An IV Test for a Unit Root in Generally Trending and Correlated Panels
| Author | Joakim Westerlund |
| Published date | 01 October 2016 |
| Date | 01 October 2016 |
| DOI | http://doi.org/10.1111/obes.12141 |
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©2016 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 78, 5 (2016) 0305–9049
doi: 10.1111/obes.12141
An IV Test for a Unit Root in GenerallyTrending and
Correlated Panels*
Joakim Westerlund†,‡
†Department of Economics, Lund University, P. O. Box 7082 S-220 07, Lund, Sweden
(e-mail: joakim.westerlund@nek.lu.se)
‡Centre for Financial Econometrics, Deakin University, Melbourne, Australia
Abstract
This paper proposes an IV-based panel unit root test that is general enough to accommodate
general error serial and cross-section dependence, and a potentially nonlinear deterministic
trend function. These allowances make the new test one of the most general around. It is
also very simple to implement. Indeed, the IV statistic is asymptotically invariant to not
only to all nuisance parameters characterizing the dependence of the errors and the true
trend function, but also the deterministic specification of the fitted test regression.
I. Introduction
This paper proposes a test statistic of the null hypothesis of a unit root in panel data
where the number of time periods, T, and cross-sectional units, N, are large. The frame-
work is general enough to include most deterministic trend functions that are linear in
parameters, including polynomial trend functions, and trigonometric functions. The inno-
vations may be both serially and cross-sectionallycor related in a very unrestricted fashion
through a multivariate common factor model. A priori knowledge as to the extent of trend-
ing, and innovation serial and cross-sectional dependence is not required, provided that
the chosen model specification is general enough to encompass the true one. Under this
assumption the proposed test statistic, which is based on the instrumental variables (IV)
principle, has the practically very useful property that it is asymptotically invariant to not
only all nuisance parameters characterizing the dependence of the innovationsand the tr ue
trend function, but also the deterministic specification of the test regression. The standard
requirement of (at most) a liner trend is therefore not needed, and the otherwise so common
mean and variance correction factors reflecting the chosen deterministic specification can
JEL Classification numbers: C12; C13; C33.
*Previousversions of the paper were presented at seminars at University of Maastricht, Deakin University,Queens-
land University of Technology, and Macquarie University.The author thanks seminar participants and in par ticular
Joerg Breitung, Jean-Pierre Urbain, Stan Hurn, Mehdi Hosseinkouchack, Adam Clements, Chris Doucouliagos,
Prasad Bhattacharya, Francesco Zanetti (Editor) and two anonymous referees for manyconstr uctivecomments. Our
sincere thanks also to the Knut andAlice Wallenberg Foundationfor financial suppor t through aWallenberg Academy
Fellowshipand to the Jan Wallander and TomHedelius Foundation for financial support under research grant number
P20140112:1.
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