Skew-normal shocks in the linear state space form DSGE model

Observed macroeconomic data – notably GDP growth rate, inflation and interest rates – can be, and usually are skewed. Economists attempt to fit models to data by matching first and second moments or co-moments, but skewness is usually neglected. It is so probably because skewness cannot appear in linear (or linearized) models with Gaussian shocks, and shocks are usually assumed to be Gaussian. Skewness requires non-linearities or non-Gaussian shocks. In this paper we introduce skewness into the DSGE framework assuming skewed normal distribution for shocks while keeping the model linear (or linearized). We argue that such a skewness can be perceived as structural, since it concerns the nature of structural shocks. Importantly, the skewed normal distribution nests the normal one, so that skewness is not assumed, but only allowed for. We derive elementary facts about skewness propagation in the state space model and, using the well-known Lubik-Schorfheide model, we run simulations to investigate how skewness propagates from shocks to observables in a standard DSGE model. We also assess properties of an ad hoc two-steps estimator of models’ parameters, shocks’ skewness parameters among them.