Signature
V = g / (1 - g) * K_E
| Inputs | Definition | Unit |
|---|---|---|
g | Sample average payment rate: total compulsory health payments divided by total pre-payment income | proportion, for example 0.05 for 5 per cent |
K_E | Kakwani index of the payment that would arise if households with equal pre-payment income paid equally, computed from the between-groups concentration index of payments minus the Gini coefficient of income | index without unit |
V | Vertical redistribution: the fall in the Gini coefficient of income that the payment would cause if there were horizontal equity in payments. Positive values mean redistribution from richer to poorer households | Gini points, without unit |
|---|
Function
Vertical equity in health financing: progressivity and redistribution function
Maps the distribution of health care payments and of ability to pay, across households ranked from poorest to richest, to measures of vertical equity in financing: the Kakwani index of progressivity for each source of finance, the revenue-weighted index for the whole financing mix, and the vertical redistributive effect of compulsory payments on the Gini coefficient of income. Progressivity is measured as a departure from proportionality between payments and ability to pay. Vertical equity in delivery is judged against a need norm that the analyst chooses and defends, so it has no single formula and is not covered here.
Try this function
Implementations
Excel
Vertical redistributive effect of a health payment in one cell
With the average payment rate as a proportion in a cell named PaymentRate and the Kakwani index under horizontal equity in a cell named KakwaniE, Excel returns V.
=PaymentRate/(1-PaymentRate)*KakwaniE
Assumptions
Compulsory payments independent of use of care
The formula applies 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 in this sense, although how far out-of-pocket payments are voluntary is open to question.
Vertical component only of the redistributive effect
V equals the whole fall in the Gini coefficient only when there is no horizontal inequity and no reranking of households. Otherwise the total redistributive effect is V minus horizontal inequity minus reranking, and both subtracted terms are never negative.
Worked examples
Vertical redistribution from illustrative tax finance at a 5 per cent payment rate
Tax payments for health care take 5 per cent of income and have a Kakwani index of 0.100, with no horizontal inequity and no reranking. The vertical effect is about 0.0053, so the income Gini coefficient falls from 0.352 to about 0.347.
g = 0.05; K_E = 0.100; V = 0.0053
Vertical redistribution from public health finance in the Netherlands in 1992
In the World Bank guide's decomposition for the Netherlands in 1992, compulsory payments for public health care took 8.21 per cent of income with a Kakwani index of minus 0.0999 under horizontal equity. The vertical effect is about minus 0.0089, redistribution from poorer to richer households.
g = 0.0821; K_E = -0.0999; V = -0.0089
Common errors
Entering the health payment rate as a percentage
Entering 5 instead of 0.05 makes the scaling factor 5 divided by minus 4. With a Kakwani index of 0.100 the result is minus 0.125, the wrong sign and more than twenty times the correct size of 0.0053.
Reporting the vertical effect as the whole redistributive effect
V ignores horizontal inequity and reranking, which can only reduce redistribution. For the Netherlands in 1992 the guide reports a vertical effect of minus 0.0089 but a total redistributive effect of minus 0.0096.
Sources
World Bank guide on 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: the redistributive effect as the reduction in the Gini coefficient caused by the payment (equation 17.1), its decomposition into vertical redistribution, horizontal inequity and reranking (equation 17.2), V as g over one minus g times K_E (equation 17.4), and Box 17.1 with results for the Netherlands, the United Kingdom and the United States.
Canonical Identity
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