In this paper, we propose new cointegration tests for single equations and panels. In both cases, the asymptotic distributions of the tests, which are derived with N fixed and T→∞, are shown to be standard normals. The effects of serial correlation and cross-sectional dependence are mopped out via long-run variances. An effective bias correction is derived which is shown to work well in finite samples; particularly when N is smaller than T. Our panel tests are robust to possible cointegration across units.