Predictive Regressions: A Reduced-Bias Estimation Method

Abstract

We propose a direct and convenient reduced-bias estimator of predictive regression coefficients, assuming that the regressors are Gaussian first-order autoregressive with errors that are correlated with the error series of the dependent variable. For the single-regressor model, Stambaugh (1999) shows that the ordinary least squares estimator of the predictive regression coefficient is biased in small samples. Our estimation method employs an augmented regression which uses a proxy for the errors in the autoregressive model. We also develop a heuristic estimator of the standard error of the estimated predictive coefficient which performs well in simulations, and show that the estimated coefficient of the errors and its squared standard error are unbiased. We analyze the case of multiple predictors that are first-order autoregressive and derive bias expressions for both the ordinary least squares and our reduced-bias estimated coefficients. The effectiveness of our estimation method is demonstrated by simulations.