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Misspecification Testing in a Class of Conditional Distributional Models

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  • Rothe, Christoph

    ()
    (Columbia University)

  • Wied, Dominik

    ()
    (TU Dortmund)

Abstract

We propose a specification test for a wide range of parametric models for the conditional distribution function of an outcome variable given a vector of covariates. The test is based on the Cramer-von Mises distance between an unrestricted estimate of the joint distribution function of the data, and a restricted estimate that imposes the structure implied by the model. The procedure is straightforward to implement, is consistent against fixed alternatives, has non-trivial power against local deviations of order n^-1/2 from the null hypothesis, and does not require the choice of smoothing parameters. In an empirical application, we use our test to study the validity of various models for the conditional distribution of wages in the US.

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Bibliographic Info

Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 6364.

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Length: 38 pages
Date of creation: Feb 2012
Date of revision:
Publication status: published in: Journal of the American Statistical Association
Handle: RePEc:iza:izadps:dp6364

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Keywords: Cramer-von Mises distance; quantile regression; distributional regression; location-scale model; bootstrap; wage distribution;

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References

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  1. Dinardo, J. & Fortin, N.M. & Lemieux, T., 1994. "Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach," Cahiers de recherche 9406, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
  3. Foresi, S. & Paracchi, F., 1992. "The Conditional Distribution of Excess Returns: An Empirical Analysis," Working Papers 92-49, C.V. Starr Center for Applied Economics, New York University.
  4. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  5. J. Carlos Escanciano & Carlos Velasco, 2010. "Specification tests of parametric dynamic conditional quantiles," Post-Print peer-00732534, HAL.
  6. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  7. Victor Chernozhukov & Ivan Fernandez-Val & Blaise Melly, 2009. "Inference on counterfactual distributions," CeMMAP working papers CWP09/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Jim Albrecht & Aico van Vuuren & Susan Vroman, 2007. "Counterfactual Distributions with Sample Selection Adjustments: Econometric Theory and an Application to the Netherlands," Working Papers gueconwpa~07-07-06, Georgetown University, Department of Economics.
  9. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper 1995-124, Tilburg University, Center for Economic Research.
  10. Juan Carlos Escanciano & Chuan Goh, 2010. "Specification Analysis of Structural Quantile Regression Models," Working Papers tecipa-415, University of Toronto, Department of Economics.
  11. Fortin, Nicole & Lemieux, Thomas & Firpo, Sergio, 2011. "Decomposition Methods in Economics," Handbook of Labor Economics, Elsevier.
  12. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
  13. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  14. Herman J. Bierens & Donna K. Ginther, 2001. "Integrated Conditional Moment testing of quantile regression models," Empirical Economics, Springer, vol. 26(1), pages 307-324.
  15. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
  16. José Mata & José A. F. Machado, 2005. "Counterfactual decomposition of changes in wage distributions using quantile regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(4), pages 445-465.
  17. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
  18. Melly, Blaise, 2005. "Decomposition of differences in distribution using quantile regression," Labour Economics, Elsevier, vol. 12(4), pages 577-590, August.
  19. Christoph Rothe, 2012. "Partial Distributional Policy Effects," Econometrica, Econometric Society, vol. 80(5), pages 2269-2301, 09.
  20. Zheng, John Xu, 1998. "A Consistent Nonparametric Test Of Parametric Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 14(01), pages 123-138, February.
  21. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
  22. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, April.
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Citations

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Cited by:
  1. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
  2. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
  3. Roger Koenker & Samantha Leorato & Franco Peracchi, 2013. "Distributional vs. Quantile Regression," EIEF Working Papers Series 1329, Einaudi Institute for Economics and Finance (EIEF), revised Dec 2013.
  4. Igor Kheifets, 2014. "Specification Tests for Nonlinear Dynamic Models," Cowles Foundation Discussion Papers 1937, Cowles Foundation for Research in Economics, Yale University.
  5. Wied, Dominik & Dehling, Herold & van Kampen, Maarten & Vogel, Daniel, 2014. "A fluctuation test for constant Spearman’s rho with nuisance-free limit distribution," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 723-736.
  6. Rothe, Christoph, 2012. "Decomposing the Composition Effect," IZA Discussion Papers 6397, Institute for the Study of Labor (IZA).

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