In the recent years, the study of cointegrated time seriesand the use of error correction models have become extremelypopular in the econometric literature. This book provides ananalysis of the notion of (weak) exogeneity, which isnecessary to sustain valid inference in sub-systems, intheframework of error correction models (ECMs).In many practical situations, the applied econometricianwants to introduce "structure" on his/her model in order toget economically meaningful coefficients. For thispurpose,ECMs in structural form provide an appealing framework,allowing the researcher to introduce (theoreticallymotivated) identification restrictions on the long runrelationships. In this case, the validity of the inferencewill depend on a number of conditions which are investigatedhere. In particular,we point out that orthogonality tests,often used to test for weak exogeneity or for generalmisspecification, behave poorly in finite samples and areoften not very useful in cointegrated systems.