A Generalized Framework for Multivariate Predictive Regressions

Predictive regressions are subject to small‐sample bias when innovations in persistent predictors are correlated with predictive errors. One approach to bias reduction is the multi‐predictor augmented regression method (mARM), which augments the predictive regression with bias‐corrected proxies for predictor innovations. We extend this framework to allow for first‐order autocorrelation in predictive errors, first‐order autocorrelation in predictor innovations, and contemporaneous correlations between shocks to the two processes. Simulations show that the mARM estimator can exhibit substantial bias, whereas our proposed extended mARM estimator significantly reduces bias relative to both mARM and ordinary least squares. Looking at predictive regressions of stock returns on several widely used financial ratios, we find that the mARM approach yields spurious statistical significance for some predictive coefficients, which is not observed with the proposed extended mARM.