Acknowledging Misspecification in Macroeconomic

We explore methods for confronting model misspeci cation in macroeconomics. We construct dynamic equilibria in which private agents and policy makers recognize that models are approximations. We explore two generalizations of rational expectations equilibria. In one of these equilibria, decision-makers use dynamic evolution equations that are imperfect statistical approximations, and in the other misspeci cation is impossible to detect even from in nite samples of time series data. In the rst of these equilibria, decision rules are tailored to be robust to the allowable statistical discrepancies. Using frequency domain methods, we show that robust decision-makers treat model misspeci cation like time series econometricians. 1. Rational expectations versus misspecification Subgame perfect and rational expectations equilibrium models do not permit a self-contained analysis of model misspeci cation. But sometimes model builders suspect misspeci cation, and so might the agents in their model. To study that we must modify rational expectations. But in doing so, we want to respect and extend the inspiration underlying rational expectations, which was to deny that a model builder knows more about the data generating mechanism than do the agents inside his model. This paper describes possible reactions of model builders and agents to two different types of model misspeci cation. The rst type is diÆcult to detect in time series samples of the moderate sizes typically at our disposable. A second type of model misspeci cation is impossible to detect even in in nite samples drawn from an equilibrium. Date: January 25, 2001.