Noncausal Bayesian Vector Autoregression

We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution as a by-product. We apply the methods to postwar quarterly U.S. inflation and GDP growth series. The noncausal VAR model turns out to be superior in terms of both in-sample fit and out-of-sample forecasting performance over its conventional causal counterpart. In addition, we find GDP growth to have predictive power for the future distribution of inflation over and above the own history of inflation, but not vice versa. This may be interpreted as evidence against the new Keynesian model that implies Granger causality from inflation to GDP growth, provided GDP growth is a reasonable proxy of the marginal cost.