Estimation for Partially Linear Single-index Instrumental Variables Models |
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| Authors: | Yousheng Zhou Jian Han Peixin Zhao |
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| Affiliation: | 1. College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China;2. School of Electronic Engineering, Dublin City University, Dublin, Ireland;3. School of Finance and Taxation, Zhongnan University of Economics and Law, Wuhan, China;4. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, China |
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| Abstract: | In this article, we generalize the partially linear single-index models to the scenario with some endogenous covariates variables. It is well known that the estimators based on the existing methods are often inconsistent because of the endogeneity of covariates. To deal with the endogenous variables, we introduce some auxiliary instrumental variables. A three-stage estimation procedure is proposed for partially linear single-index instrumental variables models. The first stage is to obtain a linear projection of endogenous variables on a set of instrumental variables, the second stage is to estimate the link function by using local linear smoother for given constant parameters, and the last stage is to obtain the estimators of constant parameters based on the estimating equation. Asymptotic normality is established for the proposed estimators. Some simulation studies are undertaken to assess the finite sample performance of the proposed estimation procedure. |
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| Keywords: | Endogenous variables Instrumental variables Local linear smoother Partially linear single-index model |
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