Global Identification in DSGE Models Allowing for Indeterminacy

This paper presents a framework for analyzing global identification 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 identification fails if and only if the minimized distance equals zero. This result has three features. (1) It can be applied across DSGE models with different structures. (2) It permits checking whether a subset of frequencies can deliver identification. (3) It delivers parameter values that yield observational equivalence if there is identification failure. Next, the paper proposes a measure for the empirical closeness between two DSGE models for a further understanding of the strength of identification. The measure gauges the feasibility of distinguishing one model from another based on a finite number of observations generated by the two models. It is shown to be equal to the highest possible power in a Gaussian model under a local asymptotic framework. The above theory is illustrated using two small scale and one medium scale DSGE models. The results document that certain parameters can be identified under indeterminacy but not determinacy, that different monetary policy rules can be (nearly) observationally equivalent, and that identification properties can differ 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 findings reported in the empirical applications. Although the paper focuses on DSGE models, the results are also applicable to other vector linear processes with well defined spectra, such as the (factor augmented) vector autoregression.