Using an independent variable correlated with the residuals in quantile regression If an independent variable correlates with the residuals in quantile regression, does it produce biased coefficient estimates?
In ordinary least squares regression, if the independent variable is correlated with the residuals, it may suggest that there is a missing confounding variable.  Does it suggest the same in quantile regression?

In principle yes - there is no difference between quantile and normal lm in that respect.
Note, however, that omitted variable bias only occurs if you have collinearity among predictors. That means that if your residuals correlate with a variable that is not in the regression, including this variable will only change regression estimates of the previous predictors if the new variable correlates with them (collinearity).
