High-Order Consumption Moments and Asset Pricing

This paper investigates the role of consumer heterogeneity in explaining asset returns. Using a Taylor series expansion of the individual's marginal utility of consumption around the conditional expectation of consumption, we derive an approximate equilibrium model for expected returns. In this model, the priced risk factors are the cross-moments of return with the moments of the cross-sectional distribution of individual consumption and the signs of the risk factor coefficients are driven by preference assumptions. That allows to avoid an ad hoc specification of preferences and to consider a general class of utility functions when addressing the question of the effect of a particular cross-sectional moment of individual consumption on the expected equity premium and risk-free rate. We demonstrate that if consumers exhibit decreasing and convex absolute prudence, then the cross-sectional mean and skewness of individual consumption yield a higher equity premium if their cross-moments with the excess market portfolio return are positive, while the cross-sectional variance and kurtosis always lower the equity premium explained by the model. Using data from the U.S. Consumer Expenditure Survey, we find that, in contrast to the complete consumption insurance case, the model with heterogeneous consumers reproduces the observed equity premium and risk-free rate with economically plausible values of the relative risk aversion coefficient (between 0.6 and 1.6) and the time discount factor when the cross-sectional skewness of individual consumption, combined with the cross-sectional mean and variance, is taken into account