Tests for Exogeneity

Abstract

Engle, Hendry and Richard (1983) and Hendry and Richard (1983) argue in a convincing manner that their notion of exogeneity is the natural one to use instead of classical (strict) exogeneity if the goal of the econometric ian is to use the simplest possible model without loss of relevant statistical information. Geweke (1984) on the other hand reveals the opposite side of the coin: while it is weak exogeneity that we are really after, that concept by itself cannot generate refutable hypotheses (see also Basmann (1965)). In other words, a model can always be constructed and parameters of interest can be chosen for which a designated set of variables is weakly exogenous — a simple way to do this is to specify the conditional model and the marginal model independently. Therefore weak exogeneity by itself does not supply enough restrictions that it can be subjected to statistical tests. So, in order to make weak exogeneity operational, concepts that generate empirically refutable hypotheses and which under reasonable assumptions are compatible with weak exogeneity are needed. And here is where we come a full circle: strict exogeneity is such a concept — though not the only one. Testing for strict exogeneity is possible (Sims (1972), Williams, Goodhart and Gowland (1976), Ciccolo (1978)), and such tests can be interpreted as joint tests of strict exogeneity and the assumptions that link weak exogeneity to strict exogeneity.