The need for non-nested tests arises when the models under consideration belong
to separate parametric families in the sense that no single model can be obtained from
the others by means of a suitable limiting process. This situation, which is particularly
prevalent in econometric research, may arise when models differ with respect to their
theoretical underpinnings and/or their auxiliary assumptions. Unlike the general specifi-
cation tests and diagnostic tests, the application of non-nested tests is appropriate when
specific but rival hypotheses for the explanation of the same economic phenomenon have
been advanced. Although non-nested tests can also be used as general specification tests,
they are designed primarily to have high power against specific models that are seriously entertained in the literature. Building on the pioneering work of Cox (1961, 1962), a
number of such tests for single equation models and systems of simultaneous equations
have been proposed. (Pesaran and Weeks, 2001).