On the Properties of Regression Tests of Stock Return Predictability Using Dividend-Price Ratios

This article investigates, both in finite samples and asymptotically, statistical inference on predictive regressions where time series are generated by present value models of stock prices. We show that regression-based tests, including robust tests such as the conditional test and the Q-test, are inconsistent and thus suffer from lack of power in local-to-unity models for the regressor persistence. The main reason is that, despite the near-integrated dividend-price ratio, the convergence rates of the estimates are slowed down because the present value model implies a shrinking innovation variance on the predictor, an effect which is masked in a predictive regression analysis with exogenous constant covariance of innovations. We illustrate these properties in a simulation study.