Discretizing unobserved heterogeneity

We develop two-step and iterative panel data estimators based on a discretization of unobserved heterogeneity. We view discrete estimators as approximations, and study their properties in environments where population heterogeneity is individual-specific and un- restricted, letting the number of types grow with the sample size. Bias reduction methods can improve the performance of discrete estimators. We also show that discrete estimation may strictly dominate fixed-effects approaches when unobservables are high-dimensional, provided their underlying dimension is low. We study two applications: a structural dy- namic discrete choice model of migration, and a model of wage determination with worker and firm heterogeneity. These applications to settings with continuous heterogeneity sug- gest computational and statistical advantages of the discrete methods that we advocate.