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Efficient Estimation of Missing Data Models Using Moment Conditions and Semiparametric Restrictions

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Bryan S. Graham

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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 missing outcome context, for example, such restrictions are implied by a semiparametric model for the outcome CEF given always-observed 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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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 14376.

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Date of creation: Oct 2008
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Handle: RePEc:nbr:nberwo:14376

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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