COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1435

Incidental Trends and the Power of Panel Unit Root Tests

Hyungsik Roger Moon
Department of Economics, University of Southern California
Benoit Perron
Département de sciences économiques, CIREQ, and CIRANO, Université de Montréal
Peter C.B. Phillips
Cowles Foundation, Yale University, University of Auckland and University of York

September 2003

The asymptotic local powers of various panel unit root tests are investigated. The power envelope is obtained under homogeneous and heterogeneous alternatives. It is compared with asymptotic power functions of the pooled t-test, the Ploberger–Phillips (2002) test, and a point optimal test in neighborhoods of unity that are of order n^–1/4T^–1 and n^–1/2T^^–1, depending on whether or not incidental trends are extracted from the panel data. In the latter case, when the alternative hypothesis is homogeneous across individuals, it is shown that the point optimal test and Ploberger–Phillips test both achieve the power envelope and are uniformly most powerful, in contrast to point optimal unit root tests for time series. Some simulations examining the finite sample performance of the tests are reported.

JEL Classification: C22, C23

Keywords and Phrases: Asymptotic power envelope, Common point optimal test, Heterogeneous alternatives, Incidental trends, Local to unity, Power function, Panel unit root test