The concept of cointegration (see e.g., Engle and Granger, 1987; Johansen, 1988) has extensively been used to model equilibrium relationships (see e.g., Johansen and Juselius, 1990; Ericsson, 1998). The links between economic and econometric concepts are now well understood and they have become part of the standard tools of empirical analysis. At the same time, however, the dynamics of the off-equilibrium situation have been met with relatively little interest on part of economic interpretations. This paper derives a paradox in which the econometric analysis is more likely to reveal the true causal links within an economic model the less valid this model actually is. A testing procedure is proposed and the results are illustrated using U.S., Japanese, German and Swiss data.