The equity premium puzzle and the risk-free rate puzzle at long horizons

The failure of consumption based asset pricing models to match the stochastic properties of the equity premium and the risk-free rate has been attributed by some authors to frictions, transaction costs or durability. However, such frictions would primarily affect the higher frequency data components: consumption-based pricing models that concentrate on long-horizon returns should be more successful. ; We consider three consumption-based models of the asset-pricing kernel: time-separable utility, and the models of Abel (1990) and Constantinides (1990). We estimate a vector ARCH model that includes the pricing kernel and the equity return, and use the fitted model to assess the model's implications for the equity premium and for the risk-free rate. We find that time-separable preferences fail at all horizons, and none of the models perform well at the quarterly horizon. When consumption is measured as nondurables plus services, the Abel and the Constantinides models show modest improvements at the one- and two-year horizon. However, when consumption is measured either as expenditures on nondurables or as total consumption purchases, versions the Abel and the Constantinides match the mean and the variance of the observed equity premium at the two-year horizon, capture a good deal of the time-variation of the equity premium in post-war data, and have more success matching the first and second moments of the observed risk-free rate. A major unresolved issue is to understand why the measured consumption services series perform so poorly in these models.