The cause is not gas. It is the cost of renewable energy policy.

Consumers pay for renewables three times over: first through direct carbon taxes on gas-fired generation, then through guaranteed above-market prices for wind and solar under Contracts for Difference (CfDs), and finally through a growing stack of levies for the backup capacity, grid reinforcement, and balancing services that intermittent generation requires. Together these impose an implicit carbon price of £342 per tonne on British electricity — more than double the £154/t that the academic literature estimates would maximise global welfare.

The consequences extend well beyond the bill. Household electricity costs at £911/annum today are scheduled to rise to £1,045/annum by 2030; on an all-gas grid with globally optimal carbon pricing they would be £689/annum, and with nationally optimal carbon pricing £506/annum. The overtaxation suppresses GDP by 1.0-1.8%, manufacturing output by 2.4-4.5%, and energy-intensive industries - steel, chemicals, cement - by 4.7-8.7%.

The most important step is to stop making the problem worse: have no further renewable auction rounds and commit to no further renewable construction until costs fall substantially. For the legacy of existing contracts, the government can either let them expire - yielding bill reductions of roughly £100 per household every five years - or assume the sunk costs onto general taxation immediately, lowering bills by 24-44% at a declining fiscal cost that turns net positive within a decade.

Twice shadow price

The stated purpose of renewable energy policy is almost entirely environmental: we favour wind and solar over gas because they emit less carbon. A subsidy to one megawatt-hour of renewable generation is therefore the mirror image of a tax on one megawatt-hour of gas — and the total implicit carbon price is the sum of both direct taxation and renewable subsidies, regardless of whether these are levied through bills or general taxation. Bills are high because the costs of these policies currently fall on electricity consumers, but the underlying policy choice would be equally expensive however it was funded.

The direct taxes on carbon are modest. The UK ETS charges £42 per tonne of CO2, supplemented by £18 from the Carbon Price Support, for a combined £60/t — unremarkable by European standards.1 But this barely scratches the surface of what the policy actually costs.

The primary subsidy mechanism is the CfD: a guarantee that a renewable generator will be paid a fixed price (known as a strike price) for every unit of electricity it produces, regardless of the wholesale market price.2 These contracts are awarded through competitive auctions known as allocation rounds. The seventh and most recent, AR7, concluded in early 2026, awarding 14.7 GW of capacity at strike prices of £91/MWh for offshore wind, £72/MWh for onshore wind, and £65/MWh for solar (2024 prices) - locked in for twenty years from construction until 2049. The implicit subsidy has three components.

First, strike prices are set above the average market price - the direct, visible payment from consumers to generators. Second, renewable output is highly correlated - wind farms generate at the same time as each other (output correlations well above 0.3), and every solar panel shares the same sun - so the wholesale price at the moment CfD payments are triggered (the “capture price”) is systematically lower than the average wholesale price. The ratio of the two, the capture rate, measures how much of the headline market price a renewable generator actually displaces. Third, and most importantly, every new megawatt of renewable capacity is subject to the same correlations so lowers the capture rate of all existing renewable capacity, cannibalising it. In most markets cannibalisation would merely impose losses on competing firms. Under CfDs it translates directly to higher consumer bills, because every generator is guaranteed its strike price regardless. We are very much carrying coals to Newcastle: building capacity that generates electricity precisely when we already have too much of it. If the wholesale price averages £70 but wind generates disproportionately when it’s £64, the capture price is £64 and the capture rate is 92%. The CfD pays the difference between the strike price and the capture price - so when the capture rate falls from 92% to 77%, the subsidy from consumer bills widens by £10/MWh.

Current CfD payments already reflect this: offshore wind receives subsidies roughly £90/MWh above wholesale, onshore wind and solar roughly £50/MWh, versus wholesale for gas excluding carbon pricing of £78/MWh. But these figures blend very expensive early contracts with a tranche from the late 2010s that cleared cheaply due to systematic underestimation of maintenance costs - and both effects are swamped by what is coming. The capture rate, currently 92%, will fall precipitously as new capacity enters the grid, mechanically widening the gap between strike prices and capture prices on every existing contract.

To project the subsidy forward, I use Ben James’s projections for wholesale prices and capture rates: £84/MWh wholesale and 92% capture today, falling to £70/MWh and 77% by 2030 and £60/MWh and 65% by 2040, held flat thereafter.3 Subsidies are calculated as the difference between payment and realised market price, plus cannibalisation of existing capacity.

These CfD subsidies — £81/MWh for offshore wind, £61/MWh for onshore wind, £37/MWh for solar — are large. But they capture only the direct payments to generators. The costs of intermittency itself are separate, and they are borne by consumers through an entirely different set of charges.

Intermittent generation requires backup capacity to keep the lights on when the wind drops. The Capacity Market — negligible in 2010 — will cost £3.6bn in 2027–28, equivalent to £22/MWh of renewable output. It also requires extensive balancing: curtailment (paying wind farms to switch off when output exceeds demand), frequency response, reserves, and the infrastructure to restart the grid after a total failure. Balancing costs have risen from £1.1bn in 2010 to £2.7bn today (both in 2025 prices), worth £19/MWh across 144 TWh of renewable generation, and are projected to rise a further 120% by 2030 — partly reflecting inadequate transmission capacity, but structural even after planned upgrades. That transmission is itself a further cost: because wind and solar have low capacity factors, they require far more grid infrastructure per unit of average output than firm generation. The government estimates transmission adds £14/MWh for offshore wind, £10/MWh for onshore wind, and £1/MWh for solar.4

The government also holds enabling powers under the Energy Act 2023 for a Gas Shipper Obligation - a levy on gas suppliers to fund hydrogen production subsidies - which at stated ambitions could substantially increase bills, but as rates have not yet been set these costs are not considered here.5

Aggregating all non-wholesale system costs, the government’s own estimates come to £71/MWh for offshore wind, £69/MWh for onshore wind, and £65/MWh for solar. These costs are currently socialised equally across all electricity consumers rather than attributed to the renewables that cause them. Correcting for this cross-subsidy - non-renewable generation was 60% of output in 2025 - gives effective cost gaps of £43/MWh, £41/MWh, and £39/MWh.6 Learning curve arguments - the price of renewables falling as we build more of them as we get better at their production - do not reduce these figures for a country installing less than 1% of global solar and onshore wind capacity.7

Combining the CfD subsidy, the system cost gap, and the direct carbon price gives the total cost per MWh of displacing gas with renewables. For new offshore wind at projected carbon prices: £81 + £38 + £70 = £189/MWh. For new solar: £37 + £34 + £70 = £141/MWh. At current tax rates the figures are £141/MWh and £94/MWh respectively. The wholesale cost of gas-fired electricity, excluding any carbon price, is £67/MWh.

To convert these cost premiums into an implicit carbon price, we need the emissions each MWh of renewables actually displaces. As a baseline, the IPCC estimates that new gas capacity emits 370 gCO₂/kWh directly plus 91 gCO₂/kWh from methane leakage. Emissions savings will be less than this for two reasons. First, gas plants forced to cycle up and down to accommodate intermittent renewables run less efficiently than they would at steady high load. A modern CCGT achieves 56-57% thermal efficiency at design point but only 51–52% at the reduced load factors - now averaging 30–40% - that the current grid imposes.8 This 5–6 percentage point gap adds roughly 40–45 gCO₂ to each MWh of gas generation currently, and would be removed in a primary gas grid. Allocated across renewable output at current penetration (47% renewable), this reduces the effective CO₂ displacement by about 10%.9 Second, renewables themselves have lifecycle infrastructure emissions: 15–17 gCO₂/kWh for wind, 66 gCO₂/kWh for utility solar, per the IPCC.

