ABSTRACT We study the ability of SVARs to match impulse responses of a well‐established DSGE model where the information of agents can be imperfect. We derive conditions for the solution of a linearized NK‐DSGE model to be invertible given this information set. In the absence of invertibility, an approximate measure is constructed. An SVAR is estimated using artificial data generated from the model and three forms of identification restrictions: zero, sign and bounds on the forecast error variance. We demonstrate that a VAR may not recover a subset of structural shocks when imperfect information causes the underlying model to be non‐invertible.