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

Author

Listed:
  • Charles Beach
  • Russell Davidson

    (McGill University = Université McGill [Montréal, Canada], AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Charles Beach & Russell Davidson, 2025. "Quantile means and quantile share standard errors and a toolbox of distributional statistics," Post-Print hal-05072779, HAL.
    • Handle: RePEc:hal:journl:hal-05072779
    DOI: 10.1080/07474938.2025.2486993
    as

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