Maximum Likelihood Inference in Weakly Identified DSGE Models

Abstract

This paper examines the problem of weak identification in maximum likelihood, motivated by problems with estimation and inference a multi-dimensional, non-linear DSGE model. We suggest a test for a simple hypothesis concerning the full parameter vector which is robust to weak identification. We also suggest a test for a composite hypothesis regarding a sub-vector of parameters. The suggested test is shown to be asymptotically exact when the nuisance parameter is strongly identified, and in some cases when the nuisance parameter is weakly identified. We pay particular attention to the question of how to estimate Fisher's information, and make extensive use of martingale theory.