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Cross-Validation Selection of Regularization Parameter(s) for Semiparametric Transformation Models

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  • Senay Sokullu
  • Sami Stouli

Abstract

We propose cross-validation criteria for the selection of regularisation parameter(s) in the semiparametric instrumental variable transformation model proposed in Florens and Sokullu (2016). In the presence of an endogenous regressor, this model is characterized by the need to choose two regularisation parameters, one for the structural function and one for the transformation of the outcome. We consider two-step and simultaneous criteria, and analyze the finite-sample performance of the estimator using the corresponding regularisation parameters by means of several Monte-Carlo simulations. Our numerical experiments show that simultaneous selection of regularisation parameters provides significant improvements in the performance of the estimator. We also apply our methods to the choice of regularisation parameters in the estimation of two-sided network effects in the German magazine industry.

Suggested Citation

  • Senay Sokullu & Sami Stouli, 2016. "Cross-Validation Selection of Regularization Parameter(s) for Semiparametric Transformation Models," Bristol Economics Discussion Papers 16/672, School of Economics, University of Bristol, UK, revised 08 Nov 2017.
    • Handle: RePEc:bri:uobdis:16/672
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    References listed on IDEAS

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    1. Frédérique Fève & Jean-Pierre Florens, 2010. "The practice of non-parametric estimation by solving inverse problems: the example of transformation models," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 1-27, October.
    2. Florens, Jean-Pierre & Sokullu, Senay, 2017. "Nonparametric Estimation Of Semiparametric Transformation Models," Econometric Theory, Cambridge University Press, vol. 33(4), pages 839-873, August.
    3. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82(5), pages 1749-1797, September.
    4. Sokullu, Senay, 2016. "Network effects in the German magazine industry," Economics Letters, Elsevier, vol. 143(C), pages 77-79.
    5. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    6. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    7. Qi Li & Jeffrey Scott Racine, 2006. "Density Estimation, from Nonparametric Econometrics: Theory and Practice," Introductory Chapters, in: Nonparametric Econometrics: Theory and Practice, Princeton University Press.
    8. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
    9. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, School of Economics, University of Bristol, UK.
    10. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The Nonparametric Identification of Treatment Effects in Duration Models," Econometrica, Econometric Society, vol. 71(5), pages 1491-1517, September.
    11. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
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    More about this item

    Keywords

    Nonparametric IV Regression; Transformation models; Cross-Validation; Tikhonov Regularization; Ill-posed inverse problems.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • L14 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Transactional Relationships; Contracts and Reputation

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