the views of subsequent commentators.

In doing so, I hope to dispel perhaps the oldest and certainly the most enduring misunderstanding about Say’s Law: that it somehow was meant to assert that depressions cannot occur, or that they are necessarily self-correcting if market forces are allowed to operate freely. As I have tried to suggest with the title of this paper, Say’s Law was actually an element of Classical insights into the causes of depressions. Indeed, a version of the same idea expressed by Say’s Law implicitly underlies those modern explanations of depressions that emphasize coordination failures, though Say’s Law actually conveys an additional insight missing from most modern explanations.

The conception of Say’s Law articulated in this paper bears a strong resemblance to what Clower (1965, 1967) and Leijonhufvud (1968, 1981) called Say’s Principle. However, their artificial distinction between Say’s Law and Say’s Principle suggests a narrower conception and application of Say’s principle than, I believe, is warranted.  Moreover, their apparent endorsement of the idea that the validity of Say’s Law somehow depends in a critical way on the absence of money implied a straightforward misinterpretation of Say’s Law earlier propounded by, among other, Hayek, Lange and Patinkin in which only what became known as Walras’s Law and not Say’s Law is a logically necessary property of a general-equilibrium system. Finally, it is appropriate to note at the outset that, in most respects, the conception of Say’s Law for which I shall be arguing was anticipated in a quirky, but unjustly neglected, work by Hutt (1975) and by the important, and similarly neglected, work of Earl Thompson (1974).

In the next section, I offer a restatement of the Classical conception of Say’s Law. That conception was indeed based on the insight that, in the now familiar formulation, supply creates its own demand. But to grasp how this insight was originally understood, one must first understand the problem for which Say’s Law was proposed as a solution. The problem concerns the relationship between a depression and a general glut of all goods, but it has two aspects. First, is a depression in some sense caused by a general glut of all goods? Second, is a general glut of all goods logically conceivable in a market economy? In section three, I shall consider the Classical objections to Say’s Law and the responses offered by the Classical originators of the doctrine in reply to those objections. In section four, I discuss the modern objections offered to Say’s Law, their relation to the earlier objections, and the validity of the modern objections to the doctrine. In section five, I re-examine the Classical doctrine, relating it explicitly to a theory of depressions characterized by “inadequate aggregate demand.” I also elaborate on the subtle, but important, differences between my understanding of Say’s Law and what Clower and Leijonhufvud have called Say’s Principle. In section six, I show that when considered in the context of a temporary-equilibrium model in there is an incomplete set of forward and state-contingent markets, not even Walras’s Law, let alone Say’s Law, is logically necessary property of the model. An understanding of the conditions in which neither Walras’s Law nor Say’s Law is satisfied provides an important insight into financial crises and the systemic coordination failures that are characteristic of the deep depression to which they lead.

And here are the last two sections of the paper.

VI. Say’s Law Violated

            I have just argued that Clower, Leijonhufvud and Hutt explained in detail how the insight provided by Say’s Law into the mechanism whereby disturbances causing disequilibrium in one market or sector can be propagated and amplified into broader and deeper economy-wide disturbances and disequilibria. I now want to argue that by relaxing the strict Walrasian framework in which since Lange (1942) articulated Walras’s Law and Say’s Law, it is possible to show conditions under which neither Walras’s Law nor Say’s Law is satisfied.

            I relax the Walrasian framework by assuming that there is not a complete set of forward and state-contingent markets in which future transactions can be undertaken in the present. Because there a complete set of markets in which future prices are determined and visible to everyone, economic agents must formulate their intertemporal plans for production and consumption relying not only on observed current prices, but also on their expectations of currently unobservable future prices. As already noted, the standard proof of Walras’s Law and a fortiori of Say’s Law (or Identity) are premised on the assumption that all agents make their decisions about purchases and sales on their common knowledge of all prices.

