Endogeneity in Weakly Separable Models without Monotonicity

TL;DR

This paper introduces a new method for identifying and estimating treatment effects in weakly separable models with endogenous treatments, removing the need for monotonicity by utilizing full outcome distribution information.

Contribution

It develops a novel identification strategy that exploits the entire outcome distribution, applicable to complex models with multiple unobserved factors, unlike previous mean-based approaches.

Findings

Method identifies treatment effects where existing methods fail

Applicable to models with multiple unobserved disturbances

Establishes consistency and asymptotic normality of estimators

Abstract

We identify and estimate treatment effects when potential outcomes are weakly separable with a binary endogenous treatment. Vytlacil and Yildiz (2007) proposed an identification strategy that exploits the mean of observed outcomes, but their approach requires a monotonicity condition. In comparison, we exploit full information in the entire outcome distribution, instead of just its mean. As a result, our method does not require monotonicity and is also applicable to general settings with multiple indices. We provide examples where our approach can identify treatment effect parameters of interest whereas existing methods would fail. These include models where potential outcomes depend on multiple unobserved disturbance terms, such as a Roy model, a multinomial choice model, as well as a model with endogenous random coefficients. We establish consistency and asymptotic normality of our estimators.