02327cam a22002657 4500001000700000003000500007005001700012008004100029100002100070245012200091260006600213490004200279500001800321520099700339530006101336538007201397538003601469690011001505690009901615690015301714710004201867830007701909856003801986856003702024w14376NBER20170818181955.0170818s2008 mau||||fs|||| 000 0 eng d1 aGraham, Bryan S.10aEfficiency bounds for missing data models with semiparametric restrictionsh[electronic resource] /cBryan S. Graham. aCambridge, Mass.bNational Bureau of Economic Researchc2008.1 aNBER working paper seriesvno. w14376 aOctober 2008.3 aThis 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC1 - Econometric and Statistical Methods and Methodology: General2Journal of Economic Literature class. 7aC14 - Semiparametric and Nonparametric Methods: General2Journal of Economic Literature class. 7aC21 - Cross-Sectional Models • Spatial Models • Treatment Effect Models • Quantile Regressions2Journal of Economic Literature class.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w14376.4 uhttp://www.nber.org/papers/w1437641uhttp://dx.doi.org/10.3386/w14376