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

Abstract

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.

Frequency Domain Analysis of Medium Scale DSGE Models with Application to Smets and Wouters (2007)

“…In this paper, we show that the methods in Qu and Tkachenko (2012) can be applied in a straightforward manner to SW (2007) to deliver informative results. We structure our identi…cation analysis into the following steps: (1) Identi…cation based on the second order properties.…”

“…Although such sophistication holds promise for delivering rich and empirically relevant results, it also poses substantial challenges for identi…cation, estimation, and inference. This paper shows how these issues can be tackled from a frequency domain perspective, using the framework recently developed by Qu and Tkachenko (2012). We use SW (2007) as the working example throughout the paper, motivated by the fact that it has become a workhorse model in the DSGE literature.…”

“…Iskrev (2010) gives su¢ cient conditions for the local identi…cation of structural parameters based on the mean and a set of autocovariances. Komunjer and Ng (2011) and Qu and Tkachenko (2012) are the …rst to provide necessary and su¢ cient conditions for local identi…cation. Qu and Tkachenko (2012) shows that taking a frequency domain perspective can deliver simple identi…cation conditions applicable to both singular and nonsingular DSGE systems without relying on a particular (say, the minimum state) representation.…”

“…Next, we consider estimating SW (2007) from a frequency domain perspective using the methodology developed in Qu and Tkachenko (2012). The method has two features.…”

Assessing Bayesian Model Comparison in Small Samples

“…Several methods already exist to check identi…cation in linearized models using: (i) the autocovariogram (Iskrev (2010), Andrle (2010)); 15 (ii) the spectral density (Komunjer and Ng (2011) and Qu and Tkachenko (2012)); and (iii) Bayesian indicators (Koop et al (2013)). For a review and methodological comparison of these techniques, the interested reader is referred to Mutschler (2014).…”