This paper studies dynamic identification of parameters of a dynamic stochastic general equilibrium model from the first and second moments of the data. Classical results for dynamic simultaneous equations do not apply because the state space solution of the model does not constitute a standard reduced form. Full rank of the Jacobian matrix of derivatives of the solution parameters with respect to the parameters of interest is necessary but not sufficient for identification. We use restrictions implied by observational equivalence to obtain two sets of rank and order conditions: one for stochastically singular models and another for nonsingular models. Measurement errors, mean, long-run, and a priori restrictions can be accommodated. An example is considered to illustrate the results.

This paper proposes a method for testing complementarities between explanatory and dependent variables in a large class of economic models. The proposed test is based on the monotone comparative statics (MCS) property of equilibria. Our main result is that MCS produces testable implications on the (small and large) quantiles of the dependent variable, despite the presence of multiple equilibria. The key features of our approach are: (1) we work with a nonparametric structural model of a continuous dependent variable in which the unobservable is allowed to be correlated with the explanatory variable in a reasonably general way; (2) we do not require the structural function to be known or estimable; (3) we remain fairly agnostic on how an equilibrium is selected. We illustrate the usefulness of our result for policy evaluation within Berry, Levinsohn, and Pakes’s (AER, 1999) model.