Treatment Effect Models with Strategic Interaction in Treatment Decisions

TL;DR

This paper develops a model for treatment effects in strategic two-player interactions, identifying effects under equilibrium selection and proposing a semiparametric estimation method, with an empirical application to adolescent risky behaviors.

Contribution

It introduces a novel framework for treatment effect estimation in strategic settings with multiple equilibria and provides a consistent estimation procedure.

Findings

Identified marginal treatment effects under equilibrium selection.

Proposed a consistent semiparametric estimator.

Empirical analysis on adolescent risky behaviors and academic performance.

Abstract

This study considers treatment effect models in which others' treatment decisions can affect both one's own treatment and outcome. Focusing on the case of two-player interactions, we formulate treatment decision behavior as a complete information game with multiple equilibria. Using a latent index framework and assuming a stochastic equilibrium selection, we prove that the marginal treatment effect from one's own treatment and that from the partner are identifiable on the conditional supports of certain threshold variables determined through the game model. Based on our constructive identification results, we propose a two-step semiparametric procedure for estimating the marginal treatment effects using series approximation. We show that the proposed estimator is uniformly consistent and asymptotically normally distributed. As an empirical illustration, we investigate the impacts of risky behaviors on adolescents' academic performance.