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Testing for common trends in semi‐parametric panel data models with fixed effects

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  • Yonghui Zhang
  • Liangjun Su
  • Peter C. B. Phillips

Abstract

This paper proposes a nonparametric test for common trends in semiparametric panel data models with fixed effects based on a measure of nonparametric goodness-of-fit (R^2). We first estimate the model under the null hypothesis of common trends by the method of profile least squares, and obtain the augmented residual which consistently estimates the sum of the fixed effect and the disturbance under the null. Then we run a local linear regression of the augmented residuals on a time trend and calculate the nonparametric R^2 for each cross section unit. The proposed test statistic is obtained by averaging all cross sectional nonparametric R^2's, which is close to zero under the null and deviates from zero under the alternative. We show that after appropriate standardization the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of Pitman local alternatives. We prove test consistency and propose a bootstrap procedure to obtain p-values. Monte Carlo simulations indicate that the test performs well in finite samples. Empirical applications are conducted exploring the commonality of spatial trends in UK climate change data and idiosyncratic trends in OECD real GDP growth data. Both applications reveal the fragility of the widely adopted common trends assumption.

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Bibliographic Info

Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 15 (2012)
Issue (Month): 1 (02)
Pages: 56-100

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Handle: RePEc:wly:emjrnl:v:15:y:2012:i:1:p:56-100

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References

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  1. Peter C.B. Phillips & Donggyu Sul, 2007. "Transition Modeling and Econometric Convergence Tests," Cowles Foundation Discussion Papers 1595, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. Jia Chen & Jiti Gao & Degui Li, 2011. "Semiparametric Trending Panel Data Models with Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 15/11, Monash University, Department of Econometrics and Business Statistics.
  4. Bruce E. Hansen, 1998. "Testing for Structural Change in Conditional Models," Boston College Working Papers in Economics 310., Boston College Department of Economics.
  5. Vogelsang, Timothy J. & Franses, Philip Hans, 2001. "Testing for Common Deterministic Trend Slopes," Working Papers 01-15, Cornell University, Center for Analytic Economics.
  6. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
  7. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521725200.
  8. 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.
  9. 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.
  10. Peter C. B. Phillips & Donggyu Sul, 2009. "Economic transition and growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(7), pages 1153-1185.
  11. de la Grandville,Olivier, 2009. "Economic Growth," Cambridge Books, Cambridge University Press, number 9780521898010.
  12. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(04), pages 557-614, August.
  13. White Halbert & Granger Clive W.J., 2011. "Consideration of Trends in Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-40, February.
  14. 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.
  15. Sun, Yixiao, 2011. "Robust trend inference with series variance estimator and testing-optimal smoothing parameter," Journal of Econometrics, Elsevier, vol. 164(2), pages 345-366, October.
  16. Banerjee, Anindya, 1999. " Panel Data Unit Roots and Cointegration: An Overview," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 607-29, Special I.
  17. 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.
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