Archive for the 'Arrow-Debrew-McKenzie model' Category

A Tale of Two Syntheses

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

14. Hence, the term “comparative statics.”

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

On Equilibrium in Economic Theory

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

 

Hayek and Intertemporal Equilibrium

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Roger Farmer’s Prosperity for All

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A Primer on Equilibrium

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

In Praise of Israel Kirzner

Over the holiday weekend, I stumbled across, to my pleasant surprise, the lecture given just a week ago by Israel Kirzner on being awarded the 2015 Hayek medal by the Hayek Gesellschaft in Berlin. The medal, it goes without saying, was richly deserved, because Kirzner’s long career spanning over half a century has produced hundreds of articles and many books elucidating many important concepts in various areas of economics, but especially on the role of competition and entrepreneurship (the title of his best known book) in theory and in practice. A student of Ludwig von Mises, when Mises was at NYU in the 1950s, Kirzner was able to recast and rework Mises’s ideas in a way that made them more accessible and more relevant to younger generations of students than were the didactic and dogmatic pronouncements so characteristic of Mises’s own writings. Not that there wasn’t and still isn’t a substantial market niche in which such didacticism and dogmatism is highly prized, but there are also many for whom those features of the Misesian style don’t go down quite so easily.

But it would be very unfair, and totally wrong, to think of Kirzner as a mere popularizer of Misesian doctrines. Although in his modesty and self-effacement, Kirzner made few, if any, claims of originality for himself, his application of ideas that he learned from, or, having developed them himself, read into, Mises, Kirzner’s contributions in their own way were not at all lacking originality and creativity. In a certain sense, his contribution was, in its own way, entrepreneurial, i.e., taking a concept or an idea or an analytical tool applied in one context and deploying that concept, idea, or tool in another context. It’s worth mentioning that a reverential attitude towards one’s teachers and intellectual forbears is not only very much characteristic of the Talmudic tradition of which Kirzner is also an accomplished master, but it’s also characteristic, or at least used to be, of other scholarly traditions, notably Cambridge, England, where such illustrious students of Alfred Marshall as Frederick Lavington and A. C. Pigou viewed themselves as merely elaborating on doctrines that had already been expounded by Marshall himself, Pigou having famously said of his own voluminous work, “it’s all in Marshall.”

But rather than just extol Kirzner’s admirable personal qualities, I want to discuss what Kirzner said in his Hayek lecture. His main point was to explain how, in his view, the Austrian tradition, just as it seemed to be petering out in the late 1930s and 1940s, evolved from just another variant school of thought within the broader neoclassical tradition that emerged late in the 19th century from the marginal revolution started almost simultaneously around 1870 by William Stanley Jevons in England, Carl Menger in Austria, and Leon Walras in France/Switzerland, into a completely distinct school of thought very much at odds with the neoclassical mainstream. In Kirzner’s view, the divergence between Mises and Hayek on the one hand and the neoclassical mainstream on the other was that Mises and Hayek went further in developing the subjectivist paradigm underlying the marginal-utility theory of value introduced by Jevons, Menger, and Walras in opposition to the physicalist, real-cost, theory of value inherited from Smith, Ricardo, Mill, and other economists of the classical school.

The marginal revolution shifted the focus of economics from the objective physical and technological forces that supposedly determine cost, which, in turn, supposedly determines value, to subjective, not objective, mental states or opinions that characterize preferences, which, in turn, determine value. And, as soon became evident, the new subjective marginalist theory of value implied that cost, at bottom, is nothing other than a foregone value (opportunity cost), so that the classical doctrine that cost determines value has it exactly backwards: it is really value that determines cost (though it is usually a mistake to suppose that in complex systems causation runs in only one direction).

