We use meta-analytic procedures to develop new tests for panel cointegration, combining p-values from time-series cointegration tests on the units of the panel. The tests are robust to heterogeneity and cross-sectional dependence between the panel units. To achieve the latter, we employ a sieve bootstrap procedure with joint resampling of the units' residuals. A simulation study shows that the tests can have substantially smaller size distortion than tests ignoring the presence of cross-sectional dependence while preserving high power. We apply the tests to a panel of post-Bretton Woods data to test for weak purchasing power parity.