Weak Inference for Dynamic Stochastic General Equilibrium Models with Time-Varying Parameters

This paper studies proper inference and asymptotically accurate structural break tests for parameters in Dynamic Stochastic General Equilibrium (DSGE) models in a maximum likelihood framework. Two empirically relevant issues may invalidate the conventional inference procedures and structural break tests for parameters in DSGE models: (i) weak identification and (ii) moderate parameter instability. DSGE literatures focus on dealing with weak identification issue, but ignore the impact of moderate parameter instability. This paper contributes to the literature via considering the joint impact of two issues in DSGE framework. The main results are: in a weakly identified DSGE model, (i) moderate instability from weakly identified parameters would not affect the validity of standard inference procedures or structural break tests; (ii) however, if strongly identified parameters are featured with moderate time-variation, the asymptotic distributions of test statistics would deviate from standard ones and would no longer be nuisance parameter free, which renders standard inference procedures and structural break tests invalid and provides practitioners misleading inference results; (iii) as long as I concentrate out strongly identified parameters, the instability impact of them would disappear as the sample size goes to infinity, which recovers the power of conventional inference procedure and structural break tests for weakly identified parameters. To illustrate my results, I simulate and estimate a modified version of the Hansen (1985) Real Business Cycle model and find that my theoretical results provide reasonable guidance for finite sample inference of the parameters in the model. I show that confidence intervals that incorporate weak identification and moderate parameter instability reduce the biases of confidence intervals that ignore those effects. While I focus on DSGE models in this paper, all of my theoretical results could be applied to any linear dynamic models or nonlinear GMM models