A simple panel unit root test in the presence of cross‐section dependence

TLDR

Panel unit root tests that account for cross‑section dependence often rely on orthogonalization procedures to eliminate cross‑dependence before applying standard tests. This paper proposes a simpler alternative that augments standard ADF regressions with cross‑section averages of lagged levels and first differences. The authors investigate the small‑sample properties of this test through Monte Carlo experiments. They derive asymptotic results for the cross‑sectionally augmented ADF statistics, showing these are asymptotically similar and independent of factor loadings, establish the existence of the average CADF limit distribution with tabulated critical values, and validate the test on OECD real exchange rates and PSID household earnings. © 2007 John Wiley & Sons, Ltd.

Abstract

A number of panel unit root tests that allow for cross-section dependence have been proposed in the literature that use orthogonalization type procedures to asymptotically eliminate the cross-dependence of the series before standard panel unit root tests are applied to the transformed series. In this paper we propose a simple alternative where the standard augmented Dickey–Fuller (ADF) regressions are augmented with the cross-section averages of lagged levels and first-differences of the individual series. New asymptotic results are obtained both for the individual cross-sectionally augmented ADF (CADF) statistics and for their simple averages. It is shown that the individual CADF statistics are asymptotically similar and do not depend on the factor loadings. The limit distribution of the average CADF statistic is shown to exist and its critical values are tabulated. Small sample properties of the proposed test are investigated by Monte Carlo experiments. The proposed test is applied to a panel of 17 OECD real exchange rate series as well as to log real earnings of households in the PSID data. Copyright © 2007 John Wiley & Sons, Ltd.