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Semiparametric single-index panel data models with cross-sectional dependence

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  • Dong, Chaohua
  • Gao, Jiti
  • Peng, Bin

Abstract

In this paper, we consider a semiparametric single-index panel data model with cross-sectional dependence and stationarity. Meanwhile, we allow fixed effects to be correlated with the regressors to capture unobservable heterogeneity. Under a general spatial error dependence structure, we then establish some consistent closed-form estimates for both the unknown parameters and the link function for the case where both cross-sectional dimension (N) and temporal dimension (T) go to infinity. Rates of convergence and asymptotic normality are established for the proposed estimates. Our experience suggests that the proposed estimation method is simple and thus attractive for finite-sample studies and empirical implementations. Moreover, both the finite-sample performance and the empirical applications show that the proposed estimation method works well when the cross-sectional dependence exists in the data set.

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  • Dong, Chaohua & Gao, Jiti & Peng, Bin, 2015. "Semiparametric single-index panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 188(1), pages 301-312.
    • Handle: RePEc:eee:econom:v:188:y:2015:i:1:p:301-312
    DOI: 10.1016/j.jeconom.2015.06.001
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    Cited by:

    1. Dong, Chaohua & Linton, Oliver, 2018. "Additive nonparametric models with time variable and both stationary and nonstationary regressors," Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
    2. Fei Liu & Jiti Gao & Yanrong Yang, 2019. "Nonparametric Estimation in Panel Data Models with Heterogeneity and Time Varyingness," Monash Econometrics and Business Statistics Working Papers 24/19, Monash University, Department of Econometrics and Business Statistics.
    3. Dong, Chaohua & Gao, Jiti & Linton, Oliver, 2023. "High dimensional semiparametric moment restriction models," Journal of Econometrics, Elsevier, vol. 232(2), pages 320-345.
    4. Gao, Jiti & Liu, Fei & Peng, Bin & Yan, Yayi, 2023. "Binary response models for heterogeneous panel data with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 1654-1679.
    5. Dong, Chaohua & Linton, Oliver, 2018. "Additive nonparametric models with time variable and both stationary and nonstationary regressors," Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
    6. Lin, Yingqian & Tu, Yundong, 2020. "Sieve extremum estimation of a semiparametric transformation model," Economics Letters, Elsevier, vol. 189(C).
    7. Feng, Guohua & Gao, Jiti & Peng, Bin & Zhang, Xiaohui, 2017. "A varying-coefficient panel data model with fixed effects: Theory and an application to US commercial banks," Journal of Econometrics, Elsevier, vol. 196(1), pages 68-82.
    8. Lin, Yingqian & Tu, Yundong, 2024. "Functional coefficient cointegration models with Box–Cox transformation," Economics Letters, Elsevier, vol. 234(C).
    9. Chaohua Dong & Jiti Gao & Yundong Tu & Bin Peng, 2023. "Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models," Papers 2301.06631, arXiv.org.
    10. Jiti Gao & Fei Liu & Bin peng, 2020. "Binary Response Models for Heterogeneous Panel Data with Interactive Fixed Effects," Monash Econometrics and Business Statistics Working Papers 44/20, Monash University, Department of Econometrics and Business Statistics.
    11. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    12. Ma, Yingying & Guo, Shaojun & Wang, Hansheng, 2023. "Sparse spatio-temporal autoregressions by profiling and bagging," Journal of Econometrics, Elsevier, vol. 232(1), pages 132-147.
    13. Fei Liu & Jiti Gao & Yanrong Yang, 2020. "Time-Varying Panel Data Models with an Additive Factor Structure," Monash Econometrics and Business Statistics Working Papers 42/20, Monash University, Department of Econometrics and Business Statistics.
    14. Jiang, Bin & Yang, Yanrong & Gao, Jiti & Hsiao, Cheng, 2021. "Recursive estimation in large panel data models: Theory and practice," Journal of Econometrics, Elsevier, vol. 224(2), pages 439-465.
    15. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," LSE Research Online Documents on Economics 103830, London School of Economics and Political Science, LSE Library.
    16. Jiti Gao & Kai Xia, 2017. "Heterogeneous panel data models with cross-sectional dependence," Monash Econometrics and Business Statistics Working Papers 16/17, Monash University, Department of Econometrics and Business Statistics.
    17. Weilun Zhou & Jiti Gao & David Harris & Hsein Kew, 2019. "Semiparametric Single-index Predictive Regression," Monash Econometrics and Business Statistics Working Papers 25/19, Monash University, Department of Econometrics and Business Statistics.
    18. Chaohua Dong & Jiti Gao & Bin Peng, 2018. "Varying-coefficient panel data models with partially observed factor structure," Monash Econometrics and Business Statistics Working Papers 1/18, Monash University, Department of Econometrics and Business Statistics.
    19. Ma, Shujie & Linton, Oliver & Gao, Jiti, 2021. "Estimation and inference in semiparametric quantile factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 295-323.
    20. Xuan Liang & Jiti Gao & Xiaodong Gong, 2019. "Time-Varying Coefficient Spatial Autoregressive Panel Data Model with Fixed Effects," Monash Econometrics and Business Statistics Working Papers 26/19, Monash University, Department of Econometrics and Business Statistics.
    21. Pei, Youquan & Huang, Tao & You, Jinhong, 2018. "Nonparametric fixed effects model for panel data with locally stationary regressors," Journal of Econometrics, Elsevier, vol. 202(2), pages 286-305.
    22. Gao, Jiti & Xia, Kai & Zhu, Huanjun, 2020. "Heterogeneous panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 219(2), pages 329-353.
    23. Dong, Chaohua & Linton, Oliver & Peng, Bin, 2021. "A weighted sieve estimator for nonparametric time series models with nonstationary variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 909-932.
    24. Shan Dai & Ngai Hang Chan, 2023. "Testing of Constant Parameters for Semi‐Parametric Functional Coefficient Models with Integrated Covariates," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(5-6), pages 474-486, September.

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    More about this item

    Keywords

    Asymptotic theory; Closed-form estimation; Nonlinear panel data model; Orthogonal series expansion method;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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