Two important practical aspects of microeconometric modeling are determining whether a model is correctly specified and selecting from alternative models. For these purposes it is often possible to use the hypothesis testing methods presented in the previous chapter, especially when models are nested. In this chapter we present several other methods.
First, m-tests such as conditional moment tests are tests of whether moment conditions imposed by a model are satisfied. The approach is similar in spirit to GMM, except that the moment conditions are not imposed in estimation and are instead used for testing. Such tests are conceptually very different from the hypothesis tests of Chapter 7, as there is no explicit statement of an alternative hypothesis model.
Second, Hausman tests are tests of the difference between two estimators that are both consistent if the model is correctly specified but diverge if the model is incorrectly specified.
Third, tests of nonnested models require special methods because the usual hypothesis testing approach can only be applied when one model is nested within another.
Finally, it can be useful to compute and report statistics of model adequacy that are not test statistics. For example, an analogue of R 2 may be used to measure the goodness of fit of a nonlinear model.
Ideally, these methods are used in a cycle of model specification, estimating, testing, and evaluation.