## Definitions and tests

Let X and Y be two income variables at either two different points in time, before and after taxes, or for different regions or countries. Let X1, X2,…, Xn be n not necessarily iid observations on X, and Y1, Y2,…, Ym be similar observations on Y. Let U1 denote the class of all utility functions u such that u’ > 0, (increasing). Also, let U2 denote the subset of all utility functions in U1 for which u" < 0 (strict concavity), and U3 denote a subset of U2 for which u”’ > 0. Let X0 and Y^ denote the ith order statistics, and assume F(x) and G(x) are continuous and monotonic cumulative distribution functions (cdfs) of X and Y, respectively. Let the quantile functions X(p) and Y(p) be defined by, for example, Y(p) = inf{y : F(y) > p}.

Proposition 1...

Read More