However, as the neoclassical research program evolved, the subjective character of the underlying theory was increasingly de-emphasized, a de-emphasis that was probably driven by two factors: 1) the profoundly paradoxical nature of the idea that value determines cost, not the reverse, and b) the mathematicization of economics and the increasing adoption, in the Walrasian style, of functional representations of utility and production, leading to the construction of models of economic equilibrium that, under appropriate continuity and convexity assumptions, could be shown to have a theoretically determinate and unique solution. The false impression was created that economics was an objective science like physics, and that economics should aim to create objective and deterministic scientific representations (models) of complex economic systems that could then yield quantitatively precise predictions, in the same way that physics produced models of planetary motion yielding quantitatively precise predictions.

What Hayek and Mises objected to was the idea, derived from the functional approach to economic theory, that economics is just a technique of optimization subject to constraints, that all economic problems can be reduced to optimization problems. And it is a historical curiosum that one of the chief contributors to this view of economics was none other than Lionel Robbins in his seminal methodological work An Essay on the Nature and Significance of Economic Science, written precisely during that stage of his career when he came under the profound influence of Mises and Hayek, but before Mises and Hayek adopted the more radically subjective approach that characterizes their views in the late 1930s and 1940s. The critical works are Hayek’s essays reproduced as The Counterrevolution of Science and his essays “Economics and Knowledge,” “The Facts of the Social Sciences,” “The Use of Knowledge in Society,” and “The Meaning of Competition,” all contained in the remarkable volume Individualism and Economic Order.

What neoclassical economists who developed this deterministic version of economic theory, a version wonderfully expounded in Samuelson Foundations of Economic Analysis and ultimately embodied in the Arrow-Debreu general-equilibrium model, failed to see is that the model could not incorporate in an intellectually satisfying or empirically fruitful way the process of economic growth and development. The fundamental characteristic of the Arrow-Debreu model is its perfection. The solution of the model is Pareto-optimal, and cannot be improved upon; the entire unfolding of the model from beginning to end proceeds entirely according to a plan (actually a set of perfectly consistent and harmonious individual plans) with no surprises and no disappointments relative to what was already foreseen and planned — in detail — at the outset. Nothing is learned in the unfolding and execution of those detailed, perfectly harmonious plans that was not already known at the beginning, whatever happens having already been foreseen. If something truly new would have been learned in the course of the unfolding and execution of those plans, the new knowledge would necessarily have been surprising, and a surprise would necessarily have generated some disappointment and caused some revision of a previously formulated plan of action. But that is precisely what the Arrow-Debreu model, in its perfection, disallows. And that is what, from the perspective of Mises, Hayek, and Kirzner, is exactly wrong with the entire development of neoclassical theory for the past 80 years or more.

The specific point of the neoclassical paradigm on which Kirzner has focused his criticism is the inability of the neoclassical paradigm to find a place for the entrepreneur and entrepreneurial activity in its theoretical apparatus. Profit is what is earned by the entrepreneur, but in full general equilibrium, all income is earned by factors of production, so profits have been exhausted and the entrepreneur euthanized.

Joseph Schumpeter, who was torn between his admiration for the Walrasian general equilibrium system and his Austrian education in economics, tried to reintroduce the entrepreneur as the disruptive force behind the process of creative destruction, the role of the entrepreneur being to disrupt the harmonious equilibrium of the Walrasian system by innovating – introducing either new techniques of production or new consumer products. Kirzner, however, though not denying that disruptive Schumpeterian entrepreneurs may come on the scene from time to time, is focused on a less disruptive, but more pervasive and more characteristic type of entrepreneurship, the kind that is on the lookout for – that is alert to – the profit opportunities that are always latent in the existing allocation of resources and the current structure of input and output prices. Prices in some places or at some times may be high relative to other places and other times, so the entrepreneurial maxim is: buy cheap and sell dear.

Not so long ago, someone noticed that used book prices on Amazon are typically lower at the end of the semester or the school year, when students are trying to unload the books that they don’t want to keep, than they are at the beginning of the semester, when students are buying the books that they will have to read in the new semester. By buying the books students are selling at the end of the school year and selling them at the beginning of the school year, the insightful entrepreneur reduces the cost to students of obtaining the books they use during the school year. That bit of insight and alertness is classic Kirznerian entrepreneurship in action; it was rewarded by a profit, but the activity was equilibrating, not disruptive, reducing the spread between prices for the same, or very similar, commodities paid by buyers or received by sellers at different times of the year.

