Constructing empirical specifications for structural economic models is difficult, if not impossible. As shown in this paper, even minor misspecifications may lead to large distortions for parameter estimates and implied model properties. We propose a novel concept, namely an agnostic structural disturbance (ASD), that can be used to both detect and correct for misspecification of structural disturbances and is easy to implement. While agnostic in nature, the estimated coefficients and associated impulse response functions of the ASDs allow us to give them an economic interpretation. We adopt the methodology to the Smets–Wouters model and formulate an improved risk-premium and an improved investment-specific productivity disturbance.