Concentration Curve and Index

Both are twice the area between a cumulative curve and the line of equality, but they rank the population differently. The Gini ranks people by the variable being measured (income by income), so it captures pure dispersion and is always nonnegative. The concentration index ranks people by a separate socioeconomic variable and measures how the health variable co-varies with that ranking, so it is signed: negative when the variable concentrates among the poor and positive when among the rich. The concentration index is therefore a bivariate measure of the socioeconomic gradient, not of dispersion alone.

A negative index means the health variable is concentrated among the poor (the concentration curve lies above the diagonal); a positive index means it is concentrated among the rich. The welfare reading depends on the variable. For a good-health variable (e.g., having insurance), a negative index is adverse because the poor have less. For an ill-health variable (e.g., illness or mortality), a negative index is also adverse because the poor bear more bad health. Always state whether the variable measures health or ill-health when interpreting the sign.

When the health variable is binary (or otherwise bounded), the minimum and maximum attainable values of the standard concentration index depend on the mean prevalence, so the raw index cannot reach plus or minus one and is not comparable across populations with different prevalence. Normalized versions — the Wagstaff index, which rescales by the mean, and the Erreygers index, which rescales by the variable's range — restore comparability and a full range. The choice between them depends on whether relative or absolute inequality is the quantity of interest.