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On Testing the Equality of Mean and Quantile Effects

Author

Listed:
  • Bera Anil K.

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

  • Galvao Antonio F.

    (Department of Economics, University of Iowa, W210 Pappajohn Business Building, 21 E. Market Street, Iowa City, IA 52242, USA)

  • Wang Liang

    (Department of Economics, University of Wisconsin-Milwaukee, Bolton Hall 821, 3210 N. Maryland Ave., Milwaukee, WI 53201, USA)

Abstract

This paper proposes tests for equality of the mean regression (MR) and quantile regression (QR) coefficients. The tests are based on the asymptotic joint distribution of the ordinary least squares and QR estimators. First, we formally derive the asymptotic joint distribution of these estimators. Second, we propose a Wald test for equality of the MR and QR coefficients considering a single fixed quantile, and also describe a more general test using multiple quantiles simultaneously. A very salient feature of these tests is that they produce asymptotically distribution-free nature of inference. In addition, we suggest a sup-type test for equality of the coefficients uniformly over a range of quantiles. For the estimation of the variance-covariance matrix, the use sample counterparts and bootstrap methods. An important attribute of the proposed tests is that they can be used as a heteroskedasticity test. Monte Carlo studies are conducted to evaluate the finite sample properties of the tests in terms of size and power. Finally, we briefly illustrate the implementation of the tests using Engel data.

Suggested Citation

  • Bera Anil K. & Galvao Antonio F. & Wang Liang, 2014. "On Testing the Equality of Mean and Quantile Effects," Journal of Econometric Methods, De Gruyter, vol. 3(1), pages 47-62, January.
    • Handle: RePEc:bpj:jecome:v:3:y:2014:i:1:p:47-62:n:1
    DOI: 10.1515/jem-2012-0003
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    References listed on IDEAS

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    1. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(2), pages 173-205, April.
    2. 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.
    3. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
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    Cited by:

    1. Gabriel Montes-Rojas & Lucas Siga & Ram Mainali, 2017. "Mean and quantile regression Oaxaca-Blinder decompositions with an application to caste discrimination," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 15(3), pages 245-255, September.
    2. Karsten Schweikert, 2019. "Asymmetric price transmission in the US and German fuel markets: a quantile autoregression approach," Empirical Economics, Springer, vol. 56(3), pages 1071-1095, March.
    3. Gabriel Montes Rojas & Andrés Sebastián Mena, 2020. "Density estimation using bootstrap quantile variance and quantile-mean covariance," Documentos de trabajo del Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET) 2020-50, Universidad de Buenos Aires, Facultad de Ciencias Económicas, Instituto Interdisciplinario de Economía Política IIEP (UBA-CONICET).
    4. Kuck, Konstantin & Maderitsch, Robert & Schweikert, Karsten, 2015. "Asymmetric over- and undershooting of major exchange rates: Evidence from quantile regressions," Economics Letters, Elsevier, vol. 126(C), pages 114-118.

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