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

Anil K. Bera, Antonio F. Galvao, Gabriel V. Montes-Rojas, Sung Y. Park

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)79-101
Number of pages23
JournalJournal of Econometric Methods
Issue number1
StatePublished - 2016


  • asymmetric Laplace distribution
  • quantile regression
  • treatment effects

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Applied Mathematics


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