Accounting for missing data in M-estimation: a general matching approach

This paper addresses M-estimation of conditional mean functions when observations are missing at random. The usual approach of correcting for missing data, when the missing data mechanism is ignorable, is inverse probability weighting (IPW). An alternative semiparametric M-estimator which involves local polynomial matching techniques is proposed and its asymptotic distribution is derived. Like IPW, the proposed estimation approach has a double robustness property for the estimation of unconditional means. Monte Carlo evidence suggests slightly better finite sample properties of the semiparametric M-estimator relatively to IPW. A version of the proposed estimator is applied to estimate the impact of noncognitive skills on wages in Germany for two different educational treatment regimes.