4 - Tests for misspecification of regression equations

Summary

Chapters 1 and 3 were devoted to fairly general discussions of test procedures. This chapter is concerned with the application of these methods to the problem of evaluating the adequacy of regression models. The number of possible misspecifications that could be made when formulating a regression model is very large, but most of those usually considered fall into one of the following categories:

(i) omitted variables (OV)

(ii) incorrect functional form

(iii) autocorrelation

(iv) heteroscedasticity

(v) lack of regression parameter constancy

(vi) non-normality of disturbances

(vii) invalid assumptions about the exogeneity of one or more regressors.

Although much of this chapter is taken up with a detailed account of parametric tests designed for alternative hypotheses included in (i) to (vii), some results on pure significance checks for regression models are also considered. Indeed, one point made is that such general checks can often be interpreted as classical tests for some specific specification error. Appropriate tests are discussed for each of the problems considered, and where possible a unifying theme (often based upon the LM principle) is provided, along with a summary of relevant Monte Carlo evidence.