A Joint Top Income and Wealth Distribution

Abstract

Top distributions of income and wealth are still incompletely measured in many national statistics, particularly when using survey data. This paper develops the technique of incorporating the joint distributional relationship to enhance the estimation of these two top distributions by using the best data available for Germany. We leverage the bivariate copula to extrapolate both income and wealth distributions from German PHF (Panel on Household Finance) data under the incidental truncation model. The copula modelling grants the separability in choosing the estimation domain as well as the parametric specification between the marginal distribution and dependence structure. One distinct feature of our paper is to complement the model fit with external validation. The copula estimate can help us to perform out-of-sample prediction on the very top of the tail distribution from one margin conditional on the characteristics of the other. The validation exercises show that our copula-based approach can approximate much closer to the top tax data and wealth “rich list” than those unconditional marginal extrapolations. The data and effectiveness of our copula-based approach also verify our presumption of incidental truncation and differential detectability in the top lists.