Non-nested Hypotheses

Abstract

In recent years considerable attention has been paid to the role of hypothesis testing in econometrics and its links with the problem of model selection in econometrics. One important topic considered in this recent work is the testing of ‘non-nested’ or separate models. Broadly speaking, two models (or hypotheses) are said to be ‘non-nested’ if neither can be obtained from the other by the imposition of appropriate parametric restrictions or as a limit of a suitable approximation; otherwise they are said to be ‘nested’. (A more formal definition can be found in Pesaran, 1987.) Non-nested models can arise from differences in the underlying theoretical paradigms and/or from differences in the way a particular relationship suggested by economic theory is modelled. Examples of non-nested econometric models abound in the literature: demand systems (Deaton, 1978; Murray, 1984), Keynesian and new classical models of unemployment (Pesaran, 1982a; Dadkhah and Valbuena, 1985), effects of dividend taxes on corporate investment decisions (Poterba and Summers, 1983), money demand functions (McAleer, Fisher and Volker, 1982) and empirical models of exchange rate determination (Backus, 1984), to mention just a few. Other examples of non-nested hypotheses arise when the probability distributions under consideration belong to separate parametric families, such as log-normal versus exponential, or Poisson versus geometric distributions.