Archive for the 'Abraham Wald' Category

Robert Lucas and the Pretense of Science

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

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

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

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

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

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

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

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

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

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

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

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

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

The 2017 History of Economics Society Conference in Toronto

I arrived in Toronto last Thursday for the History of Economics Society Meeting at the University of Toronto (Trinity College to be exact) to give talks on Friday about two papers, one of which (“Hayek and Three Equilibrium Concepts: Sequential, Temporary and Rational Expectations”) I have been posting over the past few weeks on this blog (here, here, here, here, and here). I want to thank those of you who have posted your comments, which have been very helpful, and apologize for not responding to the more recent comments. The other paper about which I gave a talk was based on a post from three of years ago (“Real and Pseudo Gold Standards: Did Friedman Know the Difference?”) on which one of the sections of that paper was based.

Here I am talking about Friedman.

Here are the abstracts of the two papers:

“Hayek and Three Equilibrium Concepts: Sequential, Temporary, and Rational Expectations”

Almost 40 years ago, Murray Milgate (1979) drew attention to the neglected contribution of F. A. Hayek to the concept of intertemporal equilibrium, which had previously been associated with Erik Lindahl and J. R. Hicks. Milgate showed that although Lindahl had developed the concept of intertemporal equilibrium independently, Hayek’s original 1928 contribution was published before Lindahl’s and that, curiously, Hicks in Value and Capital had credited Lindahl with having developed the concept despite having been Hayek’s colleague at LSE in the early 1930s and having previously credited Hayek for the idea of intertemporal equilibrium. Aside from Milgate’s contribution, few developments of the idea of intertemporal equilibrium have adequately credited Hayek’s contribution. This paper attempts to compare three important subsequent developments of that idea with Hayek’s 1937 refinement of the key idea of his 1928 paper. In non-chronological order, the three developments of interest are: 1) Radner’s model of sequential equilibrium with incomplete markets as an alternative to the Arrow-Debreu-McKenzie model of full equilibrium with complete markets; 2) Hicks’s temporary equilibrium model, and 3) the Muth-Lucas rational expectations model. While Hayek’s 1937 treatment most closely resembles Radner’s sequential equilibrium model, which Radner, echoing Hayek, describes as an equilibrium of plans, prices, and price expectations, Hicks’s temporary equilibrium model seems to be the natural development of Hayek’s approach. The Muth-Lucas rational-expectations model, however, develops the concept of intertemporal equilibrium in a way that runs counter to the fundamental Hayekian insight about the nature of intertemporal equilibrium

“Milton Friedman and the Gold Standard”

Milton Friedman discussed the gold standard in a number of works. His two main discussions of the gold standard appear in a 1951 paper on commodity-reserve currencies and in a 1961 paper on real and pseudo gold standards. In the 1951 paper, he distinguished between a gold standard in which only gold or warehouse certificates to equivalent amounts of gold circulated as a medium of exchange and one in which mere fiduciary claims to gold also circulated as media of exchange. Friedman called the former a strict gold standard and the latter as a partial gold standard. In the later paper, he distinguished between a gold standard in which gold is used as money, and a gold standard in which the government merely fixes the price of gold, dismissing the latter as a “pseudo” gold standard. In this paper, I first discuss the origin for the real/partial distinction, an analytical error, derived from David Hume via the nineteenth-century Currency School, about the incentives of banks to overissue convertible claims to base money, which inspired the Chicago plan for 100-percent reserve banking. I then discuss the real/pseudo distinction and argue that it was primarily motivated by the ideological objective of persuading libertarian and classical-liberal supporters of the gold standard to support a fiat standard supplemented by the k-percent quantity rule that Friedman was about to propose.

And here is my concluding section from the Friedman paper:

Milton Friedman’s view of the gold standard was derived from his mentors at the University Chicago, an inheritance that, in a different context, he misleadingly described as the Chicago oral tradition. The Chicago view of the gold standard was, in turn, derived from the English Currency School of the mid-nineteenth century, which successfully promoted the enactment of the Bank Charter Act of 1844, imposing a 100-percent marginal reserve requirement on the banknotes issued by the Bank of England, and served as a model for the Chicago Plan for 100-percent-reserve banking. The Currency School, in turn, based its proposals for reform on the price-specie-flow analysis of David Hume (1742).

The pure quantity-theoretic lineage of Friedman’s views of the gold standard and the intellectual debt that he owed to the Currency School and the Bank Charter Act disposed him to view the gold standard as nothing more than a mechanism for limiting the quantity of money. If the really compelling purpose and justification of the gold standard was to provide a limitation on the capacity of a government or a monetary authority to increase the quantity of money, then there was nothing special or exceptional about the gold standard.

I have no interest in exploring the reasons why supporters of, and true believers in, the gold standard feel a strong ideological or emotional attachment to that institution, and even if I had such an interest, this would not be the place to enter into such an exploration, but I conjecture that the sources of that attachment to the gold standard go deeper than merely to provide a constraint on the power of the government to increase the quantity of money.

But from Friedman’s quantity-theoretical perspective, if the primary virtue of the gold standard was that it served to limit the ability of the government to increase the quantity of money, if another institution could perform that service, it would serve just as well as the gold standard. The lesson that Friedman took from the efforts of the Currency School to enact the Bank Charter Act was that the gold standard, on its own, did not provide a sufficient constraint on the ability of private banks to increase the quantity of money. Otherwise, the 100-percent marginal reserve requirement of the Bank Charter Act would have been unnecessary.

Now if the gold standard could not function well without additional constraints on the quantity of money, then obviously the constraint on the quantity of money that really matters is not the gold standard itself, but the 100-percent marginal reserve requirement imposed on the banking system. But if the relevant constraint on the quantity of money is the 100 percent marginal reserve requirement, then the gold standard is really just excess baggage.

That was the view of Henry Simons and the other authors of the Chicago Plan. For a long time, Friedman accepted the Chicago Plan as the best prescription for monetary stability, but at about the time that he was writing his paper on real and pseudo gold standards, Friedman was frcoming to position that a k-percent rule would be a superior alternative to the old Chicago Plan. His paper on Pseudo gold standards for the Mont Pelerin Society was his initial attempt to persuade his libertarian and classical-liberal friends and colleagues to reconsider their support for the gold standard and prepare the ground for the k-percent rule that he was about to offer. But in his ideological enthusiasm he, in effect, denied the reality of the historical gold standard.

Aside from the getting to talk about my papers, the other highlights of the HES meeting for me included the opportunity to renew a very old acquaintance with the eminent Samuel Hollander whom I met about 35 years ago at the first History of Economics Society meeting that I ever attended and making the acquaintance for the first time with the eminent Deidre McCloskey who was at both of my sessions and with the eminent E. Roy Weintraub who has been doing important research on my illustrious cousin Abraham Wald, the first one to prove the existence of a competitive equilibrium almost 20 years before Arrow, Debreu and McKenzie came up with their proofs. Doing impressive and painstaking historical research Weintraub found a paper, long thought to have been lost in which Wald, using the fixed-point theorem that Arrow, Debreu and McKenzie had independently used in their proofs, gave a more general existence proof than he had provided in his published existence proofs, clearly establishing Wald’s priority over Arrow, Debreu and McKenzie in proving the existence of general equilibrium.

HT: Rebeca Betancourt

 


About Me

David Glasner
Washington, DC

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

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

Follow me on Twitter @david_glasner

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