Measures whether exposure to pollution is concentrated among lower-income or higher-income people. The index runs from -1 (all the exposure borne by the poorest) through 0 (exposure shared evenly across income) to +1 (all of it borne by the richest); environmental-justice analyses report it next to the burden.
Value
A list of class rmbl_equity (plot() draws the
concentration curve) with concidx (a number in
\([-1, 1]\)), interpretation (a sentence),
expomean, citation (a string) and extra, a
list with n (rows used), cov_h_R (the covariance) and
curve, a data frame of the concentration curve. Its column
population is the cumulative population share, poorest first, and
exposure the cumulative share of total exposure.
Details
Wagstaff, Paci and van Doorslaer (1991): $$CI = (2 / \mu) \, \mathrm{cov}(h_i, R_i)$$ with \(R_i = (rank_i - 0.5) / n\) the fractional income rank (tied incomes share their average rank, so the index does not depend on row order) and the population covariance. Negative values mean lower-income units bear more exposure. Both columns must be numeric: a factor or character income is refused rather than ranked by its level codes, and exposures must be non-negative.
Rows with a missing exposure or income are dropped. The interpretation
calls an index below -0.01 a burden on the poor, above 0.01 a burden on
the rich, and anything between an even distribution. Refusals: column
names that are not single strings or not in data; fewer than 2
complete rows; a non-numeric or infinite value; a negative exposure; an
income that takes one value only (no income gradient, so the index is
undefined); and a mean exposure of zero (the index divides by it). Income
only needs an
order: an amount, a quintile number or a rank all give the same index.
References
Wagstaff, A., Paci, P. and van Doorslaer, E. (1991). On the measurement of inequalities in health. Social Science and Medicine 33(5), 545-557.
Examples
d <- data.frame(exposure = c(30, 25, 20, 15, 10), income = 1:5)
ci <- expconcidx(d, "exposure", "income")
ci$concidx
#> [1] -0.2
ci$interpretation
#> [1] "CI = -0.2000. Pro-poor exposure burden: lower-income individuals bear disproportionately higher pollution."
# Even exposure across income gives 0; tied incomes share a rank.
expconcidx(data.frame(exposure = 20, income = c(1, 1, 2, 3)),
"exposure", "income")$concidx
#> [1] 0
# A text income cannot be ranked.
try(expconcidx(data.frame(exposure = 1:3, income = c("a", "b", "c")),
"exposure", "income"))
#> Error : expconcidx: `income` must be numeric, got character