Distribution-free statistical inference for generalized Lorenz dominance based on grouped data

Abstract

One income distribution is preferable to another under any increasing and Schur-concave (S-concave) social welfare function (SWF) if and only if the generalized Lorenz (GL) curve of the first distribution lies above that of the second. Thus, testing for GL dominance of one distribution over another is of interest. The paper focuses on inference based on grouped data and makes two contributions: (i) it gives a new formula for the asymptotic variance–covariance matrix of a vector of sample GL curve ordinates, interpreting it as a method-of-moments (MM) estimator, and (ii) it proposes a new test for multivariate inequality restrictions, of which GL dominance is a special case. For the Japanese household income data grouped into deciles, the test accepts the null hypothesis that income distribution in Japan improved from 1979 to 1994.