Implementing Box-Cox Quantile Regression

The Box-Cox quantile regression model introduced by Powell (1991) is a flexible and numerically attractive extension of linear quantile regression techniques. Chamberlain (1994) and Buchinsky (1995) suggest a two stage estimator for this model but the objective function in stage two of their method may not be defined in an application. We suggest a modification of the estimator which is easy to implement. A simulation study demonstrates that the modified estimator works well in situations, where the original estimator is not well defined.