Alternative Bayesian Estimators for Vector-Autoregressive Models

Abstract

This paper compares frequentist risks of several Bayesian estimators of the VAR lag parameters and covariance matrix under alternative priors. With the constant prior on the VAR lag parameters, the asymmetric LINEX estimator for the lag parameters does better overall than the posterior mean. The posterior mean of covariance matrix performs well in most cases. The choice of prior has more significant effects on the estimates than the form of estimators. The shrinkage prior on the VAR lag parameters dominates the constant prior, while Yang and Berger's reference prior on the covariance matrix dominates the Jeffreys prior. Estimation of a VAR using the U.S. macroeconomic data reveals significant differences between estimates under the shrinkage and constant priors.