The Statistics of Long‐horizon Regressions Revisited¹

This paper compares commonly used approaches for estimating the relation between long‐horizon returns and a predetermined variable X 1 , such as dividend yields. Specifically, we look at regression of (i) nonoverlapping multiperiod returns on X t (ii) overlapping multiperiod returns on X t , (iii) single‐period returns on multiperiod X t , and (iv) single‐period returns on X t and its implied long‐horizon regression coefficient. We provide analytical formulae which quantify the efficiency of the estimators used in the various approaches. Using the formulae, as well as Monte Carlo simulations, we demonstrate that the relative efficiency of the estimators used in the various approaches differs remarkably, depending on the dynamic structure of the regressor. of special interest for financial economists, when the regressors are highly autocorrelated, we find that the regressions (ii) (iii), and (iv) provide only marginal efficiency gains above and beyond the nonoverlapping long‐horizon regression.