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Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects

Author

Listed:
  • Chen, Xiaohong

    (New York U)

  • Hong, Han

    (Duke U)

  • Tarozzi, Alessandro
Abstract
We study semiparametric efficiency bounds and efficient estimation of parameters defined through general nonlinear, possibly non-smooth and over-identified moment restrictions, where the sampling information consists of a primary sample and an auxiliary sample. The variables of interest in the moment conditions are not directly observable in the primary data set, but the primary data set contains proxy variables which are correlated with the variables of interest. The auxiliary data set contains information about the conditional distribution of the variables of interest given the proxy variables. Identification is achieved by the assumption that this conditional distribution is the same in both the primary and auxiliary data sets. We provide semiparametric efficiency bounds for both the "verify-out-of-sample" case, where the two samples are independent, and the "verify-in-sample" case, where the auxiliary sample is a subset of the primary sample; and the bounds are derived when the propensity score is unknown, or known, or belongs to a correctly specified parametric family. These efficiency variance bounds indicate that the propensity score is ancillary for the "verify-in-sample" case, but is not ancillary for the "verify-out-of-sample" case. We show that sieve conditional expectation projection based GMM estimators achieve the semiparametric efficiency bounds for all the above mentioned cases, and establish their asymptotic efficiency under mild regularity conditions. Although inverse probability weighting based GMM estimators are also shown to be semiparametrically efficient, they need stronger regularity conditions and clever combinations of nonparametric and parametric estimates of the propensity score to achieve the efficiency bounds for various cases. Our results contribute to the literature on non-classical measurement error models, missing data and treatment effects.

Suggested Citation

  • Chen, Xiaohong & Hong, Han & Tarozzi, Alessandro, 2008. "Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects," Working Papers 42, Yale University, Department of Economics.
    • Handle: RePEc:ecl:yaleco:42
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    References listed on IDEAS

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    Cited by:

    1. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2008. "Nonparametric Tests for Treatment Effect Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 389-405, August.
    2. Matias Busso & Patrick Kline, 2008. "Do Local Economic Development Programs Work? Evidence from the Federal Empowerment Zone Program," Cowles Foundation Discussion Papers 1639, Cowles Foundation for Research in Economics, Yale University.
    3. An, Yonghong & Hu, Yingyao, 2012. "Well-posedness of measurement error models for self-reported data," Journal of Econometrics, Elsevier, vol. 168(2), pages 259-269.
    4. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2006. "Moving the Goalposts: Addressing Limited Overlap in the Estimation of Average Treatment Effects by Changing the Estimand," NBER Technical Working Papers 0330, National Bureau of Economic Research, Inc.
    5. Bryan S. Graham & Keisuke Hirano, 2011. "Robustness to Parametric Assumptions in Missing Data Models," American Economic Review, American Economic Association, vol. 101(3), pages 538-543, May.
    6. Devereux, Paul J. & Tripathi, Gautam, 2009. "Optimally combining censored and uncensored datasets," Journal of Econometrics, Elsevier, vol. 151(1), pages 17-32, July.
    7. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
    8. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    9. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 1053-1079.
    10. Rohman, Ibrahim Kholilul & Bohlin, Erik, 2011. "Towards the alternative measurement: Discovering the relationships between technology adoption and quality of life in Indonesia," 22nd European Regional ITS Conference, Budapest 2011: Innovative ICT Applications - Emerging Regulatory, Economic and Policy Issues 52206, International Telecommunications Society (ITS).
    11. Cattaneo, Matias D., 2010. "Efficient semiparametric estimation of multi-valued treatment effects under ignorability," Journal of Econometrics, Elsevier, vol. 155(2), pages 138-154, April.
    12. Hu, Yingyao, 2017. "The Econometrics of Unobservables -- Latent Variable and Measurement Error Models and Their Applications in Empirical Industrial Organization and Labor Economics [The Econometrics of Unobservables]," Economics Working Paper Archive 64578, The Johns Hopkins University,Department of Economics, revised 2021.
    13. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
    14. Victor Chernozhukov & Roberto Rigobon & Thomas M. Stoker, 2010. "Set identification and sensitivity analysis with Tobin regressors," Quantitative Economics, Econometric Society, vol. 1(2), pages 255-277, November.
    15. Cañón Salazar Carlos Iván, 2016. "Distributional Policy Effects with Many Treatment Outcomes," Working Papers 2016-01, Banco de México.
    16. Rita Ginja, 2010. "Income Shocks and Investments in Human Capital," 2010 Meeting Papers 1165, Society for Economic Dynamics.
    17. Victor Chernozhukov & Roberto Rigobon & Thomas M. Stoker, 2009. "Set identification with Tobin regressors," CeMMAP working papers CWP12/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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