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<p>We introduce a Bayesian framework for estimating income inequality by combining household survey microdata (EU-SILC) with external top-income data (WID), using a flexible Pareto II distribution to model the upper tail. Unlike traditional methods that rely on fixed thresholds, our approach endogenizes the threshold separating the central part and the upper tail of the income distribution. The central part is modelled using a semi-parametric approach based on Bernstein polynomials, improving thus the accuracy of the likelihood and the resulting inequality estimates. Prior information on tail behaviour is incorporated through a Gamma prior on the Pareto II shape parameter, built informatively from WID data. Our results suggest that treating the threshold as uncertain and integrating external top-income data can substantially revise inequality estimates, offering a robust methodology for reconciling disparate data sources in income distribution analysis. Empirical applications to 23 EU countries in 2008 and 2018 show that incorporating external data has little impact in countries using administrative records as source for income variables in surveys (typically Nordic countries), but significantly raises Gini estimates in countries relying solely on surveys such as Germany and the UK. For countries relying on mixed sources for incomes, the impact can vary a lot. Our method provides in general more important corrections for the New Member States.</p>

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Bayesian inference for income inequality using a Pareto II tail with an uncertain threshold: combining EU-SILC and WID data

  • 期刊论文

  • 发表日期：

    2026年4月23日

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  • Mathias Silva,
  • Michel Lubrano

摘要

We introduce a Bayesian framework for estimating income inequality by combining household survey microdata (EU-SILC) with external top-income data (WID), using a flexible Pareto II distribution to model the upper tail. Unlike traditional methods that rely on fixed thresholds, our approach endogenizes the threshold separating the central part and the upper tail of the income distribution. The central part is modelled using a semi-parametric approach based on Bernstein polynomials, improving thus the accuracy of the likelihood and the resulting inequality estimates. Prior information on tail behaviour is incorporated through a Gamma prior on the Pareto II shape parameter, built informatively from WID data. Our results suggest that treating the threshold as uncertain and integrating external top-income data can substantially revise inequality estimates, offering a robust methodology for reconciling disparate data sources in income distribution analysis. Empirical applications to 23 EU countries in 2008 and 2018 show that incorporating external data has little impact in countries using administrative records as source for income variables in surveys (typically Nordic countries), but significantly raises Gini estimates in countries relying solely on surveys such as Germany and the UK. For countries relying on mixed sources for incomes, the impact can vary a lot. Our method provides in general more important corrections for the New Member States.