            Thus, in the temporary-equilibrium framework, economic agents make their production and consumption decisions not on the basis of their common knowledge of future market prices common, but on their own conjectural expectations of those prices, expectations that may, or may not, be correct, and may, or may not, be aligned with the expectations of other agents. Unless the agents’ expectations of future prices are aligned, the expectations of some, or all, agents must be disappointed, and the plans to buy and sell formulated based on those expectations will have to be revised, or abandoned, once agents realize that their expectations were incorrect.

            Consider a simple two-person, two-good, two-period model in which agents make plans based on current prices observed in period 1 and their expectations of what prices will be in period 2. Given price expectations for period 2, period-1 prices are determined in a tatonnement process, so that no trading occurs until a temporary- equilibrium price vector for period 1 is found. Assume, further, that price expectations for period 2 do not change in the course of the tatonnement. Once a period-1 equilibrium price vector is found, the two budget constraints subject to which the agents make their optimal decisions, need not have the same values for expected prices in period 2, because it is not assumed that the period-2 price expectations of the two agents are aligned. Because the proof of Walras’s Law depends on agents basing their decisions to buy and sell each commodity on prices for each commodity in each period that are common to both agents, Walras’s Law cannot be proved unless the period-2 price expectations of both agents are aligned.

            The implication of the potential violation of Walras’s Law is that when actual prices turn out to be different from what they were expected to be, economic agents who previously assumed obligations that are about to come due may be unable to discharge those obligations. In standard general-equilibrium models, the tatonnement process assures that no trading takes place unless equilibrium prices have been identified. But in a temporary-equilibrium model, when decisions to purchase and sell are based not on equilibrium prices, but on actual prices that may not have been expected, the discharge of commitments is not certain.

            Of course, if Walras’s Law cannot be proved, neither can Say’s Law. Supply cannot create demand when the insolvency of economic agents obstructs mutually advantageous transactions between agents when some agents have negative net worth. The negative net worth of some agents can be transmitted to other agents holding obligations undertaken by agents whose net worth has become negative.

            Moreover, because the private supply of a medium of exchange by banks depends on the value of money-backing assets held by banks, the monetary system may cease to function in an economy in which the net worth of agents whose obligations are held banks becomes negative. Thus, the argument made in section IV.A for the validity of Say’s Law in the Identity sense breaks down once a sufficient number of agents no longer have positive net worth.

VII.      Conclusion

            My aim in this paper has been to explain and clarify a number of the different ways in which Say’s Law has been understood and misunderstood. A fair reading of the primary and secondary literature allows one to understand that many of the criticisms of Say’s Law have been not properly understood the argument that Say’s Law was either intended or could be reasonably interpreted to have said. Indeed, Say’s Law, properly understood, can actually help one understand the cumulative process of economic contraction whose existence supposedly proved its invalidity. However, I have also been able to show that there are plausible conditions in which a sufficiently serious financial breakdown, associated with financial crises in which substantial losses of net worth lead to widespread and contagious insolvency, when even Walras’s Law, and a fortiori Say’s Law, no longer hold. Understanding how Say’s Law may be violated may thus help in understanding the dynamics of financial crises and the cumulative systemic coordination failures of deep depressions.

I will soon be posting the paper on SSRN. When it’s posted I will post a link to an update to this post.

 

On Equilibrium in Economic Theory

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

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

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

The model of a stationary economy at rest in which all economic activity simply repeats what has already happened before did not seem very satisfying or informative to economists, but that view of equilibrium remained dominant in the nineteenth century and for perhaps the first quarter of the twentieth. Equilibrium was not an actual state that an economy could achieve, it was just an end state that economic processes would move toward if given sufficient time to play themselves out with no disturbing influences. This idea of a stationary timeless equilibrium is found in the writings of the classical economists, especially Ricardo and Mill who used the idea of a stationary state as the end-state towards which natural economic processes were driving an an economic system.

