A shilling of benefit next year is worth less than a shilling today, so future costs and benefits are discounted to present value before they are summed. The rate at which we discount — the social discount rate (SDR) — is the single most consequential and contested number in CBA: for a long-lived project, the choice of rate can change the answer entirely. This module is about getting it right, or at least being honest about it.
Why discount at all?
- Time preference — people (and societies) prefer benefits sooner rather than later; a pure rate of impatience.
- Opportunity cost of capital — resources invested in the project could instead earn a return elsewhere, so future benefits must clear that hurdle.
- Growing consumption — if the economy grows, future people will be richer, and an extra shilling means less to a richer person (diminishing marginal utility of consumption), so future benefits accruing to richer future people are weighted less.
The Ramsey formula
The social discount rate, decomposed
Frank Ramsey's framework (1928) gives the SDR as: r = δ + η · g • δ (delta) = the pure rate of time preference — society's impatience, the rate at which we discount future welfare just because it is in the future. (Ethically contested: should a future person's welfare count less merely because they are later?) • η (eta) = the elasticity of marginal utility of consumption — how fast the value of an extra shilling falls as people get richer (also a measure of inequality aversion). • g = the expected growth rate of per-capita consumption. The η·g term says: if future people will be richer (g > 0), discount their benefits more, by an amount that depends on how much less an extra shilling means to them (η). The formula separates the ethical parameters (δ, η) from the empirical one (g), which is what makes the discount-rate debate tractable — most disagreement is about δ and η, not g.
Prescriptive versus descriptive
How should δ and η be set? Two camps. The descriptive view: read the discount rate off observed market behaviour — the returns people actually require, the market interest rate — on the grounds that appraisal should reflect society's revealed preferences and the real opportunity cost of capital. This yields higher rates (say 5–10%). The prescriptive view: derive the rate from ethical first principles, arguing that a pure time-preference rate δ that discounts future generations' welfare is unethical (why should a person born later count less?), so δ should be near zero, yielding a low rate (1–3%). The choice is not technical; it is a value judgement about how to treat the future, and it cannot be settled by data alone.
The climate flashpoint
Nowhere does the discount rate matter more than climate change, where costs are borne now and benefits accrue over centuries. The Stern Review (2007) used a near-zero pure time-preference rate (δ ≈ 0.1%, on the prescriptive ethical ground that future generations matter equally), yielding a low discount rate and a strong case for aggressive, immediate action. William Nordhaus used a higher, market-based descriptive rate, yielding more gradual action. The two reached very different policy conclusions from largely the same climate science — because they chose different discount rates. The Stern-Nordhaus debate is the clearest demonstration that the SDR is where ethics, not just economics, decides the answer. Whenever a long-horizon CBA reaches a strong conclusion, check the discount rate first.
Declining discount rates
For very long horizons, theory and practice increasingly favour a discount rate that declines with time rather than a constant rate. The argument (Weitzman; the UK Green Book's schedule): under uncertainty about the future rate, the certainty-equivalent discount factor is dominated in the far future by the lowest possible rates, so the effective discount rate falls as the horizon lengthens. Practically, the UK Green Book applies 3.5% for years 0–30, falling in steps to 1% beyond 300 years. Declining rates raise the present value of far-future costs and benefits (climate, nuclear waste, long-lived infrastructure) relative to constant exponential discounting, partially answering the charge that conventional discounting renders the distant future worthless. For most ordinary projects (decades, not centuries) a constant rate is fine; for the very long-lived, declining rates matter.
Exercise
A government appraises a large coastal sea-wall that costs heavily now and yields benefits (avoided flood damage) spread over the next 150 years, rising as sea levels rise. At a 3% discount rate the NPV is strongly positive; at an 8% rate it is negative. (1) Explain why the discount rate is decisive for this project specifically. (2) Use the Ramsey formula to lay out what would justify the low (3%) versus high (8%) rate. (3) Frame the choice as the prescriptive-vs-descriptive debate and connect it to Stern-Nordhaus. (4) Explain how a declining discount-rate schedule would affect this appraisal and why it might be appropriate.