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

Open access


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.

Ashmead, R. 2014. “Propensity Score Methods for Estimating Causal Effects from Complex Survey Data.” Ph.D. Dissertation, Ohio State University. Retrieved from

Berg, E., J.K. Kim, and C. Sinner. 2016. “Imputation under Informative Sampling.” Journal of Survey Statistics and Methodology 4: 436–462. Doi: 10.1093/jssam/smw032.

Breidt, F.J., G. Claeskens, and J.D. Opsomer. 2005. “Model-Assisted Estimation for Complex Surveys Using Penalised Splines.” Biometrika 92(4): 831–846. Doi: 10.1093/biomet/92.4.831.

Cattaneo, M.D. 2010. “Efficient Semiparametric Estimation of Multi-valued Treatment Effects under Ignorability.” Journal of Econometrics 155(2): 138–154. Doi: 10.1016/j.jeconom.2009.09.023.

DuGoff, E., M. Schuler, and E. Stuart. 2014. “Generalizing Observational Study Results: Applying Propensity Score Methods to Complex Surveys.” Health Services Research 49(1): 284–303. Doi: 10.1111/1475-6773.12090.

Fuller, W.A. 2009. Sampling Statistics, Vol. 56, John Wiley and Sons. Doi: 10.1002/9780470523551.

Hahn, J. 1998. “On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects.” Econometrica 66(2): 315–331. Doi: 10.2307/2998560.

Haziza, D. and J.N.K. Rao. 2006. “A Nonresponse Model Approach to Inference Under Imputation for Missing Survey Data.” Survey Methodology 32(1): 53. Doi: 12-001-X20060019257.

Hirano, K., G. Imbens, and G. Ridder. 2003. “Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score.” Econometrica 71(4): 1161–1189. Doi: 10.1111/1468-0262.00442.

Horvitz, D.G. and D.J. Thompson. 1952. “A Generalization of Sampling Without Replacement From a Finite Universe.” Journal of the American Statistical Association 47: 663–685. Doi: 10.1080/01621459.1952.10483446.

Isaki, C.T. and W.A. Fuller. 1982. “Survey Design under the Regression Superpopulation Model.” Journal of the American Statistical Association 77: 89–96. Doi: 10.1080/01621459.1982.10477770.

Kim, J.K. and D. Haziza. 2014. “Doubly Robust Inference with Missing Data in Survey Sampling.” Statistica Sinica 24: 375–394. Doi: 10.5705/ss.2012.005.

Kim, J.K. A. Navarro, and W. Fuller. 2006. “Replication Variance Estimation for Two-Phase Stratified Sampling.” Journal of the American Statistical Association 101: 312–320. Doi: 10.1198/016214505000000763.

Little, R.J.A. 1982. “Models for Nonresponse in Sample Surveys.” Journal of the American Statistical Association 77: 237–250. Doi: 10.1080/01621459.1982.10477792.

Lorentz, G. 1986. Approximating of Functions. New York: Chelsea Publishing Company. Doi: 10.1112/jlms/s1-43.1.570b.

Pakes, A. and D. Pollard. 1989. “Simulation and the Asymptotics of Optimization Estimators.” Econometrica 57: 1027–1057. Doi: 10.2307/1913622.

Pfeffermann, D. 2011. “Modelling of Complex Survey Data: Why Model? Why is it a Problem? How Can we Approach it?” Survey Methodology 37: 115–136. Retrieved from

Pfeffermann, D. and M. Sverchkov. 1999. “Parametric and Semiparametric Estimation of Regression Models Fitted to Survey Data.” Sankhya B 61: 166–186. Retrieved from

Robins, J., M. Sued, Q. Lei-Gomez, and A. Rotnitzky. 2007. “Comment: Performance of Double-Robust Estimators When “Inverse Probability” Weights Are Highly Variable.” Statistical Science 22(4): 544–559. Doi: 10.1214/07-STS227D.

Rosenbaum, P.R. and D.B. Rubin. 1983. “The Central Role of the Propensity Score in Observational Studies for Causal Effects.” Biometrika 70: 41–55. Doi: 10.1093/biomet/70.1.41.

Ridgeway, G., S.A. Kovalchik, B.A. Griffin, and M.U. Kabeto. 2015. “Propensity Score Analysis with Survey Weighted Data.” Journal of Causal Inference 3(2): 237–249. Doi: 10.1515/jci-2014-0039.

Särndal, C.E., B. Swensson, and J. Wretman. 1992. Model Assisted Survey Sampling. Springer. Doi: 10.1007/978-1-4612-4378-6.

Tan, Z. 2006. “Regression and Weighting Methods for Causal Inference Using Instrumental Variables.” Journal of the American Statistical Association 101: 1607–1618. Doi: 10.1198/016214505000001366.

Tan, Z. 2008. “Bounded, Efficient, and Doubly Robust Estimation with Inverse Weighting.” Biometrika 94: 122. Doi: 10.1093/biomet/asq035.

Yu, C., J. Legg, and B. Liu. 2013. “Estimating Multiple Treatment Effects Using Two-phase Semiparametric Regression Estimators.” Electronic Journal of Statistics 7(2013): 2737–2761. Doi: 10.1214/13-EJS856.

Zanutto, E. 2006. “A Comparison of Propensity Score and Linear Regression Analysis of Complex Survey Data.” Journal of Data Science 4: 67–91. Retrieved from

Journal of Official Statistics

The Journal of Statistics Sweden

Journal Information

IMPACT FACTOR 2017: 0.662
5-year IMPACT FACTOR: 1.113

CiteScore 2017: 0.74

SCImago Journal Rank (SJR) 2017: 1.158
Source Normalized Impact per Paper (SNIP) 2017: 0.860


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 107 107 55
PDF Downloads 88 88 33