This paper develops methods of Bayesian inference in a cointegrating panel data model. This model involves each cross-sectional unit having a vector error correction representation. It is flexible in the sense that different cross-sectional units can have different cointegration ranks and cointegration spaces. Furthermore, the parameters which characterize short-run dynamics and deterministic components are allowed to vary over cross-sectional units. In addition to a noninformative prior, we introduce an informative prior which allows for information about the likely location of the cointegration space and about the degree of similarity in coefficients in different cross-sectional units. A collapsed Gibbs sampling algorithm is developed which allows for efficient posterior inference. Our methods are illustrated using real and artificial data.