This version: March 28, 2016 First version: February 2014
Structural DSGE models are used both for analyzing policy and the sources of business cycles. Conclusions based on full structural models are, however, potentially affected by misspecification. A competing method is to use partially identified VARs based on narrative shocks. This paper asks whether both approaches agree. First, I show that, theoretically, the narrative VAR approach is valid in a class of DSGE models with Taylor-type policy rules. Second, I quantify whether the two approaches also agree empirically, that is, whether DSGE model restrictions on the VARs and the narrative variables are supported by the data. To that end, I first adapt the existing methods for shock identification with external instruments for Bayesian VARs in the SUR framework. I also extend the DSGE-VAR framework to incorporate these instruments. Based on a standard DSGE model with fiscal rules, my results indicate that the DSGE model identification is at odds with the narrative information as measured by the marginal likelihood. I trace this discrepancy to differences both in impulse responses and identified historical shocks.