Climate Economics & Benefit-Cost Policy
Ramsey Social Cost of Carbon (SCC) Discounting Formula
Calculate the closed-form Social Cost of Carbon SCC = D_0 / (rho + (eta - 1)*g + phi) and quantify why Nordhaus (rho = 1.5%) vs Stern (rho = 0.1%) discounting shifts carbon prices 2.5x!
Demystify the Nordhaus vs Stern climate-policy debate with the Ramsey SCC formula!
Why do rigorous integrated assessment models produce Social Cost of Carbon (SCC) estimates ranging from $90/tCO2 to $225+/tCO2 on the SAME physical climate sensitivity? Golosov, Hassler, Krusell, and Tsyvinski (2014) and William Nordhaus showed why: if 1 ton of CO2 causes current annual GDP-proportional marginal damage D_0 ($/tCO2/yr), decays from the atmosphere at effective rate phi >= 0, while per-capita output grows at g >= 0 under Ramsey discount rate r_Ramsey = rho + eta * g (pure time preference rho >= 0, inequality/risk aversion eta > 0), output growth g offsets -g of discounting — leaving Net Effective Damage Discount Rate r_net = rho + (eta - 1) * g + phi and exact Present-Value Social Cost of Carbon SCC = D_0 / (rho + (eta - 1) * g + phi)!
Test BOTH famous calibrations on Initial_Annual_Damage_D0 = 3.60 $/tCO2/yr (B2), Growth_g = 0.02 (B5 = 2.0%/yr), and Carbon_Sink_Decay_phi = 0.015 (B6 = 1.5%/yr): under Nordhaus market-calibrated parameters rho = 0.015 (B3 = 1.5%) and eta = 1.5 (B4), r_Ramsey = 0.0450 (4.50%), r_net = 0.015 + 0.5*0.02 + 0.015 = 0.0400 (4.00%), and SCC = 3.60 / 0.0400 = 90.00 $/tCO2! Now switch to Nicholas Stern’s prescriptive parameters rho = 0.001 (0.1%) and eta = 1.0: r_net drops to 0.001 + 0 + 0.015 = 0.0160 (1.60%), jumping SCC 2.5x to 3.60 / 0.0160 = 225.00 $/tCO2!
| Climate Discounting Benchmark (D_0=3.60, g=2.0%, phi=1.5%) | Ramsey r & Net Effective r_net | Social Cost of Carbon ($/tCO2) |
|---|---|---|
| Nordhaus DICE Calibration (rho=1.5%, eta=1.5) | r = 4.50% | r_net = 4.00% | 90.00 $/tCO2 |
| U.S. EPA Near-Term ~2.0% Ramsey Benchmark (rho=0.5%, eta=1.25) | r = 3.00% | r_net = 2.50% | 144.00 $/tCO2 |
| Stern Review Calibration (rho=0.1%, eta=1.0) | r = 2.10% | r_net = 1.60% | 225.00 $/tCO2 (2.5x Nordhaus!) |
Ramsey Consumption Discount Rate r_Ramsey = rho + eta * g Formula
Validate D_0 > 0, rho >= 0, eta > 0, g >= 0, and phi >= 0.
=IF(OR(B2 <= 0, B3 < 0, B4 <= 0, B5 < 0, B6 < 0), "Invalid SCC Input", ROUND(B3 + B4 * B5, 4))Closed-Form Growth-Adjusted Social Cost of Carbon SCC Formula
Guard convergence r_net = rho + (eta - 1) * g + phi > 0 (if eta < 1 with high growth and zero decay, growing damages outrun discounting!).
=LET(d_0, B2, rh_t, B3, et_u, B4, g_pc, B5, ph_d, B6, IF(OR(d_0 <= 0, rh_t < 0, et_u <= 0, g_pc < 0, ph_d < 0), "Invalid SCC Input", LET(r_nt, rh_t + (et_u - 1) * g_pc + ph_d, IF(r_nt <= 0, "Non-Convergent SCC (r_net <= 0)", ROUND(d_0 / r_nt, 2)))))Try the example
Use the original values or change them to test your understanding.