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.
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