We propose a likelihood-based framework for cointegration analysis in panels of a fixed number of vector error-correction (VEC) models. We obtain likelihood ratio statistics to test for a common cointegration rank across the individual VEC models with both heterogeneous and homogeneous cointegrating vectors. Their limiting distributions are a summation of the limiting behavior of Johansen trace statistics. We extend the asymptotic distribution theory to cover the case of an infinite cross-sectional dimension. We apply the framework to a dataset of exchange rates and appropriate monetary fundamentals. We find evidence for the validity of the monetary exchange rate model within a panel of VEC models for three major European countries, whereas the results based on individual VEC models for each of these countries separately are less supportive.