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Estimation in Partially Linear Single-Index Panel Data Models with Fixed Effects

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  • Jia Chen
  • Jiti Gao

    ()

  • Degui Li

    ()

Abstract

In this paper, we consider semiparametric estimation in a partially linear single-index panel data model with fixed effects. Without taking the difference explicitly, we propose using a semiparametric minimum average variance estimation (SMAVE) based on a dummy-variable method to remove the fixed effects and obtain consistent estimators for both the parameters and the unknown link function. As both the cross section size and the time series length tend to infinity, we not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. The asymptotically normal distributions of the proposed estimators are similar to those obtained in the random effects case. In addition, we study several partially linear single-index dynamic panel data models. The methods and results are augmented by simulation studies and illustrated by an application to a cigarette-demand data set in the US from 1963-1992

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp14-11.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 14/11.

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Length: 32 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-14

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Keywords: Fixed effects; local linear smoothing; panel data; semiparametric estimation; single-index models;

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References

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  1. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
  2. Cai, Zongwu & Li, Qi, 2008. "Nonparametric Estimation Of Varying Coefficient Dynamic Panel Data Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1321-1342, October.
  3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
  4. Henderson, Daniel J. & Ullah, Aman, 2005. "A nonparametric random effects estimator," Economics Letters, Elsevier, vol. 88(3), pages 403-407, September.
  5. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(06), pages 1112-1137, December.
  6. Li, Qi & Stengos, Thanasis, 1996. "Semiparametric estimation of partially linear panel data models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 389-397.
  7. Badi H. Baltagi & Dong Li, . "Series Estimation of Partially Linear Panel Data Models with Fixed Effects," Working Papers 0109, East Carolina University, Department of Economics.
  8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
  9. Vidar Hjellvik & Rong Chen & Dag Tjøstheim, 2004. "Nonparametric Estimation and Testing in Panels of Intercorrelated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 831-872, November.
  10. Mammen, Enno & Støve, Bård & Tjøstheim, Dag, 2009. "Nonparametric Additive Models For Panels Of Time Series," Econometric Theory, Cambridge University Press, vol. 25(02), pages 442-481, April.
  11. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  12. Yingcun Xia & Howell Tong & W. K. Li & Li-Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410.
  13. Jeffrey Racine, 2008. "Nonparametric econometrics: a primer (in Russian)," Quantile, Quantile, issue 4, pages 7-56, March.
  14. 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.
  15. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
  16. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, December.
  17. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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.

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