Board of Governors of the Federal Reserve System

March 2012

An Empirical Investigation of Consumption-based Asset Pricing Models with Stochastic Habit Formation

Qiang Dai and Olesya V. Grishchenko

Abstract:

We econometrically estimate a consumption-based asset pricing model with stochastic internal habit and test it using the generalized method of moments. The model departs from existing models with deterministic internal habit (e.g., Dunn and Singleton (1983), Ferson and Constan- tinides (1991), and Heaton (1995)) by introducing shocks to the coefficients in the distributed lag specification of consumption habit and consequently an additional shock to the marginal rate of substitution. The stochastic shocks to the consumption habit are persistent and provide an additional source of time variation in expected returns. Using Treasury bond returns and broad equity market index returns, we show that stochastic internal habit formation models resolve the dichotomy between the autocorrelation properties of the stochastic discount factor and those of expected returns. Consequently, they provide a better explanation of time-variation in expected returns than models with either deterministic habit or stochastic external habit.

Keywords: Asset pricing, consumption-based asset pricing models, habit formation, stochastic internal habit, aggregate equity and bond returns

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