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Semiparametric Single-Index Panel Data Models with Cross-Sectional Dependence

Author

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  • Bin Peng
  • Chaohua Dong
  • Jiti Gao

Abstract

In this paper, we consider a semiparametric single index panel data mode with cross-sectional dependence, high-dimensionality 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 a link function for the case where both N and T go to ∞. Rates of convergence and asymptotic normality consistencies 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.

Suggested Citation

  • Bin Peng & Chaohua Dong & Jiti Gao, 2014. "Semiparametric Single-Index Panel Data Models with Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 9/14, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2014-9
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    References listed on IDEAS

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    1. Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
    2. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
    3. Donald W. K. Andrews, 2005. "Cross-Section Regression with Common Shocks," Econometrica, Econometric Society, vol. 73(5), pages 1551-1585, September.
    4. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 928-955, November.
    5. Chaohua Dong & Jiti Gao, 2014. "Specification Testing in Structural Nonparametric Cointegration," Monash Econometrics and Business Statistics Working Papers 2/14, Monash University, Department of Econometrics and Business Statistics.
    6. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    7. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    8. Chen, Jia & Gao, Jiti & Li, Degui, 2012. "Semiparametric trending panel data models with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 171(1), pages 71-85.
    9. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    10. Jia Chen & Jiti Gao & Degui Li, 2013. "Estimation in Partially Linear Single-Index Panel Data Models With Fixed Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 315-330, July.
    11. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    12. Qiying Wang & Peter C. B. Phillips, 2009. "Structural Nonparametric Cointegrating Regression," Econometrica, Econometric Society, vol. 77(6), pages 1901-1948, November.
    13. Su, Liangjun & Jin, Sainan, 2012. "Sieve estimation of panel data models with cross section dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 34-47.
    14. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    15. Badi H. Baltagi & James M. Griffin & Weiwen Xiong, 2000. "To Pool Or Not To Pool: Homogeneous Versus Hetergeneous Estimations Applied to Cigarette Demand," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 117-126, February.
    16. Chen, Jia & Gao, Jiti & Li, Degui, 2012. "A New Diagnostic Test For Cross-Section Uncorrelatedness In Nonparametric Panel Data Models," Econometric Theory, Cambridge University Press, vol. 28(5), pages 1144-1163, October.
    17. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    18. Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, vol. 176(1), pages 59-79.
    19. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    20. Chaohua Dong & Jiti Gao & Dag Tjostheim, 2014. "Estimation for Single-index and Partially Linear Single-index Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 7/14, Monash University, Department of Econometrics and Business Statistics.
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    Citations

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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Lin, Yingqian & Tu, Yundong, 2020. "Sieve extremum estimation of a semiparametric transformation model," Economics Letters, Elsevier, vol. 189(C).
    12. 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.
    13. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    14. 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.

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    More about this item

    Keywords

    symptotic theory; closed-form estimate; nonlinear panel data model; orthogonal series 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

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