Panel cointegration testing in the presence of linear time trends

We consider a class of panel tests of the null hypothesis of no cointegration and cointegration. All tests under investigation rely on single-equations estimated by least squares, and they may be residual-based or not. We focus on test statistics computed from regressions with intercept only (i.e., without detrending) and with at least one of the regressors (integrated of order 1) being dominated by a linear time trend. In such a setting, often encountered in practice, the limiting distributions and critical values provided for and applied with the situation 'with intercept only' are not correct. It is demonstrated that their usage results in size distortions growing with the panel size N. Moreover, we show which are the appropriate distributions, and how correct critical values can be obtained from the literature.