Netting these adjustments gives effective displacement of 416 gCO2/kWh for wind and 366 gCO2/kWh for solar, and therefore an implicit carbon price of £355/tCO2 for offshore wind and £270/tCO2 for solar at current tax rates — or £475/t and £408/t respectively at projected carbon prices for new capacity. Weighting by 2024 output (83 TWh wind, 14 TWh solar) gives a blended implicit carbon price of £342/tCO2 at current rates and £465/tCO2 at projected rates.

These figures are more than double the academic consensus on the globally optimal carbon price. The standard tool for estimating what carbon should cost is the Integrated Assessment Model: an economic simulation combining a climate model (how much warming does a tonne of CO2 cause?) with a damage function (how much does that warming reduce economic output?). The model finds the price at which the marginal cost of abatement equals the marginal damage avoided - the “social cost of carbon.” The result depends heavily on the discount rate, since climate damages fall mostly on future generations: at the low rates favoured by Stern, Rennert et al. (2022) - the largest recent meta-analysis - gives £154/tCO2 in 2025 prices. Resource-extraction models that instead price the atmosphere as a depletable stock converge on a similar figure.10

Importantly, this is the globally optimal price: the price at which the world as a whole is made better off. For a country responsible for 1% of global emissions, the nationally optimal price is far lower: Britain bears the full cost of abatement but captures only ~4% (share of global GDP) of the climate benefit, and is colder than average, hence less exposed to the damages of warming. In practice the nationally optimal carbon price is thus below £6/t, essentially zero as above administrative costs of any realistic implementation and hence assumed as such throughout.

British electricity policy thus prices carbon at £342/t - 2.2 times the globally optimal level, and many multiples of a nationally optimal price that is essentially zero.

All gas grid

​​It is worth stressing that these implicit carbon prices do not represent windfall profits for renewable generators - they are the minimum prices necessary to induce construction to the government’s desired levels. Absent such subsidies, renewables would not be built and the grid would be primarily gas-fired. We therefore model two counterfactual cases: one with globally optimal carbon pricing at £150/t, and one with nationally optimal carbon pricing.11 12

Gaslight

But aren’t renewables cheaper than gas at the government’s levelised cost estimates, with offshore wind at £39/MWh against gas at £139/MWh (£2025)? Both figures are misleading. The gas number includes £83/MWh of carbon costs at target-consistent appraisal prices - not the £22/MWh that generators actually pay under the UK ETS and CPS currently, but a trajectory averaging £224/tCO2 over the plant’s lifetime, reverse-engineered from the desired future emissions path. Strip this back to current carbon taxes and gas costs £78/MWh. The wind number, meanwhile, is what it costs the developer to build and run the turbine - not what it costs the consumer. The consumer pays the CfD strike price (at AR7 £91/MWh for offshore wind, £72/MWh onshore, £65 solar), plus the system cost cross-subsidies (capacity market, balancing, transmission) that DESNZ’s own report acknowledges it excludes (£71/MWh for offshore wind), plus the cannibalization costs as correlated output depresses the capture price on every existing contract (£30/MWh for wind). Even before accounting for the capture rate - which mechanically widens every one of these gaps as more capacity enters the grid - the comparison inverts at present, with offshore wind at £195/MWh, onshore wind at £171/MWh and solar at £152/MWh for a blended renewable average of £183/MWh vs gas at £78/MWh - over twice as much. Renewables are not cheap power carrying expensive subsidies. They are expensive power whose costs are hidden by an accounting framework that loads phantom carbon taxes onto the alternative.

The true counterfactual bill is built line by line from observable data. The wholesale cost of gas-fired electricity is £108/MWh at £150/t carbon or £55/MWh without, derived from DESNZ generation cost assumptions at 93% load factor and 57% LHV efficiency. All renewable subsidies (RO, FiT, CfD, Capacity Market) and green levies (ECO, WHD, NCC) are removed. Network charges - TNUoS, BSUoS, and DUoS - are set to their inflation-adjusted pre-renewables baselines, with the excess attributed to renewable integration.13 Nuclear (Sizewell C RAB at £12/household) is retained as nuclear may have other energy security advantages, and the contracts are signed regardless. Gas strategic storage at 19.5 bcm - six months of electricity-dedicated supply, compared to the UK’s current seven days of peak demand - is added. Supplier costs and the smart meter levy are held at their inflation-adjusted baselines, which closely match current levels.

Over 80% of the saving comes from removing directly observable subsidies and levies - line items in the Ofgem price cap that require no estimation. The network excess over baseline (£59) is secondary, and likely understated since the baseline periods already included some renewable integration costs. The only line that costs money in the counterfactual is wholesale electricity, because pricing carbon at £150/t roughly triples the current UK ETS rate. At zero carbon pricing, even this disappears.

Electricity bills would thus be 24% (£222) lower than today, and 34% (£356) below their projected 2030 level, under an all-gas grid with globally optimal carbon pricing. At the nationally optimal carbon price, bills would fall by 44% (£405) relative to today and by 52% (£539) relative to 2030.

Oil in the lamp

Gas does have one major drawback: supply is interruptible. 43% of the UK’s gas consumption arrives through pipelines from Norway - infrastructure that can be severed by a small team in a yacht, let alone any more capable platform. Prediction markets give roughly 21% probability of a war between Russia and one or more NATO countries by 2035.14 The UK currently has just 7 days of gas storage at peak winter demand, compared to 89 days for Germany, 103 for France, and 123 for the Netherlands. NESO’s own gas security assessment found that if any single major piece of gas infrastructure were lost - one pipeline, one terminal - supply would be unable to meet peak winter demand by 2030/31 under any scenario it modelled, and the government’s emergency planning acknowledges that in a gas deficit emergency the resulting surge in electric heating demand could overload and collapse the electricity grid in turn. The vulnerability is real - this would, however, be cheap to fix. Assuming gas covers 80% of the grid, or around 240 TWh, six months of storage - 19.5 bcm, fungible to household heating in a winter crisis - would cost £11 per household per year, well under 2% of the average energy bill.15 16 17

Dark Satanic Bills

To translate high electricity prices into a cost on GDP, we use the electricity price elasticity of output: the percentage change in output caused by a one percent change in electricity prices. Estimates in the literature range from 0.03 to 0.37, but this wide spread is largely explained by sectoral coverage. Manufacturing is far more electricity-intensive than services, so studies focused on manufacturing find much larger elasticities than those covering the whole economy. Since UK manufacturing is roughly 10% of GDP, the whole-economy elasticity must be at least a tenth of the manufacturing-only figure - and somewhat more in practice, because the UK uses as much electricity for commercial purposes as industrial.

At the low end, Bijnens et al. (2021), calibrated on European data and recalibrated to ONS input-output tables with five-year capital adjustment, give a whole-economy elasticity of 0.031. US manufacturing studies cluster higher: Wolverton, Shadbegian and Gray (2022) find 0.081 for full manufacturing and 0.158 for energy-intensive industries; Casey et al (2020) find 0.2, though explicitly short-run. Marin and Vona (2017) estimate separate French elasticities of −0.26 for employment, −0.04 for average wage, −0.11 for value added per worker, and −0.12 for TFP; compositing via employment + value added gives roughly 0.37, as does applying the Wolverton et al. employment-to-output multiplier. UK manufacturing is 10% of GDP, hence the above studies imply the whole economy elasticity should be at least one tenth of the manufacturing only share. As the UK uses as much electricity for commercial as industrial purposes, an output elasticity equal to twice this is not unreasonable. The UK figure should also sit above US estimates: the impact of electricity on output scales with the Domar weight, and the UK spends roughly 1.6x as much on industrial electricity as the US as a share of GDP, and 1.2x that of France.18 Most of the above studies run on 1–5 year horizons, insufficient for full capital stock adjustment. An output elasticity of 0.04 is accordingly favoured, although this could be higher in practice.

