Agnostic structural disturbances (ASDs): detecting and reducing misspecification in empirical macroeconomic models

Exogenous random structural disturbances are the main driving force behind fluctuations in most business cycle models and typically a wide variety is used. This paper documents that a minor misspecification regarding structural disturbances can lead to large distortions for parameter estimates and implied model properties, such as impulse response functions with a wrong shape and even an incorrect sign. We propose a novel concept, namely an agnostic structural disturbance (ASD), that can be used to both detect and correct for misspecification of the structural disturbances. In contrast to regular disturbances and wedges, ASDs do not impose additional restrictions on policy functions. When applied to the Smets-Wouters (SW) model, we find that its risk-premium disturbance and its investment-specific productivity disturbance are rejected in favor of our ASDs. While agnostic in nature, studying the estimated associated coefficients and the impulse response functions of these ASDs allows us to interpret them economically as a risk-premium/preference and an investment-specific productivity type disturbance as in SW, but our results indicate that they enter the model quite differently than the original SW disturbances. Our procedure also selects an additional wage mark-up disturbance that is associated with increased capital efficiency.