The most popular general univariate polarization indices for discrete (Esteban and Ray 1994), and continuous (Duclos, Esteban and Ray 2004) variables are combined and extended to describe the extent of polarization between agents in a distribution defined over a collection of many discrete and continuous agent characteristics. A formula for the asymptotic variance of the index is also provided. The implementation of the index is illustrated with an application to Chinese urban household data drawn from six provinces in the years 1987 and 2001 (years spanning the growth and urbanization period subsequent to the economic reforms). The data relates to household adult equivalent log income, adult equivalent living space, which are both continuous variables and the education of the head of household which is a discrete variable. For this data set combining the characteristics changes the view of polarization that would be inferred from considering the indices individually.
Paper submitted to the special issue
The Measurement of Inequality and Well-Being: New Perspectives
The data set for this article can be found at: http://hdl.handle.net/1902.1/16236