Journal Article

Testing for Unit Roots in Small Panels with Short-run and Long-run Cross-sectional Dependencies

Yoosoon Chang and Wonho Song

in The Review of Economic Studies

Published on behalf of Review of Economic Studies Ltd

Volume 76, issue 3, pages 903-935
Published in print July 2009 | ISSN: 0034-6527
Published online July 2009 | e-ISSN: 1467-937X | DOI:
Testing for Unit Roots in Small Panels with Short-run and Long-run Cross-sectional Dependencies

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  • Single Equation Models; Single Variables


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An IV approach, using as instruments non-linear transformations of the lagged levels, is explored to test for unit roots in panels with general dependency and heterogeneity across cross-sectional units. We allow not only for the cross-sectional dependencies of innovations, but also for the presence of co-integration across cross-sectional levels. Unbalanced panels and panels with differing individual short-run dynamics and cross-sectionally related dynamics are also permitted. We also more carefully formulate the unit root hypotheses in panels. In particular, using order statistics, we make it possible to test for and against the presence of unit roots in some of the individual units for a given panel. The individual IV t-ratios, which are the bases of our tests, are asymptotically and normally distributed and cross-sectionally independent. Therefore, the critical values of the order statistics as well as the usual average statistic can be easily obtained from simple elementary probability computations. We show via a set of simulations that our tests work well, whereas other existing tests fail to perform properly. As an illustration, we apply our tests to the panels of real exchange rates, and find no evidence for the purchasing power parity hypothesis, which is in sharp contrast with the previous studies.

Keywords: C22; C23

Journal Article.  12367 words.  Illustrated.

Subjects: Single Equation Models; Single Variables

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