Quantile means and quantile share standard errors and a toolbox of distributional statistics

Charles M. Beach and Russell Davidson

Econometric Reviews, 2025, vol. 44, issue 8, 1166-1185

Abstract: This article derives the (asymptotic) variances and covariances – and hence standard errors – of quantile means and quantile shares in terms of explicit formulas that are distribution-free and easily computable. The article then develops a toolbox of quantile-based disaggregative inequality measures, based on the means and shares, which allow for detailed inferential analysis of income distributions in a straightforward unified framework. The analytical formulas are applied to Canadian Census public-use microdata files on workers’ earnings for 2000 and 2005. The results highlight the statistical significance of how upper-earnings levels have advanced beyond middle earnings, how much the share of mid-range earnings has eroded over even a five-year period, and how decile mean growth rates for women were everywhere higher than for men – except at the top decile, where the opposite phenomenon was highly significant.

Date: 2025
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DOI: 10.1080/07474938.2025.2486993

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