Estimation of treatment effects under endogeneous heteroskedasticity

TL;DR

This paper develops a new instrumental variables model that accounts for heteroskedasticity dependent on treatment, allowing for heterogeneous treatment effects and providing consistent estimation methods.

Contribution

It extends the classical IV model to include endogenous heteroskedasticity, enabling identification and estimation of both mean and variance treatment effects with heterogeneity.

Findings

Standard IV can be inconsistent under endogenous heteroskedasticity.

The paper provides closed-form estimators for mean and variance treatment effects.

Simulation and empirical analysis demonstrate the method's effectiveness.

Abstract

The empirical literature on program evaluation limits its scope almost exclusively to models where treatment effects are homogenous for observationally identical individuals. This paper considers a treatment effect model in which treatment effects may be heterogeneous, even among observationally identical individuals. Specifically, extending the classical instrumental variables (IV) model with an endogenous binary treatment and a binary instrument, we allow the heteroskedasticity of the error disturbance to also depend upon the treatment variable so that treatment has both mean and variance effects on the outcome. In this endogenous heteroskedasticity IV (EHIV) model with heterogeneous individual treatment effects, the standard IV estimator can be inconsistent and lead to incorrect inference. After showing identification of the mean and variance treatment effects in a nonparametric version of the EHIV model, we provide closed-form estimators for the linear EHIV for the mean and variance treatment effects and the individual treatment effects (ITE). Asymptotic properties of the estimators are provided. A Monte Carlo simulation investigates the performance of the proposed approach, and an empirical application regarding the effects of fertility on female labor supply is considered.