Sometimes entrepreneurship involves recognizing that a resource or a factor of production is undervalued in its current use. Shifting the resource from a relatively low-valued use to a higher-value use generates a profit for the alert entrepreneur. Here, again, the activity is equilibrating not disruptive. And as others start to catch on, the profit earned on the spread between the value of the resource in its old and new uses will be eroded by the competition of copy-cat entrepreneurs and of other entrepreneurs with an even better idea derived from an even more penetrating insight.

Here is another critical point. Rarely does a new idea come into existence and cause just one change. Every change creates a new and different situation, potentially creating further opportunities to be taken advantage of by other alert and insightful individuals. In an open competitive system, there is no reason why the process of discovery and adaptation should ever come to an end state in which new insights can no longer be made and change is no longer possible.

However, it also the case that knowledge or information is often imperfect and faulty, and that incentives are imperfectly aligned with actual benefits, so that changes can be profitable even though they lead to inferior outcomes. Margarine can be substituted for butter, and transfats for saturated fats. Big mistake. But who knew? And processed carbohydrates can replace fats in low-fat diets. Big mistake. But who knew?

I myself had the pleasure of experiencing first-hand, on a very small scale to be sure, but still in a very inspiring way, this sort of unplanned, serendipitous connection between my stumbling across Kirzner’s Hayek lecture and, then, after starting to write this post a couple of days ago, doing a Google search on Kirzner plus something else (can’t remember what) and seeing a link to Deirdre McCloskey’s paper “A Kirznerian Economic History of the Modern World” in which McCloskey, in somewhat over-the-top style, waxed eloquent about the long and circuitous evolution of her views from the strict neoclassicism in which she was indoctrinated at Harvard and later at Chicago to Kirznerian Austrianism. McCloskey observes in her wonderful paean to Kirzner that growth theory (which is now the core of modern macroeconomics) is utterly incapable of accounting for the historically unique period of economic growth over the past 200 years in what we now refer to as the developed world.

I had faced repeatedly 1964 to 2010 the failure of oomph in the routine, Samuelsonian arguments, such as accumulation inspired by the Protestant ethic, or trade as an engine of growth, or Marxian exploitation, or imperialism as the last stage of capitalism, or factor-biased induced technical change, or Unified Growth Theory. My colleagues at the University of Chicago in the 1970s, Al Harberger and Bob Fogel, pioneered the point that Harberger Triangles of efficiency gain are small (Harberger 1964; Fogel 1965). None of the allocative, capital-accumulation explanations of economic growth since Adam Smith have worked scientifically, which I show in depressing detail in Bourgeois Dignity. None of them have the quantitative force and the distinctiveness to the modern world and the West to explain the Great Fact. No oomph.

What works? Creativity. Innovation. Discovery. The Austrian core. And where did discovery come from? It came from the releasing of the West from ancient constraints on the dignity and liberty of the bourgeoisie, producing an intellectual and engineering explosion of ideas. As the banker and science writer Matt Ridley has recently described it (2010; compare Storr 2008), ideas started breeding, and having baby ideas, who bred further. The liberation of the Jews in the West is a good emblem for the wider story. A people of the book began to be allowed into commercial centers in Holland and then England, and allowed outside the shtetl and the ghetto, and into the universities of Berlin and Manchester. They commenced innovating on a massive, breeding-reactor scale, in good ways (Rothschild, Einstein) and in bad (Marx, Freud).

