Estimation of Complier Expected Shortfall Treatment Effects with a Binary Instrumental Variable

TL;DR

This paper introduces a novel method to estimate the causal effect of a binary treatment on the expected shortfall, accommodating heterogeneity and using instrumental variables within a two-step estimation framework.

Contribution

It proposes the CRESTE model for binary endogenous treatments, utilizing Neyman-orthogonalization and weighted regressions, with proven asymptotic properties and practical validation.

Findings

Method accurately estimates CRESTE with robust finite-sample performance.

Simulation studies confirm the estimator's validity and robustness.

Application to a job training study demonstrates practical utility.

Abstract

Estimating the causal effect of a treatment or exposure for a subpopulation is of great interest in many biomedical and economical studies. Expected shortfall, also referred to as the super-quantile, is an attractive effect-size measure that can accommodate data heterogeneity and aggregate local information of effect over a certain region of interest of the outcome distribution. In this article, we propose the ComplieR Expected Shortfall Treatment Effect (CRESTE) model under an instrumental variable framework to quantity the CRESTE for a binary endogenous treatment variable. By utilizing the special characteristics of a binary instrumental variable and a specific formulation of Neyman-orthogonalization, we propose a two-step estimation procedure, which can be implemented by simply solving weighted least-squares regression and weighted quantile regression with estimated weights. We develop the asymptotic properties for the proposed estimator and use numerical simulations to confirm its validity and robust finite-sample performance. An illustrative analysis of a National Job Training Partnership Act study is presented to show the practical utility of the proposed method.