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Semiparametric transformation model with endogeneity: a control function approach

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  • 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
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    References listed on IDEAS

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    Cited by:

    1. Ying-Ying Lee, 2018. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Papers 1811.00157, arXiv.org.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

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