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Efficiency Bounds for Missing Data Models With Semiparametric Restrictions
Author(s) -
Graham Bryan S.
Publication year - 2011
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta7379
Subject(s) - covariate , moment (physics) , econometrics , mathematics , context (archaeology) , semiparametric model , semiparametric regression , missing data , conditional expectation , function (biology) , statistics , nonparametric statistics , geography , physics , archaeology , classical mechanics , evolutionary biology , biology
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.