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Semi-parametric Estimation in a Single-index Model with Endogenous Variables

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  • Melanie Birke
  • Sebastien Van Bellegem
  • Ingrid Van Keilegom

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.
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  • 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.
    • Handle: RePEc:bla:scjsta:v:44:y:2017:i:1:p:168-191
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    File URL: http://hdl.handle.net/10.1111/sjos.12247
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    2. 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.
    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. Zhang, Hong-Fan, 2021. "Iterative GMM for partially linear single-index models with partly endogenous regressors," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).

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