Hand-Calculating the Gini: Intuition . Gini Coefficient is the average of all possible pair-wise comparisons of income for people in the population, normalized by the mean income. . If everybody has the same income, this average will be 0. . As income differences between people get bigger, the larger Gini getsHand-Calculating the Gini: Steps 1. Calculate (absolute value of) all possible pairwise comparisons between people 2. Calculate the sum of these pairwise comparisons 3. Divide this average by mean income in the society 4. Divide this by 2 (to account for double-counting) 5. Divide this by the number of people in the society squared I'm G = j=1 ZK=Ininkly; - ykl 2 un2Gini coefficient Gini calculation using Covariance Formula: G = 2 * Cov(F(y),Y) ul What are the pieces in this equation? . First, we sort the incomes, y, from smallest to largest . F(y) is the "cumulative distribution of the population" . u is the mean incomeGini coefficient: Covariance The "tricky" term is the F(y) term. Let's look at an example (continued on next slide): Monthly Name Person (i) Income % of Total Q (Y) F(Y) Income Cum. % of Cum. % of (Y) Y Pop Ed 320 7% 7% 20% Anubhab 2 560 13% 20% 40% Javier 3 720 16% 36% 60% Xinda 4 1,200 27% 64% 80% Oscar 5 1,600 36% 100% 100%