Ridley explains how the evolutionary biologist Leigh Van Valen proposed in 1973 a Red Queen Hypothesis that would explain why commercial and mechanical ideas, when first allowed to evolve, had to run faster and faster to stay in the same place. Economists would call it the dissipation of initial rents, in the second and third acts of the economic drama. Once breeding ideas were set free in the seventeenth century they created more and more opportunities for Kirznerian alertness. The opportunities were alertly taken up, and persuasively argued for, and at length routinized. The idea of the steam engine had babies with the idea of rails and the idea of wrought iron, and the result was the railroads. The new generation of ideas-in view of the continuing breeding of ideas going on in the background-created by their very routinization still more Kirznerian opportunities. Railroads once they were routine led to Sears, Roebuck and Montgomery Ward. And the routine then created prosperous people, such as my grandfather the freight conductor on the Milwaukee Road or my great-grandfather the postal clerk on the Chicago & Western Indiana or my other great-grandfather who invented the ring on telephones (which extended the telegraph, which itself had made tight scheduling of trains possible). Some became prosperous enough to take up the new ideas, and all became prosperous enough under the Great Fact to buy them. If there was no dissipation of the rents to alertness, and no ultimate gain of income to hoi polloi, no third act, no Red Queen effect, then innovation would not have a justification on egalitarian grounds-as in the historical event it surely did have. The Bosses would engorge all the income, as Ricardo in the early days of the Great Fact had feared. But in the event the discovery of which Kirzner and the Austrian tradition speaks enriched in the third act mainly the poor-your ancestors, and Israel’s, and mine.

It is the growth and diffusion of knowledge (both practical and theoretical, but especially the former), not the accumulation of capital, that accounts for the spectacular economic growth of the past two centuries. So, all praise to the Austrian economist par excellence, Israel Kirzner. But just to avoid any misunderstanding, I will state for the record, that my admiration for Kirzner does not mean that I have gone wobbly on the subject of Austrian Business Cycle Theory, a subject on which Kirzner has been, so far as I know, largely silent — yet further evidence – as if any were needed — of Kirzner’s impeccable judgment.

Big Ideas in Macroeconomics: A Review

Steve Williamson recently plugged a new book by Kartik Athreya (Big Ideas in Macroeconomics), an economist at the Federal Reserve Bank of Richmond, which tries to explain in relatively non-technical terms what modern macroeconomics is all about. I will acknowledge that my graduate training in macroeconomics predated the rise of modern macro, and I am not fluent in the language of modern macro, though I am trying to fill in the gaps. And this book is a good place to start. I found Athreya’s book a good overview of the field, explaining the fundamental ideas and how they fit together.

Big Ideas in Macroeconomics is a moderately big book, 415 pages, covering a very wide range of topics. It is noteworthy, I think, that despite its size, there is so little overlap between the topics covered in this book, and those covered in more traditional, perhaps old-fashioned, books on macroeconomics. The index contains not a single entry on the price level, inflation, deflation, money, interest, total output, employment or unemployment. Which is not to say that none of those concepts are ever mentioned or discussed, just that they are not treated, as they are in traditional macroeconomics books, as the principal objects of macroeconomic inquiry. The conduct of monetary or fiscal policy to achieve some explicit macroeconomic objective is never discussed. In contrast, there are repeated references to Walrasian equilibrium, the Arrow-Debreu-McKenzie model, the Radner model, Nash-equilibria, Pareto optimality, the first and second Welfare theorems. It’s a new world.

The first two chapters present a fairly detailed description of the idea of Walrasian general equilibrium and its modern incarnation in the canonical Arrow-Debreu-McKenzie (ADM) model.The ADM model describes an economy of utility-maximizing households and profit-maximizing firms engaged in the production and consumption of commodities through time and space. There are markets for commodities dated by time period, specified by location and classified by foreseeable contingent states of the world, so that the same physical commodity corresponds to many separate commodities, each corresponding to different time periods and locations and to contingent states of the world. Prices for such physically identical commodities are not necessarily uniform across times, locations or contingent states.The demand for road salt to de-ice roads depends on whether conditions, which depend on time and location and on states of the world. For each different possible weather contingency, there would be a distinct market for road salt for each location and time period.

The ADM model is solved once for all time periods and all states of the world. Under appropriate conditions, there is one (and possibly more than one) intertemporal equilibrium, all trades being executed in advance, with all deliveries subsequently being carried out, as time an contingencies unfold, in accordance with the terms of the original contracts.

