Long-Run Discount Rates

Established The prize is one number, and it decides whether any century-scale project has a positive present value at all. A dollar of benefit arriving in 100 years is worth 13.8 cents at 2%, 3.2 cents at the 3.5% the UK Treasury’s appraisal guidance has used, and 0.115 cents at the 7% the 2003 US regulatory circular put beside its 3%. Same benefit, same physics, a factor of about 120 between the top and the bottom of what a Western treasury might hand an analyst. Nothing else in a long-horizon appraisal moves the answer that far.

Established The disagreement is wider than the guidance, because the experts are wider than the guidance. A survey of 197 economists returned a median recommended social discount rate of 2.00% and individual answers spanning 0% to 10%. At a hundred years those endpoints differ by a factor of about 13,800. The same project is either the best thing a government could buy or a rounding error, and which it is turns on a parameter the profession has never settled.

Frontier What is new is that the number can be measured instead of asserted. If the price gap between a 100-year leasehold and an otherwise identical freehold really is the present value of rent starting a century out — the contested step, and section 5 says why — then UK and Singapore housing markets put the discount rate on 100-year claims below 2.6%, and bond series reaching back to 1694 put the long-run real rate at 1.69% for the UK and 2.21% for the US. Those are observations, not positions. A 3.5% appraisal rate is then not a cautious default; it is a number the only two markets that price the far future do not support.

Speculative The gain is real and it is not evenly held. Lowering a regulatory rate from 3% to 2% can by itself more than double the social cost of carbon, and the fall in equilibrium real rates since the 1990s has at least doubled it again. The beneficiaries of that arithmetic are cohorts with no bid in any market, and the cost falls on identifiable people now. That asymmetry is why the parameter is fought over rather than estimated, and section 11 argues it cannot be settled by measurement at all.

A discount rate converts a future quantity into a present one. Everything downstream — a sea wall, a repository, a stockpile, an endowment, a carbon price — is an argument about what that rate is, whether or not anybody says so. This brief is about the rate itself: what has been measured, on what data, and where measurement stops and choice begins.

Established The standard decomposition is the Ramsey rule: the consumption discount rate equals the pure rate of time preference plus the elasticity of marginal utility times the growth rate of per-capita consumption. Written r = δ + ηg. The UK guidance instantiates it directly: 0.5% + (1.0 × 2.0%) = 2.5%, with a further 1.0% for systemic and catastrophic risk to reach the published 3.5%.

Established The three terms are different kinds of thing, and this is the source of most of the confusion. Growth, g, is a forecast. The elasticity η is estimable in principle, though it also carries an inequality-aversion reading. The pure rate of time preference δ is a statement about how much a planner cares about a person born later, and no dataset contains it.

Established The field’s own name for the split is descriptive versus prescriptive. The descriptive camp reads the rate off markets and observed savings behaviour; the prescriptive camp derives it from an ethical premise. Both are internally coherent. They give answers differing by a factor of 100 over a century.

Frontier The measurement problem the brief is built around is that no liquid market prices a claim a century out. Conventional government bonds run 30 to 50 years. Two workarounds exist and both are indirect: very long property leases, and very long time series of short bonds from which a long-run rate is inferred.

Established Three questions get run together and this brief keeps them apart. What rate people apply to distant claims, which is measurable. What rate a government should apply, which is not. And what rate makes a project pass, which is the one most often being answered.

Established What this brief does not own. Whether capital can be mobilised at civilizational scale, through what instruments, and what the historical record shows belong to Civilization Scale Investment, which already records the Stern–Nordhaus exchange as a dispute over a parameter. That brief owns the instrument; this one owns the rate, the evidence for its value, and the point at which evidence runs out.

Speculative This is a frontier topic rather than a settled one because the best measurements are recent, few, and drawn from an asset class with unusual contractual features. The leasehold literature is barely a decade old in its modern form, the bond-based estimates rest on series that survive because their issuers did, and the expert surveys measure opinion rather than the world. That is the whole evidence base, and section 3 lays it out.

Established The anchor result is a price gap between leaseholds and freeholds in two housing markets. Giglio, Maggiori and Stroebel exploited a contractual accident: in England and Wales and in Singapore, residential property is sold either as a freehold, which is perpetual, or as a leasehold, a pre-paid tradable claim of between 99 and 999 years. The price difference between two otherwise identical properties is the present value of perpetual rent starting at expiry. They used the universe of transactions: over eight million in the UK for 2004–2013, roughly 380,000 Singapore private residential sales for 1995–2013.

Established The headline number is an upper bound, not a point estimate, and it is routinely quoted as the latter. The paper’s own words: 100-year leaseholds are valued at more than 10% less than otherwise identical freeholds, “implying discount rates below 2.6% for 100-year claims”. The commission for this brief said “around 2.6%”; the paper says below, and the difference matters when the figure is set against a 2% official rate.

Established The discount is a ladder, and its shape carries more than the single number. The authors’ own review reports discounts to freehold of roughly 16% at 80–99 years remaining, about 10% at 100–124, about 8% at 125–149, about 3% at 150–300, and essentially nothing at 700 years and beyond. A claim with 700 years to run trades at the price of a claim with no end at all — which kills both the rational-bubble story and the mortgage-financing-friction story in one observation.

Established The rental test is the paper’s strongest internal check. If leaseholds were simply worse properties they would rent for less. They do not: “no significant and systematic difference between rental rates of freeholds and leaseholds of different maturity”. The price gap is not a gap in the flow of housing services.

Established The obvious contaminants were checked and reported small. Ground rents on English leaseholds are “small to non-existent”, with costs concentrated in the up-front price. On clientele, weekly income of leasehold-owning households sits between £3 below and £8 above that of freehold owners, reported as insignificant.

