Abstract
Campbell and Cochrane (1999) formulate a model that successfully explains a wide variety of asset pricing puzzles, including a high equity premium, procyclical variation of stock prices, countercyclical variation of stock market volatility, and a low and smooth risk-free rate. These remarkable results are achieved by augmenting the standard power utility function with a time-varying subsistence level, or “external habit,” that adapts nonlinearly to current and past average consumption in the economy. Given the breakthrough in matching key asset pricing facts as well as the successful adoption of the Campbell-Cochrane preferences in a number of other applications, it is all the more important to fully understand the implications of these modeling choices.
For marginal changes, Campbell and Cochrane (1999) assert that “habit moves nonnegatively with consumption everywhere” (212) and that “more consumption is always socially desirable” (246). We show that these implications are of a very local nature and do not extend to discrete perturbations. As a result, government interventions that occasionally destroy part of the aggregate endowment can lead to substantial welfare improvements. Large interventions are not required: welfare improves already with the rather tiny one-time destruction of less than 0.1 percent of the endowment at a steady state, which is a quarter of the standard deviation of monthly consumption in their calibration. Hence, Campbell and Cochrane’s (245–47) attempt to map their results into a version of the model with internal habit formation must be reconsidered. Households faced with such an internal habit would themselves choose to create fluctuations in their consumption.
Our results are true for Campbell and Cochrane’s specific formulation and because of their particular and nonlinear specification of the evolution for the habit. They are not true for habit specifications in general. Indeed, for a more conventional linear habit formulation, one can show that welfare must decrease along the balanced growth path if parts of the endowment are destroyed: the utility gain later is outweighed by the initial utility loss.