A competing method is to use partially identified VARs based on narrative shocks. This paper asks whether both approaches agree. First, the author shows that, theoretically, the narrative VAR approach is valid in a class of DSGE models with Taylor-type policy rules. Second, the author quantifies 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, the author first adapts the existing methods for shock identification with external instruments for Bayesian VARs in the SUR framework. The author also extends the DSGE-VAR framework to incorporate these instruments. Based on a standard DSGE model with fiscal rules, the author’s results indicate that the DSGE model identification is at odds with the narrative information as measured by the marginal likelihood. The author traces this discrepancy to differences both in impulse responses and identified historical shocks.