Signature
s_i = P - c_i
| Inputs | Definition | Unit |
|---|---|---|
P | Community-rated premium of the pool, from HE-FM-CRAT-001 | £ per member per year |
c_i | Expected annual cost of care for a member of risk group i | £ per member per year |
s_i | Cross-subsidy paid, when positive, or received, when negative, by each member of risk group i | £ per member per year |
|---|
Function
Community-rated premium, cross-subsidy and risk equalisation function
Maps the number of members and the expected annual cost of each risk group in a community-rated pool to the single premium every member pays, the implicit cross-subsidy each group gives or receives, the risk equalisation transfers that offset those cross-subsidies for insurers, and the late-entry loadings that Ireland and Australia add to the premium of people who first buy cover when older. The same difference between payment and expected cost, read from the insurer's side, is the expected profit per member on the Cream Skimming page (HE-FM-CSKM-001).
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Implementations
Excel
Community-rating cross-subsidy per member in one Excel cell
With the premium in a cell named Premium and a group's expected cost in a cell named ExpectedCost, Excel returns the cross-subsidy per member of that group.
=Premium-ExpectedCost
Assumptions
Premium set at the pool's mean expected cost for the cross-subsidy
P comes from HE-FM-CRAT-001 for the same members. If the premium includes loadings for administration and profit, they are removed first so that the cross-subsidies balance.
Expected, not realised, costs in the community-rating cross-subsidy
The cross-subsidy concerns predictable differences in expected cost between risk groups. Differences in realised costs within a group are the unpredictable risk that risk pooling spreads in any case.
Worked examples
Cross-subsidy paid by a low-risk member of the article's pool
At the article's premium of £2,000 each low-risk member, expected to cost £1,000, pays £1,000 more than their expected cost.
P = 2000; c_i = 1000; s_i = 1000
Cross-subsidy received by a high-risk member of the article's pool
Each high-risk member, expected to cost £6,000, pays £4,000 less than their expected cost. The total paid, 800 × 1,000 = 800,000, equals the total received, 200 × 4,000 = 800,000, so the pool balances.
P = 2000; c_i = 6000; s_i = -4000
Cross-subsidy paid by a low-risk member after the low-risk exit
At the post-exit premium of £3,000 each remaining low-risk member pays £2,000 above expected cost, computed here for illustration, which is the stronger reason to leave that the article describes.
P = 3000; c_i = 1000; s_i = 2000
Common errors
Treating the community-rating cross-subsidy as risk pooling
Risk pooling spreads unpredictable costs among members with similar risks. The £1,000 a year paid by each low-risk member in the article's example is predictable from the start and is a transfer between groups, which is why low-risk members have a reason to leave when buying cover is voluntary.
Measuring the community-rating cross-subsidy against a loaded premium
If loadings for administration and profit stay in the premium, every group appears to pay a positive amount and the cross-subsidies no longer sum to zero. The loadings are removed before the cross-subsidy is computed.
Sources
Low risks overpriced and high risks underpriced under a ban on premium differentiation
van de Ven WPMM, Hamstra G, van Kleef RC, Reuser M, Stam PJA. The goal of risk equalization in regulated competitive health insurance markets. European Journal of Health Economics. 2023;24(1):111-123. Sections on regulation-induced problems and on risk selection, which state that with a ban on premium differentiation the low-risk insured are overpriced and the high-risk insured underpriced, so that high-risk people generate a predictable loss for insurers and low-risk people a predictable gain.
Canonical Identity
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