Testing for Weak Exogeneity in Error Correction Models

Abstract

In the previous chapter we have mentioned how one could investigate the presence or absence of a cointegrating vector in the generating model for the conditioning variables. In particular, Johansen (1992a) and Boswijk (1991b) have proposed to test the hypothesis of weak exogeneity w.r.t. the long run parameters but do not consider any orthogonality conditions since the fact that an explanatory variable is error correcting is sufficient to reject weak exogeneity for the long run parameters. If we are in a structural framework, this condition is however not always sufficient when we are theoretically interested in the parameters of the short run dynamic in which case an additional orthogonality condition has to be verified. Although orthogonality tests will not take into account the possible violation of the variation free condition of weak exogeneity (see Engle et al., 1983), they may remain useful if the model used in empirical analysis is a structural error correction model, if the parameters of interest include both short and long run coefficients and if the cointegrating vector is known to be absent from the marginal models.