Identification and frequency domain quasi-maximum likelihood estimation of linearized dynamic stochastic general equilibrium 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 sufficient 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 between the number of observed endogenous variables and structural shocks, and is simple to verify. The extensions, including identification through a subset of frequencies, partial identification, 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 nonidentification curves. For estimation, restricting our attention to nonsingular systems, we consider a frequency domain quasi-maximum likelihood estimator and present its asymptotic properties. The limiting distribution of the estimator can be different 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.