Predictive regressions

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Abstract

When a rate of return is regressed on a lagged stochastic regressor, such as a dividend yield, the regression disturbance is correlated with the regressor's innovation. The OLS estimator's finite-sample properties, derived here, can depart substantially from the standard regression setting. Bayesian posterior distributions for the regression parameters are obtained under specifications that differ with respect to (i) prior beliefs about the autocorrelation of the regressor and (ii) whether the initial observation of the regressor is specified as fixed or stochastic. The posteriors differ across such specifications, and asset allocations in the presence of estimation risk exhibit sensitivity to those differences.

JEL classification

C32
C11
G11

Keywords

Regression
Bias
Bayesian analysis
Estimation risk
Asset allocation
Predicting returns

Cited by (0)

I am grateful for comments from Doron Avramov, John Campbell, Lubos Pastor, workshop participants at the University of Chicago and the University of Pennsylvania, and the referee. I am also grateful for support provided by my appointment during the 1997–98 academic year as a Marvin Bower Fellow at Harvard Business School, where portions of this research were conducted. This study includes results from a 1986 working paper, `Bias in Regressions with Lagged Stochastic Regressors'.