Archive for the 'James Hartley' Category

What’s Wrong with DSGE Models Is Not Representative Agency

The basic DSGE macroeconomic model taught to students is based on a representative agent. Many critics of modern macroeconomics and DSGE models have therefore latched on to the representative agent as the key – and disqualifying — feature in DSGE models, and by extension, with modern macroeconomics. Criticism of representative-agent models is certainly appropriate, because, as Alan Kirman admirably explained some 25 years ago, the simplification inherent in a macoreconomic model based on a representative agent, renders the model entirely inappropriate and unsuitable for most of the problems that a macroeconomic model might be expected to address, like explaining why economies might suffer from aggregate fluctuations in output and employment and the price level.

While altogether fitting and proper, criticism of the representative agent model in macroeconomics had an unfortunate unintended consequence, which was to focus attention on representative agency rather than on the deeper problem with DSGE models, problems that cannot be solved by just throwing the Representative Agent under the bus.

Before explaining why representative agency is not the root problem with DSGE models, let’s take a moment or two to talk about where the idea of representative agency comes from. The idea can be traced back to F. Y. Edgeworth who, in his exposition of the ideas of W. S. Jevons – one of the three marginal revolutionaries of the 1870s – introduced two “representative particulars” to illustrate how trade could maximize the utility of each particular subject to the benchmark utility of the counterparty. That analysis of two different representative particulars, reflected in what is now called the Edgeworth Box, remains one of the outstanding achievements and pedagogical tools of economics. (See a superb account of the historical development of the Box and the many contributions to economic theory that it facilitated by Thomas Humphrey). But Edgeworth’s analysis and its derivatives always focused on the incentives of two representative agents rather than a single isolated representative agent.

Only a few years later, Alfred Marshall in his Principles of Economics, offered an analysis of how the equilibrium price for the product of a competitive industry is determined by the demand for (derived from the marginal utility accruing to consumers from increments of the product) and the supply of that product (derived from the cost of production). The concepts of the marginal cost of an individual firm as a function of quantity produced and the supply of an individual firm as a function of price not yet having been formulated, Marshall, in a kind of hand-waving exercise, introduced a hypothetical representative firm as a stand-in for the entire industry.

The completely ad hoc and artificial concept of a representative firm was not well-received by Marshall’s contemporaries, and the young Lionel Robbins, starting his long career at the London School of Economics, subjected the idea to withering criticism in a 1928 article. Even without Robbins’s criticism, the development of the basic theory of a profit-maximizing firm quickly led to the disappearance of Marshall’s concept from subsequent economics textbooks. James Hartley wrote about the short and unhappy life of Marshall’s Representative Firm in the Journal of Economic Perspectives.

One might have thought that the inauspicious career of Marshall’s Representative Firm would have discouraged modern macroeconomists from resurrecting the Representative Firm in the barely disguised form of a Representative Agent in their DSGE models, but the convenience and relative simplicity of solving a DSGE model for a single agent was too enticing to be resisted.

Therein lies the difference between the theory of the firm and a macroeconomic theory. The gain in convenience from adopting the Representative Firm was radically reduced by Marshall’s Cambridge students and successors who, without the representative firm, provided a more rigorous, more satisfying and more flexible exposition of the industry supply curve and the corresponding partial-equilibrium analysis than Marshall had with it. Providing no advantages of realism, logical coherence, analytical versatility or heuristic intuition, the Representative Firm was unceremoniously expelled from the polite company of economists.

However, as a heuristic device for portraying certain properties of an equilibrium state — whose existence is assumed not derived — even a single representative individual or agent proved to be a serviceable device with which to display the defining first-order conditions, the simultaneous equality of marginal rates of substitution in consumption and production with the marginal rate of substitution at market prices. Unlike the Edgeworth Box populated by two representative agents whose different endowments or preference maps result in mutually beneficial trade, the representative agent, even if afforded the opportunity to trade, can find no gain from engaging in it.

