Inverse probability tilting and missing data problems

"This paper outlines a new minimum empirical discrepancy (MD) estimator for missing data, sample combination and related problems: inverse probability tilting (IPT). Covered examples include estimation of the average treatment effect (ATE), the average treatment effect on the treated (ATT) and the two sample instrumental variables (TSIV) model. The proposed estimator attains the semiparametric efficiency bound under two auxiliary parametric restrictions (local efficiency), but is consistent so long as one or the other holds (double robustness). A novel feature of IPT is its 'exact balancing' property: after reweighting, sample moments of always-observed covariates in the complete-case subsample equal their corresponding (unweighted) full sample means. We also show how prior restrictions on the marginal distribution of always-observed covariates can be efficiently incorporated into our procedure. We use our methods, and compare them to several alternatives, in an evaluation of the National Supported Work (NSW) demonstration using 'non-experimental' comparison groups drawn from the Panel Study of Income Dynamics (PSID) and the Current Population Survey (CPS) as in LaLonde (1986) and Dehejia and Wahba (1999). We explore the small sample properties of IPT in a Monte Carlo study. IPT performs well, relative to several alternative estimators, across a variety of data generating processes"--National Bureau of Economic Research web site.