The long-run risks model of asset prices explains stock price variation as a response to persistent fluctuations in the mean and volatility of aggregate consumption growth, by a representative agent with a high elasticity of intertemporal substitution. This paper documents several empirical difficulties for the model, as calibrated by Bansal and Yaron (BY, 2004) and Bansal et al. (BKY, 2011). U.S. data do not show as much univariate persistence in consumption or dividend growth as implied by the model. BY's calibration counterfactually implies that long-run consumption and dividend growth should be highly predictable from stock prices. BKY's calibration does better in this respect by greatly increasing the persistence of volatility fluctuations and their impact on stock prices. This calibration fits the predictive power of stock prices for future consumption volatility, but implies much greater predictive power of stock prices for future stock return volatility than is found in the data. The long-run risks model, particularly as calibrated by BKY, implies extremely low yields and negative term premia on inflation-indexed bonds. Finally, neither calibration can explain why movements in real interest rates do not generate strong predictable movements in consumption growth.