Levels, Differences and ECMs – Principles for Improved Econometric Forecasting

An avalanche of articles has described the testing of a time series for the presence of unit roots. However, economic model builders have disagreed on the value of testing and how best to operationalise the tests. Sometimes the characterization of the series is an end in itself. More often, unit root testing is a preliminary step, followed by cointegration testing, intended to guide final model specification. A third possibility is to specify a general vector autoregression model, then work to a more specific model by sequential testing and the imposition of parameter restrictions to obtain the simplest data-congruent model ‘fit for purpose’. Restrictions could be in the form of cointegrating vectors, though a simple variable deletion strategy could be followed instead. Even where cointegration restrictions are sought, some commentators have questioned the value of unit root and cointegration tests, arguing that restrictions based on theory are at least as effective as those derived from tests with low power. Such a situation is, we argue, unsatisfactory from the point of view of the practitioner. What is needed is a set of principles that limit and define the role of the tacit knowledge of the model builders. In searching for such principles, we enumerate the various possible strategies and argue for the middle ground of using these tests to improve the specification of an initial general vector-autoregression model for the purposes of forecasting. The evidence from published studies supports our argument, though not as strongly as practitioners would wish.