Toward an Inequality-Sensitive Measure of Development: The Unidimensional Case

This book seeks an inequality-sensitive measure of development. In this chapter, we review the standard theory in this regard for the case where there is a single dimension of development (say, income). Part of the theory is concerned with the question how we should measure inequality. However, inequality ranking is only one part of development ranking. The efficiency aspect is also to be taken into account. The important question for us is whether we can arrive at a complete development ranking, i.e. whether we can rank all pairs of economies in terms of development. It turns out that while the answer to the question is, in general, in the negative, for any given pair of economies, it is possible to formulate necessary and sufficient conditions (in terms of the observed data on incomes of the individuals in the economies) under which the two economies can be ranked. The notions of Lorenz dominance and generalized Lorenz dominance play important roles in these conditions. Whenever these conditions are violated, however, there would be ranking failures, i.e. we would be unable to rank the two economies in terms of their levels of development.