Conditional moment restriction models with incomplete data

A general statistical model is considered which is defined by moment restrictions when a subvector of data are missing. The main incomplete data situations we have in mind are missing at random and endogenous selection. Using the inverse probability weighting, we show that such a model is equivalent to a model for the observed variables only, augmented by a moment condition defined by the incompleteness mechanism. In particular, our framework covers parametric and semiparametric mean regressions and quantile regressions. We allow for missing responses, missing covariates and any combination of them. We present a general equivalence result, obtained under minimal technical conditions, that sheds new light on various aspects of interest in the missing data and econometric literature. It also provides guidelines for building (efficient) estimators.  This talk is based on a joint work with Marian Hristache.