Endogenous Treatment Models with Social Interactions: An Application to the Impact of Exercise on Self-Esteem

TL;DR

This paper develops a game theoretic model to estimate the effects of social interactions on individual treatment outcomes, specifically examining how exercise influences self-esteem.

Contribution

It introduces a computationally feasible method for estimating endogenous treatment models with social interactions using a Bayesian game framework.

Findings

Exercise frequency is influenced by friends' expectations.

Exercise and friends' self-esteem affect individual self-esteem.

Social expectations play a significant role at lower self-esteem levels.

Abstract

We address the estimation of endogenous treatment models with social interactions in both the treatment and outcome equations. We model the interactions between individuals in an internally consistent manner via a game theoretic approach based on discrete Bayesian games. This introduces a substantial computational burden in estimation which we address through a sequential version of the nested fixed point algorithm. We also provide some relevant treatment effects, and procedures for their estimation, which capture the impact on both the individual and the total sample. Our empirical application examines the impact of an individual's exercise frequency on her level of self-esteem. We find that an individual's exercise frequency is influenced by her expectation of her friends'. We also find that an individual's level of self-esteem is affected by her level of exercise and, at relatively lower levels of self-esteem, by the expectation of her friends' self-esteem.