From Discrete Choice to Endogenous Distributions: Selection and Heterogeneity

This paper develops a tractable framework in which heterogeneity, captured by the distribution of agent characteristics within an alternative (sector, location, or occupation), emerges endogenously in equilibrium through selection rather than being imposed exogenously. I show that widely used extreme-value and power-law distributions arise as conditional outcomes of payoff-based discrete choice with multivariate shocks. The framework delivers a one-to-one mapping between equilibrium allocation shares and within-alternative heterogeneity. Because distributions are equilibrium objects, they respond to counterfactual shocks, introducing adjustment margins absent from standard models and generating richer responses, as shown in applications to trade, economic geography, and occupational sorting.