We explore methods for confronting model misspecification in macroeconomics. We construct
dynamic equilibria in which private agents and policy makers recognize that models
are approximations. We explore two generalizations of reational expectations equilibria.
In one of these equilibria, decision-makers use dynamic evolution equations that
are imperfect statistical approximations, and in the other misspecification is impossible
to detect even from infinite samples of time series data. In the first 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 misspecification
like time series econometricians
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