An excellent example of this heuristic was provided by Jack Hirshleifer in his 1970 textbook Investment, Interest, and Capital, wherein he adapted the basic Fisherian model of intertemporal consumption, production and exchange opportunities, representing the canonical Fisherian exposition in a single basic diagram. But the representative agent necessarily represents a state of no trade, because, for a single isolated agent, production and consumption must coincide, and the equilibrium price vector must have the property that the representative agent chooses not to trade at that price vector. I reproduce Hirshleifer’s diagram (Figure 4-6) in the attached chart.

Here is how Hirshleifer explained what was going on.

Figure 4-6 illustrates a technique that will be used often from now on: the representative-individual device. If one makes the assumption that all individuals have identical tastes and are identically situated with respect to endowments and productive opportunities, it follows that the individual optimum must be a microcosm of the social equilibrium. In this model the productive and consumptive solutions coincide, as in the Robinson Crusoe case. Nevertheless, market opportunities exist, as indicated by the market line M’M’ through the tangency point P* = C*. But the price reflected in the slope of M’M’ is a sustaining price, such that each individual prefers to hold the combination attained by productive transformations rather than engage in market transactions. The representative-individual device is helpful in suggesting how the equilibrium will respond to changes in exogenous data—the proviso being that such changes od not modify the distribution of wealth among individuals.

While not spelling out the limitations of the representative-individual device, Hirshleifer makes it clear that the representative-agent device is being used as an expository technique to describe, not as an analytical tool to determine, intertemporal equilibrium. The existence of intertemporal equilibrium does not depend on the assumptions necessary to allow a representative individual to serve as a stand-in for all other agents. The representative-individual is portrayed only to provide the student with a special case serving as a visual aid with which to gain an intuitive grasp of the necessary conditions characterizing an intertemporal equilibrium in production and consumption.

But the role of the representative agent in the DSGE model is very different from the representative individual in Hirshleifer’s exposition of the canonical Fisherian theory. In Hirshleifer’s exposition, the representative individual is just a special case and a visual aid with no independent analytical importance. In contrast to Hirshleifer’s deployment of the representative-individual, representative-agent in the DSGE model is used as an assumption whereby an analytical solution to the DSGE model can be derived, allowing the modeler to generate quantitative results to be compared with existing time-series data, to generate forecasts of future economic conditions, and to evaluate the effects of alternative policy rules.

The prominent and dubious role of the representative agent in DSGE models provided a convenient target for critics of DSGE models to direct their criticisms. In Congressional testimony, Robert Solow famously attacked DSGE models and used their reliance on the representative-agents to make them seem, well, simply ridiculous.

Most economists are willing to believe that most individual “agents” – consumers investors, borrowers, lenders, workers, employers – make their decisions so as to do the best that they can for themselves, given their possibilities and their information. Clearly they do not always behave in this rational way, and systematic deviations are well worth studying. But this is not a bad first approximation in many cases. The DSGE school populates its simplified economy – remember that all economics is about simplified economies just as biology is about simplified cells – with exactly one single combination worker-owner-consumer-everything-else who plans ahead carefully and lives forever. One important consequence of this “representative agent” assumption is that there are no conflicts of interest, no incompatible expectations, no deceptions.

This all-purpose decision-maker essentially runs the economy according to its own preferences. Not directly, of course: the economy has to operate through generally well-behaved markets and prices. Under pressure from skeptics and from the need to deal with actual data, DSGE modellers have worked hard to allow for various market frictions and imperfections like rigid prices and wages, asymmetries of information, time lags, and so on. This is all to the good. But the basic story always treats the whole economy as if it were like a person, trying consciously and rationally to do the best it can on behalf of the representative agent, given its circumstances. This cannot be an adequate description of a national economy, which is pretty conspicuously not pursuing a consistent goal. A thoughtful person, faced with the thought that economic policy was being pursued on this basis, might reasonably wonder what planet he or she is on.

