On the Identification of Cointegrated Systems in Small Samples: Practical Procedures with an Application to UK Wages and Prices

This paper discusses the practical application of identification in cointegrated systems. It will argue that in a common realistic modelling situation of a limited data set and the theory requirements of a fairly rich model, the techniques proposed in the existing literature are almost impossible to implement successfully. There are crucial decisions to be made over the order in which various restrictions are imposed in the move from a general unrestricted VECM to the fully (over) identified VECM. We will argue that imposing exogeneity restrictions at the earliest possible stage of the model reduction process and then restricting the dynamic adjustment of the model hugely increases the power of tests of overidentifying restrictions on the long run cointegrating vectors. These arguments are supported by Monte Carlo evidence. In practise this means that a thorough use of economic theory at an early stage, rather than treating a model as a pure statistical artifact, can yield enormous benefits.