Discretizing Unobserved Heterogeneity

50 Pages Posted: 13 Feb 2019 Last revised: 28 Jan 2021

See all articles by Stéphane Bonhomme

Stéphane Bonhomme

University of Chicago

Thibaut Lamadon

University of Chicago

Elena Manresa

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Date Written: April 1, 2017

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 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.

Keywords: Unobserved heterogeneity, panel data, kmeans clustering, dimension reduction

JEL Classification: C23, C38

Suggested Citation

Bonhomme, Stéphane and Lamadon, Thibaut and Manresa, Elena, Discretizing Unobserved Heterogeneity (April 1, 2017). University of Chicago, Becker Friedman Institute for Economics Working Paper No. 2019-16, Available at SSRN: https://ssrn.com/abstract=3333452 or http://dx.doi.org/10.2139/ssrn.3333452

Stéphane Bonhomme (Contact Author)

University of Chicago

Thibaut Lamadon

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Elena Manresa

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

77 Massachusetts Ave. E62-663
Cambridge, MA 02142
United States

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