Marginal Effects for Probit and Tobit with Endogeneity

TL;DR

This paper investigates how structural endogeneity and measurement errors differently impact partial effects in nonlinear models like IV Probit and Tobit, proposing bounds and confidence intervals to address these issues.

Contribution

It introduces simple estimators and confidence intervals that distinguish and correct for both types of endogeneity in nonlinear models.

Findings

Bounds on partial effects effectively account for endogeneity

Confidence intervals accurately reflect uncertainty under endogeneity

Simulation and empirical results validate the proposed methods

Abstract

When evaluating partial effects, it is important to distinguish between structural endogeneity and measurement errors. In contrast to linear models, these two sources of endogeneity affect partial effects differently in nonlinear models. We study this issue focusing on the Instrumental Variable (IV) Probit and Tobit models. We show that even when a valid IV is available, failing to differentiate between the two types of endogeneity can lead to either under- or over-estimation of the partial effects. We develop simple estimators of the bounds on the partial effects and provide easy to implement confidence intervals that correctly account for both types of endogeneity. We illustrate the methods in a Monte Carlo simulation and an empirical application.