A triangular treatment effect model with random coefficients in the selection equation

TL;DR

This paper develops a model for treatment effects with complex heterogeneity and nonmonotone selection, providing identification conditions for various treatment effect measures in a triangular system with random coefficients.

Contribution

It introduces a triangular treatment effect model with random coefficients in both outcome and selection equations, allowing for nonmonotone selection and deriving identification conditions.

Findings

Identification of marginal distributions of potential outcomes

Bounds and conditions for point identification of joint distributions

Framework for deriving unconditional treatment effects

Abstract

This paper considers treatment effects under endogeneity with complex heterogeneity in the selection equation. We model the outcome of an endogenous treatment as a triangular system, where both the outcome and first-stage equations consist of a random coefficients model. The first-stage specifically allows for nonmonotone selection into treatment. We provide conditions under which marginal distributions of potential outcomes, average and quantile treatment effects, all conditional on first-stage random coefficients, are identified. Under the same conditions, we derive bounds on the (conditional) joint distributions of potential outcomes and gains from treatment, and provide additional conditions for their point identification. All conditional quantities yield unconditional effects (\emph{e.g.}, the average treatment effect) by weighted integration.