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

Zhongjian Lin and Francis Vella

Journal of Political Economy, 2026, vol. 134, issue 3, 949 - 977

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 via a game theoretic approach based on discrete Bayesian games. We employ a nested pseudo joint likelihood algorithm when obtaining the model’s parameters and provide relevant treatment effects and procedures for their estimation. Our empirical application examines the impact of an individual’s exercise frequency on their level of self-esteem. We find that an individual’s exercise frequency is influenced by their expectation of their friends’ exercise frequency. Moreover, an individual’s level of self-esteem is affected by their level of exercise and, at relatively lower levels of self-esteem, by the expectation of their friends’ self-esteem.

Date: 2026
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