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On endogeneity and shape invariance in extended partially linear single index models

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  • Jiti Gao
  • Namhyun Kim
  • Patrick W. Saart

Abstract

In this paper, the important (but so far unrevealed) usefulness of the extended generalized partially linear single-index (EGPLSI) model introduced by Xia et al. (1999) in its ability to model a flexible shape-invariant specification is elaborated. More importantly, a control function approach is proposed to address the potential endogeneity problems in the EGPLSI model in order to enhance its applicability to empirical studies. In the process, it is shown that the attractive asymptotic features of the single-index type of a semiparametric model are still valid in our proposed estimation procedure given intrinsic generated covariates. Our newly developed method is then applied to address the endogeneity of expenditure in the semiparametric analysis of a system of empirical Engel curves by using the British data, highlights the convenient applicability of our proposed method.

Suggested Citation

  • Jiti Gao & Namhyun Kim & Patrick W. Saart, 2018. "On endogeneity and shape invariance in extended partially linear single index models," Monash Econometrics and Business Statistics Working Papers 8/18, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2018-8
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    File URL: https://www.monash.edu/business/ebs/research/publications/wp08-2018.pdf
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    Keywords

    Extended generalized partially linear single-index; control function approach; endogeneity; semiparametric regression models.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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