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