Introduction

Misspecification of the model may result in inconsistency of maximum likelihood estimates and of estimators of their standard errors. We have seen examples of this in the last chapter. In this chapter we shall discuss some numerical and graphical methods for detecting such misspecification, whose implementation ought to be a routine part of the econometric analysis of transition data. Of course, the main way in which an econometrician detects whether his model is wrong is when the estimates do not make economic sense. But the purely statistical tests we describe in this chapter are important supplements to the economist's judgment and are particularly valuable when economics does not provide a clear guide to what are sensible results.

When an econometrician proposes to fit a model f(t | x) to data drawn from N people with regressor vectors x he is tentatively asserting that the data distribution, conditional on x, is in the family t - which may be specified fully or semi-parametrically - and that this is true for all people. There is both an assumption about functional forms and an assumption about homogeneity conditional on x. Much of this book has been about data that are not homogeneous and this is a natural preoccupation of a social scientist. The diversity of people is surely greater than can be accounted for by the values of five or ten regressor variables. The emphasis in this chapter will therefore again be on the problem of heterogeneity. But we shall also point out the form taken by some tests for incorrect functional form.