Long-Horizon Regressions: Theoretical Results and Applications to the Expected Returns/Dividend Yields and Fisher Effect Relations1

We analyze several ways of conducting long-horizon regressions, taken from the empirical literature. Asymptotic arguments are used to show that, in all cases, the t-statistics do not converge to well-de…ned distributions, thus explaining the tendency of long-horizon regressions to …nd ’signi…cant’ results, where previous short-term approaches have failed. Moreover, in some cases, the ordinary least squares estimator is not consistent, and the R cannot be interpreted as a measure of the goodness of …t. Those results cast doubt on the conclusions reached by most previous long-horizon regression studies. We propose a rescaled t-statistic, whose asymptotic distribution is easy to simulate, and re-visit some of the evidence on the long-horizon predictability of returns and the long-horizon tests of the Fisher E¤ect.