A Note on Implementing Box-Cox Quantile Regression

The Box-Cox quantile regression model using the two stage method introduced by Chamberlain (1994) and Buchinsky (1995) provides an attractive extension of linear quantile regression techniques. However, a major numerical problem exists when implementing this method which has not been addressed so far in the literature. We suggest a simple solution modifying the estimator slightly. This modification is easy to implement. The modified estimator is still [square root] n-consistent and its asymptotic distribution can easily be derived. A simulation study confirms that the modified estimator works well.