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

Listed author(s):
  • 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)

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.

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File URL: https://www.degruyter.com/view/j/jem.2016.5.issue-1/jem-2014-0018/jem-2014-0018.xml?format=INT
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Article provided by De Gruyter in its journal Journal of Econometric Methods.

Volume (Year): 5 (2016)
Issue (Month): 1 (January)
Pages: 79-101

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Handle: RePEc:bpj:jecome:v:5:y:2016:i:1:p:79-101:n:8
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  1. Park, Sung Y. & Bera, Anil K., 2009. "Maximum entropy autoregressive conditional heteroskedasticity model," Journal of Econometrics, Elsevier, vol. 150(2), pages 219-230, June.
  2. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
  3. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
  4. Ivana Komunjer, 2007. "Asymmetric power distribution: Theory and applications to risk measurement," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(5), pages 891-921.
  5. Sergio Firpo, 2007. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 75(1), pages 259-276, 01.
  6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  7. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
  8. Machado, José A.F., 1993. "Robust Model Selection and M-Estimation," Econometric Theory, Cambridge University Press, vol. 9(03), pages 478-493, June.
  9. Soofi, E. S. & Retzer, J. J., 2002. "Information indices: unification and applications," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 17-40, March.
  10. Howard S. Bloom & Larry L. Orr & Stephen H. Bell & George Cave & Fred Doolittle & Winston Lin & Johannes M. Bos, 1997. "The Benefits and Costs of JTPA Title II-A Programs: Key Findings from the National Job Training Partnership Act Study," Journal of Human Resources, University of Wisconsin Press, vol. 32(3), pages 549-576.
  11. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
  12. Ebrahimi, Nader & Soofi, Ehsan S. & Soyer, Refik, 2008. "Multivariate maximum entropy identification, transformation, and dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1217-1231, July.
  13. Schennach, Susanne M., 2008. "Quantile Regression With Mismeasured Covariates," Econometric Theory, Cambridge University Press, vol. 24(04), pages 1010-1043, August.
  14. Robert J. LaLonde, 1995. "The Promise of Public Sector-Sponsored Training Programs," Journal of Economic Perspectives, American Economic Association, vol. 9(2), pages 149-168, Spring.
  15. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
  16. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
  17. Samuel Kotz & Tomasz Kozubowski & Krzysztof Podgórski, 2002. "Maximum Likelihood Estimation of Asymmetric Laplace Parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 816-826, December.
  18. Wei, Ying & Carroll, Raymond J., 2009. "Quantile Regression With Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1129-1143.
  19. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
  20. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
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