Discretizing Unobserved Heterogeneity

TL;DR

This paper introduces a two-step grouped fixed-effects estimator for discrete panel data with continuous unobserved heterogeneity, utilizing kmeans clustering to classify individuals and allowing for nonlinear, time-varying heterogeneity.

Contribution

It develops a novel framework that combines clustering with fixed-effects estimation for non-discrete heterogeneity, including asymptotic analysis and a data-driven method for selecting the number of groups.

Findings

The estimator performs well in models of wages and labor participation.

Asymptotic expansions are derived for the estimator as the number of groups increases.

A data-driven rule for choosing the optimal number of groups is proposed.

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.