Title: Nonparametric regression with selectively missing covariates
Authors: Christoph Breunig - Humboldt-Universitat zu Berlin (Germany) [presenting]
Peter Haan - DIW Berlin and Freie Universitaet Berlin (Germany)
Abstract: The problem of regressions with selectively observed covariates is considered in a nonparametric framework. The proposed approach relies on instrumental variables that explain variation in the latent covariates, but have no direct effect on selection. The regression function of interest is shown to be a weighted version of observed conditional expectation where the weighting function is a fraction of selection probabilities. Nonparametric identification of the fractional probability weight (FPW) function is achieved via a partial completeness assumption. We provide primitive functional form assumptions for partial completeness to hold. The identification result is constructive for the FPW series estimator. We derive the rate of convergence and also the pointwise asymptotic distribution. In both cases, the asymptotic performance of the FPW series estimator does not suffer from the inverse problem which derives from the nonparametric instrumental variable approach. In a Monte Carlo study and an empirical illustration, we analyze the finite sample properties of our estimator and we demonstrate the usefulness of our method in analyses based on survey data.