Reprint of: Testing for unit roots in heterogeneous panels

Kyung So Im, Mohammad Pesaran and Yongcheol Shin

Journal of Econometrics, 2023, vol. 234, issue S, 56-69

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).

Keywords: Heterogeneous dynamic panels; Tests of unit roots; t-bar statistics; Finite sample properties (search for similar items in EconPapers)
JEL-codes: C12 C15 C22 C23 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:234:y:2023:i:s:p:56-69

DOI: 10.1016/j.jeconom.2023.03.002

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