Identification is an essential attribute of any models parameters, so we consider its three aspects of uniqueness, correspondence to reality and interpretability. Observationally-equivalent over-identified models can co-exist, and are mutually encompassing in the population; correctly-identified models need not correspond to the underlying structure; and may be wrongly interpreted. That a given model is over-identified with all over-identifying restrictions valid (even asymptotically) is insufficient to demonstrate that it is a unique representation. Moreover, structre (as invariance under extended information) need not be identifiable. We consider the role of structural breaks to discriminate between such representations.
