Assessing the Statistical Significance of Inequality Differences: The Problem of Heavy Tails

Nicolas Herault () and Stephen P. Jenkins ()
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Nicolas Herault: University of Bordeaux
Stephen P. Jenkins: London School of Economics

No 17973, IZA Discussion Papers from Institute of Labor Economics (IZA)

Abstract: Because finite sample inference for inequality indices based on asymptotic methods or the standard bootstrap does not perform well, Davidson and Flachaire (Journal of Econometrics, 2007) and Cowell and Flachaire (Journal of Econometrics, 2007) proposed inference based on semiparametric methods in which the upper tail of incomes is modelled by a Pareto distribution. Using simulations, they argue accurate inference is achievable with moderately large samples. We provide the first systematic application of these and other inferential approaches to real-world income data (high-quality UK household survey data covering 1977–2018), while also modifying them to deal with weighted data and a large portfolio of inequality indices. We find that the semiparametric asymptotic approach provides a greater number of statistically significant differences than the semiparametric bootstrap which in turn provides more than the conventional asymptotic approach and the ‘Student-t’ approach (Ibragimov et al., Econometric Reviews, 2025), especially for year-pair comparisons within the period from the late-1980s onwards.

Keywords: semiparametric asymptotic approach; semiparametric bootstrap approach; asymptotic approach; Pareto distribution; income inequality; t-statistic approach (search for similar items in EconPapers)
JEL-codes: C14 C46 C81 D31 (search for similar items in EconPapers)
Date: 2025-06
New Economics Papers: this item is included in nep-ltv
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