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

Author

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  • Liu Bin

    (Ant Financial, Hangzhou, China.)

  • Yu Cindy Long

    (Iowa State University – Department of Statistics, Ames, Iowa50011, United States.)

  • Price Michael Joseph

    (Iowa State University – Department of Statistics, Ames, Iowa50011, United States.)

  • Jiang Yan

    (Renmin University of China - School of Statistics and The Center for Applied Statistics, Beijing, China.)

Abstract

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.

Suggested Citation

  • Liu Bin & Yu Cindy Long & Price Michael Joseph & Jiang Yan, 2018. "Generalized Method of Moments Estimators for Multiple Treatment Effects Using Observational Data from Complex Surveys," Journal of Official Statistics, Sciendo, vol. 34(3), pages 753-784, September.
    • Handle: RePEc:vrs:offsta:v:34:y:2018:i:3:p:753-784:n:8
    DOI: 10.2478/jos-2018-0035
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    References listed on IDEAS

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    1. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    2. Kim, Jae Kwang & Navarro, Alfredo & Fuller, Wayne A., 2006. "Replication Variance Estimation for Two-Phase Stratified Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 312-320, March.
    3. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    4. Matias D. Cattaneo, 2010. "multi-valued treatment effects," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
    5. Tan, Zhiqiang, 2006. "Regression and Weighting Methods for Causal Inference Using Instrumental Variables," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1607-1618, December.
    6. F. J. Breidt & G. Claeskens & J. D. Opsomer, 2005. "Model-assisted estimation for complex surveys using penalised splines," Biometrika, Biometrika Trust, vol. 92(4), pages 831-846, December.
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