However, electricity expenditure is only 2-2.5% of UK GDP, so why would a price reduction deliver growth larger than this share?19 The answer is that electricity is not just a final input like office paper - it is an operating cost of every machine, furnace and production line in the economy. When electricity is expensive, capital equipment is expensive to run, and firms deploy less of it. But the less capital an economy has, the more productive each additional unit of it is: the first crane on a building site adds far more output than the fifth. The UK, in common with most Western economies, operates well below its optimal capital stock according to standard models, which means we are stuck in the steep part of the curve where each machine that becomes viable to run produces substantially more than its operating cost. Cheaper electricity doesn’t just save money on the power bill - it makes a tranche of currently marginal capital equipment worth building, and the output from that equipment is many times larger than the energy saving alone.

The 24% (44%) cost reduction above would thus imply a boost to GDP of 1.0% (1.8%), or £28bn (£50bn)/annum. At the Wolverton, Shadbegian and Gray (2022) estimates adjusted by 25% to account for Domar weight differences, manufacturing output generally would grow by 2.4% (4.5%), and specifically energy intensive industries (steel, chemicals, cement, glass) would grow by 4.7% (8.7%).

Policy & transition dynamics

Renewables and their infrastructure are sunk costs. The government is contractually bound to pay generators for the next several decades, and these obligations cannot be wished away. But provided no further renewables are built, these sunk costs do not change the marginal cost of producing electricity - which is determined by gas, as this would be our source of electricity at the margin. Whether the legacy payments sit on electricity bills or on general taxation, the same power stations produce the same electricity at the same cost. The only question is whether consumers and businesses are also charged for historical policy decisions on top of that marginal cost, or whether the Treasury absorbs them.

The simplest policy - and the one requiring no fiscal commitment - is to stop making the problem worse. Committing to no further CfD rounds is immediately fiscally positive: output and tax revenues grow at no cost to the state. The loss of UK ETS and CPS revenue under a zero carbon price is almost exactly offset by removing the reduced VAT rate on residential electricity (currently 5% vs the standard 20%), which could be done while still greatly lowering household bills. As existing contracts expire, bills fall by roughly £100 per household every five years - a substantial improvement requiring no new spending and no political risk.

Should the government go further and assume the legacy costs immediately? There are two arguments for doing so. First, economically, the correct price of electricity is its marginal cost; loading sunk policy costs onto bills distorts every consumption and investment decision in the economy, and taxation has an increasing marginal cost per product so slightly distorting all product prices slightly more with higher general taxation is efficiency enhancing compared to distorting one product greatly. Second, for businesses, electricity is an input into virtually everything the economy produces, and the fundamental insight of optimal tax theory - Diamond and Mirrlees (1971) - is that taxing production inputs is strictly worse than taxing final goods or income, because it distorts not just how much firms produce but how they produce it.

In the absence of competing demands on fiscal space, the costs should therefore sit on general taxation - not as a subsidy to electricity consumers, but as the removal of an unusually destructive form of revenue-raising. Three revenue sources partially offset the fiscal cost: the government captures carbon tax revenue currently dissipated to renewable generators, VAT harmonisation (replacing the 5% reduced rate with the standard 20%, which can be done while still lowering bills), and higher tax receipts from the output growth that cheaper electricity enables.

To quantify these dynamics we model two packages — one with a globally welfare-maximising carbon price of £150/tCO₂ (5% VAT retained) and one with zero carbon pricing (VAT harmonised to 20%) — each against a “wait” counterfactual in which the same carbon and VAT settings are adopted but legacy costs remain on consumer bills. The subsidy schedule is built from actual CfD contract data by auction round (LCCC strike prices, capacities, and contract lengths; generation and wholesale price forecasts from Ben James’s electricitybills.uk), plus RO, FiT, and Capacity Market obligations. Bills in the wait scenarios decline as each tranche expires on its known schedule, with network costs declining according to the RAB depreciation schedule. Under the wait-with-carbon scenario, the carbon price phases in as subsidy headroom permits, constrained so that bills never exceed their projected 2030 level. GDP is assumed to grow at 1.5% per annum (OBR medium-term potential output) and electricity demand at the same rate, reflecting electric vehicle adoption and data centre growth independently of climate policy (NESO FES 2025). Output effects are phased over five years; tax revenue is taken at the tax share of GDP, 37%. All present values use the Green Book discount rate of 3.5%.

The initial net cost is £16–20bn per year depending on carbon pricing assumptions, falling as contracts expire. Breakeven on an annual cash-flow basis arrives by 2031 (without carbon pricing) or 2035 (with), and the proposal is net positive in present value terms by 2040 and 2045 respectively.

However, fiscalisation competes with other uses of scarce fiscal space. The UK tax system contains several marginal tax rate cliffs; fixing these may buy more output per pound. And any future government that resumed renewable construction would transform a temporary fiscal bridge into a permanent subsidy, destroying the economic logic entirely - the sunk-cost argument depends completely on the costs remaining sunk.

The more conservative path - cancel AR7, let existing contracts expire, and direct the growing fiscal space toward the most binding distortions elsewhere - is therefore likely more prudent. Even without action, bills will fall at a substantial rate over the next few years after 2030 if the bleeding can be stopped, at around £100 every 5 years. The critical point is that the choice of transition mechanism does not affect the core finding: the implicit carbon price is £342/t, bills are far too high, and no further renewable capacity should be built at anything resembling current costs.

Let them eat carbon

The implicit carbon price in the UK energy system is £342 per tonne. It is unsurprising that energy is so expensive: the table above shows what this price would mean if applied to the rest of the economy. Beef prices would almost double. Heating bills would increase more than twofold. The cost of building a house would rise by 15%. Electricity is the one sector where something approaching this level has actually been implemented - and the result is prices nearly four times the US industrial level and a manufacturing sector in accelerating decline.

Restoring effective carbon prices to globally welfare-maximising levels would lower consumer bills by 24% and raise GDP by 1.0%. Moving to a nationally optimal carbon price would lower bills by 44% and raise GDP by 1.8%. The most important immediate step - cancelling AR7 and building no further renewables at anything resembling current costs - requires no fiscal commitment at all.

But electricity is not an aberration. It is a preview. The Climate Change Act requires net zero emissions by 2050, and the government’s own modelling relies on what it calls “target-consistent” carbon prices to get there. These are not estimates of the damage carbon causes - they are not derived from any model of costs and benefits at all. They are simply the prices reverse-engineered from the emissions path the target requires: whatever carbon must cost to force behaviour to change enough to hit net zero, that is the price, regardless of whether the change is worth making. This stands at £333/t today (2025 prices), rising to £485/t by 2050 - figures published by the government as the carbon prices its modelling says are required to meet the Act’s statutory targets.20 They are not yet applied economy-wide, which is precisely why the rest of the economy has not yet suffered what electricity consumers have. But the Act’s targets remain law, and if they are to be met, these prices must eventually reach every sector: heating, transport, agriculture, construction, industry. The government is candid about the disconnect: the relevant DESNZ guidance states that social cost of carbon analyses are “not aligned with the net zero target, [with] most estimations lead[ing] to emissions levels much higher than net zero in 2050.” The target was chosen first; the economics were discarded afterward.

The future of the Climate Change Act as written is the extension of our energy poverty to the whole economy.

This is wrong. Taxation discourages work, redirects activity into less productive but less taxed forms, and drives production that could be more efficiently performed through markets back into households. The MCPF captures these distortions, and it means every pound spent must generate more than a pound of benefit to justify itself.

