NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Efficiency bounds for missing data models with semiparametric restrictions

Bryan S. Graham

NBER Working Paper No. 14376
Issued in October 2008
NBER Program(s):   TWP

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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An online appendix is available for this publication.

This paper was revised on December 5, 2011

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Document Object Identifier (DOI): 10.3386/w14376

Published: Bryan S. Graham, 2011. "Efficiency Bounds for Missing Data Models With Semiparametric Restrictions," Econometrica, Econometric Society, vol. 79(2), pages 437-452, 03. citation courtesy of

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