Frontier The fitted discount function is not exponential, and this is under-reported. The authors calibrate a hyperbolic-exponential form, R(0,t) = e^(−ρt)/(1+κt), setting κ to 12% and ρ to 1.42%. That gives a very short-run rate of ρ + κ = 13.42%, a downward-sloping term structure, and a long-run per-period rate approaching 1.42%. The 2.6% is a point on a declining curve at 100 years, not a constant anybody estimated.

Established An independent historical replication broadly agrees at long horizons. Bracke, Pinchbeck and Wyatt priced 5,944 leasehold properties in prime central London over 1987–1991 and report that “very short leases imply discount rates of around 5-6%, whereas long leases, close to 100 years left, imply discount rates close to 3%”. For a later sample: “our estimate of 2% at 100 years from this exercise sits comfortably with the GMS finding of 1.9%”.

Frontier The same paper carries the most damaging fact in this literature for anyone who wants 2.6% to be a preference parameter. The measured rate moved: “The average 1987-1991 rate (4.1%) being significantly higher than the average rate in 2004-2013 (2.5%)”. Same country, same contract, same asset class, two decades apart, and the implied very-long-run rate fell by more than a percentage and a half. A deep parameter of household patience should not track the interest-rate cycle that closely.

Established That study also shows what a cleaner identification costs. To avoid statutory lease extension the authors exclude all sales after the Leasehold Reform, Housing and Urban Development Act 1993, and drop houses enfranchisable under the 1967 legislation. The price is under six thousand properties in one expensive district, with only around 15% of price observations verified against other sources.

Frontier A second Singapore study finds the term structure declines much further than the headline suggests. Fesselmeyer, Liu and Salvo, on privately developed apartments, estimate rates that “decline over time and, to accommodate the observed price differences, fall to 0.5–1.5% p.a. by year 400” — a third to a fifth of the 100-year rate.

Frontier A third Singapore study, using 79,191 leasehold and 77,270 freehold transactions from January 1995 to May 2019, contains a result hard to reconcile with a pure discounting story. Alongside a clean elasticity — “a 1% increase in the remaining lease increases prices by 1.46%” — it reports that “age has negative effects on freehold property prices but positive effects on leasehold prices”, pointing at redevelopment value capitalised into old leaseholds. A leasehold price carries at least two options a freehold does not, in opposite directions.

Frontier A different city with a different lease contract gives roughly double the rate. Gautier and van Vuuren, on Amsterdam, where privately owned land coexists with municipal land lease, find “houses on privately owned land are, on average, 11–13% more expensive”, each extra year before the lease obligation bites adds roughly 0.2% to price, and the implied annual rate is about 4%. The Dutch contract differs, but the gap between 4% and below 2.6% is not small.

Frontier The most recent English evidence says the leasehold coefficient is a bundle, not a horizon. A 2026 study applying a high-dimensional fixed effects hedonic model to five million HM Land Registry transactions spanning 2000–2025 finds “a robust reduced-form leasehold valuation discount of 17.33% at the sample mean”, with Greater London showing “a valuation penalty (32.65%) more than double that observed elsewhere in England and Wales”.

Frontier Its time profile is the tell. The discount widened sharply after 2016 and peaked in 2022, concentrated in multi-unit flats and coinciding with the building-safety cladding crisis. A discount rate on 100-year cash flows should not spike because of a cladding scandal; what moved was the value of divided control rights.

Established That study cannot separate the two because it does not observe lease length. Its appendix records the finite-duration mechanism as “Unobserved (lease length not in data)” and “Bundled into tenure coefficient”. The central data gap in the field is administrative: the register records tenure, not term.

Established The second independent line of evidence is three centuries of bond prices, and it lands in the same region. Farmer and co-authors fit an Ornstein–Uhlenbeck model to UK ten-year bond yields annually from 1694 to 2012 (309 records) and US ten-year yields from 1820 to 2012 (183 records), plus three-month bills. “The mean long-run rate is r∞ = 1.69% for the UK and 2.21% for the US”, with standard deviations near 0.45% and 5%–95% quantiles of 0.76–2.63% for the UK and 1.35–3.07% for the US.

Frontier Their comparison is pointed. “The value of 1.4% used by Stern is less than a standard deviation from our estimated long-run return rate for the UK, and less than two standard deviations of the estimated value for the US.” The rate attacked for a decade as an ethical imposition is, on three centuries of British bond prices, within the noise.

Established The market anchor has moved down by a measured amount. Bauer and Rudebusch estimate the equilibrium real rate over 1990–2019 and report a decline of 1.2 percentage points for the one-year rate, from 1.9% to 0.7%, and 1.8 points for the ten-year, from 3.1% to 1.3%.

Established The consequence for climate arithmetic is large and they state it plainly. “we estimate that the decline in r* and resulting downward shift in SDRs since the 1990s has caused the SCC to at least double in size”. One specification runs from $218.8 to $396.7 per ton of CO2 between 1990 and 2019, an 81% increase; another from $387.6 to $963.1, a 149% increase.

Established Official guidance moved too, then partly back. The 2003 US circular paired a 3% consumption rate with a 7% capital rate, both flat. The November 2023 revision set the social rate of time preference at 2.0%, declining in tenths to 1.1% for 2164–2172, with values “updated every three years”, and replaced the 7% capital rate with a shadow price of capital. Two economists involved note that “moving from a discount rate of 3 to 2 percent can itself more than double the social cost of carbon”.

Established The US then reversed course by executive action rather than by evidence. An executive order of 20 January 2025 directed agencies to use the 2003 guidance; a memorandum of 5 May 2025 directed them to stop factoring climate-related economic damage into regulation and permitting except where statute requires; a departmental working group published a report on 29 July 2025 arguing the social cost of carbon is too high, drawing over 59,000 comments; and on 30 January 2026 a district court held that group to be a federal advisory committee subject to the relevant statute. The 2023 circular has not been formally rescinded.

