By Stephen Morris
I reveal identification failures in a well-known dynamic stochastic general equilibrium (DSGE) model, and study the statistical implications of common identifying restrictions. First, I provide a fully analytical methodology for determining all observationally equivalent values of the structural parameters in any parameter space. I show that either parameter admissibility or sign restrictions may yield global identification for some parameter realizations, but not for others. Second, I derive a “plug-in” maximum likelihood estimator, which requires no numerical search. I use this tool to demonstrate that the idiosyncratic identifying restriction directly impinges on both the location and distribution of the small-sample MLE, and compute correctly sized confidence intervals.
While this paper looks at the identification for a specific paper, An and Schorfheide (2007), it highlights an issue of much broader reach. Specifically, when estimating a typical DSGE model, the identification of parameter values may only be local and not necessarily global. But this can be fixed with identifying restrictions, which have an impact on the estimator.