This paper considers issues related to identification, inference, and computation
in linearized dynamic stochastic general equilibrium (DSGE) models. We first pro-
vide a necessary and sufficient condition for the local identification of the struc-
tural parameters based on the (first and) second order properties of the process.
The condition allows for arbitrary relations between the number of observed en-
dogenous 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 fur-
ther used to trace out nonidentification curves. For estimation, restricting our at-
tention to nonsingular systems, we consider a frequency domain quasi-maximum
likelihood estimator and present its asymptotic properties. The limiting distribu-
tion 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.
Keywords. Infinite dimensional mapping, local identification, MCMC, noniden-
tification curve, rank condition, spectral domain.
JEL classification. C10, C13, C30, E1.