A Note on Implementing Box-Cox Quantile Regression

Bernd Fitzenberger, Ralf A. Wilke, Xuan Zhang
2005 Social Science Research Network  
Quantile regression is gradually evolving into a comprehensive approach to the statistical analysis of linear and nonlinear response models for conditional quantile functions. Just as classical linear regression methods based on minimizing sums of squared residuals allow one to estimate a general class of models for conditional mean functions, quantile regression methods offer a mechanism for estimating models for the conditional median function and the full range of other conditional quantile
more » ... unctions. The Box-Cox function is a nonlinear monotonic transformation including the log-linear and the linear function as special cases. The Box-Cox quantile regression model therefore provides an attractive extension of linear quantile regression techniques. Chamberlain (1994) and Buchinsky (1995) introduce a computationally convenient two stage method. 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. We derive the asymptotic distribution of the modified estimator and show that it has still standard statistical properties. Simulation studies confirm that the modified estimator works well in finite samples. Abstract 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 √ n-consistent and its asymptotic distribution can easily be derived. A simulation study confirms that the modified estimator works well. Keywords: Box-Cox quantile regression, iterative estimator JEL: C13, C14 * Financial support of the German Research Foundation (DFG) through the project "Microeconometric modelling of unemployment durations under consideration of the macroeconomic situation" is gratefully acknowledged.
doi:10.2139/ssrn.604441 fatcat:wqm6lj74obbrdclgefry25oheq