Journal of Probability and Statistics
Volume 2011 (2011), Article ID 617652, 17 pages
Research Article

Panel Unit Root Tests by Combining Dependent 𝑃 Values: A Comparative Study

1Department of Economics, American University, Washington, DC 20016, USA
2Department of Biostatistics and Epidemiology, University of Oklahoma Health Sciences Center, Oklahoma City, OK 73104, USA

Received 27 June 2011; Accepted 25 August 2011

Academic Editor: Mike Tsionas

Copyright © 2011 Xuguang Sheng and Jingyun Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We conduct a systematic comparison of the performance of four commonly used 𝑃 value combination methods applied to panel unit root tests: the original Fisher test, the modified inverse normal method, Simes test, and the modified truncated product method (TPM). Our simulation results show that under cross-section dependence the original Fisher test is severely oversized, but the other three tests exhibit good size properties. Simes test is powerful when the total evidence against the joint null hypothesis is concentrated in one or very few of the tests being combined, but the modified inverse normal method and the modified TPM have good performance when evidence against the joint null is spread among more than a small fraction of the panel units. These differences are further illustrated through one empirical example on testing purchasing power parity using a panel of OECD quarterly real exchange rates.