How much more depends on effective marginal tax rates and how sensitive behaviour is to them. However, most MCPF estimates use marginal rates capturing only income tax and national insurance. But the true rate must include consumption taxes, capital taxes, benefit withdrawal tapers, and smaller levies, all applied sequentially. As marginal tax rates are so high, small errors here matter greatly - a 1pp tax cut for the Beatles would have raised their marginal return to work by 20%. Calculated comprehensively, effective marginal rates below £50k average over 50%, and above £50k over 70%. A proper MCPF, using comprehensive rates and mainstream elasticity estimates, is in the range of 1.8–2.2: each pound spent must generate nearly two pounds of benefit to break even, twice as much above unity than income and payroll taxes alone would suggest.

The savings would be immediate, with a quarter of currently appraised expenditure not passing a properly calibrated test - implying £8 billion per year in spending does not generate sufficient return to justify its financing costs.1 And this is before considering the vast majority of public expenditure, including spending routed through utility regulation and para-fiscal channels, that is never subject to formal appraisal at all.

Death and taxes

How does the UK tax system work? Before individuals see their salaries, they pay employers national insurance at 13.8% and the apprenticeship levy at 0.5%; they then pay income tax, employees national insurance and any clawbacks for universal credit (the UK’s welfare system); before consumption, they then pay corporation tax and dividend tax on any savings in excess of the ISA limit (£20k) (plus stamp duty if they hold any shares on a UK exchange); and finally VAT and many minor consumption taxes that come to an effective rate of 23%.23 Pension saving is initially tax exempt, and then pension draw downs are taxed at the (likely lower) income tax band an individual is in when retired with no employees national insurance due.4

The system also has several clear inefficiencies, in the form of rate nonlinearities. At £50k-£60k with the High Income Child Benefit Charge resulting in child benefit being withdrawn; at £100k the tax-free portion of the personal allowance is withdrawn raising the marginal rate to 60% from £100k to £120k; at £260k, the pension allowance tapers at £1 per £2, raising the effective income tax rate by 50%; and at £100k free childcare hours, and tax rebates on childcare spending are lost. Universal Credit can also interact objectionably with income tax at very low incomes, although this is more dependent on characteristics such as the number of children.5 Under our central elasticity estimates, the net cost of removing all four is negative — these distortions are collectively beyond the revenue-maximising rate, and abolishing them would raise £2–£7bn depending on the assumed elasticity. Even under the most conservative estimate (ε=0.2), the fiscal cost is only £2.9bn, well below the £7.7bn mechanical effect.6

The effective rate barely differs for all realised compensations beyond £50k.

Marginal cost of public funds

Why does this matter? After all, the curve shape merely determines government revenue; for any fixed revenue requirement the curve can (and should) be made smoother by the reforms above, but why care about the overall level? Several reasons. Firstly, it would make you less optimistic about how much revenue a tax rise is likely to raise - and more optimistic about behavioural effects compensating for the costs of a tax cut.7 Secondly, it would also explain why various labour intensive sectors - such as childcare and food preparation - remain so frequently produced within households.8 There is a very large tax wedge even at the relatively low wages such workers usually earn, hence meaning that because time spent caring for children or cooking meals at home is untaxed it is routinely efficient for individuals to undertake this themselves rather than through the market.

However, we’ll here focus on the implications for cost-benefit analysis. When the government is choosing whether to make a public investment, the correct welfare criterion is not whether it generates £1 of benefit per pound spent. This is because the government can only gather the means to make investments via distortionary taxation, so activities must generate benefits over the costs of the resulting distortions.

The theoretical counterargument, advanced by Kaplow (1996, 2004) and Jacobs (2018), holds that the MCPF equals 1.0 under optimal taxation when accounting for the redistributive benefits of public spending. But even setting aside whether UK tax rates are optimal - and the proliferation of cliff edges documented above suggests they are far from it - this objection has limited force for most categories of spending subject to formal appraisal. Transport benefits are measured primarily in time savings, which scale roughly linearly with income, and more generally this is likely true for all goods the government provides without good private substitutes: willingness to pay for environmental quality, defence, or flood protection likely scales roughly linearly with income, so the equity benefits of most such schemes are minimal.

The most-cited UK estimate of the Marginal Cost of Public Funds (MCPF) is 1.26, from Kleven and Kreiner (2006), using income tax, National Insurance, and benefit tapers but not consumption or capital taxes in the marginal rate. This is representative of a literature that consistently produces values of 1.1–1.5 by applying the standard analytical formula to direct labour taxes alone, such as Browning (1987), Fullerton (1991) and Dahlby (2008). Higher estimates emerge only when the full tax system is modelled: Barrios, Pycroft and Saveyn (2013) obtained 1.81 for the UK using a CGE model that captures tax interactions of a subset of taxes endogenously, and Beaud (2011) showed analytically that incorporating VAT revenue leakage raises MCPF by 0.2–0.8 points, because reduced labour supply erodes the consumption tax base alongside the income tax base.

To estimate the Marginal Cost of Public Funds (MCPF), we take the tax rate at each income t and the elasticity of taxable income (ETI), and calculate 1 + ETI*t/(1-t). For the marginal tax rate we use the graph shown above. However, most previous estimates of the MCPF have only included direct taxes on labour when calculating this, and ignored such considerations as the income-tax-equivalent effect of benefit tapers, consumption taxes or capital levies.9 As the MCPF goes superlinearly in the tax rate, this is doubly costly.

The second key parameter for the MCPF is the elasticity of taxable income (ETI). This is because there are 3 channels that taxation could be economically costly. It could reduce hours worked per person, reduce the number of people in work or cause individuals to shift their compensation mix inefficiently - taking a job with a lower commute, for example.10 This is calculated as if compensation mix shifts are analogous to work shifts - they were entirely untaxed as is leisure. However, taxable income could also change due to redirection into corporate forms or redirection across time into lower tax periods, meaning that a pure figure for the ETI for a single revenue source is likely to be an overestimate.11

For estimates on the labour side, the total hours - combining both intensive and extensive elasticities - was estimated in Chetty et al (2013)’s meta-analysis at 0.9 leaning more heavily on micro evidence, Whalen and Reichling (2017)’s estimate for the CBO at 0.4 (range 0.27-0.53), and at 0.25 by Elminejad et al (2023).12 13 For the pure ETI, Feldstein (1999) finds 1.04 for the US in the 1980s; Browne and Phillips (2017) similarly found 0.98 under the broadest income measures from the UK’s 2010 additional rate of income tax reform, albeit under narrower specifications it can go as low as 0.35; and Gruber and Saez (2000) found an estimate of 0.4 in the US. Under the above estimates, the ETI seems very likely to at least exceed 0.4; a simple midpoint of the range would be around 0.6, and 0.8 would be possible. However, the ETI is likely higher in the US than UK on account of health insurance being such a large component of salary and lower statutory minimums for various workplace amenities providing greater margins of non-salary adjustment, and so for both these reasons and the sake of conservatism the 0.4-0.6 range will be emphasised.14

MCPF estimates also need to account for capital formation. The direct effect of taxation is to reduce labour supply, but this has a secondary consequence: with fewer effective workers, firms invest less. In standard growth models, the equilibrium capital stock is proportional to effective labour, so a 1% tax-induced reduction in hours worked leads to a corresponding 1% fall in the capital stock. This amplifies the welfare cost, and under a standard production function framework, the resulting capital reduction lowers wages by roughly 0.3%.15 The MCPF estimates presented below incorporate this adjustment as a multiplicative factor of 1.32 on the labour supply elasticity. For the purpose of calculating the MCPF given tax rates >90%, we cap the rate at 90% and pass over the excess to later incomes; this has a small impact on the results, with varying the cap from 80% to 99% only raising the estimate by 0.08 at ETI = 0.6. To ensure our worker is representative, we construct representative households on benefit-relevant characteristics from the 2023-2024 Family Resources Survey, and weight at population level frequency.

