Econometrica: Mar 2022, Volume 90, Issue 2

Discretizing Unobserved Heterogeneity
p. 625-643

Stéphane Bonhomme, Thibaut Lamadon, Elena Manresa

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.

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Supplement to "Discretizing Unobserved Heterogeneity"

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Supplement to "Discretizing Unobserved Heterogeneity"

In this appendix we provide the proofs of various technical lemmas, present several extensions, and give details about the Monte Carlo simulations.

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