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Semi-Parametric Estimation in a Single- Index Model with Endogenous Variables

Author

Listed:
  • BIRKE, Mélanie

    (Universit at Bayreuth)

  • VAN BELLEGEM, Sébastien

    (Université catholique de Louvain, CORE, Belgium)

  • VAN KEILEGOM, Ingrid

    (Université catholique de Louvain, CORE, Belgium)

Abstract

We consider a semiparametric single-index model, and suppose that endogeneity is present in the explanatory variables. The presence of an instrument is assumed that is non-correlated with the error term. We propose an estimator of the parametric component of the model, which is the solution of an ill-posed inverse problem. The estimator is shown to be asymptotically normal under certain regularity conditions. A simulation study is conducted to illustrate the finite sample performance of the proposed estimator.

Suggested Citation

  • BIRKE, Mélanie & VAN BELLEGEM, Sébastien & VAN KEILEGOM, Ingrid, 2016. "Semi-Parametric Estimation in a Single- Index Model with Endogenous Variables," LIDAM Discussion Papers CORE 2016022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2016022
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    Cited by:

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    2. Alan P. Ker & Abdoul G. Sam, 2018. "Semiparametric estimation of the link function in binary-choice single-index models," Computational Statistics, Springer, vol. 33(3), pages 1429-1455, September.
    3. Muhammad Qasim, 2024. "A weighted average limited information maximum likelihood estimator," Statistical Papers, Springer, vol. 65(5), pages 2641-2666, July.
    4. Irene Botosaru & Chris Muris & Senay Sokullu, 2022. "Time-Varying Linear Transformation Models with Fixed Effects and Endogeneity for Short Panels," Department of Economics Working Papers 2022-01, McMaster University.
    5. Xin Geng & Carlos Martins-Filho & Feng Yao, 2015. "Estimation of a Partially Linear Regression in Triangular Systems," Working Papers 15-46, Department of Economics, West Virginia University.
    6. Zhang, Hong-Fan, 2021. "Iterative GMM for partially linear single-index models with partly endogenous regressors," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    7. Jean-Pierre Florens & Elia Lapenta, 2024. "Partly linear instrumental variables regressions without smoothing on the instruments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 897-920, September.
    8. Xiaohui Yuan & Xinran Zhang & Wei Guo & Qian Hu, 2024. "An adapted loss function for composite quantile regression with censored data," Computational Statistics, Springer, vol. 39(3), pages 1371-1401, May.

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