In the previous chapter we discussed the specification of the linear regression model as well as its statistical analysis based on the underlying eight standard assumptions. In the next three chapters several departures from [1]–[8] and their implications will be discussed. The discussion differs somewhat from the usual textbook discussion (see Judge et al. (1982)) because of the differences in emphasis in the specification of the model.

In Section 20.1 the implications of having E(yt,/σ(Xt)) instead of E(yt,/Xt = xt) as the systematic component are discussed. Such a change gives rise to the stochastic regressors model which as a statistical model shares some features with the linear regression model, but the statistical inference related to the statistical parameters of interest θ is somewhat different. The statistical parameters of interest and their role in the context of the statistical GM is the subject of Section 20.2. In this section the so called omitted variables bias problem is reinterpreted as a parameters of interest issue. In Section 20.3 the assumption of exogeneity is briefly considered. The cases where a priori exact linear and non-linear restrictions on θ exist are discussed in Section 20.4. Estimation as well as testing when such information is available are considered. Section 20.5 considers the concept of the rank deficiency of X known as collinearity and its implications. The potentially more serious problem of ‘near collinearity’ is the subject of Section 20.6.