Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency
We apply bootstrap methodology to unit root tests for dependent panels with N cross-sectional units and T time series observations. More speciﬁcally, we let each panel be driven by a general linear process which may be diﬀerent across cross-sectional units, and approximate it by a ﬁnite order autoregressive integrated process of order increasing with T . As we allow the dependency among the innovations generating the individual panels, we construct our unit root tests from the estimation of the system of the entire N panels. The limit distributions of the tests are derived by passing T to inﬁnity, with N ﬁxed. We then apply the bootstrap method to the approximated autoregressions to obtain the critical values for the panel unit root tests, and establish the asymptotic validity of such bootstrap panel unit root tests under general conditions. The proposed bootstrap tests are indeed quite general covering a wide class of panel models. They in particular allow for very general dynamic structures which may vary across individual units, and more importantly for the presence of arbitrary cross-sectional dependency. The ﬁnite sample performance of the bootstrap tests is examined via simulations, and compared to that of the t-bar statistics by Im, Pesaran and Shin (1997), which is one of the commonly used unit root tests for panel data. We ﬁnd that our bootstrap panel unit root tests perform well relative to the t-bar statistics, especially when N is small.
Chang, Yoosoon, "Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency" (2000). Cowles Foundation Discussion Papers. 1501.