Table 1: MCPF estimates

Table 2: Distribution of MCPF & deadweight loss by income bracket

Under these elasticities, the MCPF would be ~2 in practice (unrestricted), vs ~1.4 if only income and payroll taxes were counted. This would explain the lower values common in much of the literature - as the MCPF is upward sloping in taxes, to have missed the last few components of the marginal rate would greatly reduce it. 71% of DWL comes from individuals earning below £50k, 92% from below £80k and 97% from below £125k - so this is a story of high distortionary rates affecting all workers rather than just those with high earnings.

Savings

Using data from the government’s major projects portfolio (NISTA 2024-25), there are 213 projects with total whole-life costs of £536bn. Of the 88 projects reporting monetised benefits, 69 are ongoing, representing ~£20bn in annual spending. Applying a present-value correction to whole-life costs - discounting at the Green Book rate of 3.5% assuming uniform annual spending - 64% of this expenditure has a benefit-cost ratio below 2.0 and would therefore not pass a properly calibrated cost-benefit test.16

The danger zone — projects with corrected BCRs between 1.0 and 2.0 that currently pass appraisal but would newly not automatically pass under MCPF of 2.0 — comprises 16 projects totalling £7.6bn/annum and £115bn in whole-life costs, led by the New Hospital Programme (BCR 1.26, £2.4bn/yr) (although note that this bundles the high-BCR RAAC removal that should certainly still proceed with lower-BCR new hospital construction when the return on new capital equipment for existing hospitals may be higher), the Affordable Homes Programme (BCR 1.68, £1.4bn/yr), and Smart Metering (BCR 1.35, £1.0bn/yr).17 A further 22 ongoing projects with £5.4bn in annual spending already fail at a BCR threshold of 1.0, including several major transport schemes subsequently cancelled or descoped. Infrastructure projects generally fare worst: the aggregate corrected BCR for ongoing infrastructure is just 1.30, with 77% of infrastructure spending below BCR 2.0.

These figures cover only the 5-6% of government spending that enters the GMPP and undergoes formal appraisal; the potential for savings is considerably larger if a greater share of spending were subject to cost-benefit analysis, or through implicit changes in areas such as the optimal level of subsidies and regulatory mandates.18 19 It perhaps wouldn’t be desirable to push such logic too far: the best documented parts of government are also likely the most efficient.20 However, the fact that even the most scrutinised fraction of spending contains £7.6bn of projects that would not pass a corrected cost-benefit test suggests that the true scale of mispriced public expenditure is considerably larger.

Conclusion

Marginal tax rates are frequently underestimated in policy analysis due to the need to factor in the dozens of overlapping levies, tapers and cliff edges. Beyond further raising the case for reforms to remove the largest distortions, this also implies that the threshold for public spending generating net benefits is higher than usually used. Implementing an MCPF of 2.0 in the Green Book would be an excellent opportunity for a Treasury looking to boost growth and make £8bn+ worth of savings from the expenditure judged least valuable by the departments themselves.

Today, private sector DB schemes, worth £1.2trn, hold just 18% of their assets in equities and 69% in government bonds.1 DC schemes, worth £600bn, hold 76% in equities.2 This gap exists because DB schemes must match assets to liabilities, which in practice means holding gilts.

The problem is that stocks and bonds have very different long-term returns. Since 1900 global equities have returned 5.0% per annum after inflation, compared to 1.7% for bonds.3 This 3.3 percentage point annual gap compounds relentlessly: over a 40-year career, £100 in equities grows to roughly £700 in real terms; in bonds, under £200. Equities are more volatile year-to-year, but over pension-relevant horizons of a decade or more, real equity returns actually exhibit lower variance than bonds - nominal bond values depend on the price level, which could end up almost anywhere, while equity values track GDP, which is far more predictable over decades.

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DB pensioners might receive fixed benefits, but they funded those benefits through decades of contributions.4 When that money earns 2% instead of 5%, pensioners or trustees lose the difference.

The regulatory origins of this gap trace to the 1995 Pensions Act, which introduced minimum funding requirements tied to gilt yields. The 2004 Pensions Act and subsequent guidance accelerated the shift: DB schemes went from holding 61% equities in 2006 to just 18% today. For comparison, the global average pension allocation to equities is 45% - Canada’s CPP holds 59%, Australian super funds 56%. UK DB schemes hold less than half the international norm.

This post quantifies the costs of current asset allocations. 96% of private sector DB schemes are closed to new members, with the switch generally having occurred between 2006 and 2012, hence the gains accrue to individuals who started work before 2012. We build a lifecycle model tracking cohorts of UK pensioners from 1925 to 2075, computing the consumption and welfare gains from returning DB allocations to historical norms. We find that switching to a 75% equity allocation would boost pensioner consumption by £381 billion in present value, generate £201 billion in additional tax revenue, raise bequests by £177bn and improve welfare even after accounting for increased portfolio risk.

Model

How large are the gains from returning to pre-2006 allocations? A back-of-the-envelope calculation is straightforward: shifting from 25% to 75% equities raises expected returns by just short of 3 percentage points, implying annual gains of around £40 billion on £1.4 trillion of DB assets, diminishing over time as DB schemes wind down. But this naïve approach leaves a key question unanswered: when do pensioners choose to take their consumption? To properly account for how rational savers would adjust their spending in response to improved investment prospects, we need to model optimal consumption paths, not just terminal wealth.

Individuals work from age 22 to 67, with wages growing at 1% per annum from experience (on top of 1% economy-wide real growth). They face mortality risk based on UK actuarial tables, adjusted so that life expectancy rises over time at historical rates. A fixed proportion of salary flows into pensions: pre-2006, all contributions enter DB schemes; from 2006-2012, new contributions transition linearly toward DC; post-2012, all new contributions are DC.5 Contribution rates are calibrated to match the actual observed sizes of the DB and DC pension pools, and fees are 0.4%/annum. Retirees also hold £200k of housing wealth, the average for 65-74 year olds, which returns 3.5% giving untaxed consumption via imputed rent every year.

In retirement, individuals face stochastic returns determined by their portfolio’s asset allocation and optimise their drawdown rates accordingly. Stocks return 7% pre-volatility drag with 18% standard deviation, while bonds return 1% with 5% standard deviation.6 Preferences follow a standard CRRA utility function with risk aversion η = 3 and a 3.5% discount rate. Bequests are valued at 10% of equivalent terminal consumption, and are assumed to be consumed entirely during the recipient’s working life—they therefore affect welfare but do not feed back into the retired population’s consumption.7 Individuals face a 15% probability of needing care towards the end of their life, in which case £75,000 will be subtracted from their bequest.

Results

The results of this are visible above.8 Consumption rises immediately as existing pensioners anticipate higher future returns, with the total effect coming to £381bn in present value (post-tax). Bequests also rise by £177bn present value, due to both higher wealth and higher risk encouraging greater precautionary asset holdings. The annual consumption gain peaks in the early 2040s, then declines as the DB-holding population ages and shrinks. The cohort that most benefits is those born in 1960 (aged 65 today), gaining a mean of £37,300 in expected consumption. Importantly, these gains remain positive in every period even after adjusting for risk: certainty-equivalent gains, which account for the disutility of increased portfolio volatility, are 57% (£218bn) of the headline figures.

