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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:
Handle: RePEc:iza:izadps:dp6364

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Related research

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. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, November.
  2. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly, 2013. "Inference on counterfactual distributions," CeMMAP working papers CWP17/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Albrecht, James & van Vuuren, Aico & Vroman, Susan, 2009. "Counterfactual distributions with sample selection adjustments: Econometric theory and an application to the Netherlands," Labour Economics, Elsevier, vol. 16(4), pages 383-396, August.
  4. Juan Carlos Escanciano & Carlos Velasco, 2008. "Specification Tests of Parametric Dynamic Conditional Quantiles," Caepr Working Papers 2008-021, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  5. Nicole Fortin & Thomas Lemieux & Sergio Firpo, 2010. "Decomposition Methods in Economics," NBER Working Papers 16045, National Bureau of Economic Research, Inc.
  6. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, November.
  7. Juan Carlos Escanciano & Chuan Goh, 2010. "Specification Analysis of Structural Quantile Regression Models," Working Papers tecipa-415, University of Toronto, Department of Economics.
  8. 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.
  9. Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
  10. 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.
  11. Rothe, Christoph, 2011. "Partial Distributional Policy Effects," IZA Discussion Papers 6076, Institute for the Study of Labor (IZA).
  12. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
  13. Hardle, W. & Mammen, E., 1990. "Comparing nonparametric versus parametric regression fits," CORE Discussion Papers 1990065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Nidardo, J. & Fortin, N. & Lemieux, T., 1994. "Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach," Papers 93-94-15, California Irvine - School of Social Sciences.
  15. Herman J. Bierens & Donna K. Ginther, 2001. "Integrated Conditional Moment testing of quantile regression models," Empirical Economics, Springer, vol. 26(1), pages 307-324.
  16. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  17. 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.
  18. Melly, Blaise, 2005. "Decomposition of differences in distribution using quantile regression," Labour Economics, Elsevier, vol. 12(4), pages 577-590, August.
  19. 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.
  20. 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.
  21. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
  22. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
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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. Igor Kheifets, 2014. "Specification Tests for Nonlinear Dynamic Models," Cowles Foundation Discussion Papers 1937, Cowles Foundation for Research in Economics, Yale University.
  3. Rothe, Christoph, 2012. "Decomposing the Composition Effect," IZA Discussion Papers 6397, Institute for the Study of Labor (IZA).
  4. Roger Koenker & Samantha Leorato & Franco Peracchi, 2013. "Distributional vs. Quantile Regression," CEIS Research Paper 300, Tor Vergata University, CEIS, revised 17 Dec 2013.
  5. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.

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