A Control Function Approach to Estimate Panel Data Binary Response Model

TL;DR

This paper introduces a novel control function method for estimating binary response models in panel data with unobserved heterogeneity, requiring weaker assumptions and allowing for point identification of effects under certain conditions.

Contribution

It develops a new control function approach that relaxes restrictions and enables point identification of average partial effects with discrete instruments.

Findings

The method performs well in Monte Carlo simulations.

It allows point identification with large support of endogenous regressors.

Bounds are provided when support assumptions are violated.

Abstract

We propose a new control function (CF) method to estimate a binary response model in a triangular system with multiple unobserved heterogeneities The CFs are the expected values of the heterogeneity terms in the reduced form equations conditional on the histories of the endogenous and the exogenous variables. The method requires weaker restrictions compared to CF methods with similar imposed structures. If the support of endogenous regressors is large, average partial effects are point-identified even when instruments are discrete. Bounds are provided when the support assumption is violated. An application and Monte Carlo experiments compare several alternative methods with ours.