Established The UK reopened its own rate in 2026. A Treasury-commissioned discount rate review dated 30 June 2026, by Freeman and Groom, recommends δ = 0.5%, μ = 1.25 and g = 1.5%, so that “the Ramsey Rule itself gives a risk-free STP rate of 0.5% + 1.25 × 1.5 = 2.375%”, against the existing 2.5% plus a 1% premium giving 3.5%.

Frontier Its most consequential move redefines the risk term rather than the patience term. It treats the catastrophe premium as “an adjustment for systematic risk and not specifically for catastrophic and systemic risk”, and with rare-disaster risk included estimates that adjustment at minus 0.5%, taking the risk-free rate to 1.875%.

Established It proposes an explicitly declining forward schedule and a second, lower one for a class of projects. For standard projects, “3.0% up to 30 years, 2.5% from 31–75 years, and 2.25% from 76–125 years”. For social insurance projects — pandemic protection, defence — “1.5% up to 30 years, 1.0% from 31–75 years, and 0.75% from 76–125 years”. Beyond 125 years it recommends formal welfare analysis rather than a published rate.

Established Across rich countries official rates span a factor of more than six and most now decline. The review’s international table records Australia at 7% falling to 3.7% beyond 301 years; Denmark 3.5% to 1.5% after 70; the Netherlands 2.8% to 1.8% beyond 35; Norway 4.0% to 2.0% beyond 75; Ireland 4.0% to 1.5% for 276 and beyond; New Zealand 2% falling to 1.0% beyond 100 alongside an 8% opportunity-cost rate; France 3.2% to 2070; Canada 3% and Sweden 3.5%, both flat; Germany a maturity-matched 1.2% nominal.

Established The expert distribution is the last piece, and it measures opinion rather than the world. Drupp, Freeman, Groom and Nesje surveyed 197 experts and report a mean recommended rate of 2.27%, a median and mode of 2.00%, “with a range from 0 to 10 percent”. The pure rate of time preference has a modal value of zero, a mean of 1.1% and a median of 0.5%; the elasticity of marginal utility a mean of 1.35 and a median and mode of 1; expected growth a median of 1.6%. Seventy-seven per cent include 2% in their acceptable range and “92 percent of experts report that they would be comfortable with a SDR somewhere in the interval of 1 percent to 3 percent”. And the formula everyone teaches is not the one most of them use: “only 35 percent of respondents can be reconciled with any of the representations of the Ramsey Rule”.

Established Where the record leaves the number. Two independent asset classes, housing leases and three centuries of bonds, put the long-horizon real rate between about 1.4% and about 2.6%. Expert opinion centres on 2.00%. Official guidance in use in 2026 spans 1.2% to 8%. The measured evidence sits at the bottom of the policy range, and the gap is not evidentiary — it is a disagreement about whether market evidence is the right input at all.

Frontier The first open question is whether a long leasehold is really a freehold minus a maturity. The identifying assumption is that the price gap is the present value of a perpetuity starting at expiry and nothing else. Every contaminant tested so far was reported small, and the 700-year result is a strong falsification test. But the 2026 English study shows the coefficient absorbing things with no horizon interpretation.

Frontier The sharpest version is that the leaseholder does not hold a dated claim but a claim plus a statutory option to extend it. English leaseholders can extend for a premium, with disputes going to a valuation tribunal, and the original authors note that “court enforced settlements have occurred at estimated discounts favorable to leaseholders compared to those estimated based on market values”. A statutory formula inside the price gap is a policy variable, not a preference.

Frontier Marriage value makes the statutory term discontinuous at 80 years. Under the 1993 Act, for leases below 80 years a share of the value created by combining leasehold and freehold interests must be paid to the freeholder, sharply raising extension costs. A hedonic regression through that legal kink estimates a blend of discounting and statute.

Frontier The second question is whether the rate is a parameter or a state variable. The 4.1% to 2.5% movement in one London market across two decades, and the 1.2 to 1.8 point fall in equilibrium real rates over 1990–2019, both point at the second. If the very-long-run rate is a slow-moving function of the macroeconomy, reading a century-scale appraisal rate off a 2004–2013 housing sample is a category error.

Frontier The third is whether the declining term structure is a theorem or an artefact. The theoretical case comes from three directions: uncertainty about the rate itself, uncertainty about growth with correlated shocks, and disagreement between people.

Established The first route has a measured consequence. Newell and Pizer estimated certainty-equivalent schedules from US bond data: “If we use these rates to value consequences at horizons of 400 years, the discounted value increases by a factor of 7,000 based on the random walk model and by a factor of 30 based on the mean-reverting model — both relative to conventional discounting.” The choice between two reasonable time-series models changes a 400-year valuation by more than two orders of magnitude.

Frontier The second route is the one an expert panel endorsed. Thirteen economists including Arrow, Nordhaus, Weitzman, Gollier and Pindyck concluded that “the arguments in favor of a DDR are compelling and thus merit serious consideration by regulatory agencies in the United States”, on the ground that a declining certainty-equivalent rate follows from the Ramsey formula when consumption growth is uncertain and shocks are correlated. That panel included both principals of the Stern–Nordhaus dispute.

Frontier The third route derives hyperbolic discounting from disagreement rather than psychology. Heal and Millner show a planner aggregating heterogeneous individual rates must have a representative rate converging on the lowest in the population, and that with gamma-distributed time preference the aggregate is exactly hyperbolic — licence to “reinterpret the classic behavioral models of hyperbolic discounting…in a normative light”.

