DSGE models have become a widely used tool for policymakers. This paper takes the global identification theory used for structural vectorautoregressions, and applies it to dynamic stochastic general equilibrium (DSGE) models. We use this modified theory to check whether a DSGE model structure allows for unique estimates of structural shocks and their dynamic effects. The potential cost of a lack of identification for policy oriented models along that specific dimension is huge, as the same model can generate a number of contrasting yet theoretically and empirically justifiable recommendations. The problem and methodology are illustrated using a simple New Keynesian business cycle model.