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Estimation of a semiparametric transformation model in the presence of endogeneity

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  • Van Keilegom, Ingrid
  • Vanhems, Anne

Abstract

We consider a semiparametric transformation model, in which the regression func- tion has an additive nonparametric structure and the transformation of the response is assumed to belong to some parametric family. We suppose that endogeneity is present in the explanatory variables. Using a control function approach, we show that the pro- posed model is identified under suitable assumptions, and propose a profile estimation method for the transformation. The proposed estimator is shown to be asymptotically normal under certain regularity conditions. A simulation study shows that the esti- mator behaves well in practice. Finally, we give an empirical example using the U.K. Family Expenditure Survey.

Suggested Citation

  • Van Keilegom, Ingrid & Vanhems, Anne, 2016. "Estimation of a semiparametric transformation model in the presence of endogeneity," TSE Working Papers 16-654, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:30482
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    1. Birke, M. & Van Bellegem, S. & Van Keilegom, I., 2014. "Semi-parametric estimation in a single-index model with endogenous variables," LIDAM Discussion Papers ISBA 2014043, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Jacho-Chávez, David & Lewbel, Arthur & Linton, Oliver, 2010. "Identification and nonparametric estimation of a transformed additively separable model," Journal of Econometrics, Elsevier, vol. 156(2), pages 392-407, June.
    3. 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.
    4. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    5. Joshua D. Angrist & Alan B. Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 69-85, Fall.
    6. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
    7. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    8. MANZI, Jorge & SAN MARTIN, Ernesto & VAN BELLEGEM, Sébastien, 2010. "School system evaluation by value-added analysis under endogeneity," LIDAM Discussion Papers CORE 2010046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Florens, Jean-Pierre & Sokullu, Senay, 2017. "Nonparametric Estimation Of Semiparametric Transformation Models," Econometric Theory, Cambridge University Press, vol. 33(4), pages 839-873, August.
    10. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    11. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    12. Benjamin Colling & Cédric Heuchenne & Rawane Samb & Ingrid Van Keilegom, 2015. "Estimation of the error density in a semiparametric transformation model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 1-18, February.
    13. Johannes, J. & Van Bellegem, S. & Vanhems, A., 2013. "Iterative regularisation in nonparametric instrumental regression," LIDAM Reprints ISBA 2013003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    15. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    16. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sebastien, 2012. "Instrumental regression in partially linear models," LIDAM Reprints ISBA 2012017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. 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.
    18. Jorge Manzi & Ernesto San Martín & Sébastien Van Bellegem, 2014. "School System Evaluation by Value Added Analysis Under Endogeneity," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 130-153, January.
    19. Johannes, Jan & Van Bellegem, Sébastien & Vanhems, Anne, 2010. "Iterative Regularization in Nonparametric Instrumental Regression," TSE Working Papers 10-184, Toulouse School of Economics (TSE).
    20. A. Zellner & N. S. Revankar, 1969. "Generalized Production Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(2), pages 241-250.
    21. Horowitz, Joel L, 2001. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Econometrica, Econometric Society, vol. 69(2), pages 499-513, March.
    22. Jean‐Pierre Florens & Jan Johannes & Sébastien Van Bellegem, 2012. "Instrumental regression in partially linear models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 304-324, June.
    23. repec:fth:prinin:455 is not listed on IDEAS
    24. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    25. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-137, January.
    26. Colling, Benjamin & Van Keilegom, Ingrid, 2014. "Goodness-of-fit tests in semiparametric transformation models," LIDAM Discussion Papers ISBA 2014017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    27. Joshua Angrist & Alan Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Working Papers 834, Princeton University, Department of Economics, Industrial Relations Section..
    28. Neumeyer, Natalie & Noh, Hohsuk & Van Keilegom, Ingrid, 2014. "Heteroscedastic semiparametric transformation models: estimation and testing for validity," LIDAM Discussion Papers ISBA 2014047, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    29. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, School of Economics, University of Bristol, UK.
    30. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
    31. Guang Cheng, 2015. "Moment Consistency of the Exchangeably Weighted Bootstrap for Semiparametric M-estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 665-684, September.
    32. Colling, Benjamin & Heuchenne, Cedric & Samb, Rawane & Van Keilegom, Ingrid, 2015. "Estimation of the Error Density in a Semiparametric Transformation Model," LIDAM Reprints ISBA 2015002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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