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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.
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Suggested Citation

  • Bryan S. Graham, 2011. "Efficiency Bounds for Missing Data Models With Semiparametric Restrictions," Econometrica, Econometric Society, vol. 79(2), pages 437-452, March.
    • Handle: RePEc:ecm:emetrp:v:79:y:2011:i:2:p:437-452
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    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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