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Semiparametric Trending Panel Data Models with Cross-Sectional Dependence

  • Jia Chen
  • Jiti Gao


  • Degui Li


A semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A pooled semiparametric profile likelihood dummy variable approach based on the first-stage local linear fitting is developed to estimate both the parameter vector and the nonparametric time trend function. As both the time series length T and the cross-sectional size N tend to infinity simultaneously, the resulting estimator of the parameter vector is asymptotically normal with a rate of convergence of Op(NT)^{-1/2}. Meanwhile, the asymptotic distribution for the estimator of the nonparametric trend function is also established with a rate of convergence of Op(NTh)^{-1/2}. Two simulated examples are provided to illustrate the finite sample performance of the proposed method. In addition, the proposed model and estimation method is applied to analyze a CPI data set as well as an input-output data set.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 15/11.

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Length: 34 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-15
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  1. Duffy, John & Papageorgiou, Chris, 2000. " A Cross-Country Empirical Investigation of the Aggregate Production Function Specification," Journal of Economic Growth, Springer, vol. 5(1), pages 87-120, March.
  2. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Cowles Foundation Discussion Papers 1222, Cowles Foundation for Research in Economics, Yale University.
  3. Phillips, Peter C. B., 2001. "Trending time series and macroeconomic activity: Some present and future challenges," Journal of Econometrics, Elsevier, vol. 100(1), pages 21-27, January.
  4. Jiti Gao & Kim Hawthorne, 2006. "Semiparametric estimation and testing of the trend of temperature series," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 332-355, 07.
  5. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, June.
  6. Atak, Alev & Linton, Oliver B. & Xiao, Zhijie, 2010. "A Semiparametric Panel Model for Unbalanced Data with Application to Climate Change in the United Kingdom," MPRA Paper 22079, University Library of Munich, Germany.
  7. 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.
  8. Robinson, Peter M., 2012. "Nonparametric trending regression with cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 4-14.
  9. Jia Chen & Jiti Gao & Degui Li, 2009. "A New Diagnostic Test for Cross-Section Independence in Nonparametric Panel Data Model," School of Economics Working Papers 2009-16, University of Adelaide, School of Economics.
  10. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  11. Su, Liangjun & Ullah, Aman, 2006. "Profile likelihood estimation of partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 92(1), pages 75-81, July.
  12. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
  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, 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(05), pages 1144-1163, October.
  15. Jinhong You & Xian Zhou & Yong Zhou, 2011. "Series Estimation in Partially Linear In‐Slide Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 89-107, 03.
  16. Peter C. B. Phillips, 2010. "The Mysteries of Trend," Cowles Foundation Discussion Papers 1771, Cowles Foundation for Research in Economics, Yale University.
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