Bayesian Inference of Local Projections with Roughness Penalty Priors

Abstract: A local projection is a statistical framework that accounts for the relationship between an exogenous variable and an endogenous variable, measured at different time points. Local projections are often applied in impulse response analyses and direct forecasting. While local projections are becoming increasingly popular because of their robustness to misspecification and their flexibility, they are less statistically efficient than standard methods, such as vector autoregression. In this study, we seek to improve the statistical efficiency of local projections by developing a fully Bayesian approach that can be used to estimate local projections using roughness penalty priors. By incorporating such prior-induced smoothness, we can use information contained in successive observations to enhance the statistical efficiency of an inference. We apply the proposed approach to an analysis of monetary policy in the United States, showing that the roughness penalty priors successfully estimate the impulse response functions and improve the predictive accuracy of local projections.