IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/24640.html
   My bibliography  Save this paper

Semiparametric transformation model with endogeneity: a control function approach

Author

Listed:
  • Van Keilegom, Ingrid
  • Vanhems, Anne

Abstract

We consider a semiparametric transformation model, in which the regression function 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 likelihood estimation method for the transformation. The proposed estimator is shown to be asymptotically normal under certain regularity conditions. A small simulation study shows that the estimator behaves well in practice.

Suggested Citation

  • Van Keilegom, Ingrid & Vanhems, Anne, 2011. "Semiparametric transformation model with endogeneity: a control function approach," TSE Working Papers 11-243, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:24640
    as

    Download full text from publisher

    File URL: http://www.tse-fr.eu/sites/default/files/medias/doc/wp/etrie/11-243.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    4. 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.
    5. 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.
    6. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 60-109, February.
    7. Florens, Jean-Pierre & Sokullu, Senay, 2017. "Nonparametric Estimation Of Semiparametric Transformation Models," Econometric Theory, Cambridge University Press, vol. 33(4), pages 839-873, August.
    8. 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.
    9. 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.
    10. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818728, September.
    11. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524131, September.
    12. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    13. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    14. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2010. "Nonparametric regression with nonparametrically generated covariates," SFB 649 Discussion Papers 2010-059, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    16. 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.
    17. repec:dau:papers:123456789/6486 is not listed on IDEAS
    18. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818742, September.
    19. 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.
    20. 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.
    21. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524117, September.
    22. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    23. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818735, September.
    24. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524124, September.
    25. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, School of Economics, University of Bristol, UK.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Esmeralda A. Ramalho & Joaquim J. S. Ramalho, 2017. "Moment-based estimation of nonlinear regression models with boundary outcomes and endogeneity, with applications to nonnegative and fractional responses," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 397-420, April.
    2. Samb, R. & Heuchenne, C. & Van Keilegom, I., 2011. "Estimation of the error density in a semiparametric transformation model," LIDAM Discussion Papers ISBA 2011023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. 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.
    4. Simar, Léopold & Vanhems, Anne & Van Keilegom, Ingrid, 2016. "Unobserved heterogeneity and endogeneity in nonparametric frontier estimation," Journal of Econometrics, Elsevier, vol. 190(2), pages 360-373.
    5. Melanie Birke & Sebastien Van Bellegem & Ingrid Van Keilegom, 2017. "Semi-parametric Estimation in a Single-index Model with Endogenous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 168-191, March.
    6. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
    7. Ying-Ying Lee, 2018. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Papers 1811.00157, arXiv.org.
    8. Ingrid Van Keilegom, 2013. "Comments on: Model-free model-fitting and predictive distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 234-236, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vanhems, Anne & Van Keilegom, Ingrid, 2011. "Semiparametric transformation model with endogeneity: a control function approach," LIDAM Discussion Papers ISBA 2011011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Vanhems, Anne & Van Keilegom, Ingrid, 2013. "Semiparametric transformation model with endogeneity: a control function approach," LIDAM Discussion Papers ISBA 2013018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Lewbel, Arthur & Lu, Xun & Su, Liangjun, 2015. "Specification testing for transformation models with an application to generalized accelerated failure-time models," Journal of Econometrics, Elsevier, vol. 184(1), pages 81-96.
    4. Vanhems, Anne & Van Keilegom, Ingrid, 2019. "Estimation Of A Semiparametric Transformation Model In The Presence Of Endogeneity," Econometric Theory, Cambridge University Press, vol. 35(1), pages 73-110, February.
    5. Gutknecht, Daniel, 2012. "Do Reservation Wages Decline Monotonically? A Novel Statistical Test," Economic Research Papers 270635, University of Warwick - Department of Economics.
    6. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    7. 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.
    8. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    9. Hoderlein, Stefan & Nesheim, Lars & Simoni, Anna, 2017. "Semiparametric Estimation Of Random Coefficients In Structural Economic Models," Econometric Theory, Cambridge University Press, vol. 33(6), pages 1265-1305, December.
    10. repec:wrk:warwec:991 is not listed on IDEAS
    11. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    12. Martin Huber, 2012. "Identification of Average Treatment Effects in Social Experiments Under Alternative Forms of Attrition," Journal of Educational and Behavioral Statistics, , vol. 37(3), pages 443-474, June.
    13. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.
    14. Peter C.B. Phillips & Liangjun Su, 2009. "Nonparametric Structural Estimation via Continuous Location Shifts in an Endogenous Regressor," Cowles Foundation Discussion Papers 1702, Cowles Foundation for Research in Economics, Yale University.
    15. Benjamin Williams, 2019. "Identification of a nonseparable model under endogeneity using binary proxies for unobserved heterogeneity," Quantitative Economics, Econometric Society, vol. 10(2), pages 527-563, May.
    16. Florens, Jean-Pierre & Simoni, Anna, 2012. "Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior," Journal of Econometrics, Elsevier, vol. 170(2), pages 458-475.
    17. Andrew Chesher, 2004. "Identification of sensitivity to variation in endogenous variables," CeMMAP working papers 10/04, Institute for Fiscal Studies.
    18. James J. Heckman, 2008. "The Principles Underlying Evaluation Estimators with an Application to Matching," Annals of Economics and Statistics, GENES, issue 91-92, pages 9-73.
    19. James J. Heckman & Rodrigo Pinto, 2022. "Causality and Econometrics," NBER Working Papers 29787, National Bureau of Economic Research, Inc.
    20. Feng Yao & Junsen Zhang, 2015. "Efficient kernel-based semiparametric IV estimation with an application to resolving a puzzle on the estimates of the return to schooling," Empirical Economics, Springer, vol. 48(1), pages 253-281, February.
    21. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tse:wpaper:24640. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.