Latent group structure in linear panel data models with endogenous regressors

TL;DR

This paper develops two-stage Kmeans-based estimation methods for linear panel data models with endogenous regressors and latent group structures, demonstrating their effectiveness through simulations and an application to income and democracy.

Contribution

It introduces novel two-stage estimation procedures that incorporate latent group structures into instrumental variables estimation for panel data models.

Findings

Two-stage methods achieve high classification accuracy in simulations.

Methods perform well even with fully heterogeneous first-stage regressions.

Application reveals insights into income and democracy relationships.

Abstract

This paper concerns the estimation of linear panel data models with endogenous regressors and a latent group structure in the coefficients. We consider instrumental variables estimation of the group-specific coefficient vector. We show that direct application of the Kmeans algorithm to the generalized method of moments objective function does not yield unique estimates. We newly develop and theoretically justify two-stage estimation methods that apply the Kmeans algorithm to a regression of the dependent variable on predicted values of the endogenous regressors. The results of Monte Carlo simulations demonstrate that two-stage estimation with the first stage modeled using a latent group structure achieves good classification accuracy, even if the true first-stage regression is fully heterogeneous. We apply our estimation methods to revisiting the relationship between income and democracy.