Efficient Tests for Long-Run Predictability: Do Long-Run Relations Convey Extra Information?

Short-run and long-run relations among time series can differ. In situations in which short-run constraints and information biases obscure equilibrium relations among economic variables, estimates of the long-run relations, which are free of such contaminations, become the only basis for evaluating economic hypotheses. The common approach to estimating long-run predictability has been long-horizon regressions. However, long-horizon regressions are not designed to extract long-run information efficiently, and the lack of accuracy often outweighs their robustness to short-run noise. This study suggests two methods for replacing long-horizon regressions. The corresponding tests can be viewed as long-run versions of the Q-test by Campbell and Yogo (2006) and the nearly optimal test by Elliott, Müller, and Watson (2014). We demonstrate the usefulness of long-run information in two common empirical applications. Department of Economics, Rice University, Houston, TX 77251, USA. Tel.: +1 (713) 348-5613; fax: +1 (713) 348-5278. Email: [email protected].