Ex Post Heterogeneity and the Business Cycle

The reason why the assumption of a representative agent is so popular in the equilibrium business cycle literature is mainly that equilibrium allocations are derived by solving a concave programming problem, whereas once heterogeneity is introduced it is necessary to solve for weights on individual utilities and this generally involves solving a complicated fixed point problem. The representative agent framework is extended in a way that permits workers to have different skills. The key feature is that each agent faces a stochastic productivity ex ante but a different realized productivity ex post from others'. This means that there is no ex ante heterogeneity but ex post heterogeneity, and hence an equal weight is applied to the utilities of all agents. The results show how serious the aggregation problem is in aggregate fluctuations. The responsiveness of labor supply in physical units is larger than that of labor supply in efficiency units. On the contrary, productivity in physical units responds to the aggregate productivity shock less vigorously than productivity in efficiency units. So the relative ratio of standard deviation of aggregate hours to that of productivity tends to be exaggerated in the actual data, which measures the aggregate labor supply only in physical unit. In addition, a heterogeneity helps the model economy produce a more plausible correlation structure. Furthermore, the results show that a high elasticity of intertemporal substitution of labor is not required for a real business cycle model to mimic the key feature observed in the actual economy.