Macroeconometric Modeling and the Theory of the Representative Agent

The Lucas critique of econometric policy evaluation (1976) argues that, to the extent econometric models do not capture the primitive parameters of tastes and technology, their coefficients can be expected to vary with changes in policy regimes. Several econometricians have undertaken empirical work that separates the parameters of tastes, technology, and policy, estimating models that are in principle immune from this critique. Exemplary contributors to this effort have been Thomas Sargent (1978) and Sargent and Lars Hansen (1980). The empirical work inspired by the Lucas critique has proceeded using representative agent models and aggregate data. The treatment of expectations and dynamic optimization has been careful, although at times necessarily limited by the analytical requirements of attaining closed-form solutions for dynamic programming problems under uncertainty. Potential problems due to aggregation have usually been ignored, although when preferences and technology are quadratic it appears that they can be disposed of quickly: "assuming a representative firm is only a convenience, as the model admits a tidy theory of aggregation" (Sargent, 1978, p. 1016). It is ironic that a paradigm that emphasizes the isolation of the primitive parameters of tastes and technology has led to empirical work that has ben conducted almost exclusively with aggregate data. (There are exceptions: T. MaCurdy, 1983; J. Biddle, 1984.) There are several difficulties with this development. First, the fact that representative agent models with exact aggregation can be constructed is unrelated to whether or not these models are adequate; we can also construct models in which agents' behavior is unaffected by the policy regime. To exclusively model and test one but not the other appears to be a misplacement of emphasis. Second, some of this work has proceeded using representative agents whose behavior cannot be aggregated exactly (see, M. Eichenbaum, Hansen, and Kenneth Singleton, 1984, for an example). There is a third and most fundamental objection to empirical work which seeks to avoid the Lucas critique, yet uses aggregate data. Whenever econometric policy evaluation is undertaken using models estimated with aggregate data, it is implicitly presumed that the aggregator function is structural with respect to the policy intervention in question. Formally, aggregator functions are no more structural than are within-regime, reducedform relations of endogenous to policy variables. As a modeling strategy, ignoring the sensitivity of aggregators to policy changes seems no more compelling than ignoring the dependence of expectations on the policy regime. This paper describes a very modest econometric model in which the effects of ignoring aggregation and of ignoring expectations, each within the context of several representative agent models, can be appreciated. Objective functions are quadratic and prices are disparate across agents; in these respects the model's assumptions are in the mainstream of Lucas and subsequent empirical work. The model is carefully contrived so that exact aggregation is always possible. This is not essential to the argument in any way, but it drastically reduces the number of circumstances to be examined in constructing numerical examples. The example pertains to neoclassical production, and in each case there are three distinct representative agents: one for production, one for factor demand, *Professor of Economics, Duke University, Durham, NC 27706. Financial support from NSF Grant SES8318778 and a Sloan Research Fellowship are gratefully acknowledged. A more detailed version of this paper is available on request from the author.