Testing for Unit Roots in Heterogeneous Panels

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performances of the t-bar test is reasonably satisfactory and generally better than the test proposed by Levin and Lin (Unpublished manuscript, University of California, San Diego, 1993).

Im K., Pesaran H., and Shin Y. (2003) Testing for Unit Roots in Heterogeneous Panels. Journal of Econometrics, 115, 53-74.