Frontier The strongest case against declining rates is not that they are ad hoc but that they are inconsistent. Gollier shows the gamma-discounting construction “is in fact equivalent to the Local Expectations Hypothesis, a hypothesis globally rejected in empirical finance”, and that when growth shocks persist, gamma discounters are time-inconsistent and short-termist because they ignore the correlation between future consumption and spot rates — the opposite of what the method is adopted to achieve.

Frontier The two protagonists closed most of the gap themselves. The Weitzman–Gollier puzzle — two apparently equivalent ways of handling an uncertain rate giving opposite answers — was resolved jointly: once agents optimise consumption plans, the long-run rate declines toward its lowest possible value.

Speculative Whether the time inconsistency matters in practice is unsettled. A declining schedule means a planner in 2100 will not want to honour the 2026 plan. Whether renegotiation proofness binds a real government is institutional, and Long-Term Institutions owns it.

Frontier Fat tails may dominate the discount rate entirely. Weitzman’s argument is that low-probability, high-impact outcomes are not a footnote to climate cost-benefit analysis but its main term. If expected loss is driven by a tail, the rate applied to the central case is second order, and the apparatus of this brief answers a question that is not binding.

Frontier The bounding result is the honest summary of the theory. Freeman and Groom, examining how much the declining-rate arguments pin down, find that “even with considerable agreement on these features, these bounds are widely spread for horizons beyond 75 years”, and that the resulting present values “typically remain so imprecise as to provide little practical guidance”. The people who built the theory report that it does not deliver a number.

Speculative Finally, the estimates rest on survivors. The UK series runs from 1694 because the issuer never defaulted or was conquered. A long-run rate estimated from the institutions that lasted is conditioned on lasting, and no correction for that appears in the work read for this brief.

Established The binding constraint is that the transaction register does not record the term. The 2026 English study had five million sales and could not use them for horizon estimation because lease length is not in the data. The variable that would turn the largest property dataset in the country into a discount-rate instrument is an administrative field nobody has been asked to publish.

Established The clean samples are therefore small. The historical London study that does control for extension rights works with 5,944 leasehold properties in one district, only around 15% of whose price observations were verified against other sources. Precision and cleanliness trade against each other here and no dataset delivers both.

Frontier The second constraint is that identification depends on a legal regime that keeps changing. Lease extension rights, marriage value, ground rent reform and enfranchisement have all been legislated in England since 1967, and each change moves the price of a short lease for reasons unrelated to discounting.

Established The third is that no liquid instrument prices a claim beyond about a century. Bond-based estimates infer a long-run rate from short maturities via a time-series model, which is why model choice does the work: a random walk and a mean-reverting process, both defensible, give 400-year valuations differing by more than two orders of magnitude.

Established The fourth is measuring the real rate itself over long spans. Real UK three-month rates are negative 32% of the time and ten-year rates 38% of the time, which rules out the standard lognormal machinery, and inflation indices over three centuries are themselves reconstructions.

Frontier The fifth is that leasehold prices carry options in both directions. Redevelopment and collective-sale value is capitalised into old Singapore leaseholds — building age raising leasehold prices while lowering freehold prices is hard to read any other way — while divided control rights subtract value in England. Two option values of opposite sign sit inside the coefficient being read as a discount rate.

Speculative The sixth is thin trading at the maturities that matter. The result that leases beyond 700 years trade at freehold prices is decisive only if those leases trade often enough to be priced, and no paper read for this brief reports the count of 700-year-plus transactions underlying that comparison.

Frontier The seventh is not a data problem. Even with perfect measurement of what buyers do, the step from a household’s revealed rate to a planner’s rate is normative, and the expert survey shows the profession does not take it: the modal pure rate of time preference was zero while market rates were not.

Established The eighth is institutional churn on the output side. A rate set in November 2023, directed to revert in January 2025 and still unrescinded in 2026 is not a parameter a fifty-year appraisal can rest on; Public Policy Foresight carries the consequences.

Established The first dependency is an estimate of the equilibrium real rate, because that is the anchor. Bauer and Rudebusch make the claim explicit: the steady-state real interest rate is the fundamental anchor for market-based social discount rates, so every market-based schedule inherits the uncertainty in r* estimation wholesale.

Frontier The second is a credible long-run growth forecast, and the 2026 UK review moved it. Its recommendation cuts expected per-capita consumption growth from 2.0% to 1.5%, taking 0.5 percentage points off the Ramsey rate before any argument about patience. A discount rate is only as good as a century-ahead growth projection, and nobody has one.

Frontier The third is an identified estimate of the elasticity of marginal utility, which the same review moved from 1.0 to 1.25. The expert survey shows why that is contestable: a mean of 1.35, a median and mode of 1, and recommendations the authors describe as “widely dispersed”. The parameter does double duty as risk aversion, inequality aversion and consumption smoothing.

Established The fourth is damage estimation, because the rate only matters against a stream. The social cost of carbon figures that move with it — $218.8 to $396.7 in one specification, $387.6 to $963.1 in another — are model outputs whose damage functions are contested independently. Climate Overshoot and Lock-In and Carbon Removal Verification carry that side.

Established The fifth is a linked property dataset. Lease term must be joined to transaction price at scale before the largest samples can speak to horizon. This is the one dependency that is purely administrative and could be discharged in a year by a land registry publishing a field it already holds.

Frontier Nothing on this map is blocking the parameter. There is no missing physical measurement, no instrument to build, no theoretical result anybody is waiting on. What is missing is a data join, a natural experiment nobody has exploited, and a normative decision evidence cannot make. Section 14 types those honestly.

