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One for All and All for One: Regression Checks With Many Regressors

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  • Lavergne, Pascal
  • Patilea, Valentin

Abstract

We develop a novel approach to build checks of parametric regression models when many regressors are present, based on a class of sufficiently rich semiparametric alternatives, namely single-index models. We propose an omnibus test based on the kernel method that performs against a sequence of directional nonparametric alternatives as if there was one regressor only, whatever the number of regressors. This test can be viewed as a smooth version of the integrated conditional moment (ICM) test of Bierens. Qualitative information can be easily incorporated into the procedure to enhance power. In an extensive comparative simulation study, we find that our test is little sensitive to the smoothing parameter and performs well in multidimensional settings. We then apply it to a cross-country growth regression model.

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Bibliographic Info

Paper provided by University of Toulouse 1 Capitole in its series Open Access publications from University of Toulouse 1 Capitole with number http://neeo.univ-tlse1.fr/3282/.

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Date of creation: 2012
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Publication status: Published in Journal of Business and Economic Statistics (2012) v.30, p.41-52
Handle: RePEc:ner:toulou:http://neeo.univ-tlse1.fr/3282/

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Web page: http://www.univ-tlse1.fr/

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  1. Juan Carlos Escanciano, 2005. "A Consistent Diagnostic Test for Regression Models Using Projections," Faculty Working Papers 09/05, School of Economics and Business Administration, University of Navarra.
  2. Godfrey, Leslie G. & Orme, Chris D., 2004. "Controlling the finite sample significance levels of heteroskedasticity-robust tests of several linear restrictions on regression coefficients," Economics Letters, Elsevier, vol. 82(2), pages 281-287, February.
  3. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
  4. Miguel A. DELGADO & Manuel A. DOMINGUEZ & Pascal LAVERGNE, 2006. "Consistent Tests of Conditional Moment Restrictions," Annales d'Economie et de Statistique, ENSAE, issue 81, pages 33-67.
  5. King, Robert G. & Levine, Ross, 1993. "Finance and growth : Schumpeter might be right," Policy Research Working Paper Series 1083, The World Bank.
  6. Emmanuel Guerre & Pascal Lavergne, 2004. "Data-Driven Rate-Optimal Specification Testing In Regression Models," Econometrics 0411008, EconWPA.
  7. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra.
  8. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
  9. Mankiw, N Gregory & Romer, David & Weil, David N, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 407-37, May.
  10. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  11. King, Robert G. & Levine, Ross, 1993. "Finance and growth : Schumpeter might be right," Policy Research Working Paper Series 1083, The World Bank.
  12. 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.
  13. Gozalo, Pedro L., 1997. "Nonparametric bootstrap analysis with applications to demographic effects in demand functions," Journal of Econometrics, Elsevier, vol. 81(2), pages 357-393, December.
  14. Juan Mora & Daniel Miles, 2002. "On The Performance Of Nonparametric Specification Tests In Regression Models," Working Papers. Serie AD 2002-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  15. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
  16. Guerre, Emmanuel & Lavergne, Pascal, 2002. "Optimal Minimax Rates For Nonparametric Specification Testing In Regression Models," Econometric Theory, Cambridge University Press, vol. 18(05), pages 1139-1171, October.
  17. Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Open Access publications from University of Toulouse 1 Capitole http://neeo.univ-tlse1.fr, University of Toulouse 1 Capitole.
  18. Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
  19. Liu, Zhenjuan & Stengos, Thanasis, 1999. "Non-linearities in Cross-Country Growth Regressions: A Semiparametric Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 527-38, Sept.-Oct.
  20. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
  21. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
  22. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
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