Given the existence of an equilibrium, i.e., a set of prices subject to which all agents are individually optimizing, and all markets are clearing, there are two classical welfare theorems stating that any such equilibrium involves a Pareto-optimal allocation and any Pareto-optimal allocation could be supported by an equilibrium set of prices corresponding to a suitably chosen set of initial endowments. For these optimality results to obtain, it is necessary that markets be complete in the sense that there is a market for each commodity in each time period and contingent state of the world. Without a complete set of markets in this sense, the Pareto-optimality of the Walrasian equilibrium cannot be proved.

Readers may wonder about the process by which an equilibrium price vector would actually be found through some trading process. Athreya invokes the fiction of a Walrasian clearinghouse in which all agents (truthfully) register their notional demands and supplies at alternative price vectors. Based on these responses the clearinghouse is able to determine, by a process of trial and error, the equilibrium price vector. Since the Walrasian clearinghouse presumes that no trading occurs except at an equilibrium price vector, there can be no assurance that an equilibrium price vector would ever be arrived at under an actual trading process in which trading occurs at disequilibrium prices. Moreover, as Clower and Leijonhufvud showed over 40 years ago (“Say’s Principle: What it Means and What it Doesn’t Mean”), trading at disequilibrium prices may cause cumulative contractions of aggregate demand because the total volume of trade at a disequilibrium price will always be less than the volume of trade at an equilibrium price, the volume of trade being constrained by the lesser of quantity supplied and quantity demanded.

In the view of modern macroeconomics, then, Walrasian general equilibrium, as characterized by the ADM model, is the basic and overarching paradigm of macroeconomic analysis. To be sure, modern macroeconomics tries to go beyond the highly restrictive assumptions of the ADM model, but it is not clear whether the concessions made by modern macroeconomics to the real world go very far in enhancing the realism of the basic model.

Chapter 3, contains some interesting reflections on the importance of efficiency (Pareto-optimality) as a policy objective and on the trade-offs between efficiency and equity and between ex-ante and ex-post efficiency. But these topics are on the periphery of macroeconomics, so I will offer no comment here.

In chapter 4, Athreya turns to some common criticisms of modern macroeconomics: that it is too highly aggregated, too wedded to the rationality assumption, too focused on equilibrium steady states, and too highly mathematical. Athreya correctly points out that older macroeconomic models were also highly aggregated, so that if aggregation is a problem it is not unique to modern macroeconomics. That’s a fair point, but skirts some thorny issues. As Athreya acknowledges in chapter 5, an important issue separating certain older macroeconomic traditions (both Keynesian and Austrian among others) is the idea that macroeconomic dysfunction is a manifestation of coordination failure. It is a property – a remarkable property – of Walrasian general equilibrium that it achieves perfect (i.e., Pareto-optimal) coordination of disparate, self-interested, competitive individual agents, fully reconciling their plans in a way that might have been achieved by an omniscient and benevolent central planner. Walrasian general equilibrium fully solves the coordination problem. Insofar as important results of modern macroeconomics depend on the assumption that a real-life economy can be realistically characterized as a Walrasian equilibrium, modern macroeconomics is assuming that coordination failures are irrelevant to macroeconomics. It is only after coordination failures have been excluded from the purview of macroeconomics that it became legitimate (for the sake of mathematical tractability) to deploy representative-agent models in macroeconomics, a coordination failure being tantamount, in the context of a representative agent model, to a form of irrationality on the part of the representative agent. Athreya characterizes choices about the level of aggregation as a trade-off between realism and tractability, but it seems to me that, rather than making a trade-off between realism and tractability, modern macroeconomics has simply made an a priori decision that coordination problems are not a relevant macroeconomic concern.