Frontier The decisive experiment is a matched leasehold–freehold sample in which the maturity extension is exogenous to property quality, replicated in a second very-long-claim asset class. Everything the field rests on is a hedonic comparison across properties differing in tenure, and the strongest objection is that tenure correlates with unobserved quality, contractual burden and institutional risk. The test that settles it does not compare properties at all: it compares the same property before and after its term changes, for a reason unrelated to the property.

Frontier The variation exists and is legal rather than economic. English statute has repeatedly changed who may extend a lease, on what formula and at what threshold, from the 1967 enfranchisement regime to the 1993 Act and the reforms that followed. Each change is a shock to remaining term assigned by eligibility rather than by the state of the building.

Established The design is standard and has never been run at scale on this question. Take repeat sales of the same unit, identify the extension event, and estimate the price change against a matched control of ineligible or not-yet-extended units. The historical London study came closest and went the other way, excluding every post-1993 transaction to avoid extension effects: it treated as contamination the thing that is actually the instrument.

Established The prediction is sharp and falsifiable. If the leasehold gap is a discount rate, extending a 90-year lease to 990 years should raise its price by the freehold gap for a 90-year term and no more — roughly the 10% to 16% range reported at those maturities — and the implied rate should match the cross-sectional estimate. If the gap is institutional risk, extension changes the term but not the divided control, and the price should move by materially less.

Frontier The 2026 English evidence makes the second outcome a live possibility rather than a straw man. A tenure discount of 17.33% that widens after 2016, peaks in 2022, reaches 32.65% in London and concentrates in flats during a building-safety crisis is not behaving like a horizon effect. If extension events move price by a fraction of the cross-sectional gap, the 2.6% figure bounds something that is not a discount rate.

Established The replication leg is already half done, in bonds. The long bond series give a long-run real rate of 1.69% for the UK and 2.21% for the US with standard deviations near 0.45%, from an asset with no control rights, no maintenance obligation, no redevelopment option and no statutory extension formula. Two asset classes with disjoint contamination sets agreeing within a percentage point is stronger evidence than either alone.

Frontier The bond leg has its own identifying problem. The long-run rate is a model extrapolation from short maturities, and model choice does visible work: random walk and mean-reverting specifications differ by a factor of more than 200 in the 400-year valuation. A pre-registered horse race scored out of sample would make that choice evidential.

Frontier A third replication is available in Singapore. The two existing studies disagree informatively — one finding rates falling to 0.5–1.5% by year 400, the other that building age raises leasehold prices. Estimating both on the same transactions would separate the redevelopment option from the horizon.

Speculative A fourth test costs nothing and nobody has published it. The 2023 US revision and its 2025 reversal are a policy natural experiment: the same agencies, the same projects, appraised at 2% and then at 3% and 7% within two years. Comparing which projects flipped sign would measure the real-world elasticity of decisions to the parameter rather than the arithmetic elasticity of present values.

Established A fifth has just been run and its microdata should be released. The 2026 UK review surveyed academics and practitioners between 19 January and 27 February 2026 across thirteen questions on time-preference versus opportunity-cost approaches, Ramsey parameters, declining rates and risk premia. Publishing the response distribution would give the first directly comparable successor to the 197-expert survey.

Speculative What would not settle anything. Another calibration on the same UK transaction universe, another derivation of a declining schedule, another survey of the same population. The binding constraint is whether the leasehold gap is a horizon effect, and only an exogenous change in horizon answers it.

Frontier None of this is funded or scheduled. The statutory variation exists, the bond series are public, and the registry field that would make the English test possible is already in title documents. What is missing is somebody commissioning the join: not a hard experiment, an unrun one.

Established Implementing a declining rate is a forward-rate problem, not a spot-rate problem, and the 2026 UK review is explicit about it. Its schedule is stated as forward discount rates by band — 3.0% to 30 years, 2.5% from 31 to 75, 2.25% from 76 to 125 — which compound into a spot curve. Appraisal spreadsheets that apply a band rate to the whole horizon get the wrong answer.

Established The US schedule is a spot schedule by emission year and looks nothing like it, running 2.0% for 2023–2079 down in tenths to 1.1% for 2164–2172. Two countries can hold identical views about the far future and publish schedules that are not comparable line by line.

Established The capital side needs separate machinery. The shadow price of capital that replaced the 7% rate requires estimating how much of a project’s cost displaces investment rather than consumption — a harder empirical object than a discount rate, now load-bearing in US regulatory arithmetic.

Frontier The risk adjustment is where the engineering is least settled. The UK review proposes a separate schedule for social insurance projects at 1.5%, 1.0% and 0.75% across the three bands, arguing that projects protecting against rare severe disasters have negative risk premia.

Established That second schedule is the most consequential engineering change on the table. A pandemic stockpile or defence capability appraised at 0.75% over 76 to 125 years rather than 3.5% flat goes from unfundable to obviously worth buying, on a risk classification rather than a new estimate of patience. Existential Risk Governance and Economic Resilience are the briefs whose arithmetic this rewrites.

Frontier Beyond 125 years the review declines to publish a rate at all, recommending formal welfare analysis instead. That is honest and operationally awkward: deep geological disposal, land-use commitments and archives sit past the point where guidance stops, and Nuclear Waste Solutions and Civilizational Archives both need a number there.

Established On the measurement side the engineering is a data join, not an instrument. Term must be attached to price: in England by linking registered lease particulars to the price paid dataset, in Singapore by releasing remaining-lease length alongside the transaction record, which studies have already done at samples of 79,191 and 77,270 transactions.

Established The short-end market anchor is already published. The UK review takes the risk-free component from the Bank of England real yield curve, which “giv[es] a current rate of approximately 2%”, and concludes the risk-free component for maturities of 30 years or shorter should be 2%. The entire difficulty is beyond the longest traded maturity.

