We develop identification and estimation methods for treatment effect models with strategic interaction in the treatment decisions . We consider models where one's treatment choice and outcomecan be endogenously affected by others' treatment choices. We formulate the interaction of the treatment decisions as a two-player  complete information game with potential multiple equilibria. For this model, using a latent index framework and the assumption of a stochastic equilibrium selection rule , we prove that the marginal treatment effect from one's own treatment and that from his/her partner 's can be separately point-identified with potential over-identifiability . Based on our constructive identification results, we propose a two-step semiparametric procedure for estimating the marginal treatment effects using series approximation. The proposed estimator is shown to be uniformly consistent and asymptotically normal. As an empirical illustration, we investigate the impacts of risky behaviors on adolescents' academic performance.
This study considers treatment effect models in which others' treatment decisions can affect 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 can be over-identified separately . 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 normal. As an empirical illustration, we investigate the impacts of risky behaviors on adolescents' academic performance.
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