Polarization: Concepts, Measurement, Estimation

Abstract

We develop the measurement theory of polarization for the case in which income distributions can be described using density functions. The main theorem uniquely characterizes a class of polarization measures that fit into what we call the "identity-alienation" framework, and simultaneously satisfies a set of axioms. Second, we provide sample estimators of population polarization indices that can be used to compare polarization across time or entities.Distribution-free statistical inference results are also used in order to ensure that the orderings of polarization across entities are not simply due to samplingnoise. An illustration of the use of these tools using data from 21 countries shows that polarization and inequality orderings can often differ in practice.

Constructing indices of multivariate polarization

“…These pioneering papers have been followed by many others, among them Chakravarty and Majumder (2001), Esteban et al (1999), Wang and Tsui (2000), D´Ambrosio (2001), Gradín (2000), Duclos et al (2004). All these papers study polarization in terms of the distribution of incomes and measure how much this distribution spreads out from its center, dividing the population into at least two groups that are homogeneous and well separated from each other.…”

Effects of Income Inequality on Growth through Efficiency Improvement and Capital Accumulation

“…investigating whether a newly developed income inequality index such as a polarization index (Duclos et al 2004, Esteban et al 2007), affects efficiency improvement and capital accumulation. As well, how other socio-economic factors are related to them needs to be examined.…”

“…This data is widely used in previous works (e.g., Banerjee and Duflo 2003, Barro 2000, Forbes 2000, Li and Zou 1998. Recently, new indicators for inequality ((Duclos et al 2004, Esteban et al 2007) and ethnic composition (Montalvo and Reynal-Querol 2005) have been developed. However, the cross country panel data, which is called for the present paper, have not been constructed before.…”

Boats and Tides and 'Trickle Down' Theories: What Economists Presume About Wellbeing When They Employ Stochastic Process Theory in Modeling Behavior

“…Interestingly enough no such debate seems to have taken place regarding relative versus absolute inequality, though invariably relative inequality measures (Coefficient of Variation, Gini and Shutz coefficients for example) seem to have been favored and recently the concept of polarization which is related to, but distinctly different from, relative inequality has gained favour (see Duclos, Esteban and Ray (2004) for details).…”