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Equivalent models for observables under the assumption of missing at random

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  • Hristache, Marian
  • Patilea, Valentin

Abstract

An equivalence result for a general class of models when some variables are missing at random is established. The initial model and the missingness mechanism could be equivalently defined under the form of a system of moment equations. The equivalence means the same sets of probability measures for the observed variables. This type of equivalence greatly simplifies the analysis of the initial model under the missingness mechanism.

Suggested Citation

  • Hristache, Marian & Patilea, Valentin, 2021. "Equivalent models for observables under the assumption of missing at random," Econometrics and Statistics, Elsevier, vol. 20(C), pages 153-165.
    • Handle: RePEc:eee:ecosta:v:20:y:2021:i:c:p:153-165
    DOI: 10.1016/j.ecosta.2020.03.002
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    References listed on IDEAS

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    1. MacKinnon, James G & Magee, Lonnie, 1990. "Transforming the Dependent Variable in Regression Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 315-339, May.
    2. Bryan S. Graham, 2011. "Efficiency Bounds for Missing Data Models With Semiparametric Restrictions," Econometrica, Econometric Society, vol. 79(2), pages 437-452, March.
    3. 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.
    4. Lavergne, Pascal & Patilea, Valentin, 2013. "Smooth minimum distance estimation and testing with conditional estimating equations: Uniform in bandwidth theory," Journal of Econometrics, Elsevier, vol. 177(1), pages 47-59.
    5. Prokhorov, Artem & Schmidt, Peter, 2009. "GMM redundancy results for general missing data problems," Journal of Econometrics, Elsevier, vol. 151(1), pages 47-55, July.
    6. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    7. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.
    8. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    9. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, vol. 170(2), pages 442-457.
    10. Jeffrey M. Wooldridge, 2002. "Inverse probability weighted M-estimators for sample selection, attrition, and stratification," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 1(2), pages 117-139, August.
    11. Hitomi, Kohtaro & Nishiyama, Yoshihiko & Okui, Ryo, 2008. "A Puzzling Phenomenon In Semiparametric Estimation Problems With Infinite-Dimensional Nuisance Parameters," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1717-1728, December.
    12. Whitney K. Newey, 2004. "Efficient Semiparametric Estimation via Moment Restrictions," Econometrica, Econometric Society, vol. 72(6), pages 1877-1897, November.
    13. Hristache, Marian & Patilea, Valentin, 2016. "Semiparametric Efficiency Bounds For Conditional Moment Restriction Models With Different Conditioning Variables," Econometric Theory, Cambridge University Press, vol. 32(4), pages 917-946, August.
    14. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2009. "Choosing instrumental variables in conditional moment restriction models," Journal of Econometrics, Elsevier, vol. 152(1), pages 28-36, September.
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