On the Uses of Misspecification Checks and Tests of Non-Nested Hypotheses in Emperical Econometrics

In recent years, there has been an increased emphasis on the need to subject econometric models to rigorous testing. Many checks for misspecification have been derived as Lagrange multiplier (LM) tests by viewing the model under scrutiny as being a special case of (nested in) some more general specification.' While it seems likely that careful and thorough use of such checks will be helpful in empirical research, a poor choice of alternative hypothesis may lead to a low probability of rejecting an inadequate null model. In view of our lack of knowledge about the true data generating process (DGP), it is not sensible to regard tests of a model against simple extensions as being infallible and standard diagnostic checks cannot be expected to reject inappropriate specifications with high probability in every application. It follows that it is possible that quite different economic models will sometimes be put forward, estimated and declared 'data consistent' after routine testing for, say, autocorrelation and parameter constancy. In such circumstances, it is natural to think of using these competing models to provide additional checks of each other's specification. Indeed, Davidson et al. (1978) and Hendry and Richard (1983) have emphasised the need for an adequate model to account for or encompass the results obtained by estimating alternative specifications. Tests of separate or non-nested alternatives may, therefore, prove valuable. The purpose of this paper is to consider tests of a model's specification based upon both nested and non-nested hypotheses. Theoretical results and Monte Carlo evidence are discussed, and particular attention is paid to the question of the potential constructive use of such tests in model reformulation. As full information estimators are not widely used in empirical work and suffer from several practical disadvantages, only statistical procedures for single equations will be considered.2 It will be further supposed that individual structural relations from a (possibly incomplete) simultaneous equation system are estimated by an instrumental variable/two stage least squares (IV/2SLS) technique and that (non-simultaneous) regression equations are estimated by ordinary least squares (OLS).

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