Results (v1)
A run defaults if, in any year, a benefit goes unpaid or solvency falls below 1. The minimum seed capital is the smallest injection that keeps the default probability at or below 5% (50 runs per scenario, search resolution about 4 million yuan). Amounts in million yuan.
Conclusions
- Once membership is mandatory, one seed injection is enough for the long run. With the switch in year 10, median solvency at the end is about 1.8 and none of 50 runs defaults.
- Voluntary membership alone stays small. After 50 years participation is about 13% and never reaches the 30% needed to switch. A small voluntary fund needs no seed money and runs a surplus — but it does not grow into county-wide coverage on its own. Policy has to set the date for mandatory membership.
- The financial risk sits in the year membership becomes mandatory. Every child in the county starts drawing education benefits at once, and the education pool runs short that year. The seed money covers that year, not a long-run deficit.
- Pooling cuts the seed money needed sharply. With the switch in year 10, separate pools need about 35 million yuan; pooled lending needs none.
- The seed money is small next to the county's budget. The largest case (mandatory from year 1, separate pools) needs about 94 million yuan: 11.8% of the county's own 2025 budget revenue and 2.0% of its spending.
- Stress tests barely change the seed money needed. Only a long period of low interest rates raises it, by about 11% with separate pools.
Minimum seed capital
| Scenario | Separate pools | Pooled |
|---|---|---|
| Mandatory from year 1 | 93.75 (475 yuan per resident) | 27.34 (138 yuan per resident) |
| Mandatory from year 10 | 35.16 (178 yuan per resident) | 0 |
| Year 10 + epidemic | 35.16 | 0 |
| Year 10 + recession | 35.16 | 0 |
| Year 10 + run (30% of members leave at once) | 35.16 | 0 |
| Year 10 + low rates (1% for 20 years) | 39.06 | 0 |
| Voluntary only | 0 | 0 |
Where the gap appears
Without seed capital (mean of 20 runs):
| Scenario | Gap |
|---|---|
| Year 10, separate pools | Education pool short by 11.77 in year 10 |
| Year 10, pooled | No gap; about 3.8 borrowed from the other pools that year |
| Year 1, separate pools | Year 1: education short by 21.86, medical by 4.11 |
| Year 1, pooled | Year 1: education short by 19.64, medical by 5.48 |
When membership is mandatory from year 1, all three pools are empty and there is nothing to borrow. When the switch comes in year 10, the voluntary members have already built up the medical and pension pools, which lend to education. Starting voluntary and switching later is itself a source of start-up money.
Other scenarios
Mandatory from year 10, pooled, 200 million yuan seed:
| Scenario | Median solvency at the end |
|---|---|
| Base | 1.80 |
| Medical split 50/50 | 1.47 |
| Reinsurance of large medical claims | 1.73 |
| Epidemic | 1.75 |
| Recession | 1.78 |
| Run | 1.80 |
| Low rates | 1.70 |
- A 50/50 medical split shrinks the shared pool and cuts the margin most.
- With these parameters the reinsurance premium costs more than the claims it carries.
- Automatic adjustment triggers at 105% solvency, which the simulation never reached.
The cost
- The average contributor pays 2,463 yuan a year, about 5.4% of earned income, on top of the existing resident medical insurance (400 yuan) and resident pension (from 200 yuan).
- Rural disposable income in the study county is only 16,155 yuan per head. For low-income rural households even the lowest tier, 530 yuan, is a real cost.
- Much of the fund's long-run surplus comes from one rule: personal balances move to the shared pools at death.