A Unified Approach to Measuring Poverty and Inequality
g LPM (x, y; p) =
WLPM (y; p) − WLPM (x; p) × 100%. WLPM (x; p)
(2.14)
If every quantile income registers an increase over time, then gLPM(x, y; p) > 0 for all p. Given that GLx(p) = pWLPM(x; p), the growth of the lower partial mean at a certain percentile is equal to the growth of the generalized Lorenz curve at that percentile. So the height of the generalized Lorenz growth curve at p = 20 percent is the rate at which the mean income of the lowest 20 percent of the population changed over time. Unlike the growth incidence curve, this curve provides information about the growth rate of mean income, which is the height of the curve at p = 100 percent. Again, varying p allows us to examine whether this growth rate is robust to the choice of income standard, or whether the low-income standards grew at a different rate than that of the rest. If the growth rates of the lower-income standards are found to be lower than the mean income, then overall growth, indeed, has not been pro-poor. However, if all lesser “lower partial means” grow at a faster rate than the higher “lower partial means,” then growth is assumed to be pro-poor. Figure 2.11 depicts the growth curves of lower partial mean incomes. The vertical axis denotes the growth rate of lower partial mean income, and the horizontal axis denotes the cumulative population share. Following the same notations as the growth incidence curve, suppose that there are two
Growth rate of partial mean income
Figure 2.11: Growth Rate of Lower Partial Mean Income
C D
C′
0
78
gLPM(x,y)
g
20
D′
gLPM(x ′,y ′)
40 60 80 Cumulative population share
100