Which quantile is the most informative? Maximum likelihood, maximum entropy and quantile regression
AbstractThis 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.
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Bibliographic InfoPaper provided by Department of Economics, City University London in its series Working Papers with number 10/08.
Date of creation: 2010
Date of revision:
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Postal: Department of Economics, Social Sciences Building, City University London, Whiskin Street, London, EC1R 0JD, United Kingdom,
Phone: +44 (0)20 7040 8500
Web page: http://www.city.ac.uk
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quantile regression; treatment effects; asymmetric laplace distribution;
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