Identification and Frequency Domain QML Estimation of Linearized DSGE Models

This paper considers issues related to identification, inference and computation in linearized Dynamic Stochastic General Equilibrium (DSGE) models. We first provide a necessary and su¢ cient condition for the local identification of the structural parameters based on the (first and) second order properties of the process. The condition allows for arbitrary relations be- tween the number of observed endogenous variables and structural shocks and is simple to verify. The extensions, including identification through a subset of frequencies, partial iden- tification, conditional identification and identification under general nonlinear constraints, are also studied. When lack of identification is detected, the method can be further used to trace out non-identification curves. For estimation, restricting our attention to nonsingular systems, we consider a frequency domain quasi-maximum likelihood (FQML) estimator and present its asymptotic properties. The limiting distribution of the estimator can be di¤erent from results in the related literature due to the structure of the DSGE model. Finally, we discuss a quasi- Bayesian procedure for estimation and inference. The procedure can be used to incorporate relevant prior distributions and is computationally attractive.