Journal of Econometrics 115 (2003) 53–74 www.elsevier.com/locate/econbase Testing for unit roots in heterogeneous panels  Kyung So Im a ; ∗ , M. Hashem Pesaran b , Yongcheol Shin c a Department of Economics, University of Central Florida, P.O. Box 161400, Orlando, FL 32816-1400, USA b Trinity College, Cambridge CB2 1TQ, UK c School of Economics and Management, University of Edinburgh, 50, George Square, Edinburgh EH8 9JY, UK Accepted 12 January 2003 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 nite non-negative constant, is also conjectured. In the special case where errors in individual Dickey–Fuller (DF) regressions are serially uncorrelated a modied version of the standardized t -bar statistic is shown to be distributed as standard normal as N →∞ for a xed 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 xed 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of the t -bar test is reasonably satisfactory and generally better than the test proposed by Levin and Lin (Unpublished manuscript, University of California, San Diego, 1993). c  2003 Elsevier Science B.V. All rights reserved. JEL classication: C12; C15; C22; C23 Keywords: Heterogeneous dynamic panels; Tests of unit roots; t -bar statistics; Finite sample properties  This is a substantially revised version of the DAE Working Papers Amalgamated Series No. 9526, University of Cambridge. ∗ Corresponding author. E-mail addresses: kim@bus.ucf.edu (K.S. Im), mhp1@econ.cam.ac.uk (M.H. Pesaran), y.shin@ed.ac.uk (Y. Shin). 0304-4076/03/$-see front matter c  2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-4076(03)00092-7