Measuring inequality with interval data

This paper employs the axiomatic approach underpinning the literature on income inequality measurement to analyze measures of dispersion in interval data. We find that some widely employed measures fail to properly measure dispersion when data are not of the ratio type. We go on to prove that, under reasonable conditions, variance is the only decomposable measure that can be used to consistently measure inequality of interval data. Moreover, the only proper Lorenz dominance condition for interval data is absolute Lorenz dominance that Moyes [Moyes, P., 1987. A new concept of Lorenz domination. Economics Letters 23, 203–207] introduced.