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

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

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

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

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

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

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

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

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

Hayek and Temporary Equilibrium

Published June 11, 2017 Axel Leijonfuvud , C. J. Bliss , expectations , general equilibrium , Hayek , incomplete markets , intertemporal equilibrium , J. R. Hicks , temporary equilibrium , Uncategorized 8 Comments

In my three previous posts (here, here, and here) about intertemporal equilibrium, I have been emphasizing that the defining characteristic of an intertemporal equilibrium is that agents all share the same expectations of future prices – or at least the same expectations of those future prices on which they are basing their optimizing plans – over their planning horizons. At a given moment at which agents share the same expectations of future prices, the optimizing plans of the agents are consistent, because none of the agents would have any reason to change his optimal plan as long as price expectations do not change, or are not disappointed as a result of prices turning out to be different from what they had been expected to be.

The failure of expected prices to be fulfilled would therefore signify that the information available to agents in forming their expectations and choosing optimal plans conditional on their expectations had been superseded by newly obtained information. The arrival of new information can thus be viewed as a cause of disequilibrium as can any difference in information among agents. The relationship between information and equilibrium can be expressed as follows: differences in information or differences in how agents interpret information leads to disequilibrium, because those differences lead agents to form differing expectations of future prices.

Now the natural way to generalize the intertemporal equilibrium model is to allow for agents to have different expectations of future prices reflecting their differences in how they acquire, or in how they process, information. But if agents have different information, so that their expectations of future prices are not the same, the plans on which agents construct their subjectively optimal plans will be inconsistent and incapable of implementation without at least some revisions. But this generalization seems incompatible with the equilibrium of optimal plans, prices and price expectations described by Roy Radner, which I have identified as an updated version of Hayek’s concept of intertemporal equilibrium.

The question that I want to explore in this post is how to reconcile the absence of equilibrium of optimal plans, prices, and price expectations, with the intuitive notion of market clearing that we use to analyze asset markets and markets for current delivery. If markets for current delivery and for existing assets are in equilibrium in the sense that prices are adjusting in those markets to equate demand and supply in those markets, how can we understand the idea that  the optimizing plans that agents are seeking to implement are mutually inconsistent?

The classic attempt to explain this intermediate situation which partially is and partially is not an equilibrium, was made by J. R. Hicks in 1939 in Value and Capital when he coined the term “temporary equilibrium” to describe a situation in which current prices are adjusting to equilibrate supply and demand in current markets even though agents are basing their choices of optimal plans to implement over time on different expectations of what prices will be in the future. The divergence of the price expectations on the basis of which agents choose their optimal plans makes it inevitable that some or all of those expectations won’t be realized, and that some, or all, of those agents won’t be able to implement the optimal plans that they have chosen, without at least some revisions.

In Hayek’s early works on business-cycle theory, he argued that the correct approach to the analysis of business cycles must be analyzed as a deviation by the economy from its equilibrium path. The problem that he acknowledged with this approach was that the tools of equilibrium analysis could be used to analyze the nature of the equilibrium path of an economy, but could not easily be deployed to analyze how an economy performs once it deviates from its equilibrium path. Moreover, cyclical deviations from an equilibrium path tend not to be immediately self-correcting, but rather seem to be cumulative. Hayek attributed the tendency toward cumulative deviations from equilibrium to the lagged effects of monetary expansion which cause cumulative distortions in the capital structure of the economy that lead at first to an investment-driven expansion of output, income and employment and then later to cumulative contractions in output, income, and employment. But Hayek’s monetary analysis was never really integrated with the equilibrium analysis that he regarded as the essential foundation for a theory of business cycles, so the monetary analysis of the cycle remained largely distinct from, if not inconsistent with, the equilibrium analysis.

I would suggest that for Hayek the Hicksian temporary-equilibrium construct would have been the appropriate theoretical framework within which to formulate a monetary analysis consistent with equilibrium analysis. Although there are hints in the last part of The Pure Theory of Capital that Hayek was thinking along these lines, I don’t believe that he got very far, and he certainly gave no indication that he saw in the Hicksian method the analytical tool with which to weave the two threads of his analysis.