Speculative The instrument that would fix this does not exist. A liquid, indexed, very-long-dated claim would replace the whole inference apparatus with a price. Future Capital Markets owns whether such an instrument can be placed, and Civilization Scale Investment records what happened to the closest existing attempt.

Established Within this map, four briefs meet this one at defined seams. Civilization Scale Investment owns the instrument and the historical record of mobilisation; this brief owns the rate. Future Capital Markets owns tenor and intermediation. Long-Term Institutions owns whether a commitment made at a declining rate survives the planner who made it. Megaproject Governance owns whether appraised benefits arrive.

Established Three more depend on the output without contributing to the input. Climate Adaptation Finance, Nuclear Waste Solutions and Carbon Removal Verification each carry a benefit stream whose sign under appraisal is set here, and none can resolve it internally.

Frontier Outside the map the adjacent technical literatures are term-structure finance and real estate economics. Ornstein–Uhlenbeck processes, unobserved-components models of the equilibrium rate and certainty-equivalent schedules are standard fixed-income econometrics applied at horizons the field was not built for; hedonic pricing, repeat-sales indices and high-dimensional fixed effects supply the other half, and that field’s own worries about unobserved quality are exactly what decides whether a leasehold coefficient is a discount rate.

Speculative Behavioural economics is adjacent but less useful here than it looks. Hyperbolic discounting was built to describe individual present-bias over months; the version in this brief is derived from aggregation and is a statement about a planner, not a psychology. Importing experimental present-bias parameters into a century-scale appraisal is a category error the literature has mostly avoided.

Established Legal scholarship is adjacent in an unusual way: it is upstream of the measurement. The size of the leasehold discount depends on enfranchisement statute, marriage value thresholds, ground rent regulation and building-safety liability. The 2026 study reaching a 17.33% tenure discount is published in a law and economics journal, which is the right home for it.

Established Almost every number in this brief comes from a party with an interest, and the directions differ. The 2023 US rate cut was made by the office whose regulations benefit from a lower rate; the 2025 reversal by an administration whose deregulatory programme benefits from a higher one. Neither move came with a new estimate. Both are cited here for what they did.

Established Two sources used here are advocacy organisations and are weighted accordingly. A policy centre arguing for lower rates supplied the rescission timeline and the observation that a 7% rate devalues an effect 50 years out by more than 97%: the arithmetic is checkable, the framing is not neutral.

Established The UK review is commissioned work and its authors are participants in the literature it reviews. Freeman and Groom wrote the 2026 Treasury review, are two of the four authors of the 197-expert survey, and co-authored the bounding result showing the theory does not pin down a number beyond 75 years. That is less a conflict than an unavoidable feature of a field with a few dozen specialists.

Frontier The institutional question that matters is who may change the number. In the US it is the executive, and it has changed twice in three years by order rather than by evidence. In the UK it is the Treasury, advised by commissioned academics, on a roughly decadal cycle. The 2023 US circular’s commitment to restate values every three years is the only automatic revision rule in the guidance reviewed here.

Established Formal rescission is harder than direction. The 2023 circular stands unrescinded in 2026 even though agencies were directed in January 2025 to use the 2003 version, because proper rescission requires expert scrutiny under statutory peer review. The practical result is two live standards.

Frontier The international pattern is convergence in form and divergence in level. Australia, Denmark, the Netherlands, Norway, Ireland and New Zealand all publish declining schedules while Canada and Sweden remain flat, and headline rates span 1.2% to 8%. Adopting a term structure has proved much easier politically than agreeing a level.

Speculative The institutional design problem nobody has solved is insulation. A parameter changeable by executive order that changes appraised values by a factor of 100 over a century is a standing invitation to set the rate to reach the answer. Central bank independence is the obvious template and nobody has proposed its equivalent here; Long-Term Institutions and Scientific Advisory Institutions hold the comparable cases.

Frontier The evidence base is small enough to be a governance risk in itself. Two housing markets, two bond series, one expert survey and a handful of replications underpin a parameter used in every long-horizon appraisal in the rich world.

Established The choice of a social discount rate is not an empirical question and no measurement will make it one. The Ramsey decomposition makes the boundary visible: g is a forecast and η is estimable in principle, but δ is a statement about how much weight a planner gives to a person who does not exist yet. No dataset contains that number, and this brief does not adjudicate it.

Established The profession’s own distribution shows the disagreement is concentrated exactly there. In the 197-expert survey the modal recommended pure rate of time preference is zero — the Ramsey position — while the mean is 1.1% and the median 0.5%, and the authors explicitly report this does not confirm a claimed broad consensus for a zero or near-zero rate. The mode is an ethical stance; the mean is a compromise with observed behaviour.

Frontier The prescriptive case at its strongest. If δ is positive, a planner assigns less weight to a person purely because of when they were born. On three centuries of British bond prices the 1.4% rate this reasoning produced is less than one standard deviation from the estimated long-run return, so the ethical position is not even in tension with the UK market evidence.

Frontier The descriptive case at its strongest. A planner using a rate far below the return on capital will recommend projects a private investor would reject and, at scale, direct saving away from higher-return uses that would have made future people richer. The objection to a near-zero rate is not that the future does not matter but that the arithmetic implies savings rates no society has chosen.

Established Both sides sat on the same panel and agreed on the shape. Thirteen economists including the principals of the dispute jointly concluded the case for a declining rate is compelling. The disagreement is about the level of the near-term rate, not about whether the far future should be discounted more gently than the near.

Frontier The distributional question hidden inside η is rarely stated. A high elasticity says an extra unit of consumption matters much more to a poor person than a rich one. Raised for intergenerational purposes it lowers the weight on a richer future; applied within a generation it argues for redistribution now. The 2026 UK review raises μ to 1.25 for the first reason without discussing the second, and Wealth Distribution Systems is where that argument lives.

