Frequency Domain Analysis of Medium Scale DSGE Models with Application to Smets and Wouters (2007)

The paper considers parameter identification, estimation and inference in medium scale DSGE models from a frequency domain perspective using the framework developed in Qu and Tkachenko (2010). 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 identification, in additional to checking parameter identifiably, we derive the non-identification curve to depict parameter values that yield observational equivalence, revealing which and how many parameters need to be fixed to achieve local identification. For estimation and inference, we contrast estimates obtained using the full spectrum with those using only the business cycle frequencies to find 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 in handling subsets of frequencies, constitutes a fiexible framework for studying medium scale DSGE models.