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Reprint of: Testing for unit roots in heterogeneous panels

Author

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  • Im, Kyung So
  • Pesaran, M. Hashem
  • Shin, Yongcheol

Abstract

This paper proposes unit root tests for dynamic heterogeneous panels based on the mean of individual unit root statistics. In particular it proposes a standardized t-bar test statistic based on the (augmented) Dickey–Fuller statistics averaged across the groups. Under a general setting this statistic is shown to converge in probability to a standard normal variate sequentially with T (the time series dimension) →∞, followed by N (the cross sectional dimension) →∞. A diagonal convergence result with T and N→∞ while N/T→k,k being a finite non-negative constant, is also conjectured. In the special case where errors in individual Dickey–Fuller (DF) regressions are serially uncorrelated a modified version of the standardized t-bar statistic is shown to be distributed as standard normal as N→∞ for a fixed T, so long as T ¿ 5 in the case of DF regressions with intercepts and T ¿ 6 in the case of DF regressions with intercepts and linear time trends. An exact fixed N and T test is also developed using the simple average of the DF statistics. Monte Carlo results show that if a large enough lag order is selected for the underlying ADF regressions, then the small sample performances of the t-bar test is reasonably satisfactory and generally better than the test proposed by Levin and Lin (1993).

Suggested Citation

  • Im, Kyung So & Pesaran, M. Hashem & Shin, Yongcheol, 2023. "Reprint of: Testing for unit roots in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 234(S), pages 56-69.
  • Handle: RePEc:eee:econom:v:234:y:2023:i:s:p:56-69
    DOI: 10.1016/j.jeconom.2023.03.002
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    References listed on IDEAS

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    1. Kaddour Hadri, 2000. "Testing for stationarity in heterogeneous panel data," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 148-161.
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    More about this item

    Keywords

    Heterogeneous dynamic panels; Tests of unit roots; t-bar statistics; Finite sample properties;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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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