Statistical inference of heterogeneous treatment effects using semiparametric single-index model

TL;DR

This paper introduces a novel semiparametric single-index model for estimating heterogeneous treatment effects using doubly robust methods, avoiding traditional constraints and demonstrating superior performance through simulations and real data application.

Contribution

It develops a flexible estimation approach for HTE that relaxes conventional assumptions and provides theoretical and empirical validation of its effectiveness.

Findings

The proposed estimator has desirable asymptotic properties.

Simulation studies show superior finite-sample performance.

Application reveals significant insights into health intervention impacts.

Abstract

In recent years, with the rapid development of science and technology, heterogeneous treatment effects have emerged as a focal research topic in statistics, econometrics, and sociology. This paper investigates HTE through semiparametric single-index models based on doubly robust estimation. Departing from conventional approaches, we neither impose boundedness constraints on the link function in single-index models nor restrict its support range. By employing the sieve method to approximate the link function, we achieve simultaneous estimation of both the link function and index parameters. Our study not only establishes the asymptotic properties of the proposed estimator but also systematically evaluates its finite-sample performance through comprehensive simulation studies. Numerical results demonstrate that our method significantly outperforms other commonly used competing estimators. Furthermore, we apply the proposed approach to the National Health and Nutrition Examination Survey dataset to assess the impact of participation in school lunch programs on body mass index.