TY - JOUR

T1 - Reprint of: Testing for unit roots in heterogeneous panels

AU - Im, Kyung So

AU - Pesaran, M.H

AU - Shin, Yongcheol

PY - 2023/3/7

Y1 - 2023/3/7

N2 - 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).

AB - 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).

U2 - https://doi.org/10.1016/j.jeconom.2023.03.002

DO - https://doi.org/10.1016/j.jeconom.2023.03.002

M3 - Article

SN - 0304-4076

VL - 234

SP - 56

EP - 69

JO - Journal of Econometrics

JF - Journal of Econometrics

ER -