1. Health insurance claims distributions Robert Cole NZ Society of Actuaries conference Nov 2010

2. Disclaimer Thanks to my former employer for making the data available for this analysis All opinions, errors & omissions are my own

3. Exec summary – why claims distributions are important Proportion of nil-claimers Member behaviour and value perceptions Low claims rewards Claim size distribution Member anti-selection Product design (maximums, excesses, etc) Pricing (rate cards, rating factors, large corporate schemes) Multi-year correlations in claiming A very significant component of claims costs

4. Exec summary – key findings Significance of high-claiming members 80/20 (or 80/8) - in any year >80% of total claims $ from 20% of claiming (about 8% of all) members Total costs over large $ thresholds (eg $10k) growing faster than average Material differences by factor Age, gender, plan type Multi-year correlations in claiming High-claiming members tend to remain high- claiming for long periods of time, and vice versa

5. Analysis method Total amount of claims paid summed up for every member by financial year from 03/04 to 09/10 Can be zero or $ amount (up to about $110,000) Member attributes at mid year (ie 31 December) Age, gender, plan type, excess, individual or group, subsidy

6. 20% claiming members (8% all) = 80% claims $, share of $ from high-claimers is growing

7. Claim $ paid for members claiming large $ a year is growing faster than overall (>$0)

8. Lower proportions of nil-claimers old ages, female, comprehensive plans

9. Older ages have more members with large annual claims than at younger ages

10. More high-claiming males

11. Higher proportions of females claiming up to about $15,000 in a year

12. Claim difference is smaller than excess amount for major medical excess plans …

13. … and also for comprehensive excess plan

14. Serial correlations High-claiming members in a period are more likely to be high-claiming members in next period Low (or nil)-claiming members in a period are more likely to be low (or nil)-claiming members in next period holds if period is 1-year, 2-years or 3-years holds if consecutive periods are overlapping or non- overlapping Relevant for low claims reward design proportions of members gaining or losing reward proportions qualifying

15. 1-year claims conditional on prior 1-year eg $0 given $0 =1.3 times as likely, $30+k given $30+k = 18.5 times

16. 1-year claims conditional on prior 2-years bigger effect than prior 1-year

17. 1-year claims conditional on prior 3-years bigger effect still

18. Any questions?