This paper introduces some new methods to test for panel cointegration in the error correction framework. These methods are proposed since the previous approaches do not perform well when the number of cross-sectional units (N) is approximately equal to the number of time periods (T). By means of Monte Carlo simulations we investigate the size and power properties when N and T increase simultaneously, i.e., N/T -> c where 0 < c <= 1. Based on the simulated results we may recommend a test for panel cointegration in high dimensional setting with cross-sectional dependency.