Established There is a measured distributional fact about who is being discounted. A policy brief arguing for the lower rate notes that applying a 7% rate to an effect 50 years out devalues it by more than 97%. Under that rate, effects on people alive today and in their seventies are worth about three cents on the dollar to the appraisal deciding whether to prevent them.

Speculative The symmetric objection deserves the same weight. A near-zero rate over a long horizon can justify very large present sacrifices for distant gains, and the people bearing them are alive, identifiable and frequently poorer than the future beneficiaries the arithmetic protects. Neither direction of error is obviously the safe one.

Frontier The step to zero is a real position and it appears in official guidance. A 2026 study of transport appraisal for Russia and post-Soviet countries recommends 3.2% for the first 60 years, with an interval of 1.7% to 4% and a 7.4% opportunity cost of capital, and zero beyond 60 years. That is defensible as intergenerational neutrality, and it also makes a long-lived benefit stream unbounded in present value, which is why most schedules decline to a floor instead.

Speculative The deepest normative problem is that the planner will not honour the plan. A declining rate is time inconsistent by construction, and renegotiation proofness is a claim about Pareto improvement, not about what a future government will do.

Established What this brief will say, and where it stops. The measured leasehold discounts are real and replicated. The identification is genuinely open. The declining shape has broad theoretical and official support. And the level a society writes into its guidance is a values decision the evidence constrains and does not determine. Anyone claiming the data settles it is overclaiming in whichever direction they prefer.

Established The parameter is upstream of every long-horizon commitment a civilization can make, and the leverage is arithmetic rather than rhetorical. At 2% a dollar in a century is worth 13.8 cents; at 7% it is worth 0.115 cents. A society setting the rate at the top of the published range has, by that act alone, made 99.2% of a century-out benefit disappear relative to one setting it at 2%.

Frontier The choice selects which projects are even proposed. Deep geological disposal, coastal realignment, seed and genetic archives, pandemic stockpiles, orbital debris remediation and multi-century land-use commitments all concentrate their benefits past the point where the rate dominates. At 3.5% they fail appraisal; at 1% they pass. The pipeline is shaped before any of them reaches a decision-maker.

Established The 2026 UK proposal shows how much of that is classification rather than economics. Moving a project from the standard schedule to the social-insurance schedule takes its 76-to-125-year forward rate from 2.25% to 0.75%. Same project, same evidence, a third of the discounting, decided by which list it is on.

Frontier The instability is as consequential as the level. An investor facing a parameter that went to 2% in November 2023 and was directed back to 3% and 7% in January 2025 prices the political risk, not the physics, and Civilization Scale Investment records what that does to the instruments.

Speculative There is a reflexive loop nobody has modelled. If the equilibrium real rate fell 1.2 to 1.8 points since 1990 partly through a scarcity of safe assets, and a lower rate justifies more long-horizon public investment, then acting on the measurement changes the quantity measured.

Frontier The distributional consequence runs opposite to the usual framing. A lower rate moves resources toward the future and away from the present, and the present includes every poor person alive. The discount rate forces a society to say which claim it holds stronger.

Handwave The strongest version of the case for caring about this is not provable and should be labelled. If a civilization’s long-run trajectory is decided by a small number of century-scale investments, and if those are gated by a parameter chosen on grounds nobody can defend as measurement, then the discount rate is among the highest-leverage numbers in public administration. Every step is plausible and none is demonstrated. Civilization Timelines examines the survival assumption those prices embed.

These horizons track guidance revisions, data releases and the arrival of usable natural experiments, not technology.

• 10 yr: Frontier The dated items are hard. The 2026 UK review’s recommendations — δ = 0.5%, μ = 1.25, g = 1.5%, and a forward schedule of 3.0%, 2.5% and 2.25% — are either adopted or not, and that decision is a published fact within this window. Frontier The US 2023 schedule commits to restating values every three years; whether that happens under an administration directing the 2003 guidance is the cleanest available test of whether an automatic revision rule binds. Speculative Expect at least one replication of the leasehold–freehold estimate on English enfranchisement events, because the statutory variation and the transaction data both now exist.
• 25 yr: Speculative If equilibrium real rates stay near the 0.7% one-year and 1.3% ten-year levels estimated for 2019, official schedules converge downward toward the 1.69% to 2.21% region the bond series imply. Speculative The social-insurance schedule, or something like it, spreads: a separate lower rate for catastrophe-avoiding projects is an easier political sale than cutting the headline rate. Frontier A repeat of the 197-expert survey shows whether a median of 2.00% was a parameter or a snapshot.
• 50 yr: Speculative The leasehold cohorts observed in the 2004–2013 samples reach maturities where the original estimates made sharp predictions, turning a cross-sectional inference into a panel with realised outcomes. Speculative Whether any guidance publishes a rate beyond 125 years, which the 2026 UK review declines to do, is the boundary at which appraisal hands over to explicit welfare argument.
• 100 / 250+ yr: Handwave The 2120 and 2164 bands in current schedules stop being projections and become data, and whether the institutions that wrote them still exist is answered rather than assumed. Handwave Any statement about what rate a society uses in 2270 is assertion: the oldest continuous evidence base here, UK bond yields from 1694, is itself only 330 years long, and contains two centuries in which the question was not asked.

