Consumption-Based Asset Pricing with Incomplete Markets

This paper shows that consumption-based asset pricing theory imposes no testable restrictions on either macroeconomic or cross-sectional data if one allows for uninsurable idiosyncratic income shocks which are persistent and not normally distributed. More precisely, this paper shows that any “observed” joint process of arbitrage-free asset prices and payoffs, aggregate consumption, and moments of the cross-sectional distribution of consumption (income) growth is an equilibrium outcome for some incomplete-markets economy (some subjective discount factor and process of individual income). The proof heavily relies on the fact that second moments might be a poor measure of risk once the assumptions (normal distribution or quadratic utility) leading to a mean-variance framework are relaxed. More specifically, this paper introduces a “personal-disaster process” and shows that this process completely determines idiosyncratic risk in equilibrium without affecting the higher (second) moments of the cross-sectional distribution of consumption and income growth.