世行的文献，里面包含计算The Concentration Index的理论以及STATA程序The Concentration Index
Concentration curves can be used to identify whether socioeconomic inequality in
some health sector variable exists and whether it is more pronounced at one point
in time than another or in one country than another. But a concentration curve does
not give a measure of the magnitude of inequality that can be compared conveniently
across many time periods, countries, regions, or whatever may be chosen
for comparison. The concentration index (Kakwani 1977, 1980), which is directly
related to the concentration curve, does quantify the degree of socioeconomicrelated
inequality in a health variable (Kakwani, Wagstaff, and van Doorslaer 1997;
Wagstaff, van Doorslaer, and Paci 1989). It has been used, for example, to measure
and to compare the degree of socioeconomic-related inequality in child mortality
(Wagstaff 2000), child immunization (Gwatkin et al. 2003), child malnutrition
(Wagstaff, van Doorslaer, and Watanabe 2003), adult health (van Doorslaer et al.
1997), health subsidies (O’Donnell et al. 2007), and health care utilization (van
Doorslaer et al. 2006). Many other applications are possible.
In this chapter we defi ne the concentration index, comment on its properties,
and identify the required measurement properties of health sector variables to
which it can be applied. We also describe how to compute the concentration index
and how to obtain a standard error for it, both for grouped data and for microdata.
绘制曲线的，世行的文献，包含STATA程序的
Concentration Curves
In previous chapters, we assessed health inequality through variation in mean
health across quintiles of some measure of living standards. Although convenient,
such a grouped analysis provides only a partial picture of how health varies across
the full distribution of living standards. A complete picture can be provided using
a concentration curve, which displays the share of health accounted for by cumulative
proportions of individuals in the population ranked from poorest to richest
(Kakwani 1977; Kakwani et al. 1997; Wagstaff et al. 1991). The concentration curve
can be used to examine inequality not just in health outcomes but in any health sector
variable of interest. It can also be used to assess differences in health inequality
across time and countries. For example, it has been used to assess whether subsidies
to the health sector are targeted toward the poor and whether the targeting is
better in some countries than in others (O’Donnell et al. 2007; Sahn and Younger
2000). It has also been used to assess whether child mortality is more unequally
distributed to the disadvantage of poor children in one country than in another
(Wagstaff 2000) and whether inequalities in adult health are more pronounced in
some countries than in others (van Doorslaer et al. 1997). Many other applications
are possible.
In this chapter we explain how to compute a concentration curve. We also
explain how to test whether a concentration curve departs signifi cantly from an
equal distribution and whether there is a statistically signifi cant difference between
two concentration curves that may represent different health services, time periods,
or countries. This
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