Discretizing unobserved heterogeneity

We study panel data estimators based on a discretization of unobserved heterogeneity when individual heterogeneity is not necessarily discrete in the population. We focus on two-step grouped-fixed effects estimators, where individuals are classified into groups in a first step using kmeans clustering, and the model is estimated in a second step allowing for group-specific heterogeneity. We analyze the asymptotic properties of these discrete estimators as the number of groups grows with the sample size, and we show that bias reduction techniques can improve their performance. In addition to reducing the number of parameters, grouped fixed-effects methods provide effective regularization. When allowing for the presence of time-varying unobserved heterogeneity, we show they enjoy fast rates of convergence depending of the underlying dimension of heterogeneity. Finally, we document the finite sample properties of two-step grouped fixed-effects estimators in two applications: a structural dynamic discrete choice model of migration, and a model of wages with worker and firm heterogeneity.