A Comparative Study of Unit Root Tests with Panel Data and a New Simple Test

TLDR

The Levin–Lin panel unit root test, widely used in economic applications, relies on a restrictive hypothesis rarely of practical interest, and the Im–Pesaran–Shin test relaxes this assumption, a problem with a long statistical history. This study argues that the IPS test should be seen as a summary of independent tests and proposes using the Fisher test for stationarity and cointegration in panel data. The authors introduce a Fisher panel unit root test, comparing it with the LL, IPS, and Bonferroni bounds tests, and employ bootstrap‑based critical values. Overall, evidence points to the Fisher test with bootstrap‑based critical values as the preferred choice.

Abstract

The panel data unit root test suggested by Levin and Lin (LL) has been widely used in several applications, notably in papers on tests of the purchasing power parity hypothesis. This test is based on a very restrictive hypothesis which is rarely ever of interest in practice. The Im–Pesaran–Shin (IPS) test relaxes the restrictive assumption of the LL test. This paper argues that although the IPS test has been offered as a generalization of the LL test, it is best viewed as a test for summarizing the evidence from a number of independent tests of the sample hypothesis. This problem has a long statistical history going back to R. A. Fisher. This paper suggests the Fisher test as a panel data unit root test, compares it with the LL and IPS tests, and the Bonferroni bounds test which is valid for correlated tests. Overall, the evidence points to the Fisher test with bootstrap-based critical values as the preferred choice. We also suggest the use of the Fisher test for testing stationarity as the null and also in testing for cointegration in panel data.