Habit Formation as a Resolution to the Equity Premium Puzzle: What Is in the Data, What Is Not

Abstract

The consumption based asset pricing model of Lucas [14] defines a theoretical relationship between streams of consumption and equilibrium asset prices. Since data of both aggregate consumption and asset prices are available, theory can be tested. Empirical tests of Lucas model using standard time separable utility functions indicate mismatches between theory and data. For example, in GMM (Generalized Method of Moments) estimation of Hansen and Singleton [9], overidentifying constraints implied by model were rejected. Mehra and Prescott [16] demonstrated difficulty of explaining a particular statistic: theoretical expected equity premium (the yield differential between stocks and risk-free bonds) is much higher than observed one if a standard utility function is used. They called mismatch the equity premium puzzle. To improve performance of model, several authors have relaxed time-separability of preferences. In a stimulating paper, Constantinides [1] argued that equity premium puzzle can be resolved through assumption of The idea is that consumption in past reduces utility in present because it establishes habits. His model can match observed mean and variance of both equity premium and consumption growth rate. The match of low moments is consistent with bound tests of Heaton [11], Gallant, Hansen, and Tauchen [7], and Hansen and Jagannathan [10]. On other hand, GMM estimations using monthly aggregate consumption of nondurable goods and leisure by Eichenbaum, Hansen, and Singleton [3], and that using consumption of nondurable goods and durable goods by Dunn and Singleton [2] and Eichenbaum and Hansen [4], showed that if current utility depends on current and past consumption, then current utility increases in past consumption, i.e., consumption has durability, opposite of that implied by habit formation. A particularly strong result was obtained by Gallant and Tauchen [6]. They estimated a general form of utility functions with a general law of motion of data and found that source of time-non-separability is local durability. Since it is known that local durability