Companion to NCOS Working Paper v1.0 · Reference calibration Rmax 10%, m 6.00 ($1M) · ncos.world · November 2026
Intended audience: SSA actuaries, CMS analysts, independent actuarial reviewers
The Social Security contribution sigmoid (S2), the benefit sigmoid (S3), the Civic Healthcare Contribution (S11) and the Subsidy Coefficient (S12) replace the capped payroll tax and the fragmented premium structure with continuous functions. This note sets out their reference parameters, the reference results computed by the D2 model embedded in the working paper, the solvency conditions that formal actuarial certification must test, and the stress scenarios. Every figure is on an FY2024 basis and is reproduced by the working paper build. Formal certification by SSA, CMS and independent actuaries remains a requirement for a future version.
Revision note (October 2026). This edition supersedes the April 2026 note. Earlier editions stated that removing the wage cap produced a "modestly positive" revenue effect under the original S2 parameters, assumed the National Healthcare Fund was self-funding from S11, and contained an S11 parameter table inconsistent with the working paper. All three are corrected here.
C(y) = Cmax · σ(k(log₁₀ y − m)), applied to all wages with no cap, paid in full by the employer under the Parity Protocol. Reference parameters (October 2026): Cmax = 15%, k = 1.2, m = 4.0 (inflection $10,000).
| Annual wages | S2 rate | Today (OASDI, employee + employer) |
|---|---|---|
| $20,000 | 8.8% | 12.4% |
| $45,000 | 10.3% | 12.4% |
| $100,000 | 11.5% | 12.4% |
| $184,500 (2026 cap) | 12.3% | 12.4% |
| $300,000 | 12.8% | 7.6% |
| $1.00M | 13.8% | 2.3% |
Result: S2 raises approximately $1.33T on FY2024 wages, compared with $1.30T from today’s OASDI payroll tax and $1.47T of benefits. S2 covers about 91% of benefits (today: about 88%). Every worker earning less than about $185,000 (the 2026 wage cap of $184,500) pays a lower rate than today; high earners pay the same smooth rate on all wages. The “Today” column in the table above uses the 2026 cap; the revenue figures use the FY2024 wage base, consistent with the working paper.
Workers aged 50 or older at implementation retire under the current benefit formula (Retirement Certainty Clause, §14.3). S3 applies to younger cohorts. Solvency requires PV(S2 contributions) ≥ PV(S3 benefits) + trust-fund floor over 75 years. The long-run cost of the S3 benefit floor (Blow $2,500/month) for post-transition cohorts has not yet been modeled and is the principal open item for SSA review.
Per-person NEB cost by age (working paper Table 15.1 midpoints): 0–18 $5,000; 19–44 $7,500; 45–64 $15,000; 65+ $28,500. Across the 2024 population the NEB costs about $4.28T a year (average ≈ $12,500 per person, consistent with the $12,000 National Standard Premium).
H(w) = Hmax · σ(kH(log₁₀ w − mH)), with Hmax = 0.821%, kH = 0.4, mH = 5.5 (inflection ≈ $316K). The curve is gentle: H rises from about 0.37% at $100K toward its ceiling only at very high wealth.
| Net wealth | H(w) | Contribution |
|---|---|---|
| $100,000 | 0.37% | $370 |
| $500,000 | 0.43% | $2,134 |
| $1.00M | 0.45% | $4,514 |
| $5.00M | 0.51% | $25,355 |
| $15M | 0.54% | $81,476 |
| $1.00B | 0.66% | $6.59M |
Aggregate S11: $0.72T gross, $0.51T after the 30% behavioral haircut.
Bill(w) = min( (1 − S(w)) × NEBhousehold, C(w) ), where S(w) = max(20%, 95% · (1 − σ(0.9(log₁₀ w − 6.5)))) is the share curve and C(w) = $60,000 · σ(1.6(log₁₀ w − 7.0)) is the affordability ceiling. The subsidy is fixed at the standard-plan premium. Households in the 50+ transition cohort keep Medicare-level coverage (85%) for life; for the wealthiest, IRMAA-style, that extra help fades toward the 20% floor under the Standard High-Wealth Taper, Taper(W) = 1 − σ(k(log₁₀ W − m)), set to keep 90% of the help at $5M and 10% at $25M (Working Paper §4.6, §15.6). Low-wealth households pay small per-visit co-payments, waived under S8.
| Net wealth | Share S(w) | Ceiling C(w) | Working-age household bill | Retiree household bill (50+ cohort) |
|---|---|---|---|---|
| $50,000 | 79% | $1,474 | $1,474 | $1,474 |
| $500,000 | 64% | $6,654 | $6,654 | $6,565 |
| $1.00M | 58% | $10,079 | $10,079 | $6,598 |
| $5.00M | 43% | $22,912 | $16,085 | $9,401 |
| $15M | 33% | $34,198 | $18,857 | $26,184 |
| $100M | 20% | $49,921 | $22,678 | $34,908 |
| Flow | $T / yr (FY2024 basis) |
|---|---|
| NEB cost, all citizens | 4.28 |
| Household S12 bills | 0.60 |
| NHF subsidy outlay | 3.68 |
| Financed by: S11 (net) | 0.51 |
| Financed by: state contributions (federal takeover offer, all states accepting) | 0.34 |
| Financed by: S9 employer bridge, year 1 (declining to 20% in year 5 and zero thereafter) | 0.75 |
| Financed by: S1 general revenue | balance |
| Replaced federal outlays (Medicare net, Medicaid, CHIP, ACA) | 1.62 |
The NHF outlay exceeds the federal programs it replaces because it brings into the federal budget the financing that employers (about $0.75T in premiums) and the employer tax exclusion provide today; households pay about what they pay in premiums now. For an average working-age household, S11 exceeds the subsidy received above approximately $2.82M of net wealth (the self-funding breakeven).
The certifiable condition is: S11 + state contributions + S1 allocation ≥ Σ (NEB cost − household bill) + administrative margin, with an NHF stabilization buffer of one to two years of outlay funded from S1 in surplus years. Actuarial work must confirm the NEB cohort costs, the ceiling and share parameters, the age factors, and the 50+ cohort cost path.
Illustrative household with $50M of net wealth and $2M of wages: S1 ≈ $4.59M a year; S2 ≈ $282,163 paid by the employer. S1 flows to general revenue and S2 to the Social Security trust fund; the NVL accounting keeps the streams separate, so there is no double counting.
Technical Note A1 — NCOS Working Paper v1.0 companion document · Actuarial Series · Cross-reference: Working Paper §14, §15, Appendix A · ncos.world · November 2026