Scandinavian Working Papers in Economics

Working Paper Series,
IFAU - Institute for Evaluation of Labour Market and Education Policy

No 2017:21: Discretizing Unobserved Heterogeneity

St├ęphane Bonhomme (), Thibaut Lamadon () and Elena Manresa ()
Additional contact information
St├ęphane Bonhomme: University of Chicago, Postal: USA
Thibaut Lamadon: University of Chicago, Postal: USA
Elena Manresa: Massachusetts Institute of Technology and The Sloan School of Mangement, Postal: USA

Abstract: 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 groups in 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. When allowing for the presence of time-varying unobserved heterogeneity, we show they enjoy fast rates of convergence depending of 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.

Keywords: dimension reduction; panel data; structural models; kmeans clustering

JEL-codes: C23; C38

110 pages, November 21, 2017

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