Cointegration ideas as introduced by Granger (1981) are commonly embodied in empirical macroeconomic modelling through the vector error correction model (VECM). It has also become common practice in these models to treat some variables as weakly exogenous, resulting in conditional VECMs. This paper studies the consequences of different approaches to weak exogeneity for the dynamic properties of such models, in the context of two models of the UK economy, one a national-economy model, the other the UK submodel of a global model. Impulse response and common trend analyses are shown to be sensitive to these assumptions and other specification choices.