Quantile Regression with Generated Regressors

This paper studies estimation and inference for linear quantile regression models with generated regressors. We suggest a practical two-step procedure, where the regressors are computed in first step. The asymptotic properties of estimator, namely, consistency normality established. show that variance-covariance matrix needs to be adjusted account first-step error. propose general estimator variance-covariance, establish its consistency, develop testing procedures hypotheses these models. Monte Carlo simulations evaluate finite-sample performance provided. Finally, we apply proposed methods study Engel curves various commodities using data from UK Family Expenditure Survey. document strong heterogeneity estimated along conditional distribution budget share each commodity. empirical application also emphasizes correctly estimating confidence intervals by is importance inference.