This paper by Russell Davidson and James G. MacKinnon proposes several procedures for testing the specification of an econometric model when there are one or more alternative models that also purport to explain the same phenomenon. These procedures, which are closely related to the non-nested hypothesis tests proposed by Pesaran and Deaton, are conceptually and computationally simpler than the CPD test. The authors demonstrate that their tests can be used to test against multiple alternative models simultaneously and present empirical results showing their effectiveness in rejecting false hypotheses. The paper also discusses the asymptotic properties of these tests and compares them to those of the CPD test, concluding that all tests are capable of rejecting both the null and alternative hypotheses asymptotically. The authors recommend the J-test for linear models, the P-test for nonlinear models, and the C-test as a preliminary test for nonlinear models. The paper concludes by emphasizing the simplicity and ease of implementation of these tests, suggesting they could be widely used in applied econometric work.This paper by Russell Davidson and James G. MacKinnon proposes several procedures for testing the specification of an econometric model when there are one or more alternative models that also purport to explain the same phenomenon. These procedures, which are closely related to the non-nested hypothesis tests proposed by Pesaran and Deaton, are conceptually and computationally simpler than the CPD test. The authors demonstrate that their tests can be used to test against multiple alternative models simultaneously and present empirical results showing their effectiveness in rejecting false hypotheses. The paper also discusses the asymptotic properties of these tests and compares them to those of the CPD test, concluding that all tests are capable of rejecting both the null and alternative hypotheses asymptotically. The authors recommend the J-test for linear models, the P-test for nonlinear models, and the C-test as a preliminary test for nonlinear models. The paper concludes by emphasizing the simplicity and ease of implementation of these tests, suggesting they could be widely used in applied econometric work.