The reform generates £201 billion in present value tax revenue (6.4% of GDP). This estimate is conservative: it assumes all pension income is taxed at the basic rate, that all retirees take their full 25% tax-free lump sum, and ignores inheritance tax entirely.9

Debt financing

The gains above flow from assets that currently sit in government bonds—so any reform is simultaneously a fiscal event. Shifting £500+ billion out of gilts would reduce captive demand for public debt, pushing up yields at a time when the UK’s fiscal position is already strained. This cost must be modelled directly. That said, DB schemes are winding down regardless: the Treasury will eventually lose this captive buyer whether or not reform accelerates the timeline.10

The cumulative reallocation represents 349 1% GDP demand shock years. What yield impact should we expect? Moretti et al. (2024) estimate a price elasticity of demand for emerging market sovereign debt of -0.3, implying a 1% GDP demand reduction raises yields by around 4.7 basis points. Other studies find smaller elasticities (-0.05 (EU) to -0.15 (US)). However, if the yield-demand relationship is stable in levels rather than elasticities, then higher debt stocks mechanically reduce the per-unit elasticity—and modern developed economies carry roughly twice the debt-to-GDP ratios of the emerging market sample (mean 54.7% in Moretti et al. (2024)). This suggests a plausible range of 1.6-4.7bp per 1% GDP demand shock, worth 5.5%-16.7% of GDP present value (£171-492 billion). The true figure is likely towards the lower end of that range as the lowest estimates refer to European countries directly comparable to the UK while the highest refer to emerging markets with much less institutional credibility.11

In fact, this cost could be fully offset by adjusting the maturity structure of government debt. The UK’s weighted average maturity (WAM) stands at 15 years—double that of any other G7 country and 2.5 times the US average of 6 years. This is no coincidence: the UK has been able to issue at such long maturities precisely because pension funds were required to buy duration-matched assets. In effect, the Treasury took the benefit of captive demand in the form of longer maturities rather than lower yields. But most models suggest this was not optimal - Greenwood et al. (2015) find that shorter-maturity debt minimises expected financing costs, and provides a natural hedge in recessions when interest rates fall and fiscal needs rise. Extrapolating from Belton et al (2018), the UK’s maturity premium costs approximately 30 basis points in yield - worth 9% of GDP in present value.12 Combined with the £201 billion in additional tax revenue, this would fully fund the proposal even under the most pessimistic assumptions about yield sensitivity.

Policy implications

How could reform be enacted? For LGPS, implementation is straightforward: the Secretary of State can issue directives under Regulation 7 of The Local Government Pension Scheme (Management and Investment of Funds) Regulations 2016 that all council investment strategies must be compatible with, and could mandate a 75% equity target tomorrow. As such pensions are DB, this would only improve their funding ratio however, with the surplus accruing to the government or local councils. Similar modest incentives to those proposed below could be used to encourage individual conversion to DC.

For private sector DB schemes, an existing mechanism - Cash Equivalent Transfer Value (CETV) transfers - already gives individuals a statutory right to move from DB to DC schemes.13 But current rules stack the deck against transferring: members must accept an implicit haircut if the scheme is underfunded, and must obtain financial advice that, following Pensions Regulator guidance, is highly likely to recommend against switching.14 Moreover, the same arguments for holding equities that apply to pension funds apply to a similar extent to individuals’ own savings, yet the UK public holds remarkably little in stocks, implying some public information efforts would be necessary to induce take-up.

To reduce these frictions, three changes would help. First, remove the underfunding haircut: if a scheme is 90% funded in expectation, let members transfer the full value of their assets and whatever entity previously would have been liable retains responsibility for the shortfall they would have borne had the individual stayed. Second, reverse the regulatory presumption on advice for switches to regulated DC schemes - the Pensions Regulator could update its guidance to reflect the long-term case for equities, reducing both the cost and the friction of mandatory advice. Third, offer a modest incentive: a £1,000 lump sum payment today for those who switch to regulated schemes, with the government informing every potentially affected household about the offer. Even if 10 million people took this offer up, the cost would be under 2% of the expected consumption benefits. The machinery for implementation does exist.

Conclusion

Pension misallocation has substantially reduced the retirement consumption of a generation of UK savers, having cost DB members over half their potential asset value since 2006 - and the supposedly “safe” gilt-heavy strategy still managed to trigger emergency Bank of England intervention in September 2022. The implicit subsidy from forced gilt purchases is a highly inefficient means of financing government debt - and one that could be entirely offset by shortening the maturity structure to international norms. DB reform could thus deliver over £600 billion in additional consumption and bequests to British retirees and older workers over the coming decades at no net fiscal cost.

People don’t flock to expensive, crowded cities primarily because they love urban living. They move there for higher wages. While cities offer museums and restaurants, this is in practice fully offset by higher crime, commute time and other disamenities, resulting in there being no net effect of city size on amenities. Most major cities aren’t located in places with exceptional natural beauty or ideal climates—they grew where they did for historical reasons of trade, ports, and industry.1 If AI significantly reduces the wage premium that cities offer, the economic logic that keeps millions packed into urban centers weakens dramatically. We might expect a meaningful shift toward areas that people actually prefer to live in—places with more space, lower costs, and better natural amenities.

To test this hypothesis, we’ll adapt Hsieh and Moretti’s (2019)’s model of urban agglomeration by adding a parameter for exogenous capital income. This capital income is distributed uniformly across locations—everyone receives roughly the same amount regardless of where they live. Why model it thus? In a world where the return on capital remains below the economic growth rate (the r < g condition), most capital income at any point in time still represents someone’s deferred wages from earlier work, rather than inherited wealth passed down through generations.2

Specifically, we’ll redefine utility to be

Where Wi is city wages, K the transfer, Zi city amenities, Pi city prices and beta the expenditure share on housing. As dV/dWi, i.e. the marginal return to an additional $1 of wage earnings, remains constant, while dV/dZ_i has risen by K/P_i^beta, wages will be relatively less important in determining relative housing prices, so high wage areas will fall in relative price. Combining with the equation for labour demand gives a new equilibrium condition of:

Where gamma is the inverse of the city elasticity of supply, P_bar is a constant of the demand curve and theta is a parameter indicating the degree of long mobility. We can solve this using the data from Hsieh and Moretti (2019) for the US and this housing data for the UK.

We also need to establish a baseline: how much exogenous consumption do people effectively receive today? The obvious component is returns on financial assets like stocks and bonds, but for most people these are fairly small. The larger piece comes from government transfers—both cash payments like Social Security and in-kind benefits like Medicare. These transfers are ultimately funded in part by returns to capital (through corporate taxes, capital gains taxes, and general taxation of capital income), making them effectively a form of redistributed capital income from the perspective of recipients. Calculating the exact equivalent flows through several channels. Capital ownership is highly unequal, then gets taxed at various rates, then gets redistributed through government spending—some as cash transfers, some as services like healthcare or education. Working through this implies the average person in the UK effectively receives capital income equivalent to about 28% of their total income, while in the US it’s about 21%.3

The model produces several striking results. Firstly, aggregate housing prices fall in the UK but rise in the US. This is because in the US, many of the most supply-constrained cities—places like Los Angeles and San Diego with strict zoning—also happen to have genuinely desirable amenities. These cities can maintain their value even as wage premia decline.4 The UK’s curtailed cities, by contrast, are constrained more by historical accident than natural appeal, and see much less movement than American cities with more liberal planning regimes.5 Second, in both countries’ larger cities see bigger drops in both prices and population. This makes intuitive sense—big cities today are big precisely because they offer large wage premiums, and as that advantage erodes, so does their pull. Third, US cities show much steeper price and population swings than UK cities when we account for their size, as US cities differ much more in amenities than UK cities so changes in the desirability of amenities are much more important. This is perhaps unsurprising given the massively greater variance in climatic conditions, and larger variance in local policy, in the US compared to the UK.

