Chasing the Tail: A Generalized Pareto Distribution Approach to Estimating Wealth Inequality

Abstract

Abstract Since the work reported in Vermeulen [2018], a literature has developed on using the simple Pareto distribution along with “rich list” information to make improved estimates of the upper tail of the wealth distribution measured in surveys. Because the construction of such external data is typically opaque and subject to potentially serious measurement error, it may be best not to depend exclusively on this approach. This paper develops an alternative approach, using the generalized Pareto distribution (GPD), of which the simple Pareto is a subset, extending an estimation strategy developed by Castillo and Hadi [1997]. The greater flexibility of the GPD allows the possibility of modeling the tail of the wealth distribution, using a larger set of data for support than is typically the case with the simple Pareto. Moreover, the elaboration of the estimation method presented here allows explicitly for the possibility that the extreme of the observed upper tail is measured with error or that it is not captured at all. The approach also allows the incorporation of external data on total wealth as a constraint on the estimation. For the applications considered here using Austrian and U.S. micro data, the model relies on an estimate of total household wealth from national accounts, rather than rich-list information. The results suggest that where sufficiently comparable and reliable estimates of aggregate wealth are available, this approach can provide a useful way of mitigating problems in comparing distributional estimates across surveys that differ meaningfully in their effective coverage of the upper tail of the wealth distribution. The approach may be particularly useful in the construction of distributional national accounts.