A Static and Microfounded Theory of Zipf's Law for Firms and of the Top Labor Income Distribution

I propose a theory of Zipf's Law for firm sizes and Pareto distributions for top labor incomes based on arbitrarily small differences in skills between workers, and no functional form assumption. A version of Garicano (2000)'s knowledge-based production hierarchies model is shown to generate Pareto distributions for high span of control of intermediary managers with coefficients equal to 2L/(2L-1) between L levels of management, under very limited assumptions on the underlying distribution of agents' skills. This breakdown of the aggregate firm size distribution receives considerable empirical support in the French matched employer-employee administrative data. The model provides a method to structurally estimate the relative importance of different factors in the recent rise in labor income inequality: the tail index of the Pareto top labor income distribution depends on a notion of race between education and technology, while the scale parameter depends on communication costs and heterogeneity. It also has striking implications for the literature in trade and macroeconomics on firm heterogeneity: in the model, heterogeneity in firm sizes grows when underlying productivity heterogeneity decreases.