Both graphs in levels assume that the income elasticity of demand of housing is zero, or equivalently that the shock is purely to shares with no effect on aggregate income. In practice, any likely shock here would almost certainly boost overall output, and with it housing prices given a rise in housing demand with income.6

City populations could adjust downward fairly substantially in many worlds with higher capital shares, and would plausibly do so more in worlds with more egalitarian distributions of income. Many institutions—political, economic, and financial—are implicitly built around assumptions of a capital share substantially below the labor share. If that assumption doesn’t hold, much else may change.

Location: Harkstead Hall, 2 hours from London Liverpool Street

✨ Apply here! Applications are due August 31st, EOD AoE. ✨

What is Second Order?

A three‑day residential unconference for ~20 early‑career economists, policy wonks and kindred thinkers. At an unconference, the schedule is participant driven: we collaboratively craft the content at the beginning of each day, so you can run whatever you are most enthusiastic about! The classic case for this is that conversations in corridors between sessions are often the most valuable part of traditional conferences, hence unconferences aim to transform the entire conference in this manner. Some sessions from a previous iteration:

• A step by step guide for how you won’t build a house in London

• Informational supply chains

• A history of cybernetics

• Uncertainties on optimal immigration policy

• Frequentism’s insanity in two diagrams (1st, 2nd)

• Evaluating mechanisms for fertility decline

• Why the horses were fine after all

• Introduction to mechanism design

• Will AI be a decisive strategic advantage?

Plus many others, along with an evening panoply of Wikipedia bluffing games, supply chain simulations, giving someone else’s lightning talk topic, late night conversations and much more.

Who should apply?

We're primarily looking for curious people with some economics-adjacent interests. Note that some of our most valuable participants previously had no formal economics training, and we're seeking a diverse group with varied backgrounds—so when in doubt, apply!

A few other things we value are demonstrated excellence in other areas, super reasoning / critical thinking ability, and desire to understand the world as an entire system rather than just one particular part.

Logistics

We expect we’ll need to charge around £200 for students, and £300 for non-students. We’ll finalise the cost by the time of the acceptance email. If cost is a barrier for you, please apply anyway and make a note of it in the additional comments section of the form. We may be able to subsidise places for people who need them.

Venue: We’re staying at Harkstead Hall. Check-in will be Friday, September 26th, at 4 PM. We will leave the venue on Monday, 29th September, at 10:00. Should that be inconvenient, you’re welcome to join us there instead. All beds will be singles, and single gender rooms will be available should that be your preference. The venue has a pool, hot tub and sauna, so you may wish to bring swimming costumes.

Travel: The train from London Liverpool Street to Ipswich takes around 90 minutes. We will be booking a coach from central Ipswich to travel to the venue.

Contact

Please email second.order.retreat@gmail.com if you have any questions or concerns.

✨ Apply here! Applications are due August 31st, EOD AoE.

Britain’s slide from global hegemony to irrelevance wasn’t because it once had the world in GDP per capita, but is now doing famously badly relative to other developed countries. Income gaps among rich nations are modest, and weaker economies like the USSR (never above 43 % of US GDP per capita) still packed strategic punch.1 What shrank Britain’s weight was not low fertility either—its birth rates stayed high, at least until WW1—but mass emigration. The people, and the children they would have had, simply left.

Over the 19th century, UK emigration averaged 0.5% of the population per year. About half of migrants eventually went to the US, with the remainder primarily going to Canada, Australia, New Zealand, with smaller numbers going to various African colonies, primarily what is now South Africa. In this post, I model a counterfactual where emigration of British citizens was zero since 1815, and compute the corresponding UK population.

Model and results

How can we estimate the population absent emigration? The naive solution—just add every emigrant back into the headcount—ignores the children those emigrants would have had. A cleaner method strips migration out of the growth rate itself: start with the observed population, subtract net migration each year as a share of the total, and let that adjusted growth rate compound forward. The result is a population path that implicitly assumes net migration is zero for the entire period.2

The core emigration series was pieced together from A History of Emigration for 1815-1911 data, some 1920s Parliamentary questions on migration, a statistics handbook for 1948-1950, the post-1960 UK emigration records. Data for 1930-1947 was not readily available and was assumed to be zero for the sake of conservatism, and data for 1951-1960 was inferred from the net migration rate, meaning for both these periods actual outflows were likely notably higher. Data pre-1870 refers to every person who left via ports in Great Britain to emigrate to a long distance destination, and thus includes some individuals who transited through British ports for immigration purposes without being British themselves. Post-1870 data refers to British citizens only (or British subjects as they were known before 1949). Pre-1850 net migration was not available directly, and was imputed at 60% of the level of emigration, on the grounds that 40% of emigrants later permanently returned. All of Ireland is excluded from the data pre-1922, but post-1922 data includes Northern Ireland.

This methodology would imply a population of the UK today at slightly above 150mn. However, this ignores the potential effects of any emigration on fertility. Firstly, might there be some effect lowering the standard of living from the higher population, which could lower fertility? Under the classic Solow model of economic growth, this would occur, but not by much. The higher rate of population growth would depress the capital stock per capita - fewer machines per worker - reducing GDP per capita by about 4.7%.3 Substantial, but not large enough to interrupt this population boom in its tracks. Secondly, the higher population would enable larger scale effects for cities - about 4% per doubling per Duranton and Puga (2020). If this larger population was sorted into cities at exactly the current distribution of size, this would by now have more than counteracted this decline, although it would have reduced fertility in the interim, and is hence included.4 Additionally, a majority of migrants were male, causing a demographic imbalance in the UK - in 1850 there were 500k more women than men, implying 0.9% higher fertility in the 19th century without this (assuming monogamy).

Most of these effects are fairly small in magnitude however - adding up to a 5mn change in expected population. This is because the elasticity of fertility to income in the 18th century was fairly small - Klemp (2012) found 0.31 to wages, while Foreman-Peck (2015) found 0.13 and Clark (2007) found essentially zero - implying minimal changes in TFR given the already small changes in wages. 0.2 will be used here for the sake of conservativism.

The biggest upward revision comes from the emigrants’ own future families. Most left as adults: they had already survived the brutal childhood mortality of the 1800s, yet 80 % were still in the 15-50 age band, with the bulk clustering in their twenties. That means they carried more unspent fertility than the average Briton at home. Adjusting the model for this higher expected childbearing (and noting that our lack of fine-grained age data likely understates the gap) pushes the population trajectory to the higher line shown in the next figure.

With the fertility boost included, Britain would now house just over 200 million people instead of 70 million. How would that reshape the Anglo-American balance? The chart below offers a clue—though it likely understates the change. Our UK-to-US migration counts cover only 1815-1920 and 2000-2022, and the earlier series records passengers sailing directly from British ports, missing those who detoured through Canada for cheaper fares. Even with these gaps, emigrants from Britain over the period summed to 13.4 % of the 1920 U.S. population, implying that America today would be roughly 23 % smaller had those people, and thus their descendants, stayed put. A bigger Britain and a shrunken United States would bring their economies much closer in scale.

