Public Policy, Health & Labor Economics
Value of a Statistical Life (VSL) & VSLY Formula
Calculate Thaler-Rosen / Viscusi hedonic wage-risk VSL = (Delta_w / Delta_r_100k)*100,000, micromort willingness-to-pay, and real-annuity Value of a Statistical Life-Year (VSLY).
Translate occupational wage-risk differentials into regulatory VSL, micromorts, and VSLY!
In Richard Thaler & Sherwin Rosen (1976) and W. Kip Viscusi’s hedonic labor-market methodology (used by EPA, DOT, and health-technology evaluators), Value of a Statistical Life (VSL) measures aggregate marginal willingness-to-pay across a large population for small mortality-risk reductions — NOT the price of an identified individual’s life! If workers require an annual compensating wage differential Delta_w to accept an extra Delta_r_100k annual fatalities per 100,000 workers, implied VSL is (Delta_w / Delta_r_100k) * 100,000, implied Micromort Value (1-in-1,000,000 acute risk) is VSL / 1,000,000, and constant real Value of a Statistical Life-Year (VSLY) over T_rem remaining life-years at real discount rate r is (r * VSL) / (1 - (1 + r)^(-T_rem)) (or VSL / T_rem when r = 0)!
Check by hand BEFORE writing formulas: Annual_Wage_Premium_dw = 960 (B2) for an occupational risk gap of Delta_r_100k = 8 per 100,000 workers (B3), Remaining_Years_T = 40 (B4), and Real_Discount_Rate_r = 0.03 (B5). Per 1/100,000 unit risk, each worker is paid 960 / 8 = 120.00; across 100,000 workers (preventing 1.0 statistical fatality), VSL = 12,000,000.00, 1 Micromort = 12.00, and 3%-discounted VSLY = (0.03 * 12,000,000) / (1 - 1.03^(-40)) = 519,148.53 (avoiding the common undiscounted mistake 12,000,000 / 40 = 300,000.00 when r > 0!).
| Benefit-Cost Metric (dw=960, dr=8/100k, T=40, r=3%) | Formula | Verified Output |
|---|---|---|
| Value of a Statistical Life (VSL) | (Delta_w / Delta_r_100k) * 100,000 | 12,000,000.00 |
| Value of One Micromort (10^-6 Risk) | VSL / 1,000,000 | 12.00 |
| Discounted VSLY (r = 3%, T = 40 yr) | (r * VSL) / (1 - (1 + r)^(-T)) | 519,148.53 / life-year |
| Zero-Discount VSLY Benchmark (r = 0%) | VSL / T | 300,000.00 / life-year |
Hedonic Wage-Risk Value of a Statistical Life (VSL) Formula
Always verify the denominator scale (per 100,000 vs per 10,000 full-time equivalents — a 10x unit slip is the #1 regulatory spreadsheet error!).
=LET(dw_yr, B2, dr_100k, B3, IF(OR(dw_yr <= 0, dr_100k <= 0), "Invalid VSL Input", ROUND((dw_yr / dr_100k) * 100000, 2)))Discounted Real-Annuity Value of a Statistical Life-Year (VSLY) Formula
Branch cleanly on r = 0 so sensitivity tables never trigger #DIV/0! when testing undiscounted life-years.
=LET(dw_yr, B2, dr_100k, B3, t_rem, B4, r_rl, B5, IF(OR(dw_yr <= 0, dr_100k <= 0, t_rem <= 0, r_rl < 0), "Invalid VSL Input", LET(vsl_v, (dw_yr / dr_100k) * 100000, vsly_v, IF(r_rl = 0, vsl_v / t_rem, (r_rl * vsl_v) / (1 - ((1 + r_rl)^(-t_rem)))), ROUND(vsly_v, 2))))Try the example
Use the original values or change them to test your understanding.