Signature
pi_total = sum_(j=1)^J [w_j * pi_j]
| Inputs | Definition | Unit |
|---|---|---|
w_j | Share of total health payments raised by source j, so that the J shares add to 1 | proportion |
pi_j | Kakwani index of source j, computed against the same ability to pay ranking and Gini coefficient as every other source | index without unit, from minus 2 to 1 |
pi_total | Kakwani index for total health financing | index without unit, from minus 2 to 1 |
|---|
JNumber of sources of finance, for example general taxation, social insurance, private insurance and out-of-pocket payments (count)
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.
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Implementations
Excel
Revenue-weighted Kakwani index with SUMPRODUCT
With the revenue shares in a range named RevenueShare and the matching source Kakwani indices in a range named KakwaniSource, SUMPRODUCT returns the weighted index.
=SUMPRODUCT(RevenueShare,KakwaniSource)
Assumptions
Revenue weights covering all health finance
The weights are each source's share of total health payments and add to 1, ideally taken from National Health Accounts. Sources that survey data cannot assign to households need an explicit assumption about their distribution, for example that they are distributed like a similar tax, and the result is tested for sensitivity to that assumption.
Common ability to pay ranking across sources of finance
Every source index uses the same households, the same ability to pay variable and the same Gini coefficient. The weighted average then equals the Kakwani index of the combined payment, because both indices are linear in the payment shares.
Worked examples
Sixty per cent tax and forty per cent out-of-pocket financing mix
With 60 per cent of revenue from tax (Kakwani 0.100) and 40 per cent from out-of-pocket payments (Kakwani minus 0.168), the overall index is 0.060 minus 0.0672, or minus 0.0072. The system is very slightly regressive although its larger source is progressive.
J = 2; w_j = [0.6,0.4]; pi_j = [0.100,-0.168]; pi_total = -0.0072
Common errors
Taking an unweighted average of source Kakwani indices
Averaging the source indices without revenue weights gives minus 0.034 in the article's example, nearly five times the correct value of minus 0.0072, and overstates the regressivity of the system.
Judging the financing system by its largest source
The direction of the largest source does not settle the direction of the system. In the article's example tax raises 60 per cent of revenue and is progressive, yet the system as a whole is slightly regressive.
Sources
World Bank guide on overall progressivity of health financing
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 16, pages 193 to 194: progressivity of total health financing as a weighted average of the source Kakwani indices with weights equal to each source's share of total payments, macroweights from National Health Accounts, and assumptions for revenues that cannot be allocated to households.
Canonical Identity
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