A Statistical Characterization of Median-Based Inequality Measures

Charles M. Beach and Russell Davidson ()
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Charles M. Beach: Department of Economics, Queen’s University, Kingston, ON K7L 3N6, Canada
Russell Davidson: Department of Economics and CIREQ, McGill University, Montréal, QC H3A 2T7, Canada

Econometrics, 2025, vol. 13, issue 3, 1-33

Abstract: For income distributions divided into middle, lower, and higher regions based on scalar median cut-offs, this paper establishes the asymptotic distribution properties—including explicit empirically applicable variance formulas and hence standard errors—of sample estimates of the proportion of the population within the group, their share of total income, and the groups’ mean incomes. It then applies these results for relative mean income ratios, various polarization measures, and decile-mean income ratios. Since the derived formulas are not distribution-free, the study advises using a density estimation technique proposed by Comte and Genon-Catalot. A shrinking middle-income group with declining relative incomes and marked upper-tail polarization among men’s incomes are all found to be highly statistically significant.

Keywords: median-based inequality; income shares; population shares; income polarization (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2025
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