A panel cointegration rank test with structural breaks and cross-sectional dependence

This paper proposes a new likelihood-based panel cointegration rank test which allows for a linear time trend with heterogeneous breaks and cross sectional dependence. It is based on a novel modification of the inverse normal method which combines the p-values of the individual likelihood-ratio trace statistics of Trenkler et al. (2007). We call this new test a correlation augmented inverse normal (CAIN) test. It infers the unknown correlation between the probits of the individual p-values from an estimate of the average absolute correlation between the VAR processes' innovations, which is readily observable in practice. A Monte Carlo study demonstrates that this simple test is robust to various degrees of cross-sectional dependence generated by common factors. It has better size and power properties than other meta-analytic tests in panels with dimensions typically encountered in macroeconometric analysis.