# Discount Rates as Policy Choices A dollar of benefit fifty years from now is worth less than a dollar today. Cost-benefit analysis handles this by discounting: dividing future values by `(1 + r)^t`, where *r* is the discount rate and *t* is years out. The exponent is the whole story. **Discounting is exponential, so small differences in *r* produce enormous differences over long horizons — and every policy whose benefits arrive decades later is decided by this parameter rather than by any fact about the policy.** ## The arithmetic $1 million arriving in 100 years, in present-value terms: | Discount rate | Present value | |---|---| | 1% | ~$370,000 | | 3% | ~$52,000 | | 7% | ~$1,150 | At 7%, a century of future benefit is worth about a tenth of a percent of its face value. **Any regulation whose payoff is intergenerational fails cost-benefit analysis at a 7% discount rate almost regardless of how large the payoff is.** Nothing about the regulation determined that. The exponent did. ## Where the numbers came from Federal regulatory analysis under OMB Circular A-4, administered through the [[Office of Information and Regulatory Affairs]], long directed agencies to present results at **3% and 7%**. The 7% figure was intended to approximate the pre-tax return on private capital — the opportunity cost of resources drawn out of the private sector. The 3% figure approximates the rate at which individuals trade present for future consumption, proxied by returns on low-risk government securities. Both have defenders. But they answer different questions, and the choice between them is not resolvable by measurement: - If the question is *what else could this capital have earned*, a market-return rate is arguable. - If the question is *how much do we owe people who do not exist yet*, market returns are not obviously relevant at all. Future generations are not parties to the transaction and cannot bid. That second point is why the discount rate is genuinely an **ethical parameter wearing a financial costume.** A high rate is a statement that the distant future counts for very little. Stated that way it would be contested. Stated as a technical assumption in an appendix, it is not. ## The climate case This is where it bites hardest. The costs of emissions abatement are near-term; the benefits are spread across centuries. The social cost of carbon — the dollar damage per additional ton — is therefore almost entirely a function of the discount rate chosen. The Stern Review (2006) used a very low rate on explicitly ethical grounds, arguing that discounting future welfare merely for being future is indefensible, and derived a large social cost of carbon implying aggressive immediate action. William Nordhaus used a higher, market-calibrated rate and derived a much smaller figure implying gradual action. **Both were doing the arithmetic correctly.** The disagreement was entirely about the parameter, and it was a disagreement about intergenerational obligation, not about climate science or economics. Successive American administrations have revised the social cost of carbon sharply up and sharply down. Very little of that movement reflected new physical science. Most of it was discount-rate selection and the choice between domestic-only and global damages. ## The pattern Discounting is the clearest available instance of the [[Mathematics and Power Hub]] thesis, because the value judgment is not merely hidden — it is *encoded as a number in a spreadsheet cell*, where it acquires the appearance of a technical input and becomes nearly impossible to contest politically. There is no hearing on the discount rate. There is no vote. There is a footnote. Paired with the treatment of mortality benefits (see [[The Value of a Statistical Life]]), discount-rate selection determines the outcome of essentially all federal regulatory cost-benefit analysis on long-horizon questions, and both parameters are set administratively. ## Related [[The Value of a Statistical Life]] · [[Dynamic Scoring]] · [[CBO Baselines and Scoring Windows]] · [[Rate Versus Level]] · [[Office of Information and Regulatory Affairs]] · [[Climate Change]] · [[Deregulation]] · [[Mathematics and Power Hub]]