It has long been known that conventional approaches to finite sample inference for inequality measures based on asymptotic methods or the standard bootstrap do not perform well, even in large samples. See, e.g., Davidson and Flachaire (Journal of Econometrics, 2007) and Cowell and Flachaire (Journal of Econometrics, 2007). The source of the problem is the heavy-tailed nature of income distributions, with a relatively high prevalence of influential high-income outliers in datasets. Can researchers do better? The answer is yes, in principle. Davidson and Flachaire (DF, 2007) and Cowell and Flachaire (CF, 2007) propose inference based on a semi-parametric percentile-t bootstrap in which the upper tail is modelled parametrically by a Pareto distribution, and show using simulated data that accurate inference is achievable with moderately large samples. (For a related approach, see also Alfons et al., JRSS(A) 2011.) In this paper, we provide the first systematic application of the DF-CF inferential approach to real-world income data for multiple years (yearly, 1977-2018), i.e., the same survey data as used by the UK Office for National Statistics for official statistics on inequality. As part of this work, we extend the DF-CF approach to deal with weighted data and a range of inequality indices (Gini, Generalised Entropy family, percentile ratios, and top income shares). We confirm that inequality indices are more precisely estimated using the DF-CF approach rather than the conventional asymptotic approach. But according to our DF-CF estimates, we cannot reject the null hypothesis of no inequality difference between most pairs of years over the period 1977-2018 at conventional levels of statistical significance.

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