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In this article, we consider a generalized method moments (GMM) estimator to estimate treatment effects defined through estimation equations using an observational data set from a complex survey. We demonstrate that the proposed estimator, which incorporates both sampling probabilities and semiparametrically estimated self-selection probabilities, gives consistent estimates of treatment effects. The asymptotic normality of the proposed estimator is established in the finite population framework, and its variance estimation is discussed. In simulations, we evaluate our proposed estimator and its variance estimator based on the asymptotic distribution. We also apply the method to estimate the effects of different choices of health insurance types on healthcare spending using data from the Chinese General Social Survey. The results from our simulations and the empirical study show that ignoring the sampling design weights might lead to misleading conclusions.

Generalized Method of Moments Estimators for Multiple Treatment Effects Using Observational Data from Complex Surveys