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Efficiency bounds for missing data models with semiparametric restrictions

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  • Bryan S. Graham

Abstract

This paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random (MAR) coincides with that of a particular augmented moment condition problem. The augmented system consists of the inverse probability weighted (IPW) original moment restriction and an additional conditional moment restriction which exhausts all other implications of the MAR assumption. The paper also investigates the value of additional semiparametric restrictions on the conditional expectation function (CEF) of the original moment function given always- observed covariates. In the program evaluation context, for example, such restrictions are implied by semiparametric models for the potential outcome CEFs given baseline covariates. The efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem. Some implications of these results for estimation are briefly discussed.

Suggested Citation

  • Bryan S. Graham, 2008. "Efficiency bounds for missing data models with semiparametric restrictions," NBER Working Papers 14376, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:14376
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Saraswata Chaudhuriy & David T. Frazierz & √Čric Renault, 2016. "Indirect Inference with Endogenously Missing Exogenous Variables," CIRANO Working Papers 2016s-15, CIRANO.
    2. Bryan S. Graham & Guido Imbens & Geert Ridder, 2016. "Identification and efficiency bounds for the average match function under conditionally exogenous matching," CeMMAP working papers CWP10/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Bryan S. Graham & Cristine Campos de Xavier Pinto & Daniel Egel, 2016. "Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 288-301, April.
    4. Ying-Ying Lee, 2015. "Efficient propensity score regression estimators of multi-valued treatment effects for the treated," Economics Series Working Papers 738, University of Oxford, Department of Economics.
    5. Thomas MaCurdy & Xiaohong Chen & Han Hong, 2011. "Flexible Estimation of Treatment Effect Parameters," American Economic Review, American Economic Association, vol. 101(3), pages 544-551, May.
    6. repec:oup:biomet:v:104:y:2017:i:3:p:735-742. is not listed on IDEAS
    7. repec:eee:econom:v:204:y:2018:i:2:p:207-222 is not listed on IDEAS

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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