A Unified Approach to Measuring Poverty and Inequality
In fact, each of the three dominance curves presented earlier suggests an associated growth curve. First, the growth incidence curve assesses how the quantile incomes are changing over time. Second, the generalized Lorenz growth curve indicates how the lower partial means are changing over time. Finally, the general mean growth curve plots the rate of growth of each general mean over time against parameter a. In the remainder of this section, we discuss the concepts of these different growth curves in greater detail. Growth Incidence Curve We start with the growth incidence curve. Consider two income distributions, x and y, at two different periods of time, where x is the initial income distribution. The quantile incomes of distribution x and distribution y at percentile p are denoted by WQI(x; p) and WQI(y; p), respectively. The growth of quantile income at percentile p is denoted by g QI (x, y; p) =
WQI (y; p) − WQI (x; p) WQI (x; p)
× 100%.
(2.13)
If every quantile registers an increase over time, then gQI(x, y; p) > for all p. The curve’s height at p = 50 percent gives the median income’s growth rate. Note that no part of this growth curve provides any information about the growth of mean income. Varying p allows us to examine whether this growth rate is robust to the choice of income standard, or whether the lowincome standards grew at a different rate than the rest. Figure 2.10 depicts the growth curves of quantile incomes. The vertical axis denotes the growth rate of quantile income and the horizontal axis denotes the cumulative population share. Suppose there are two societies, X and X'. The income distributions of society X at two different points in time are x and y, while those of society X' are x' and y'. The dashed growth curve gQI(x, y) denotes the quantile income growth rates of society X over time, whereas the dotted growth curve gQI(x', y') denotes the quantile income growth rates of society X' over time. Suppose the growth rates of mean income across these two distributions are the same and are denoted by –g > 0. Thus, the solid horizontal line at –g denotes the growth rate if the growth rate had been the same for all percentiles or the cumulative population share.
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