Predictable Stock Returns: The Role of Small Sample Bias




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    • From the University of Washington and NBER, and the University of Alabama, respectively. We are grateful to John Campbell for providing us with the data set assembled by him and Robert Shiller. Helpful comments from Stephen Cecchetti, Gregory Chow, Tim Cogley, Robert Engle, Benjamin Friedman, Robert Hodrick, Bruce Lehmann, Andrew Lo, Richard Parks, Pierre Perron, G. William Schwert, Robert Stambaugh, Richard Startz, René Stulz (the editor), Stephen Turnovsky, Kenneth West, anonymous referees, and participants in seminars at the Federal Reserve Board, the NBER, Northwestern University, Ohio State University, Princeton University, Southern Methodist University, the University of California at Santa Barbara, and the University of Oregon are acknowledged with thanks, but responsibility for any errors is entirely the authors'.


Predictive regressions are subject to two small sample biases: the coefficient estimate is biased if the predictor is endogenous, and asymptotic standard errors in the case of overlapping periods are biased downward. Both biases work in the direction of making t-ratios too large so that standard inference may indicate predictability even if none is present. Using annual returns since 1872 and monthly returns since 1927 we estimate empirical distributions by randomizing residuals in the VAR representation of the variables. The estimated biases are large enough to affect inference in practice, and should be accounted for when studying predictability.