Nonparametric Regression with Selectively Missing Covariates

Date

Nov 8, 2018

Time

2:00 PM - 3:00 PM

Speaker

Prof. Dr. Christoph Breunig

Affiliation

HU Berlin

Series

TUD Mathematik AG Analysis & Stochastik

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. O. Okhrin

Description

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 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, we analyze the finite sam- ple properties of our estimator and we demonstrate the usefulness of our method in analyses based on survey data. In the empirical application, we estimate the association between income and health using linked data from the SHARE survey data and administrative pension information. The pension information which is a function of the full earnings history is used as an instrument. We show that income is selectively missing and we demonstrate that standard methods that do not account for the non- random selection process are strongly downward biased, in particular for high income individuals.

Links

• AG Analysis & Stochastik

Last modified: Oct 29, 2018, 12:29:38 PM