A similar argument applies to Athreya’s defense of rational expectations and the use of equilibrium in modern macroeconomic models. I would not deny that there are good reasons to adopt rational expectations and full equilibrium in some modeling situations, depending on the problem that theorist is trying to address. The question is whether it can be appropriate to deviate from the assumption of a full rational-expectations equilibrium for the purposes of modeling fluctuations over the course of a business cycle, especially a deep cyclical downturn. In particular, the idea of a Hicksian temporary equilibrium in which agents hold divergent expectations about future prices, but markets clear period by period given those divergent expectations, seems to offer (as in, e.g., Thompson’s “Reformulation of Macroeconomic Theory“) more realism and richer empirical content than modern macromodels of rational expectations.

Athreya offers the following explanation and defense of rational expectations:

[Rational expectations] purports to explain the expectations people actually have about the relevant items in their own futures. It does so by asking that their expectations lead to economy-wide outcomes that do not contradict their views. By imposing the requirement that expectations not be systematically contradicted by outcomes, economists keep an unobservable object from becoming a source of “free parameters” through which we can cheaply claim to have “explained” some phenomenon. In other words, in rational-expectations models, expectations are part of what is solved for, and so they are not left to the discretion of the modeler to impose willy-nilly. In so doing, the assumption of rational expectations protects the public from economists.

This defense of rational expectations plainly belies betrays the methodological arrogance of modern macroeconomics. I am all in favor of solving a model for equilibrium expectations, but solving for equilibrium expectations is certainly not the same as insisting that the only interesting or relevant result of a model is the one generated by the assumption of full equilibrium under rational expectations. (Again see Thompson’s “Reformulation of Macroeconomic Theory” as well as the classic paper by Foley and Sidrauski, and this post by Rajiv Sethi on his blog.) It may be relevant and useful to look at a model and examine its properties in a state in which agents hold inconsistent expectations about future prices; the temporary equilibrium existing at a point in time does not correspond to a steady state. Why is such an equilibrium uninteresting and uninformative about what happens in a business cycle? But evidently modern macroeconomists such as Athreya consider it their duty to ban such models from polite discourse — certainly from the leading economics journals — lest the public be tainted by economists who might otherwise dare to abuse their models by making illicit assumptions about expectations formation and equilibrium concepts.

Chapter 5 is the most important chapter of the book. It is in this chapter that Athreya examines in more detail the kinds of adjustments that modern macroeconomists make in the Walrasian/ADM paradigm to accommodate the incompleteness of markets and the imperfections of expectation formation that limit the empirical relevance of the full ADM model as a macroeconomic paradigm. To do so, Athreya starts by explaining how the Radner model in which a less than the full complement of Arrow-Debreu contingent-laims markets is available. In the Radner model, unlike the ADM model, trading takes place through time for those markets that actually exist, so that the full Walrasian equilibrium exists only if agents are able to form correct expectations about future prices. And even if the full Walrasian equilibrium exists, in the absence of a complete set of Arrow-Debreu markets, the classical welfare theorems may not obtain.

To Athreya, these limitations on the Radner version of the Walrasian model seem manageable. After all, if no one really knows how to improve on the equilibrium of the Radner model, the potential existence of Pareto improvements to the Radner equilibrium is not necessarily that big a deal. Athreya expands on the discussion of the Radner model by introducing the neoclassical growth model in both its deterministic and stochastic versions, all the elements of the dynamic stochastic general equilibrium (DSGE) model that characterizes modern macroeconomics now being in place. Athreya closes out the chapter with additional discussions of the role of further modifications to the basic Walrasian paradigm, particularly search models and overlapping-generations models.

I found the discussion in chapter 5 highly informative and useful, but it doesn’t seem to me that Athreya faces up to the limitations of the Radner model or to the implied disconnect between the Walraisan paradigm and macroeconomic analysis. A full Walrasian equilibrium exists in the Radner model only if all agents correctly anticipate future prices. If they don’t correctly anticipate future prices, then we are in the world of Hicksian temporary equilibrium. But in that world, the kind of coordination failures that Athreya so casually dismisses seem all too likely to occur. In a world of temporary equilibrium, there is no guarantee that intertemporal budget constraints will be effective, because those budget constraint reflect expected, not actual, future prices, and, in temporary equilibrium, expected prices are not the same for all transactors. Budget constraints are not binding in a world in which trading takes place through time based on possibly incorrect expectations of future prices. Not only does this mean that all the standard equilibrium and optimality conditions of Walrasian theory are violated, but that defaults on IOUs and, thus, financial-market breakdowns, are entirely possible.

