Discretizing Unobserved Heterogeneity
Stéphane Bonhomme, Thibaut Lamadon, Elena Manresa
Econometrica · 2022 · Volume 90 · Issue 2
Abstract
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 ontwo-step grouped fixed-effects(GFE) estimators, where individuals are first classified into groups usingkmeansclustering, 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.
Keywords
Unobserved heterogeneity, panel data, kmeans clustering, dimension reduction
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