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Goodness of Fit and Misspecification in Quantile Regressions

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  • Marilena Furno

Abstract

The article considers a test of specification for quantile regressions. The test relies on the increase of the objective function and the worsening of the fit when unnecessary constraints are imposed. It compares the objective functions of restricted and unrestricted models and, in its different formulations, it verifies (a) forecast ability, (b) structural breaks, and (c) exclusion restrictions. The quantile-based tests are more informative than their ordinary least squares (OLS) analogues because they allow to analyze the model not only at the center but also in the tails of the conditional distribution. In this example, contrarily to the OLS findings, the quantile-based test uncovers in (a) the forecast weakness of the selected model at the upper quantile; (b) a break occurring in the tails and not in the center of the conditional distribution; and (c) that the excluded variable has a relevant impact at the upper quantile. Monte Carlo experiments analyze the behavior of the different definitions of the test with non-normal errors, comparing least squares and quantile regression results.

Suggested Citation

  • Marilena Furno, 2011. "Goodness of Fit and Misspecification in Quantile Regressions," Journal of Educational and Behavioral Statistics, , vol. 36(1), pages 105-131, February.
    • Handle: RePEc:sae:jedbes:v:36:y:2011:i:1:p:105-131
    DOI: 10.3102/1076998610379134
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    1. Tae-Hwan Kim & Halbert White, 2003. "Estimation, Inference, And Specification Testing For Possibly Misspecified Quantile Regression," Advances in Econometrics, in: Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later, pages 107-132, Emerald Group Publishing Limited.
    2. Qu, Zhongjun, 2008. "Testing for structural change in regression quantiles," Journal of Econometrics, Elsevier, vol. 146(1), pages 170-184, September.
    3. Marilena Furno, 2012. "Tests for structural break in quantile regressions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(4), pages 493-515, October.
    4. 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.
    5. Gagliardini, Patrick & Trojani, Fabio & Urga, Giovanni, 2005. "Robust GMM tests for structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 139-182.
    6. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    7. Clark, Todd E. & McCracken, Michael W., 2005. "The power of tests of predictive ability in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 124(1), pages 1-31, January.
    8. Marilena Furno, 2008. "Quantile regressions analysis of the Italian school system," Working Papers 2008-06, Universita' di Cassino, Dipartimento di Scienze Economiche.
    9. He X. & Zhu L-X., 2003. "A Lack-of-Fit Test for Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1013-1022, January.
    10. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(3), pages 403-436, June.
    11. Leslie G. Godfrey & Chris D. Orme, 2000. "Controlling the significance levels of prediction error tests for linear regression models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 66-83.
    12. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
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