The dividend-growth based test of return predictability, proposed by Cochrane (2008), is similar to a likelihood-based test of the standard return-predictability model, treating the autoregressive (AR) parameter of the dividend-price ratio as known. In comparison to standard OLS-based inference, both tests can achieve power gains by using restrictions or prior information on the value of the AR parameter. When compared to the likelihood-based test, there are no power advantages for the dividend-growth based test. In common implementations, with the AR parameter set equal to the corresponding OLS estimate, Cochrane’s test suffers from severe size distortions.