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ASYMPTOTICALLY UMP PANEL UNIT ROOT TESTS—THE EFFECT OF HETEROGENEITY IN THE ALTERNATIVES

Published online by Cambridge University Press:  23 September 2014

I. Gaia Becheri ,
Feike C. Drost  and
Ramon van den Akker
I. Gaia Becheri
Affiliation:
Delft University of Technology
Feike C. Drost
Affiliation:
Tilburg University
Ramon van den Akker*
Affiliation:
Tilburg University
*
*Address correspondence to Ramon van den Akker, Econometrics Group, CentER, Tilburg University, Tilburg, the Netherlands; e-mail: [email protected].
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Abstract

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.

Type
ARTICLES
Information
Econometric Theory , Volume 31 , Issue 3 , June 2015 , pp. 539 - 559
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

The authors wish to thank the referees and a co-editor for constructive comments. In particular, we are grateful for suggesting optimality of a test based on Breitung and Meyer (1994).

References

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