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Estimation in Single-Index Panel Data Models with Heterogeneous Link Functions

  • Jia Chen
  • Jiti Gao

    ()

  • Degui Li

    ()

In this paper, we study semiparametric estimation for a single-index panel data model where the nonlinear link function varies among the individuals. We propose using the refined minimum average variance estimation method to estimate the parameter in the single-index. As the cross-section dimension N and the time series dimension T tend to infinity simultaneously, we establish asymptotic distributions for the proposed estimator. In addition, we provide a real-data example to illustrate the finite sample behaviour of the proposed estimation method.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp12-11.pdf
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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 12/11.

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Length: 28 pages
Date of creation: Sep 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-12
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Web page: http://www.buseco.monash.edu.au/depts/ebs/
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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Horowitz, Joel & Hardle, Wolfgang, 1994. "Direct Semiparametric Estimation of Single-Index Models With Discrete Covariates," Working Papers 94-22, University of Iowa, Department of Economics.
  6. 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.
  7. Li, Qi & Stengos, Thanasis, 1996. "Semiparametric estimation of partially linear panel data models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 389-397.
  8. 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.
  9. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(02), pages 258-289, February.
  10. 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.
  11. Abrevaya, Jason, 1999. "Leapfrog estimation of a fixed-effects model with unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 93(2), pages 203-228, December.
  12. 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.
  13. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
  14. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  15. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  16. 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.
  17. Hardle, W. & Hall, P. & Ichimura, H., 1991. "Optimal smoothing in single index models," CORE Discussion Papers 1991007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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