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Journal of Econometric Methods

Ed. by Giacomini, Raffaella / Li, Tong

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Asymmetric Laplace Regression: Maximum Likelihood, Maximum Entropy and Quantile Regression

Anil K. Bera / Antonio F. Galvao Jr.
  • Department of Economics, University of Iowa, W334 Pappajohn Business Building, 21 E. Market Street, Iowa City, IA 52242, USA
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 / Gabriel V. Montes-Rojas / Sung Y. Park
Published Online: 2015-03-03 | DOI: https://doi.org/10.1515/jem-2014-0018

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Abstract

This paper studies the connections among the asymmetric Laplace probability density (ALPD), maximum likelihood, maximum entropy and quantile regression. 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. The ALPD score functions lead to joint estimating equations that delivers estimates for the slope parameters together with a representative quantile. Asymptotic properties of the estimator are derived under the framework of the quasi maximum likelihood estimation. With a limited simulation experiment we evaluate the finite sample properties of our estimator. Finally, we illustrate the use of the estimator with an application to the US wage data to evaluate the effect of training on wages.

Keywords: asymmetric Laplace distribution; quantile regression; treatment effects

JEL Classification:: C14; C31

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About the article

Corresponding author: Gabriel V. Montes-Rojas, Department of Economics, City University London, 10 Northampton Square, London EC1V 0HB, UK, E-mail:

Published Online: 2015-03-03

Published in Print: 2016-01-01

Citation Information: Journal of Econometric Methods, Volume 5, Issue 1, Pages 79–101, ISSN (Online) 2156-6674, ISSN (Print) 2194-6345, DOI: https://doi.org/10.1515/jem-2014-0018.

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