Evaluating Trade Reforms with Model with Heterogeneous Firms

Theories in which firms have heterogeneous productivities, such as those of Melitz (2003) and Chaney (2008), have been successful in capturing this empirical regularity that the average exporting firm is larger than the average nonexporter, but they fail to capture the richness of the distributions of exporters and nonexporters. We develop a simple model in which firms face heterogeneous fixed costs as well as having heterogeneous productivities. With a C.E.S. utility function and a Pareto distribution of productivities, this model has analytical solutions independently of the functional form chosen for the distribution of fixed costs. We show how this model can be reinterpreted as a model of occupation choice between being a worker or a manager in the spirit of Lucas (1978), thus providing a model for studying the impact of changes in trade policy on income distribution. Unfortunately, industrial census data indicate that the distribution of firm sizes is more consistent with a log normal distribution of productivities than it is with a Pareto distribution. We can solve a model with a log normal distribution of productivity numerically, but this model lacks many of the stark features of the model with a Pareto distribution of productivities.