I will now try to explain how the temporary-equilibrium method makes it possible to understand  the conditions for a cumulative monetary disequilibrium. I make no attempt to outline a specifically Austrian or Hayekian theory of monetary disequilibrium, but perhaps others will find it worthwhile to do so.

As I mentioned in my previous post, agents understand that their price expectations may not be realized, and that their plans may have to be revised. Agents also recognize that, given the uncertainty underlying all expectations and plans, not all debt instruments (IOUs) are equally reliable. The general understanding that debt – promises to make future payments — must be evaluated and assessed makes it profitable for some agents to specialize in in debt assessment. Such specialists are known as financial intermediaries. And, as I also mentioned previously, the existence of financial intermediaries cannot be rationalized in the ADM model, because, all contracts being made in period zero, there can be no doubt that the equilibrium exchanges planned in period zero will be executed whenever and exactly as scheduled, so that everyone’s promise to pay in time zero is equally good and reliable.

For our purposes, a particular kind of financial intermediary — banks — are of primary interest. The role of a bank is to assess the quality of the IOUs offered by non-banks, and select from the IOUs offered to them those that are sufficiently reliable to be accepted by the bank. Once a prospective borrower’s IOU is accepted, the bank exchanges its own IOU for the non-bank’s IOU. No non-bank would accept a non-bank’s IOU, at least not on terms as favorable as those on which the bank offers in accepting an IOU. In return for the non-bank IOU, the bank credits the borrower with a corresponding amount of its own IOUs, which, because the bank promises to redeem its IOUs for the numeraire commodity on demand, is generally accepted at face value.

Thus, bank debt functions as a medium of exchange even as it enables non-bank agents to make current expenditures they could not have made otherwise if they can demonstrate to the bank that they are sufficiently likely to repay the loan in the future at agreed upon terms. Such borrowing and repayments are presumably similar to the borrowing and repayments that would occur in the ADM model unmediated by any financial intermediary. In assessing whether a prospective borrower will repay a loan, the bank makes two kinds of assessments. First, does the borrower have sufficient income-earning capacity to generate enough future income to make the promised repayments that the borrower would be committing himself to make? Second, should the borrower’s future income, for whatever reason, turn out to be insufficient to finance the promised repayments, does the borrower have collateral that would allow the bank to secure repayment from the collateral offered as security? In making both kinds of assessments the bank has to form an expectation about the future — the future income of the borrower and the future value of the collateral.

In a temporary-equilibrium context, the expectations of future prices held by agents are not the same, so the expectations of future prices of at least some agents will not be accurate, and some agents won’tbe able to execute their plans as intended. Agents that can’t execute their plans as intended are vulnerable if they have incurred future obligations based on their expectations of future prices that exceed their repayment capacity given the future prices that are actually realized. If they have sufficient wealth — i.e., if they have asset holdings of sufficient value — they may still be able to repay their obligations. However, in the process they may have to sell assets or reduce their own purchases, thereby reducing the income earned by other agents. Selling assets under pressure of obligations coming due is almost always associated with selling those assets at a significant loss, which is precisely why it usually preferable to finance current expenditure by borrowing funds and making repayments on a fixed schedule than to finance the expenditure by the sale of assets.

Now, in adjusting their plans when they observe that their price expectations are disappointed, agents may respond in two different ways. One type of adjustment is to increase sales or decrease purchases of particular goods and services that they had previously been planning to purchase or sell; such marginal adjustments do not fundamentally alter what agents are doing and are unlikely to seriously affect other agents. But it is also possible that disappointed expectations will cause some agents to conclude that their previous plans are no longer sustainable under the conditions in which they unexpectedly find themselves, so that they must scrap their old plans replacing them with completely new plans instead. In the latter case, the abandonment of plans that are no longer viable given disappointed expectations may cause other agents to conclude that the plans that they had expected to implement are no longer profitable and must be scrapped.

