University of California, Berkeley
and University of Wisconsin, Madison
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.