Working Paper: NBER ID: w14376
Authors: Bryan S. Graham
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 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.
Keywords: missing data; semiparametric models; efficiency bounds
JEL Codes: C1; C14; C21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| semiparametric efficiency bound under MAR (C51) | efficiency bound from augmented moment condition problem (C51) |
| unconditional moment restriction with MAR (C30) | specific augmented moment condition problem (C30) |
| additional semiparametric restrictions on conditional expectation function (C51) | more efficient estimators (C51) |
| proposed methods (C90) | enhance precision of parameter estimates (C51) |