A robust sign test for panel unit roots under cross sectional dependence

A robust sign test is proposed for testing unit roots in cross-sectionally dependent panel data. Large sample Gaussian null asymptotics of the test are established under (fixed NN, large TT) and, for serially uncorrelated error cases, under (large NN, fixed TT), where NN is the number of panel units and TT is the length of time span. The limiting null distribution is valid, even if the error processes are subject to any type of conditional heteroscedasticity. A Monte-Carlo experiment reveals that, compared with other existing tests, the proposed test has a very stable size property for wider classes of error distributions, type of conditional heteroscedasticities, type of cross-sectional correlations, and values of (N,TN,T) while having reasonable power. Especially, for small TT like T=5,10,20T=5,10,20, the proposed test shows much stabler size performance than other existing tests. The unemployment rates of the 51 states of the USA are analyzed by the proposed method, which reveals some evidence for unit roots in the presence of factor and spatial cross-section correlation.