A Simple Panel Unit Root Test in the Presence of Cross Section Dependence

A Simple Panel Unit Root Test in the Presence of Cross Section Dependence

September 24, 2003 | M. Hashem Pesaran
This paper proposes a simple panel unit root test that accounts for cross-sectional dependence. The test involves augmenting standard Dickey-Fuller (DF) or Augmented Dickey-Fuller (ADF) regressions with cross-sectional averages of lagged levels and first differences of individual series. A truncated version of the CADF statistic is also considered. The paper derives new asymptotic results for the individual CADF statistics and their simple averages. It is shown that the CADF statistics are asymptotically similar and do not depend on factor loadings under joint asymptotics where N (cross-sectional dimension) and T (time-series dimension) both tend to infinity such that N/T approaches a fixed finite non-zero constant. However, they are asymptotically correlated due to their dependence on the common factor. Despite this, the limit distribution of the average CADF statistic exists and its critical values are tabulated. The paper also investigates the small sample properties of the proposed tests through Monte Carlo experiments, showing that the cross-sectionally augmented panel unit root tests have satisfactory size and power even for relatively small values of N and T. This is particularly true of cross-sectionally augmented and truncated versions of the simple average t-test of Im, Pesaran and Shin, and Choi's inverse normal combination test. The paper also discusses the implications of cross-sectional dependence on the asymptotic properties of the CADF test and the use of truncated versions of the test to avoid the influence of extreme outcomes. The paper concludes that the proposed tests are simple to compute and have good finite sample properties.This paper proposes a simple panel unit root test that accounts for cross-sectional dependence. The test involves augmenting standard Dickey-Fuller (DF) or Augmented Dickey-Fuller (ADF) regressions with cross-sectional averages of lagged levels and first differences of individual series. A truncated version of the CADF statistic is also considered. The paper derives new asymptotic results for the individual CADF statistics and their simple averages. It is shown that the CADF statistics are asymptotically similar and do not depend on factor loadings under joint asymptotics where N (cross-sectional dimension) and T (time-series dimension) both tend to infinity such that N/T approaches a fixed finite non-zero constant. However, they are asymptotically correlated due to their dependence on the common factor. Despite this, the limit distribution of the average CADF statistic exists and its critical values are tabulated. The paper also investigates the small sample properties of the proposed tests through Monte Carlo experiments, showing that the cross-sectionally augmented panel unit root tests have satisfactory size and power even for relatively small values of N and T. This is particularly true of cross-sectionally augmented and truncated versions of the simple average t-test of Im, Pesaran and Shin, and Choi's inverse normal combination test. The paper also discusses the implications of cross-sectional dependence on the asymptotic properties of the CADF test and the use of truncated versions of the test to avoid the influence of extreme outcomes. The paper concludes that the proposed tests are simple to compute and have good finite sample properties.
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