An obvious example is that the DSGE story has no real room for unemployment of the kind we see most of the time, and especially now: unemployment that is pure waste. There are competent workers, willing to work at the prevailing wage or even a bit less, but the potential job is stymied by a market failure. The economy is unable to organize a win-win situation that is apparently there for the taking. This sort of outcome is incompatible with the notion that the economy is in rational pursuit of an intelligible goal. The only way that DSGE and related models can cope with unemployment is to make it somehow voluntary, a choice of current leisure or a desire to retain some kind of flexibility for the future or something like that. But this is exactly the sort of explanation that does not pass the smell test.

While Solow’s criticism of the representative agent was correct, he left himself open to an effective rejoinder by defenders of DSGE models who could point out that the representative agent was adopted by DSGE modelers not because it was an essential feature of the DSGE model but because it enabled DSGE modelers to simplify the task of analytically solving for an equilibrium solution. With enough time and computing power, however, DSGE modelers were able to write down models with a few heterogeneous agents (themselves representative of particular kinds of agents in the model) and then crank out an equilibrium solution for those models.

Unfortunately for Solow, V. V. Chari also testified at the same hearing, and he responded directly to Solow, denying that DSGE models necessarily entail the assumption of a representative agent and identifying numerous examples even in 2010 of DSGE models with heterogeneous agents.

What progress have we made in modern macro? State of the art models in, say, 1982, had a representative agent, no role for unemployment, no role for Financial factors, no sticky prices or sticky wages, no role for crises and no role for government. What do modern macroeconomic models look like? The models have all kinds of heterogeneity in behavior and decisions. This heterogeneity arises because people’s objectives dier, they differ by age, by information, by the history of their past experiences. Please look at the seminal work by Rao Aiyagari, Per Krusell and Tony Smith, Tim Kehoe and David Levine, Victor Rios Rull, Nobu Kiyotaki and John Moore. All of them . . . prominent macroeconomists at leading departments . . . much of their work is explicitly about models without representative agents. Any claim that modern macro is dominated by representative-agent models is wrong.

So on the narrow question of whether DSGE models are necessarily members of the representative-agent family, Solow was debunked by Chari. But debunking the claim that DSGE models must be representative-agent models doesn’t mean that DSGE models have the basic property that some of us at least seek in a macro-model: the capacity to explain how and why an economy may deviate from a potential full-employment time path.

Chari actually addressed the charge that DSGE models cannot explain lapses from full employment (to use Pigou’s rather anodyne terminology for depressions). Here is Chari’s response:

In terms of unemployment, the baseline model used in the analysis of labor markets in modern macroeconomics is the Mortensen-Pissarides model. The main point of this model is to focus on the dynamics of unemployment. It is specifically a model in which labor markets are beset with frictions.

Chari’s response was thus to treat lapses from full employment as “frictions.” To treat unemployment as the result of one or more frictions is to take a very narrow view of the potential causes of unemployment. The argument that Keynes made in the General Theory was that unemployment is a systemic failure of a market economy, which lacks an error-correction mechanism that is capable of returning the economy to a full-employment state, at least not within a reasonable period of time.

The basic approach of DSGE is to treat the solution of the model as an optimal solution of a problem. In the representative-agent version of a DSGE model, the optimal solution is optimal solution for a single agent, so optimality is already baked into the model. With heterogeneous agents, the solution of the model is a set of mutually consistent optimal plans, and optimality is baked into that heterogenous-agent DSGE model as well. Sophisticated heterogeneous-agent models can incorporate various frictions and constraints that cause the solution to deviate from a hypothetical frictionless, unconstrained first-best optimum.

The policy message emerging from this modeling approach is that unemployment is attributable to frictions and other distortions that don’t permit a first-best optimum that would be achieved automatically in their absence from being reached. The possibility that the optimal plans of individuals might be incompatible resulting in a systemic breakdown — that there could be a failure to coordinate — does not even come up for discussion.

One needn’t accept Keynes’s own theoretical explanation of unemployment to find the attribution of cyclical unemployment to frictions deeply problematic. But, as I have asserted in many previous posts (e.g., here and here) a modeling approach that excludes a priori any systemic explanation of cyclical unemployment, attributing instead all cyclical unemployment to frictions or inefficient constraints on market pricing, cannot be regarded as anything but an exercise in question begging.

 

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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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