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The effect of recursive detrending on panel unit root tests

journal contribution
posted on 2015-04-01, 00:00 authored by Joakim WesterlundJoakim Westerlund
This paper analyzes the properties of panel unit root tests based on recursively detrended data. The analysis is conducted while allowing for a (potentially) non-linear trend function, which represents a more general consideration than the current state of affairs with (at most) a linear trend. A new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis, and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple. Indeed, the test statistic is not only asymptotically independent of the true trend polynomial, but also is in fact unique in that it is independent also of the degree of the fitted polynomial. However, this invariance property does not carry over to the local alternative, under which it is shown that local power is a decreasing function of the trend degree. But while power does decrease, the rate of shrinking of the local alternative is generally constant in the trend degree, which goes against the common belief that the rate of shrinking should be decreasing in the trend degree. The above results are based on simplifying assumptions. To compensate for this lack of generality, a second, robust, test statistic is proposed, whose validity does not require that the trend function is a polynomial or that the errors are iid.

History

Journal

Journal of econometrics

Volume

185

Pagination

453-467

Location

Amsterdam, The Netherlands

ISSN

0304-4076

eISSN

1872-6895

Language

eng

Publication classification

C1 Refereed article in a scholarly journal, C Journal article

Copyright notice

2014, Elsevier

Issue

2

Publisher

Elsevier