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To Smooth or Not to Smooth? The Case of Discrete Variables in Nonparametric Regressions

  • Valentin Zelenyuk

    (CEPA - School of Economics, The University of Queensland)

  • Leopold Simar

    (CEPA - School of Economics, The University of Queensland)

In a seminal paper, Racine and Li, (Journal of Econometrics, 2004) introduce a tool which admits discrete and categorical variables as regressors in nonparametric regres- sions. The method is similar to the smoothing techniques for continuous regressors but uses discrete kernels. In the literature, it is generally admitted that it is always better to smooth the discrete variables. In this paper we investigate the potential problem linked to the bandwidths selection for the continuous variable due to the presence of the discrete variables. We find that in some cases, the performance of the resulting regression estimates may be deteriorated by smoothing the discrete variables in the way addressed so far in the literature, and that a fully separate estimation (without any smoothing of the discrete variable) may provide significantly better results, and we explain why this may happen. The problem being posed, we then suggest how to use the Racine and Li approach to overcome these difficulties and to provide estimates with better performances. We investigate through some simulated data sets and by more ex- tensive Monte-Carlo experiments the performances of all the proposed approaches and we find that, as expected, our suggested approach has the best performances. We also briefly illustrate the consequences of these issues on the estimation of the derivatives of the regression. Finally, we exemplify the phenomenon with an empirical illustration. Our main objective is to warn the practitioners of the potential problems posed by smoothing discrete variables by using the so far available softwares and to suggest a safer approach to implement the procedure.

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Paper provided by School of Economics, University of Queensland, Australia in its series CEPA Working Papers Series with number WP102011.

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Date of creation: 2011
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Handle: RePEc:qld:uqcepa:76
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  1. Daniel J. Henderson & Christopher F. Parmeter & Subal C. Kumbhakar, 2007. "Nonparametric estimation of a hedonic price function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 695-699.
  2. 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, November.
  3. Jeffery Racine & Jeffrey Hart & Qi Li, 2006. "Testing the Significance of Categorical Predictor Variables in Nonparametric Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 523-544.
  4. Ozkan Eren & Daniel J. Henderson, 2008. "The impact of homework on student achievement," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 326-348, 07.
  5. E. Zacharias & T. Stengos, 2006. "Intertemporal pricing and price discrimination: a semiparametric hedonic analysis of the personal computer market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 371-386.
  6. Cheng Hsiao & Qi Li & Jeff Racine, 2006. "A Consistent Model Specification Test with Mixed Discrete and Continuous Data," IEPR Working Papers 06.47, Institute of Economic Policy Research (IEPR).
  7. Daniel J. Henderson & R. Robert Russell, 2005. "Human Capital And Convergence: A Production-Frontier Approach ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(4), pages 1167-1205, November.
  8. 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.
  9. 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.
  10. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, vol. 99(1), pages 63-106, November.
  11. Daniel J. Henderson & Valentin Zelenyuk, 2007. "Testing for (Efficiency) Catching-up," Southern Economic Journal, Southern Economic Association, vol. 73(4), pages 1003–1019, April.
  12. Simar, Leopold & Zelenyuk, Valentin, 2004. "On testing equality of distributions of technical efficiency scores," MPRA Paper 28003, University Library of Munich, Germany.
  13. Subodh Kumar & R. Robert Russell, 2002. "Technological Change, Technological Catch-up, and Capital Deepening: Relative Contributions to Growth and Convergence," American Economic Review, American Economic Association, vol. 92(3), pages 527-548, June.
  14. Byeong U. Park & Leopold Simar & Valentin Zelenyuk, 2010. "Local Maximum Likelihood Techniques with Categorical Data," CEPA Working Papers Series WP142010, School of Economics, University of Queensland, Australia.
  15. repec:cup:cbooks:9780521586115 is not listed on IDEAS
  16. Daniel J. Henderson, 2010. "A test for multimodality of regression derivatives with application to nonparametric growth regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(3), pages 458-480.
  17. Valentina Hartarska & Christopher F. Parmeter & Denis Nadolnyak, 2010. "Economies of Scope of Lending and Mobilizing Deposits in Microfinance Institutions: A Semiparametric Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 93(2), pages 389-398.
  18. Oleg Badunenko & Daniel J. Henderson & Valentin Zelenyuk, 2007. "Technological Change and Transition: Relative Contributions to Worldwide Growth during the 1990s," Discussion Papers of DIW Berlin 740, DIW Berlin, German Institute for Economic Research.
  19. repec:cup:cbooks:9780521355643 is not listed on IDEAS
  20. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355, April.
  21. W. Walls, 2009. "Screen wars, star wars, and sequels," Empirical Economics, Springer, vol. 37(2), pages 447-461, October.
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