Identities and their Role in Econometric Modeling

One important feature of econometric macro-models is their structural equations include several identities. The main aim of this paper is to attempt a critical look at the nature and role of identities in empirical modeling. The argument, in a nutshell, is that most of the identities included as an integral part of the model are just accounting identities that have no place in such models. This is because accounting identities constitute equalities among data series and not the variables behind the data. In this sense accounting identities represent measurement information which is already satisfied by the data for the whole of the sample period. When they are explicitly used as additional equations in an econometric model, they are misleadingly treated as behavioral relations like an equilibrium condition, a theoretical constraint or a theoretical definition. Such misinterpretations are not innocuous because the inclusion of such identities can lead to highly misleading results by imposing inappropriate restrictions on the statistical model, giving rise to unreliable inference results. ∗This is a updated version of the 1983 Birkbeck College discussion paper No. 110. The updating has been primarily focused on bringing the citations up to date because the original paper included several unpublished references.