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A Consistent Model Specification Test with Mixed Discrete and Continuous Data

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Author Info
Cheng Hsiao
Qi Li
Jeff Racine

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Abstract

In this paper we propose a nonparametric kernel-based model specification test that can be used when the regression model contains both discrete and continuous regressors. We employ discrete variable kernel functions and we smooth both the discrete and continuous regressors using least squares cross-validation methods. The test statistic is shown to have an asymptotic normal null distribution. We also prove the validity of using the wild bootstrap method to approximate the null distribution of the test statistic, the bootstrap being our preferred method for obtaining the null distribution in practice. Simulations show that the proposed test has significant power advantages over conventional kernel tests which rely upon frequency-based nonparametric estimators that require sample splitting to handle the presence of discrete regressors.

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File URL: http://www.usc.edu/dept/LAS/economics/IEPR/Working%20Papers/IEPR_06.47_%5BHsiao,Li,Racine%5D.pdf
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Publisher Info
Paper provided by Institute of Economic Policy Research (IEPR) in its series IEPR Working Papers with number 06.47.

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Length: 31 pages
Date of creation: Apr 2006
Date of revision:
Handle: RePEc:scp:wpaper:06-47

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Related research
Keywords: Consistent test; parametric functional form; nonparametric estimation;

Other versions of this item:

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    Other versions:
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  8. Joel Horowitz, 2000. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Econometric Society World Congress 2000 Contributed Papers 0166, Econometric Society. [Downloadable!]
  9. Hidehiko Ichimura, . "Asymptotic Distribution of Non-Parametric and Semi-Parametric Estimators with Data Dependent Smoothing Parameters," Working Papers _001, University of California at Berkeley, Econometrics Laboratory Software Archive. [Downloadable!]
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    Other versions:
  13. Enno Mammen, . "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin. [Downloadable!]
  14. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March. [Downloadable!] (restricted)
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    Other versions:
  19. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, 08. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Henderson, Daniel J. & Papageorgiou, Chris & Parmeter, Christopher F., 2008. "Are any growth theories linear? Why we should care about what the evidence tells us," MPRA Paper 8767, University Library of Munich, Germany. [Downloadable!]
  2. Maasoumi, Esfandiar & Racine, Jeff, 2006. "Growth And Convergence: A Profile Of Distribution Dynamics And Mobility," Departmental Working Papers 0605, Southern Methodist University, Department of Economics. [Downloadable!]
    Other versions:
  3. Lawrence Dacuycuy, 2006. "The effects of bandwidth changes on model validity: an empirical study," Applied Economics Letters, Taylor and Francis Journals, vol. 13(10), pages 629-633, August. [Downloadable!] (restricted)
  4. Millimet, Daniel & Henderson, Daniel, 2006. "Is Gravity Linear?," Departmental Working Papers 0517, Southern Methodist University, Department of Economics. [Downloadable!]
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  5. W. D. Walls, 2008. "Screen Wars, Star Wars, and Sequels: Nonparametric Reanalysis of Movie Profitability," Working Papers 2008-28, Department of Economics, University of Calgary, revised 24 Jan 2008. [Downloadable!]
  6. Henderson, Daniel J., 2008. "A Test for Multimodality of Regression Derivatives with an Application to Nonparametric Growth Regressions," MPRA Paper 8768, University Library of Munich, Germany. [Downloadable!]
  7. Eren,Ozkan & Henderson,J. Daniel, 2006. "The Impact of Homework on Student Achievement," Departmental Working Papers 0518, Southern Methodist University, Department of Economics, revised 12 May 2006. [Downloadable!]
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  8. Lawrence Dacuycuy, 2005. "On distribution approximation: a simple comparative study on procedural variations of the Zheng test," Economics Bulletin, Economics Bulletin, vol. 3(11), pages 1-10. [Downloadable!]
  9. Andrea Vaona, 2008. "The sensitivity of nonparametric misspecification tests to disturbance autocorrelation," Quaderni della facoltà di Scienze economiche dell'Università di Lugano 0803, Biblioteca universitaria di Lugano (University Library of Lugano). [Downloadable!]
  10. Henderson, Daniel J., 2008. "A Nonparametric Examination of Capital-Skill Complementarity," IZA Discussion Papers 3865, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  11. Livanis, Grigorios T. & Salois, Matthew J. & Moss, Charles B, 2009. "A Nonparametric Kernel Representation of the Agricultural Production Function: Implications for Economic Measures of Technology," 83rd Annual Conference, March 30-April 1, 2009, Dublin, Ireland 51063, Agricultural Economics Society. [Downloadable!]
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