The Paper provides new tools for the evaluation of DSGE models, and applies it to a large-scale New Keynesian dynamic stochastic general equilibrium (DSGE) model with price and wage stickiness and capital accumulation. Specifically, we approximate the DSGE model by a vector autoregression (VAR), and then systematically relax the implied cross-equation restrictions. Let delta denote the extent to which the restrictions are being relaxed. We document how the in- and out-of-sample fit of the resulting specification (DSGE-VAR) changes as a function of delta. Furthermore, we learn about the precise nature of the misspecification by comparing the DSGE model’s impulse responses to structural shocks with those of the best-fitting DSGE-VAR. We find that the degree of misspecification in large-scale DSGE models is no longer so large to prevent their use in day-to-day policy analysis, yet it is not small enough that it cannot be ignored.