Testing for unit roots in heterogeneous panels (Reprinted from Journal of Econometrics, vol 115, pg 53-74, 2003)

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) -> infinity, followed by N (the cross sectional dimension) -> infinity. A diagonal convergence result with T and N -> infinity 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 -> infinity 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). (c) 2023 Published by Elsevier B.V.