Do we really need heterogeneous agent models?

We investigate the existence of representative agent under various heterogeneities in a recursive utility framework. We provide the analytical solution of household allocations. We numerically explore whether we can find a representative agent whose income is the aggregate income of the society and whose allocations are the aggregate allocations of the society under heterogeneity in the parameter of risk aversion and/or parameter of intertemporal substitution, or discount rate or survival probability. We find that there is no representative agent when the heterogeneity is in survival probability. From the data, we know that there is heterogeneity among people in terms of survival probability. For instance, women tend to live longer than men, rich people tend to live longer than poor people. We conclude that it may be better to use heterogeneous agents models than the representative agent models under the recursive utility framework. Our results support the idea that we do need the heterogeneous agent models indeed.