A long tradition in macro-finance studies the joint dynamics of aggregate stock returns and dividends using vector autoregressions (VARs), imposing the cross-equation restrictions of the Campbell-Shiller (CS) identity to sharpen inference. We take a Bayesian perspective and develop methods to draw from the posterior distribution of Bayesian VARs that encode a priori skepticism about large amounts of return predictability while imposing the CS restrictions exactly. In doing so, we show how a common empirical practice of omitting dividend growth from the system amounts to imposing the extra restriction that dividend growth is not persistent. We highlight that persistence in dividend growth induces a previously overlooked channel for return predictability, which we label \dividend momentum". Compared to estimation based on OLS, the Bayesian approach leads to a much more moderate, but still significant, degree of return predictability, with forecasts that would have been helpful out-of-sample and realistic asset allocation prescriptions.