Congruence and encompassing

Abstract

This paper considers the relationship between congruence and encompassing. Congruence is defined formally, and though it is not testable directly, it can be tested indirectly via tests of misspecification. Empirically more than one model can appear congruent, but that which encompasses its rivals is dominant, will encompass all models nested within it, and accurately predict the misspecifications of non-congruent models. These results are consistent with a general-to-specific modelling strategy being successful in practice. An empirical example illustrates these points.