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

When estimated from survey data alone, the distribution of high incomes in a population may be misrepresented, as surveys typically provide detailed coverage of the lower part of the income distribution, but offer limited information on top incomes. Tax data, in contrast, better capture top incomes, but lack contextual information. To combine these data sources, Pareto models are often used to represent the upper tail of the income distribution. In this paper, we propose a Bayesian approach for this purpose, building on extreme value theory. Our method integrates a Pareto II tail with a semi-parametric model for the central part of the income distribution, and it selects the income threshold separating them endogenously. We incorporate external tax data through an informative prior on the Pareto II coefficient to complement survey micro-data. We find that Bayesian inference can yield a wide range of threshold estimates, which are sensitive to how the central part of the distribution is modelled. Applying our methodology to the EU-SILC micro-data set for 2008 and 2018, we find that using tax-data information from WID introduces no changes to inequality estimates for Nordic countries or The Netherlands, which rely on administrative registers for income data. However, tax data significantly revise survey-based inequality estimates in new EU member states.