Confidence Contours For 2 Test Statistics For Non-nested Regression-models

Abstract

In this note we use the concept of implicit null hypotheses introduced by Mizon and Richard (1982) to clarify the relationship between the two test procedures discussed by Pesaran (1974) for testing non-nested regression models. These procedures are, firstly, Pesaran¿s version of the Cox (1961,1962) modified likelihood ratio test statistic and, secondly, the `comprehensive test¿ which is the usual classical test obtained from combining the two competing models. In particular, we suggest that the two testing procedures have markedly different confidence contours as a result of having different implicit null hypotheses,