Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2022, Volume 90, Issue 2

Discretizing Unobserved Heterogeneity

https://doi.org/10.3982/ECTA15238
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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Supplemental Material

Supplement to "Discretizing Unobserved Heterogeneity"

Bonhomme, Stéphane, Thibaut Lamadon and Elena Manresa

This zip file contains the replication files for the manuscript.

Supplement to "Discretizing Unobserved Heterogeneity"

Bonhomme, Stéphane, Thibaut Lamadon and Elena Manresa

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