A Unified Approach on the Local Power of Panel Unit Root Tests

TL;DR

This paper introduces a unified, characteristic function-based method to derive the exact local asymptotic power of popular panel unit root tests, enhancing understanding of their performance under various conditions.

Contribution

It provides a novel, unified approach to analyze the local power of LLC and IPS tests, including new results for the IPS test and Edgeworth expansions.

Findings

Derived exact local asymptotic power for LLC and IPS tests.

Provided new results for the non-admissible IPS test.

Illustrated theoretical findings with simulations.

Abstract

In this paper, a unified approach is proposed to derive the exact local asymptotic power for panel unit root tests, which is one of the most important issues in nonstationary panel data literature. Two most widely used panel unit root tests known as Levin-Lin-Chu (LLC, Levin, Lin and Chu (2002)) and Im-Pesaran-Shin (IPS, Im, Pesaran and Shin (2003)) tests are systematically studied for various situations to illustrate our method. Our approach is characteristic function based, and can be used directly in deriving the moments of the asymptotic distributions of these test statistics under the null and the local-to-unity alternatives. For the LLC test, the approach provides an alternative way to obtain the results that can be derived by the existing method. For the IPS test, the new results are obtained, which fills the gap in the literature where few results exist, since the IPS test is non-admissible. Moreover, our approach has the advantage in deriving Edgeworth expansions of these tests, which are also given in the paper. The simulations are presented to illustrate our theoretical findings.