Recursive Risk Sharing: Microfoundations for Representative-Agent Asset Pricing

We explore the properties of Pareto optimal allocations when agents have heterogeneous recursive preferences. The dynamics of individual consumption growth reflect not just standard mean-variance tradeoffs as in the expected-utility model, but also tradeoffs involving the timing of the resolution of uncertainty. We also explore the implications of these optimal allocations for the aggregate asset-pricing kernel. In our specific Gaussian log-linear environment, the representative agent will appear to have recursive preferences of the same form as the individual agents. However, the representative agent's preference parameters will reflect both the heterogeneous preference parameters of the individuals and the parameters governing the stochastic process for income growth. Empirical findings of unusual values for the representative agent's preference parameters, therefore, can be a reflection of this commingling of individual preferences and the dynamics of the opportunity set. Moreover, evidence of parameter instability of the representative agent's preferences may simply reflect changes in the dynamics of income growth.