Non-nested Hypothesis Testing: An Overview

In econometric analysis, non-nested models arise naturally when rival economic theories are used to explain the same phenomenon, such as unemployment, inflation or output growth. The authors examine the problem of hypothesis testing when the models under consideration are ‘non-nested’ or belong to ‘separate’ families of distributions in the sense that none of the individual models may be obtained form the remaining, either by imposition of parameter restrictions or through a limiting process. Although the primary focus is on non-nested hypothesis testing, the authors briefly discuss the problem of model selection and the differences and similarities between the two approaches. By using the linear regression model as a convenient framework, the authors examine three broad approaches to non-nested hypothesis testing: the modified (centred) long-likelihood ratio procedure, the comprehensive models approach, and the encompassing procedure. Finally, they consider a number of practical problems which arise in the application of non-nested tests to non-linear models such as the probit and logit qualitative response models.