Discretizing Unobserved Heterogeneity

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Link to the paper: www.dropbox.com/s/mbybh9o53ipnky0/Discrete_Hetero_18.pdf?dl=0

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 group sin 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. For instance, when allowing for the presence of
time-varying unobserved heterogeneity we show they enjoy fast rates of
convergence depending on 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.