Abstract
This paper proposes a simple algorithm based on a matrix formulation to compute the Esteban and Ray (ER) polarization index. It then shows how the algorithm introduced leads to quite a simple decomposition of polarization by income sources. Such a breakdown was not available hitherto. The decomposition we propose will thus allow one to determine the sign, as well as the magnitude, of the impact of the various income sources on the ER polarization index. A simple empirical illustration based on EU data is provided.
Highlights
During the past 25 years, many studies attempted to measure the extent of the middle class and stressed the link between the concept of bipolarization and the importance of the middle class
The basic contribution here is that of Esteban and Ray (1994) who linked the concept of polarization to the notions of identification, alienation, and potential social conflict
The main contribution of the present paper is to introduce a simple algorithm to compute the Esteban and Ray (1994) polarization index
Summary
During the past 25 years, many studies attempted to measure the extent of the middle class and stressed the link between the concept of bipolarization and the importance of the middle class. The main contribution of the present paper is to introduce a simple algorithm to compute the Esteban and Ray (1994) polarization index We derive this algorithm from the simple matrix formulation suggested by Silber (1989) to compute the Gini index. The expression v0 Gη is a kind of Gini index, comparing a priori shares, the actual population shares, with a posteriori shares, the ‘identification modified income shares’ of the various population subgroups. This comparison is made again via the linear operator G, the G-matrix.
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