Bayesian model averaging and principal component regression forecasts in a data rich environment

Abstract

This study revisits the accuracy of the point and density forecasts of monthly US inflation and output growth that are generated using principal components regression (PCR) and Bayesian model averaging (BMA). I run a forecasting horse race between 24 BMA specifications and two PCR alternatives in an out-of-sample, 10-year rolling event evaluation. The differences in mean-square forecast errors between BMA and PCR are mostly insignificant but predictable. PCR methods perform best for predicting deviations of output and inflation from their expected paths, whereas BMA methods perform best for predicting “tail” events. This dichotomy implies that risk-neutral policy-makers may prefer the classical PCR approach, while the BMA approach would belong in the toolkit of a prudential, risk-averse forecaster.