Exogeneity in Error Correction Models

In recent years, the study of cointegrated time series and the use of error correction models have become extremely popular in the econometric literature. This is an analysis of the notion of (weak) exogeneity, which is necessary to sustain valid inference in sub-systems, in the framework of error correction models (ECMs). In many practical situations, the applied econometrician wants to introduce "structure" to a model in order to get economically meaningful coefficients. For this purpose, ECMs in structural form provide an appealing framework, allowing the researcher to introduce (theoretically motivated) identification restrictions on the long run relationships. In this case, the validity of the inference will depend on a number of conditions which are investigated here. In particular, it is stressed that orthogonality tests, often used to test for weak exogeneity or for general misspecification, behave poorly in finite samples and are often not very useful in cointegrated systems.