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

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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