Modeling Money

Kjell DoksumUniversity of California, Berkeleyand University of Wisconsin, Madison

Abstract

Lorenz and Bonferroni introduced measures of the concentration of

income that indicate how much the incomes below the uth quantile fall

short of the egalitarian situation where everyone has the same income.

As u changes, these measures become curves on [0,1].Gini introduced an

index that is the average over u of the difference between the Lorenz

curve and its egalitarian version.Bonferroni similarly introduced an

index based on the Bonferroni curve. In this paper we consider the

situation where the Lorenz and Bonferroni curves as well as the Gini

and Bonferroni indices are functions of covariates. We consider the

estimation of these functions for parametric, semiparametric and

nonparametric models. In particular, we consider a semiparametric model

involving regression coefficients and an unknown baseline income

distribution. In this model, which combines ideas from Pareto, Lehmann,

and Cox, we find partial likelihood estimates of Gini and Bonferroni

regression indices as well as the baseline income distribution.This is joint work with Rolf Aaberge and Steinar Bjerve.