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.

This paper presents a framework for analyzing global identi…cation in log linearized DSGE models that encompasses both determinacy and indeterminacy. First, it considers a frequency domain expression for the Kullback-Leibler distance between two DSGE models, and shows that global identi…cation fails if and only if the minimized distance equals zero. This result has three features. (1) It can be applied across DSGE models with di¤erent structures. (2) It permits checking whether a subset of frequencies can deliver identi…cation. (3) It delivers parameter values that yield observational equivalence if there is identi…cation failure. Next, the paper proposes a measure for the empirical closeness between two DSGE models for a further understanding of the strength of identi…cation. The measure gauges the feasibility of distinguishing one model from another based on a …nite number of observations generated by the two models. It is shown to represent the highest possible power under Gaussianity when considering local alternatives. The above theory is illustrated using two small scale and one medium scale DSGE models. The results document that certain parameters can be identi…ed under indeterminacy but not determinacy, that di¤erent monetary policy rules can be (nearly) observationally equivalent, and that identi…cation properties can di¤er substantially between small and medium scale models. For implementation, two procedures are developed and made available, both of which can be used to obtain and thus to cross validate the …ndings reported in the empirical applications. Although the paper focuses on DSGE models, the results are also applicable to other vector linear processes with well de…ned spectra, such as the (factor augmented) vector autoregression.

The paper considers parameter identi…cation, estimation, and model diagnostics in medium scale DSGE models from a frequency domain perspective using the framework developed in Qu and Tkachenko (2012). The analysis uses Smets and Wouters (2007) as an illustrative example, motivated by the fact that it has become a workhorse model in the DSGE literature. For identi…cation, in addition to checking parameter identi…ability, we derive the non-identi…cation curve to depict parameter values that yield observational equivalence, revealing which and how many parameters need to be …xed to achieve local identi…cation. For estimation and inference, we contrast estimates obtained using the full spectrum with those using only the business cycle frequencies to …nd notably di¤erent parameter values and impulse response functions. A further comparison between the nonparametrically estimated and model implied spectra suggests that the business cycle based method delivers better estimates of the features that the model is intended to capture. Overall, the results suggest that the frequency domain based approach, in part due to its ability to handle subsets of frequencies, constitutes a ‡exible framework for studying medium scale DSGE models.

This paper considers issues related to identi…cation, inference and computation in linearized Dynamic Stochastic General Equilibrium (DSGE) models. We …rst provide a necessary and su¢ cient condition for the local identi…cation of the structural parameters based on the (…rst 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 identi…cation through a subset of frequencies, partial identi…cation, conditional identi…cation and identi…cation under general nonlinear constraints are also studied. When lack of identi…cation is detected, the method can be further used to trace out non-identi…cation 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 quasiBayesian procedure for estimation and inference. The procedure can be used to incorporate relevant prior distributions and is computationally attractive.Keywords: structural identi…cation, in…nite dimensional mapping, non-identi…cation curve, frequency domain estimation, MCMC.We thank Pierre Perron and Hsueh-Ling Huynh for useful comments and suggestions.

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