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Semiparametric Estimation of Average Treatment Effect with Sieve Method

Correctly identifying treatment effects in observational studies is very difficult due to the fact that the outcome model or the treatment assignment model must be correctly specified. Taking advantages of semiparametric models in this article, we use single-index models to establish the outcome model and the treatment assignment model, which can allow the link function to be unbounded and have unbounded support. The link function is regarded as a point in an infinitely dimensional function space, and we can estimate the link function and the index parameter simultaneously. The sieve method is used to approximate the link function and obtain the estimator of the average treatment effect by the simple linear regression. We establish the asymptotic properties of the proposed estimator. The finite-sample performance of the proposed estimator is evaluated through simulation studies and an empirical example.