This note derives the bias of the quantile regression estimator in the presence of classical additive measurement error, and show its connection to least squares models. The bias structure suggests that the instrumental variables estimator proposed for least squares can be applied to the...

We derive the variance of the Hirano, Imbens and Ridder (Econometrica 66, 315--31, 2003) average treatment effects estimator when the true propensity score is known. This variance is used in the derivation of the variance of a similar two-step estimator, where a M-estimator is used in the first...