  We study linear quantile regression models when regressors and/or dependent
variable are not directly observed but estimated in an initial first step and
used in the second step quantile regression for estimating the quantile
parameters. This general class of generated quantile regression (GQR) covers
various statistical applications, for instance, estimation of endogenous
quantile regression models and triangular structural equation models, and some
new relevant applications are discussed. We study the asymptotic distribution
of the two-step estimator, which is challenging because of the presence of
generated covariates and/or dependent variable in the non-smooth quantile
regression estimator. We employ techniques from empirical process theory to
find uniform Bahadur expansion for the two step estimator, which is used to
establish the asymptotic results. We illustrate the performance of the GQR
estimator through simulations and an empirical application based on auctions.