In a key passage in chapter 5, Athreya dismisses coordination-failure explanations, invidiously characterized as Keynesian, for inefficient declines in output and employment. While acknowledging that such fluctuations could, in theory, be caused by “self-fulfilling pessimism or fear,” Athreya invokes the benchmark Radner trading arrangement of the ADM model. “In the Radner economy, Athreya writes, “households and firms have correct expectations for the spot market prices one period hence.” The justification for that expectational assumption, which seems indistinguishable from the assumption of a full, rational-expectations equilibrium, is left unstated. Athreya continues:

Granting that they indeed have such expectations, we can now ask about the extent to which, in a modern economy, we can have outcomes that are extremely sensitive to them. In particular, is it the case that under fairly plausible conditions, “optimism” and “pessimism” can be self-fulfilling in ways that make everyone (or nearly everyone) better off in the former than the latter?

Athreya argues that this is possible only if the aggregate production function of the economy is characterized by increasing returns to scale, so that productivity increases as output rises.

[W]hat I have in mind is that the structure of the economy must be such that when, for example, all households suddenly defer consumption spending (and save instead), interest rates do not adjust rapidly to forestall such a fall in spending by encouraging firms to invest.

Notice that Athreya makes no distinction between a reduction in consumption in which people shift into long-term real or financial assets and one in which people shift into holding cash. The two cases are hardly identical, but Athreya has nothing to say about the demand for money and its role in macroeconomics.

If they did, under what I will later describe as a “standard” production side for the economy, wages would, barring any countervailing forces, promptly rise (as the capital stock rises and makes workers more productive). In turn, output would not fall in response to pessimism.

What Athreya is saying is that if we assume that there is a reduction in the time preference of households, causing them to defer present consumption in order to increase their future consumption, the shift in time preference should be reflected in a rise in asset prices, causing an increase in the production of durable assets, and leading to an increase in wages insofar as the increase in the stock of fixed capital implies an increase in the marginal product of labor. Thus, if all the consequences of increased thrift are foreseen at the moment that current demand for output falls, there would be a smooth transition from the previous steady state corresponding to a high rate of time preference to the new steady state corresponding to a low rate of time preference.

Fine. If you assume that the economy always remains in full equilibrium, even in the transition from one steady state to another, because everyone has rational expectations, you will avoid a lot of unpleasantness. But what if entrepreneurial expectations do not change instantaneously, and the reduction in current demand for output corresponding to reduced spending on consumption causes entrepreneurs to reduce, not increase, their demand for capital equipment? If, after the shift in time preference, total spending actually falls, there may be a chain of disappointments in expectations, and a series of defaults on IOUs, culminating in a financial crisis. Pessimism may indeed be self-fulfilling. But Athreya has a just-so story to tell, and he seems satisfied that there is no other story to be told. Others may not be so easily satisfied, especially when his just-so story depends on a) the rational expectations assumption that many smart people have a hard time accepting as even remotely plausible, and b) the assumption that no trading takes place at disequilibrium prices. Athreya continues:

Thus, at least within the context of models in which households and firms are not routinely incorrect about the future, multiple self-fulfilling outcomes require particular features of the production side of the economy to prevail.

Actually what Athreya should have said is: “within the context of models in which households and firms always predict future prices correctly.”

In chapter 6, Athreya discusses how modern macroeconomics can and has contributed to the understanding of the financial crisis of 2007-08 and the subsequent downturn and anemic recovery. There is a lot of very useful information and discussion of various issues, especially in connection with banking and financial markets. But further comment at this point would be largely repetitive.

Anyway, despite my obvious and strong disagreements with much of what I read, I learned a lot from Athreya’s well-written and stimulating book, and I actually enjoyed reading it.


About Me

David Glasner
Washington, DC

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

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