Why Surplus Consumption in the Habit Model May Be Less Persistent than You Think

In U.S. data, value stocks have higher expected excess returns and higher CAPM alphas than growth stocks. This paper finds the external-habit model of Campbell and Cochrane (1999) can generate a value premium in both CAPM alpha and expected excess return when the log surplus- consumption ratio is allowed to be not very persistent. In contrast, Lettau and Wachter (2007) find that when the log surplus-consumption ratio is assumed to be highly persistent as in Campbell and Cochrane (by assuming that the price-of-risk state variable is highly persistent), the external-habit model generates a growth premium in expected excess return. However, there is a good economic reason for why the persistence of the log surplus-consumption ratio is likely to be low, and the micro evidence also favors a less persistent log surplus-consumption ratio. In particular, the high persistence assumed by Lettau and Wachter's specification implies that the contribution of the most recent 5 years of log consumption to log habit is just a little over 50% and so the contribution of log consumption more than 5 years ago is almost 50%, which seems very high. We choose a value for this persistence which is su±ciently low that the most recent 2 years of log consumption contribute over 98% of all past consumption to log habit, which is a much more reasonable number than the 25% contribution generated by the Lettau-Wachter value. In our specification, expected consumption is slowly mean-reverting, as in the long-run risk model of Bansal and Yaron (2004), which is why our model is able to generate a price-dividend ratio for aggregate equity that exhibits the high autocorrelation found in the data, despite the very low persistence of the price-of-risk state variable. Our results suggest that external-habit preferences and long-run risk consumption may both play important roles in explaining the time-series and cross-sectional properties of equity returns and prices. The one important dimension of equity return behavior that low persistence of the price-of-risk state variable cannot replicate is the predictability of long-horizon equity return using the price-dividend ratio for aggregate equity