A Joint Top Income and Wealth Distribution

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. We leverage the bivariate parametric/non-parametric copula to extrapolate both income and wealth distributions from German PHF (Panel on Household Finance) data. The copula modelling potentially reduces the ad hocery in choosing the estimation domain as well as in the parametric specification (eg Pareto family) imposed by almost all the marginal approaches. 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 properness of copula and conditioning criterion seems to convince the asymmetric joint association between (labor) income and wealth (capital income) distributions as recently evidenced by other countries.