Signature
RE = V - H - R
| Inputs | Definition | Unit |
|---|---|---|
V | Vertical redistribution: the redistributive effect there would be if households with equal pre-payment income paid equally | Gini points, without unit |
H | Horizontal inequity: the weighted sum of the post-payment Gini coefficients within groups of pre-payment income equals, each weighted by the group's population share times its share of post-payment income. Never negative | Gini points, without unit |
R | Reranking: the Gini coefficient of post-payment income minus the concentration index of post-payment income with households ranked by pre-payment income group and then by post-payment income. Never negative | Gini points, without unit |
RE | Redistributive effect: the Gini coefficient of pre-payment income minus the Gini coefficient of post-payment income. Positive values mean redistribution from richer to poorer households | Gini points, without unit |
|---|
Function
Horizontal equity measurement function for health care delivery and finance
Maps data on the use of health care, proxies of need and compulsory health payments, for people ranked by income or another measure of living standards, to measures of horizontal equity: need-expected use from a need regression, need-standardised use, the horizontal inequity index for the delivery of care, its rule-of-75 reading, and the horizontal inequity term in the decomposition of the redistributive effect of health finance. Equal treatment for equal need is judged against the average relationship between need and use in the sample, so the vertical norm is assumed rather than tested. The grouped-data concentration index (HE-FM-HINQ-005 on the Health Inequality page and HE-FM-VEQ-002 on the Vertical Equity page) and the Kakwani index (HE-FM-VEQ-001) have their own records and are not repeated here.
Try this function
Implementations
Excel
Redistributive effect from its three components in one Excel cell
With the vertical effect in a cell named VerticalEffect, horizontal inequity in HorizontalInequity and reranking in Reranking, Excel returns the total redistributive effect.
=VerticalEffect-HorizontalInequity-Reranking
Assumptions
Compulsory payments independent of use in the horizontal equity decomposition
The decomposition is applied to payments that are compulsory and independent of use, such as taxes and social insurance contributions. Voluntary payments made in return for care are not treated as redistributing income.
Income intervals defining groups of pre-payment equals
Few households have exactly the same income, so equals are defined by intervals of pre-payment income. The choice of interval leaves H plus R unchanged but shifts the split between them: wider intervals give a larger H and a smaller R.
Worked examples
Illustrative redistributive effect with horizontal inequity and reranking
Illustrative figures: a tax for health care with a vertical effect of 0.0053, as in the tax example on the Vertical Equity page, horizontal inequity of 0.0003 and reranking of 0.0002 has a total redistributive effect of 0.0048. Unequal treatment of equals and reranking reduce the fall in income inequality by about 9 per cent.
V = 0.0053; H = 0.0003; R = 0.0002; RE = 0.0048
Redistributive effect with horizontal equity in payments and no reranking
When households with equal pre-payment income pay equally and no household changes rank, the redistributive effect equals the vertical effect, 0.0053 in the same example.
V = 0.0053; H = 0; R = 0; RE = 0.0053
Common errors
Adding the horizontal inequity and reranking terms to vertical redistribution
H and R are subtracted. Adding them in the illustrative example gives 0.0058, more than the vertical effect, although horizontal inequity can only reduce redistribution.
Comparing horizontal inequity terms computed with different income intervals
H alone depends on the width of the income intervals used to define equals. Studies or years compared on H need the same intervals; otherwise H plus R, which equals V minus RE, is the comparable quantity.
Sources
World Bank guide on the decomposition of the redistributive effect of health finance
O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation. Washington, DC: World Bank; 2008. Chapter 17, pages 197 to 199: redistribution by compulsory payments independent of use, the redistributive effect as the fall in the Gini coefficient (equation 17.1), its decomposition into vertical redistribution, horizontal inequity and reranking shown by Aronson, Johnson and Lambert (1994) (equation 17.2), H as a weighted sum of within-group post-payment Gini coefficients (equation 17.5), R (equation 17.6), the effect of the income intervals on H and R, and Box 17.1 for the Netherlands, the United Kingdom and the United States.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0