Journal of Financial and Quantitative Analysis

Research Article

Predictive Regressions: A Reduced-Bias Estimation Method

Yakov Amihuda1 and Clifford M. Hurvicha2

a1 yamihud@stern.nyu.edu, Department of Finance, and Hurvich

a2 churvich@stern. nyu.edu, Department of Operations and Management Science, New York University, Stern School of Business, 44 W 4th St, New York, NY 10012

Abstract

Standard predictive regressions produce biased coefficient estimates in small samples when the regressors are Gaussian first-order autoregressive with errors that are correlated with the error series of the dependent variable. See Stambaugh (1999) for the single regressor model. This paper proposes a direct and convenient method to obtain reduced-bias estimators for single and multiple regressor models by employing an augmented regression, adding a proxy for the errors in the autoregressive model. We derive bias expressions for both the ordinary least-squares and our reduced-bias estimated coefficients. For the standard errors of the estimated predictive coefficients, we develop a heuristic estimator that performs well in simulations, for both the single predictor model and an important specification of the multiple predictor model. The effectiveness of our method is demonstrated by simulations and empirical estimates of common predictive models in finance. Our empirical results show that some of the predictive variables that were significant under ordinary least squares become insignificant under our estimation procedure.

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