Method and data
Study county: a mountain county in western China
We compared 3 candidate counties and chose a mountain county in western China as the study county, with a plains county in eastern China as the control.
| Indicator | Study county | Control county |
|---|---|---|
| Residents, 2020 census | 197,500 | 289,500 |
| Aged 0–14 | 21.4% | 11.5% |
| Aged 65 and over | 15.9% | 21.4% |
| Residents ÷ registered population | 81% (strong youth out-migration) | 87% |
| Disposable income per head, 2025 | 25,881 yuan | 43,585 yuan |
| Own general budget revenue, 2025 | 795 million yuan | 3.49 billion yuan |
Why this county:
- Its county-level public data is the most complete; it is the only candidate that publishes its own medical insurance fund accounts.
- Many children and strong youth out-migration put the most pressure on the design: many beneficiaries, few contributors.
- Its budget is weak, so it is the hardest test of whether a seed injection is affordable.
If the design works in this county, the conclusion carries weight.
Data
Public data only:
- Population: population and deaths by age and sex from the provincial-level 2020 Census Yearbook. The yearbook is a scan; we extracted it with OCR and checked the sums: 197,497 residents, the male and female totals match the census bulletin, and the age groups add up.
- Life table: the age pattern of the provincial-level single-year death rates, first scaled to the official provincial-level life expectancy of 79.39 years (census deaths are under-reported), then to the county's own death level. Estimated life expectancy in the county: about 76.9 years.
- Medical: 0.22 hospital stays per person a year, 5,500 yuan per stay, about 45% paid by the patient (national medical security statistics, local insurance rules).
- Education: County kindergarten fees, local high-school and university tuition.
- Income: disposable income per head from the statistical bulletin.
Model
- An individual-level Monte Carlo simulation written in Go. Every resident has an age, sex, mother, health risk and income level.
- Each year it simulates death, out- and in-migration, employment, joining and leaving, contributions, medical care, education, pensions and births.
- Voluntary joining includes adverse selection: people with higher health risk join more readily, and members who have not drawn for a long time leave more readily.
- Each scenario runs 50 times; results give the 5th, 50th and 95th percentile of solvency and the default probability.
- A bisection search finds the smallest seed capital that keeps the default probability at or below 5%.
Calibration
The model first reproduces the study county's known statistics. Average of the first 5 model years against the targets:
| Indicator | Model | Target |
|---|---|---|
| Change in residents per year | +0.09% | 0% (flat 2020–2025) |
| Births | 1,286 | 1,314 |
| Deaths | 1,844 | 1,773 (estimate) |
| Hospital stays per person | 0.221 | 0.22 |
| Earned income per resident | 19,408 yuan | 19,400 yuan |
All within 4%. Some inputs are assumptions — the shape of migration, the share of earned income in disposable income — and the research documents mark the confidence of each.
Break-even cost
With everyone covered, each contributor carries per year:
| Item | Amount | Share of income |
|---|---|---|
| Education fees | 430–720 yuan | 1.0–1.6% |
| Medical costs left after public insurance | 1,400–1,900 yuan | 3.1–4.2% |
Ageing raises the medical cost per contributor by about 35% over 50 years. The contribution tiers are set at this break-even level plus a 10% margin.