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Non‐parametric time‐varying coefficient panel data models with fixed effects

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  • Degui Li
  • Jia Chen
  • Jiti Gao

Abstract

This paper is concerned with developing a nonparametric time-varying coefficient model with fixed effects to characterize nonstationarity and trending phenomenon in nonlinear panel data analysis. We develop two methods to estimate the trend function and the coefficient function without taking the first difference to eliminate the fixed effects. The first one eliminates the fixed effects by taking cross-sectional averages, and then uses a nonparametric local linear approach to estimate the trend function and the coefficient function. The asymptotic theory for this approach reveals that although the estimates of both the trend function and the coefficient function are consistent, the estimate of the coefficient function has a rate of convergence that is slower than that of the trend function. To estimate the coefficient function more efficiently, we propose a pooled local linear dummy variable approach. This is motivated by a least squares dummy variable method proposed in parametric panel data analysis. This method removes the fixed effects by deducting a smoothed version of cross-time average from each individual. The asymptotic distributions of both of the estimates are established when T tends to infinity and N is fixed or both T and N tend to infinity. Simulation results are provided to illustrate the finite sample behavior of the proposed estimation methods.
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Suggested Citation

  • Degui Li & Jia Chen & Jiti Gao, 2011. "Non‐parametric time‐varying coefficient panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 387-408, October.
  • Handle: RePEc:ect:emjrnl:v:14:y:2011:i:3:p:387-408 DOI: j.1368-423X.2011.00350.x
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    Cited by:

    1. Afonso, A & Arghyrou, MG & Gadea, MD & Kontonikas, A, 2017. ""Whatever it takes" to resolve the European sovereign debt crisis? Bond pricing regime switches and monetary policy effects," Essex Finance Centre Working Papers 20417, University of Essex, Essex Business School.
    2. Tingting Cheng & Jiti Gao & Xibin Zhang, 2015. "Bayesian Bandwidth Estimation In Nonparametric Time-Varying Coefficient Models," Monash Econometrics and Business Statistics Working Papers 3/15, Monash University, Department of Econometrics and Business Statistics.
    3. 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.
    4. Jia Chen & Jiti Gao, 2014. "Semiparametric Model Selection in Panel Data Models with Deterministic Trends and Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 15/14, Monash University, Department of Econometrics and Business Statistics.
    5. Lee, Jungyoon & Robinson, Peter, 2015. "Panel nonparametric regression with fixed effects," LSE Research Online Documents on Economics 61431, London School of Economics and Political Science, LSE Library.
    6. Jean-Louis Combes & Rasmané Ouedraogo, 2014. "Does Pro-cyclical Aid Lead to Pro-cyclical Fiscal Policy? An Empirical Analysis for Sub-Saharan Africa," Working Papers halshs-01084600, HAL.
    7. Lin, Cunjie & Zhou, Yong, 2016. "Semiparametric varying-coefficient model with right-censored and length-biased data," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 119-144.
    8. Li, Han & O’Hare, Colin & Zhang, Xibin, 2015. "A semiparametric panel approach to mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 264-270.
    9. Boneva, Lena & Linton, Oliver & Vogt, Michael, 2015. "A semiparametric model for heterogeneous panel data with fixed effects," Journal of Econometrics, Elsevier, vol. 188(2), pages 327-345.
    10. Lee, Yoon-Jin, 2014. "Testing a linear dynamic panel data model against nonlinear alternatives," Journal of Econometrics, Elsevier, vol. 178(P1), pages 146-166.
    11. Xiangjin B. Chen & Jiti Gao & Degui Li & Param Silvapulle, 2013. "Nonparametric Estimation and Parametric Calibration of Time-Varying Coefficient Realized Volatility Models," Monash Econometrics and Business Statistics Working Papers 21/13, Monash University, Department of Econometrics and Business Statistics.
    12. Yonghui Zhang & Liangjun Su & Peter C. B. Phillips, 2012. "Testing for common trends in semi‐parametric panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 56-100, February.
    13. Jia Chen & Degui Li & Jiti Gao, 2013. "Non- and Semi-Parametric Panel Data Models: A Selective Review," Monash Econometrics and Business Statistics Working Papers 18/13, Monash University, Department of Econometrics and Business Statistics.
    14. Baltagi, Badi H. & Feng, Qu & Kao, Chihwa, 2016. "Estimation of heterogeneous panels with structural breaks," Journal of Econometrics, Elsevier, vol. 191(1), pages 176-195.
    15. repec:ecr:col070:42012 is not listed on IDEAS
    16. Lee, Jungyoon & Robinson, Peter M., 2015. "Panel nonparametric regression with fixed effects," Journal of Econometrics, Elsevier, vol. 188(2), pages 346-362.
    17. Timothy Neal, 2016. "Multidimensional Parameter Heterogeneity in Panel Data Models," Discussion Papers 2016-15, School of Economics, The University of New South Wales.

    More about this item

    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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