Introduction

An important objective in econometric modelling is to obtain congruent and encompassing models, which are thus consistent with data evidence and economic theory, and are capable of explaining the behaviour of rival models for the same economic phenomena. Hendry (1995) and Mizon (1995b) inter alia present this view of modelling, as well as recording that a general-to-simple modelling strategy is an efficient way to isolate congruent models. Indeed such a modelling strategy requires the models under consideration to be thoroughly tested and progressively evaluated within a sequence of nested hypotheses, so that each model not rejected in the process is a valid simplification of (i.e. parsimoniously encompasses) all models more general than it in the sequence. Models arrived at as the limit of the reduction process therefore contain all relevant information available in the initial models, thus rendering the latter inferentially redundant. Testing the ability of models to parsimoniously encompass more general ones, thus ensuring that no information is lost in the reduction process, creates a partially ordered sequence of models. Further, Lu and Mizon (1997) point out that the intermediate models considered while testing the parsimonious encompassing ability of models in a nested sequence are mutually encompassing models and hence observationally equivalent to each other. Note, though, that there is an important distinction between observational equivalence in the population and in a sample, which may contain weak evidence.