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Which quantile is the most informative? Maximum likelihood, maximum entropy and quantile regression

Bera, A. K., Galvao Jr, A. F., Montes-Rojas, G. and Park, S. Y. (2010). Which quantile is the most informative? Maximum likelihood, maximum entropy and quantile regression (Report No. 10/08). London, UK: Department of Economics, City University London.

Abstract

This paper studies the connections among quantile regression, the asymmetric Laplace distribution, maximum likelihood and maximum entropy. We show that the maximum likelihood problem is equivalent to the solution of a maximum entropy problem where we impose moment constraints given by the joint consideration of the mean and median. Using the resulting score functions we propose an estimator based on the joint estimating equations. This approach delivers estimates for the slope parameters together with the associated “most probable” quantile. Similarly, this method can be seen as a penalized quantile regression estimator, where the penalty is given by deviations from the median regression. We derive the asymptotic properties of this estimator by showing consistency and asymptotic normality under certain regularity conditions. Finally, we illustrate the use of the estimator with a simple application to the U.S. wage data to evaluate the effect of training on wages.

Publication Type: Monograph (Discussion Paper)
Additional Information: © 2010 the authors.
Publisher Keywords: quantile regression, treatment effects, asymmetric laplace distribution
Subjects: H Social Sciences > HB Economic Theory
Departments: School of Arts & Social Sciences > Economics > Discussion Paper Series
URI: http://openaccess.city.ac.uk/id/eprint/1483
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