Posterior Probabilities of Dominance for Wealth Distributions

Probability distributions, which are typically used to describe income distributions, are not suitable to describe a population’s distribution of wealth because of the existence of negative observations and a large concentration of values close to zero. To overcome these problems, we describe how the asymmetric Laplace distribution can be used for modelling wealth distributions and illustrate how it can be used to compute the posterior probabilities of first- and second-order stochastic dominance. Stochastic dominance concepts are useful for comparing wealth distributions and assessing whether changes in welfare have increased or decreased welfare in society. We use three distributions to make two such comparisons. The results are such that, in one comparison, one distribution clearly dominates the other. There is more uncertainty about dominance in the other comparison, with no dominance being the most likely outcome.