Why Surplus Consumption in the Habit Model May Be Less Persistent than You Think
49 Pages Posted: 18 Mar 2010
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Why Surplus Consumption in the Habit Model May Be Less Persistent than You Think
Why Surplus Consumption in the Habit Model May Be Less Persistent than You Think
Date Written: February 3, 2010
Abstract
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.
Keywords: habit preferences,value premium, fast-moving habit
JEL Classification: G12
Suggested Citation: Suggested Citation
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