Marginal effects for probit and tobit with endogeneity

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 non-linear models. We study this issue, focusing on the instrumental variable (IV) probit and tobit models. We show that even when a valid instrumental variable is available, failing to differentiate between the two types of endogeneity can lead to either under- or overestimation 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.