Tag Archives: inequality

Polarization and the Decline of the Middle Class: Canada and the US

Several recent studies have suggested that the distribution of income (earnings, jobs) is becoming more polarized. Much of the evidence presented in support of this view consists of demonstrating that the population share in an arbitrarily chosen middle income class has fallen. However, such evidence can be criticized as being range-specific – depending on the particular cutoffs selected. In this paper we propose a range-free approach to measuring the middle class and polarization, based on partial orderings. The approach yields two polarization curves which, like the Lorenz curve in inequality analysis, signal unambiguous increases in polarization. It also leads to an intuitive new index of polarization that is shown to be closely related to the Gini coefficient. We apply the new methodology to income and earnings data from the US and Canada, and find that polarization is on the rise in the US but is stable or declining in Canada. A cross-country comparison reveals the US to be unambiguously more polarized than Canada.

Citation: Foster, J. and Wolfson, M. C. (1992, revised in August 2009). “Polarization and the Decline of the Middle Class: Canada and the US.” OPHI Working Paper 31, University of Oxford.

A Class of Association Sensitive Multidimensional Welfare Indices

The last few decades have seen increased theoretical and empirical interest in multidimensional measures of welfare. This paper develops a two-parameter class of welfare indices that is sensitive to two distinct forms of inter-personal inequality in the multidimensional framework. The first form of inequality pertains to the spread of each dimensional achievement across the population, as would be reflected in the multidimensional version of the usual Lorenz criterion. The second one regards association or correlation across dimensions, reflecting the key observation that inter-dimensional association may alter evaluation of individual as well as overall inequality. Most existing multi-dimensional welfare indices are, however, either completely insensitive to inter-personal inequality or are only sensitive to the first. The class of indices developed in this paper is sensitive to both forms of multidimensional inequality. An axiomatic characterization of the class is provided, and it is shown that other multidimensional indices, such as the ones developed by Bourguignon (1999) and Foster, Lopez-Calva, and Székely (2005), are sub-classes of this new broader class. Finally, essential statistical tests are constructed to verify the reliability of the evaluations generated by the indices.

Citation: Seth, S. (2009). “A Class of Association Sensitive Multidimensional Welfare Indices.” OPHI Working Paper 27, University of Oxford.