The issue of model adequacy in mainstream econometrics is approached either as a
model selection problem or as a problem in statistical inference whereby the hypothesis
of interest is tested against general or specific alternatives. The use of absolute criteria
such as measures of fit/parsimony or formal Bayesian analysis based on posterior odds
are notable examples of model selection procedures, while likelihood ratio, Wald and
Lagrange multiplier tests of nested hypotheses and Cox’s centred log-likelihood ratio
tests of non-nested hypotheses are examples of the latter approach. The distinction
between these two general approaches basically stems from the way alternative models
are treated. In the case of model selection (or model discrimination) all the models under
consideration enjoy the same status and the investigator is not committed a priori to any
one of the alternatives. The aim is to choose the model which is likely to perform best with
respect to a particular loss function. By contrast, in the hypothesis-testing framework
the null hypothesis (or the maintained model) is treated differently from the remaining
hypotheses (or models).