Deprivation in two dimensions Sample Clauses

Deprivation in two dimensions. -1 0 - y - π y 0 π x x Let D be a class of deprivation measures formed by integrating over the distribution a function p(x, y), where this is zero when x and y are both above the poverty thresholds: π x π y D = ∫∫ p( x, y) f (x, y)dydx Following the social welfare approach this quantity has to be minimised. As show by Xxxxxxxxxxx and Xxxxxxxxxxx (2003), a deprivation measures is increased or remain the same, as a result of a correlation increasing perturbation if the cross-derivate of p with respect to x and y is positive, that is the attributes are substitutes. Conversely, when the derivate is negative, they are complements. The first-degree dominance conditions allow us to rank two distributions: for poverty measures that are substitutes F(x, y) must be lower in country A than in country B given x and y, conversely, for poverty measures that are complements [F(x) + F(y) - F(x, y)] must be lower in country A than in country B given x and x. Xxxxxxxxxxx and Xxxxxxxxxxx (2003), for example, defined a deprivation index as: p(x, y) = [g β + bg β ]α / β