• Depends on nothing on this map, and that is an adjudication rather than a gap. No brief in this corpus produces a result this one waits on: the missing pieces are a data join, an unexploited natural experiment and a normative decision. Two seams run to briefs that exist and are cross-referenced rather than restated — Civilization Scale Investment on the instrument and the historical record of mobilisation, and Long-Term Institutions on whether a commitment made at a declining rate binds a later planner.
• Requires (not on this map) six things, none of them a discovery. A price effect measured from a change in lease term assigned by statute rather than by the state of the building, which is the decisive test and has never been run. A land registry publishing remaining term alongside price, without which the five million transactions already collected cannot speak to horizon. A traded, indexed claim running beyond a century, which would replace the inference apparatus with an observable price. An estimate of the elasticity of marginal utility separating its risk, inequality and smoothing readings, since a 2026 review moved it to 1.25 on judgement. A rate that survives a change of administration, against a US record of 2% in 2023 and a directed reversion in 2025. And publication of the response distributions from official consultations, so that expert opinion becomes a series rather than a citation.
• Enables a defensible appraisal of any project whose benefits arrive beyond about fifty years: deep geological disposal, coastal realignment, pandemic and defence stockpiles, long-lived archives, and the carbon price itself, where a move from 3% to 2% can more than double the social cost of carbon and the fall in equilibrium real rates since the 1990s has at least doubled it again.
• Adjacent to Future Capital Markets on tenor and intermediation, Climate Adaptation Finance and Carbon Removal Verification on benefit streams whose sign this parameter sets, Nuclear Waste Solutions on the canonical past-125-year case, Future Taxation Models on the revenue side of anything financed by tax, and Future Philanthropy on the private version of the same question.

Established “Housing markets show the true long-run discount rate is 2.6%.” Three errors in one sentence. The paper reports discount rates below 2.6% for 100-year claims, as an upper bound. The 2.6% is a point on a fitted declining curve whose long-run limit is 1.42% and whose short-run rate is 13.42%, not a constant. And it is what property buyers in two markets did between 1995 and 2013, which is a positive fact, not a recommendation.

Frontier “The leasehold result is contaminated, so it tells us nothing.” Overcorrection. The original work tested the obvious contaminants and reported them small: rents show no systematic difference across maturities, ground rents are small to non-existent, and leases beyond 700 years trade at freehold prices, which kills both the bubble and the financing-friction stories. The open question is narrower — whether statutory extension rights and divided control are in the coefficient.

Frontier “The 17.33% English leasehold discount refutes the 2.6% estimate.” It does not, because it is not measuring the same thing. That study does not observe lease length — its own appendix records the finite-duration mechanism as unobserved and bundled into the tenure coefficient — so its number averages over all lease lengths and all contractual burdens. What it does establish is that the tenure coefficient moves for reasons with no horizon interpretation, which is why the decisive test in section 7 is an exogenous change in term rather than another cross-section.

Established “The Stern Review used an indefensibly low rate that no evidence supports.” The rate was defended on ethical grounds and attacked on that basis for a decade. On three centuries of bond prices it is also within the statistical noise: “The value of 1.4% used by Stern is less than a standard deviation from our estimated long-run return rate for the UK.” One can still think the ethical argument wrong; the empirical claim that it is far from any market rate is not supported.

Frontier “Nordhaus and Stern disagree about whether the future matters.” They disagree about whether the rate should be read off observed market returns and savings behaviour or derived from an ethical premise. Nordhaus’s stated objection is that the Review’s conclusions “will not survive the substitution of assumptions that are consistent with today’s marketplace real interest rates and savings rates”. Both men then signed a joint panel statement endorsing declining discount rates.

Established “Declining discount rates are a fringe idea.” Australia, Denmark, the Netherlands, Norway, Ireland, New Zealand and the United States all publish declining schedules, and a thirteen-author panel including Arrow, Nordhaus, Weitzman, Gollier and Pindyck called the arguments compelling. The flat rate is now the minority position.

Frontier “Declining rates are settled theory.” Also wrong, and the objection is technical rather than political. Gollier shows the gamma-discounting route “is in fact equivalent to the Local Expectations Hypothesis, a hypothesis globally rejected in empirical finance”, and that its users are time-inconsistent and short-termist when growth shocks persist.

Frontier “A declining schedule gives you the number for a 200-year project.” The people who developed the theory say it does not. Their bounding exercise finds the resulting present values “typically remain so imprecise as to provide little practical guidance” beyond 75 years. The 2026 UK review agrees in practice, publishing rates only to 125 years.

Established “Hyperbolic discounting is a human bias, so a rational planner should use an exponential rate.” Two results say otherwise. The housing estimate fits a hyperbolic-exponential form to market prices, not to experimental subjects. And a planner aggregating people who disagree must, under iso-elastic felicity and gamma-distributed time preference, discount hyperbolically — the behavioural model in a normative light.

Speculative “Lower the discount rate and long-horizon projects get built.” The rate governs appraisal, not delivery or funding. Whether promised benefits arrive belongs to Megaproject Governance, and whether capital can be raised on the relevant tenor to Civilization Scale Investment, which records that the flagship century bond cost issue-date buyers more than two-thirds of their capital.

Frontier “There is broad consensus on a zero pure rate of time preference.” The survey authors specifically decline to confirm this, reporting a modal value of zero but a mean of 1.1% and a median of 0.5%. The zero position is the single most common answer and a minority one.

Speculative “Getting the discount rate right is the main thing standing between us and good long-term policy.” Two arguments cut against it. If catastrophic outcomes have fat tails, the tail term dominates and the central rate is second order. And if integrated assessment models “create a perception of knowledge and precision that is illusory”, refining one input improves an output whose error lives elsewhere. This brief takes the parameter seriously and does not claim it is the binding constraint.

Handwave “A society that discounts the future properly will act on it.” This is the step where the argument works by assertion, and it is the implicit premise of most advocacy in this area. The US rate went to 2% in November 2023 and was directed back to the 2003 guidance in January 2025 without any new estimate. Nothing in the evidence reviewed here shows that a correct parameter produces a durable commitment.