We analyze the properties of non- and semiparametric estimation procedures involving nonparametric regression with generated covariates. Such estimators appear in numerous econometric applications, including nonparametric estimation of simultaneous equation models, sample selection models, treatment effect models, and censored regression models, but so far there seems to be no unified theory to establish their statistical properties. Our paper provides such results, allowing to establish asymptotic properties like rates of consistency or asymptotic normality for a wide range of semi- and nonparametric estimators. We also show how to account for the presence of nonparametrically generated regressors when computing standard errors.
empirical process propensity score control variable methods semiparametric estimation