When agents whose price expectations have been disappointed respond with marginal adjustments in their existing plans rather than scrapping them and replacing them with new ones, a temporary equilibrium with disappointed expectations may still exist and that equilibrium may be reached through appropriate price adjustments in the markets for current delivery despite the divergent expectations of future prices held by agents. Operation of the price mechanism may still be able to achieve a reconciliation of revised but sub-optimal plans. The sub-optimal temporary equilibrium will be inferior to the allocation that would have resulted had agents all held correct expectations of future prices. Nevertheless, given a history of incorrect price expectations and misallocations of capital assets, labor, and other factors of production, a sub-optimal temporary equilibrium may be the best feasible outcome.

But here’s the problem. There is no guarantee that, when prices turn out to be very different from what they were expected to be, the excess demands of agents will adjust smoothly to changes in current prices. A plan that was optimal based on the expectation that the price of widgets would be $500 a unit may well be untenable at a price of $120 a unit. When realized prices are very different from what they had been expected to be, those price changes can lead to discontinuous adjustments, violating a basic assumption — the continuity of excess demand functions — necessary to prove the existence of an equilibrium. Once output prices reach some minimum threshold, the best response for some firms may be to shut down, the excess demand for the product produced by the firm becoming discontinuous at the that threshold price. The firms shutting down operations may be unable to repay loans they had obligated themselves to repay based on their disappointed price expectations. If ownership shares in firms forced to cease production are held by households that have predicated their consumption plans on prior borrowing and current repayment obligations, the ability of those households to fulfill their obligations may be compromised once those firms stop paying out the expected profit streams. Banks holding debts incurred by firms or households that borrowers cannot service may find that their own net worth is reduced sufficiently to make the banks’ own debt unreliable, potentially causing a breakdown in the payment system. Such effects are entirely consistent with a temporary-equilibrium model if actual prices turn out to be very different from what agents had expected and upon which they had constructed their future consumption and production plans.

Sufficiently large differences between expected and actual prices in a given period may result in discontinuities in excess demand functions once prices reach critical thresholds, thereby violating the standard continuity assumptions on which the existence of general equilibrium depends under the fixed-point theorems that are the lynchpin of modern existence proofs. C. J. Bliss made such an argument in a 1983 paper (“Consistent Temporary Equilibrium” in the volume Modern Macroeconomic Theory edited by  J. P. Fitoussi) in which he also suggested, as I did above, that the divergence of individual expectations implies that agents will not typically regard the debt issued by other agents as homogeneous. Bliss therefore posited the existence of a “Financier” who would subject the borrowing plans of prospective borrowers to an evaluation process to determine if the plan underlying the prospective loan sought by a borrower was likely to generate sufficient cash flow to enable the borrower to repay the loan. The role of the Financier is to ensure that the plans that firms choose are based on roughly similar expectations of future prices so that firms will not wind up acting on price expectations that must inevitably be disappointed.

I am unsure how to understand the function that Bliss’s Financier is supposed to perform. Presumably the Financier is meant as a kind of idealized companion to the Walrasian auctioneer rather than as a representation of an actual institution, but the resemblance between what the Financier is supposed to do and what bankers actually do is close enough to make it unclear to me why Bliss chose an obviously fictitious character to weed out business plans based on implausible price expectations rather than have the role filled by more realistic characters that do what their real-world counterparts are supposed to do. Perhaps Bliss’s implicit assumption is that real-world bankers do not constrain the expectations of prospective borrowers sufficiently to suggest that their evaluation of borrowers would increase the likelihood that a temporary equilibrium actually exists so that only an idealized central authority could impose sufficient consistency on the price expectations to make the existence of a temporary equilibrium likely.

