This paper specifies a regression model describing homogeneous cointegrating relations between variables at the individual level. The model allows for correlation between the regressors and the regression error through shocks that are common to all cross-section units so the condition about strictly exogenous regressors is not imposed. It is shown that the estimator obtained by a cross-section regression performed at any point in time is a consistent estimator of the cointegrating parameters and its limiting distribution is normal. The model is extended to allow for the cointegrating parameters to differ randomly across units. In this case a cross-section regression will give a consistent estimator of the cointegrating parameter means.