Maybe this link helps: https://www.researchgate.net/post/Anyone_know_of_a_package_in_R_or_Stata_that_will_estimate_quantile_regression_with_endogenous_regressors_for_data_that_is_purely_cross-sectional
You can get other files (including the Journal of Econometrics paper, which discusses some advantages) under "Smoothed estimating equations for instrumental variables quantile regression" at