But from the perspective of positive macroeconomic and business-cycle theory, explicitly introducing banks that simultaneously provide an economy with a medium of exchange – either based on convertibility into a real commodity or into a fiat base money issued by the monetary authority – while intermediating between ultimate borrowers and ultimate lenders seems to be a promising way of modeling a dynamic economy that sometimes may — and sometimes may not — function at or near a temporary equilibrium.

We observe economies operating in the real world that sometimes appear to be functioning, from a macroeconomic perspective, reasonably well with reasonably high employment, increasing per capita output and income, and reasonable price stability. At other times, these economies do not function well at all, with high unemployment and negative growth, sometimes with high rates of inflation or with deflation. Sometimes, these economies are beset with financial crises in which there is a general crisis of solvency, and even apparently solvent firms are unable to borrow. A macroeconomic model should be able to account in some way for the diversity of observed macroeconomic experience. The temporary equilibrium paradigm seems to offer a theoretical framework capable of accounting for this diversity of experience and for explaining at least in a very general way what accounts for the difference in outcomes: the degree of congruence between the price expectations of agents. When expectations are reasonably consistent, the economy is able to function at or near a temporary equilibrium which is likely to exist. When expectations are highly divergent, a temporary equilibrium may not exist, and even if it does, the economy may not be able to find its way toward the equilibrium. Price adjustments in current markets may be incapable of restoring equilibrium inasmuch as expectations of future prices must also adjust to equilibrate the economy, there being no market mechanism by which equilibrium price expectations can be adjusted or restored.

This, I think, is the insight underlying Axel Leijonhufvud’s idea of a corridor within which an economy tends to stay close to an equilibrium path. However if the economy drifts or is shocked away from its equilibrium time path, the stabilizing forces that tend to keep an economy within the corridor cease to operate at all or operate only weakly, so that the tendency for the economy to revert back to its equilibrium time path is either absent or disappointingly weak.

The temporary-equilibrium method, it seems to me, might have been a path that Hayek could have successfully taken in pursuing the goal he had set for himself early in his career: to reconcile equilibrium-analysis with a theory of business cycles. Why he ultimately chose not to take this path is a question that, for now at least, I will leave to others to try to answer.

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

Published June 4, 2017 Arrow-Debrew-McKenzie model , expectations , general equilibrium , Hayek , incomplete markets , intertemporal budget constraint , intertemporal equilibrium , temporary equilibrium , Uncategorized , Walras's Law 9 Comments
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In this post I want to discuss Roy Radner’s treatment of an equilibrium of plans, prices, and price expectations (EPPPE) and its relationship to Hayek’s conception of intertemporal equilibrium, of which Radner’s treatment is a technically more sophisticated version. Although I seen no evidence that Radner was directly influenced by Hayek’s work, I consider Radner’s conception of EPPPE to be a version of Hayek’s conception of intertemporal equilibrium, because it captures essential properties of Hayek’s conception of intertemporal equilibrium as a situation in which agents independently formulate their own optimizing plans based on the prices that they actually observe – their common knowledge – and on the future prices that they expect to observe over the course of their planning horizons. While currently observed prices are common knowledge – not necessarily a factual description of economic reality but not an entirely unreasonable simplifying assumption – the prices that individual agents expect to observe in the future are subjective knowledge based on whatever common or private knowledge individuals may have and whatever methods they may be using to form their expectations of the prices that will be observed in the future. An intertemporal equilibrium refers to a set of decentralized plans that are both a) optimal from the standpoint of every agent’s own objectives given their common knowledge of current prices and their subjective expectations of future prices and b) mutually consistent.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Roger Farmer’s Prosperity for All

Published February 24, 2017 Arrow-Debrew-McKenzie model , J. R. Hicks , New Keynesians , Roger Farmer , Roy Radner , temporary equilibrium , Uncategorized 25 Comments

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

About Me

David Glasner
Washington, DC

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

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

Follow me on Twitter @david_glasner

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