Introduction and Notation

Abstract

In what follows in this book, we will denote living standards by the variable y. The indices we will use will sometimes require these living standards to be strictly positive, and, for expositional simplicity, we may assume that this is always the case. Strictly positive values of y are required, for instance, for the Watts poverty index and for many of the decomposable inequality indices. It is of course reasonable to expect indicators of living standards such as consumption or expenditures to be strictly positive. This assumption is less natural for other indicators, such as income, for which capital losses or retrospective tax payments can generate negative values. Also recall that, for expositional simplicity, we will also usually refer to living standards as incomes.