We consider the problem of regressions with selectively observed covariates in a nonparametric framework. Our approach relies on instrumental variables that explain variation in the latent covariates but have no direct e ffect on selection. The regression function of interest is shown to be a...

This paper proposes a test for missing at random (MAR). The MAR assumption is shown to be testable given instrumental variables which are independent of response given potential outcomes. A nonparametric testing procedure based on integrated squared distance is proposed. The statistic's...