.ISSN (e) 1759-7331
(print) 1759-7323
Quantitative Economics
An open-access journal in quantitative economics
Journal of the
Econometric Society
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Quantitative Economics, Volume 3, Issue 1 (March 2012)

Identification and frequency domain quasi-maximum likelihood estimation of linearized dynamic stochastic general equilibrium models

Zhongjun Qu, Denis Tkachenko


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.

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