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

Author

Listed:
  • Bera Anil K.

    (Department of Economics, University of Illinois, 1407 W. Gregory Drive, Urbana, IL 61801, USA)

  • Galvao Antonio F.

    (Department of Economics, University of Iowa, W334 Pappajohn Business Building, 21 E. Market Street, Iowa City, IA 52242, USA)

  • Montes-Rojas Gabriel V.

    (Department of Economics, City University London, 10 Northampton Square, London EC1V 0HB, UK)

  • Park Sung Y.

    (School of Economics, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul, Korea)

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.

Suggested Citation

  • Bera Anil K. & Galvao Antonio F. & Montes-Rojas Gabriel V. & Park Sung Y., 2016. "Asymmetric Laplace Regression: Maximum Likelihood, Maximum Entropy and Quantile Regression," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 79-101, January.
    • Handle: RePEc:bpj:jecome:v:5:y:2016:i:1:p:79-101:n:8
    DOI: 10.1515/jem-2014-0018
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    References listed on IDEAS

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    1. Manski, Charles F, 1991. "Regression," Journal of Economic Literature, American Economic Association, vol. 29(1), pages 34-50, March.
    2. Joshua Angrist & Victor Chernozhukov & Iván Fernández-Val, 2006. "Quantile Regression under Misspecification, with an Application to the U.S. Wage Structure," Econometrica, Econometric Society, vol. 74(2), pages 539-563, March.
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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