Structural DSGE models are used for analyzing both 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 SVARs based on narrative shocks. This paper asks whether both approaches agree. Specifically, I use narrative data in a DSGE‐SVAR that partially identify policy shocks in the VAR and assess the fit of the DSGE model relative to this narrative benchmark. In developing this narrative DSGE‐SVAR, I develop a tractable Bayesian approach to proxy VARs and show that such an approach is valid for models with a certain class of Taylor rules. Estimating a DSGE‐SVAR based on a standard DSGE model with fiscal rules and narrative data, I find that the DSGE model identification is at odds with the narrative information as measured by the marginal likelihood. I trace this discrepancy to differences in impulse responses, identified historical shocks and policy rules. The results indicate monetary accommodation of fiscal shocks.