Discretizing Unobserved Heterogeneity

We study discrete panel data methods where unobserved heterogeneity is revealed in a first step, environments population not discrete. focus on two?step grouped fixed?effects (GFE) estimators, individuals are classified into groups using kmeans clustering, and the model then estimated allowing for group?specific heterogeneity. Our framework relies two key properties: function—possibly nonlinear time?varying—of low?dimensional continuous latent type, informative moments available classification. illustrate method of wages labor market participation, probit with time?varying derive asymptotic expansions GFE estimators as number grows dimensions panel. propose data?driven rule groups, discuss bias reduction inference.