Nonparametric regression with selectively missing covariates

We consider the problem of regression with selectively observed covariates in a nonparametric framework. Our approach relies on instrumental variables that explain variation latent but have no direct effect selection. The function interest is shown to be weighted version conditional expectation where weighting fraction selection probabilities. Nonparametric identification fractional probability weight (FPW) achieved via partial completeness assumption. provide primitive functional form assumptions for hold. result constructive FPW series estimator. derive rate convergence and also pointwise asymptotic distribution. In both cases, performance estimator does not suffer from inverse which derives variable approach. Monte Carlo study, we analyze finite sample properties our compare weighting, can used alternatively unconditional moment estimation. empirical application, focus two different applications. estimate association between income health using linked data SHARE survey administrative pension information use entitlements as an instrument. second application revisit question how affects demand housing based German Socio–Economic Panel Study (SOEP). this regional residential block level applications show missing demonstrate standard methods do account nonrandom process lead significantly biased estimates individuals low income.