Archive for the 'common knowledge' 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 Rises and Falls of Keynesianism and Monetarism

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

The Explanatory Gap and Mengerian Subjectivism

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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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