We use a Bayesian method to estimate a consumption-based asset pricing model featuring long-run risks. Although the model is generally consistent with consumption and dividend growth moments in annual data, the conditional mean of consumption growth (a latent process) is not persistent enough to satisfy the restriction that the price-dividend ratio be an affine function of the latent process. The model also requires relatively high intertemporal elasticity of substitution to match the low volatility of the risk-free return. These two restrictions lead to the equity volatility puzzle. The model accounts for only 50% of the total variation in asset returns.