A long tradition in macro-finance studies the dynamics of aggregate stock returns and dividends using vector autoregressions, imposing the restrictions implied by the Campbell-Shiller (CS) identity to sharpen inference. We develop Bayesian methods that encode a priori skepticism about return predictability while imposing the restrictions. We highlight that persistence in dividend growth induces “dividend momentum,” a previously overlooked channel for return predictability. By combining Bayesian shrinkage and the CS restrictions, we obtain more plausible degrees of return predictability, superior out-of-sample forecasts, and Sharpe ratios, which cannot be obtained by using either shrinkage or the CS restrictions on their own.