Introduction

The method of instrumental variables (IV) has traditionally been viewed as a response to a common problem in regression contexts, namely where one or more of the regressors on the right-hand side of the proposed equation are correlated with the equation disturbance. If this happens, the method of ordinary least squares suffers from consistency problems. The instrumental variables methods were developed to overcome these problems. It could legitimately be objected that the focus on consistency alone as a criterion of statistical effectiveness is misplaced. Thus it is often the case that estimators that are consistent possess inferior meansquare error properties to those that are not. Remarkably enough, however, the IV methodology can in many circumstances provide estimators that have superior efficiency properties all round. Indeed, it will be one of the themes of the later chapters of this book that the method of maximum likelihood may, in certain contexts of importance, itself be regarded as an instrumental variables estimator, so that IV estimators are asymptotically fully efficient. In the present chapter, however, we shall lower our sights a little and consider the motivation for instrumental variables as arising from requirements of statistical consistency.