The purpose of this paper is to describe some of the widely used non nested testing procedure such as the Cox-type family tests, the F-test and two new procedures recently proposed by Godfrey-Pesaran.
The general framework used for the analysis of these procedures is the encompassing principle which allows to classify all them into two groups: variance-encompassing and parameter-encompassing tests.
As the small sample behaviour of most of these tests is not known, Monte Carlo experimentation is required to assess the validity of different procedures. Power and size comparisons are then performed in the context of alternative dynamic models characterized by equal and unequal number of regressors. Monte Carlo simulations are however limited in the sense that they do not cover the number of all possible experiments. In this way, the results of such techniques are imprecise and characterized by specificity. To avoid this problem a possible solution is to resort to the application of response surface techniques. After a brief exposition of the main features of response surface analyses, an application is shown for the F-test and one of the Cox-type testing procedures derived by Godfrey-Pesaran.
