Structural relations, cointegration and identification: some simple results and their application

This paper presents and applies some results on the interpretation of cointegrating regressions. The key concept is the irreducible cointegrating (IC) relation, one from which no variable can be omitted without loss of the cointegration property. Extending earlier results, it is shown that under certain circumstances, IC relations are identified structural forms. It is possible, at least in principle, to learn about the structure of simultaneous long-run relations directly from cointegration analyses, in contrast with the well-known fact that no such knowledge can be obtained from the correlations between stationary variables. IC relations can also be estimated by asymptotically mixed Gaussian and median unbiased estimators, permitting standard inference. MINIMAL, an algorithm for extracting the IC subsets of a data set, is applied to variety of artificial and actual data.