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The Local Power of the IPS Test with Both Initial Conditions and Incidental Trends

Author

Listed:
  • Kajal Lahiri
  • Zhongwen Liang
  • Huaming Peng

Abstract

This paper investigates the asymptotic local power of the the averaged t-test of Im, Pesaran and Shin (2003, IPS hereafter) in the presence of both initial explosive conditions and incidental trends. By utilizing the least squares detrending methods, it is found that the initial condition plays no role in determining the asymptotic local power of the IPS test, a result strikingly different from the finding in Harris et al. (2010), who examined the impact of the initial conditions on local power of IPS test without incidental trends. The paper also presents, via an application of the Fredholm method discussed in Nabeya and Tanaka (1990a, 1990b), the exact asymptotic local power of IPS test, thereby providing theoretical justifications for its lack of asymptotic local power in the neighborhood of unity with the order of N-1/2T-1 while attaining nontrivial power in the neighborhood of unity that shrinks at the rate N-1/4T-1. This latter finding is consistent with Moon et al. (2007) and extends their results to IPS test. It is also of practical significance to empirical researchers as the presence of incidental trends in panel unit root test setting is ubiquitous.

Suggested Citation

  • Kajal Lahiri & Zhongwen Liang & Huaming Peng, 2017. "The Local Power of the IPS Test with Both Initial Conditions and Incidental Trends," CESifo Working Paper Series 6313, CESifo.
    • Handle: RePEc:ces:ceswps:_6313
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    File URL: https://www.cesifo.org/DocDL/cesifo1_wp6313.pdf
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    References listed on IDEAS

    as
    1. Choi, In, 2001. "Unit root tests for panel data," Journal of International Money and Finance, Elsevier, vol. 20(2), pages 249-272, April.
    2. Hyungsik Roger Moon & Peter C. B. Phillips, 2004. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometrica, Econometric Society, vol. 72(2), pages 467-522, March.
    3. Moon, Hyungsik Roger & Perron, Benoit & Phillips, Peter C.B., 2007. "Incidental trends and the power of panel unit root tests," Journal of Econometrics, Elsevier, vol. 141(2), pages 416-459, December.
    4. Nabeya, Seiji, 1999. "Asymptotic Moments Of Some Unit Root Test Statistics In The Null Case," Econometric Theory, Cambridge University Press, vol. 15(1), pages 139-149, February.
    5. Nabeya, Seiji & Sørensen, Bent E., 1994. "Asymptotic Distributions of the Least-Squares Estimators and Test Statistics in the Near Unit Root Model with Non-Zero Initial Value and Local Drift and Trend," Econometric Theory, Cambridge University Press, vol. 10(5), pages 937-966, December.
    6. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
    7. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(3), pages 587-636, June.
    8. Harris, David & Harvey, David I. & Leybourne, Stephen J. & Sakkas, Nikolaos D., 2010. "Local Asymptotic Power Of The Im-Pesaran-Shin Panel Unit Root Test And The Impact Of Initial Observations," Econometric Theory, Cambridge University Press, vol. 26(1), pages 311-324, February.
    9. Im, Kyung So & Pesaran, M. Hashem & Shin, Yongcheol, 2003. "Testing for unit roots in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 115(1), pages 53-74, July.
    10. Sawa, Takamitsu, 1972. "Finite-Sample Properties of the k-Class Estimators," Econometrica, Econometric Society, vol. 40(4), pages 653-680, July.
    11. G. S. Maddala & Shaowen Wu, 1999. "A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(S1), pages 631-652, November.
    12. Hyungsik Roger Moon & Benoit Perron, 2008. "Asymptotic local power of pooled t-ratio tests for unit roots in panels with fixed effects," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 80-104, March.
    13. László Mátyás & Patrick Sevestre (ed.), 2008. "The Econometrics of Panel Data," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75892-1.
    14. Levin, Andrew & Lin, Chien-Fu & James Chu, Chia-Shang, 2002. "Unit root tests in panel data: asymptotic and finite-sample properties," Journal of Econometrics, Elsevier, vol. 108(1), pages 1-24, May.
    15. repec:bla:obuest:v:61:y:1999:i:0:p:631-52 is not listed on IDEAS
    16. David I. Harvey & Stephen J. Leybourne, 2005. "On testing for unit roots and the initial observation," Econometrics Journal, Royal Economic Society, vol. 8(1), pages 97-111, March.
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    More about this item

    Keywords

    panel data; unit root test; individual heterogeneity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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