Discussion

A Britain of 200 million would have stayed neck-and-neck with the United States; its relative GDP to the US would be today roughly where it historically stood in 1899, perhaps higher had the Victorian colonies remained. But keeping everyone at home looks like a very large welfare loss. Britain’s relative poverty is probably rooted in planning rules, not people, while the emigrant destinations—Australia, Canada, New Zealand, and, above all, the US—have long out-earned the old country. Additionally, public-goods spending grows more than one-for-one with a country’s heft. America’s sheer scale makes it rational for it to invest much more as a share of GDP in defence, biomedical R&D, and green-tech subsidies than the UK or individual EU countries; trim that scale and the super-sized contribution shrinks disproportionately. Half of Britain’s outflow went elsewhere, so the net effect on global public goods is reduced but still likely negative, and although an extra boost to the Allies in two world wars is plausible, it does not outweigh the peacetime gains long enjoyed already enjoyed by the emigrants’ descendants, and the global benefits from higher public goods production.5 6

Conclusion

The UK ultimately lost international power because a very large percentage of its population left for greener and more pleasant lands overseas. However, the scale of emigration was so large that, by the 1980 census counts the US has more people of British descent than the current UK does - 75mn scaled to all who reported that year, versus only 56mn citizens in Britain proper in 1980, and 70mn today.7 8 By the absolute number of its inhabitants, the US might well have a better claim to be the successor state of Victorian Britain than the current UK does. After all, the sun sets on the US for less than a thousand hours a year.9

Modern AI models need access to internet-scale public data, which requires a liberal copyright regime to train on. Current debates around copyright reform often rely on the perceived costs to artists and writers—they provide the key inputs to making models, but receive no compensation in the process.

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We model how much they could get paid. Even if AI companies were forced to spend as much on data as all other expenses combined, artists would receive only $0.09/10 000-word essay and $0.06/image—while raising AI company costs by 65%. Considering the large amounts of anonymous data available, the fact that data varies in quality, and cheap synthetic enhancement that can be done, the median artist’s payment would be even lower.

How did we calculate this number?

There are many ways you could assign property rights for data. How much, realistically, could they pay? Training a frontier model already requires billions of dollars of compute and engineering. Whatever legal regime emerges, labs cannot afford raw data, so we therefore model outcomes under the conservative assumption that this entire current spend forms the absolute ceiling — while staying agnostic about the mechanism enforcing it.1 Competition with geopolitical rivals that care less about respecting copyright puts a hard upper limit to the maximum possible tax that AI companies will in fact pay to copyright-holders.

So, let’s explore what creators might earn if they were paid for AI companies using their work. The best publicly available data is from 2024, and with Meta’s Llama figures.

When Llama 4 Behemoth was trained, it used about 30 trillion tokens of text from roughly 1.4 petabytes of data. The training cost approximately $800 million. If creators were compensated based on this total cost, they’d receive ~$0.00003/token.

But this initial calculation doesn't tell the whole story. This 30 trillion tokens was from 120 trillion tokens of raw text, dropping the value dramatically to about $0.000007 per token. To put this in perspective, a 10,000-word essay (about 13,000 tokens) would earn only about 9 cents - or Shakespeare’s complete works $4.74.

Something wicked this way comes

We need to make several key adjustments to this estimate. Multiple AI companies run multiple training iterations, which increases the value somewhat, but not dramatically. At least 16 training runs larger than 1e25 flops took part in 2025, and 100 larger than 1e23; assuming an exponential distribution over training run size, this implies that the sum of all training runs will be 3.59x larger than the largest training run in a given year, as the largest training runs take up most compute. Additionally, compute and data trade off against each other, so companies can shift to using less data and more compute power. Under Chinchilla-optimal scaling laws, companies would respond to laws requiring a fixed cost per token by giving the model more parameters - but if they want models as effective as previous, they’ll need more compute - as their previous choices represented the optimal combination of parameters and data. This causes a 43% reduction in data usage and an 8% rise in compute used, and thus tax revenue at 57% of expected levels; with the 8% represents a pure loss to society, as AI developers' costs rise without firms compensating creators.2

Additionally, much data has an untraceable author - being an anonymous form comment, Wikipedia article or random code. This means that if firms had to pay, they could simply push towards using such anonymous data. This will be magnified by synthetic data - model-generated stand-ins - as current techniques cost relatively little extra GPU time. Once a sufficiently comprehensive seed of human works is secured, labs can pad the rest with these cheap tokens, driving royalties ever closer to bare compute cost. We won’t model either of these effects here, but this will make all discussions regarding creator compensation increasingly irrelevant over time.

Quality and variety considerations don’t substantially increase these values either. Most creative works aren’t uniquely valuable to AI systems because similar information exists in many sources.3 There may only be one ground truth for Romeo and Juliet, but the AIs can probably guess the contents of your 7000-word Harry Potter fanfic.4 Insofar as content differs in value, the payment to the median content-producer - holding the mean constant - necessarily falls. AI companies would also likely develop more synthetic data rather than pay high prices for human-created content.

After all these adjustments, a 10,000-word essay might earn about 9 cents per year — hardly Substack.

The situation for images is similar. Models like DALLE-3 trained on about 1 billion images with approximately $30 million in compute costs. This translates to about 6 cents per image. Picasso might earn $831 for his life's work, but the less accomplished, such as the little known Leonardo da Vinci, might receive less than 50 cents.

For sale: human art, never automated.

Implementing such a system would increase AI development costs by about 65% while providing minimal benefits to creators, measured at best in the single digit dollars per year. Without worldwide coordination, companies would simply relocate to countries with fewer restrictions.

In the end, these calculations suggest that data payment schemes would significantly hinder AI development while offering little meaningful compensation to the creators whose work is used in training.

Conclusion

At present, the UK copyright’s text-and-data-mining carve-out (s. 29A CDPA) is restricted to non-commercial research, meaning a frontier lab must obtain licences from every right-holder before scrapping even a single copyrighted sentence. At the trillion-token scale the transaction burden becomes unworkable, effectively shutting commercial model training out of UK jurisdiction.

We’d like AGI to be safer than current trajectories, yet if advanced models are coming anyway the a country’s tight copyright rules won’t protect its artists—they’ll just vanish from the corpus. That vacuum hands influence to looser jurisdictions, so ensuring local data is trainable is strategically vital: it imprints future systems with local norms, economic aims, and security interests.

Acknowledgements: Rudolf Laine, Jack Wiseman, Julia Willemyns, GPT-4o, millions of uncompensated artists

Oftentimes the worst case story told by your doomsayers of automation is that you might be to AI, as we horses were to the automobiles.

And indeed, in the short-run, we did suffer. Within 60 years of the release of Mr. Ford’s Model T, the first mass-manufactured car, our US population declined by 80%. Many of my ancestors were sent to the glue factory, their final contribution being to hold together furniture rather than society.

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Yet, in the long-run, we have done pretty well, thank you very much.

We find that total horse welfare, including when adjusting for population, peaked in 2000 and has stayed high since. That means that, under our best guess of the population’s happiness, both the average and total welfare was maximized in the early 21st century. Population adjusted welfare peaked in 2000, and remains higher today than at any point in the 20th century. This may be a cause for hope.1

How did we go about measuring horse welfare? The response rate on our happiness surveys weren’t high enough. What was it like to see automation as it was happening (contemporary reactions below)?

The Intuition

Our economy consists of labour (manual work like pulling) and capital (all the existing ploughs and carriages) to produce output — happy consumption hay.

We horses generally don’t control our own population. While we can choose whether to mate or not in the wild, the vast majority of our population (99.92% as of 5 years ago) is determined by your breeders.

This complicates things because, unlike humans, if we became more “productive” (i.e. able to generate more value per hour worked), the breeders, influenced by your free market, would simply breed more of us.

We are in the Malthusian trap. We don’t keep the profits from our hard labor nor do we control when we have foals. Therefore, our welfare will fall until we reach subsistence levels.

This means that each time horse productivity changes, on a short enough timescale, the free market breeds more horses until the marginal horse is worth as much as before — our total opportunity cost to be kept as low as possible. By how much? This hinges on the price elasticity of demand - how large a change in prices a 1% change in quantity would cause. Racehorse demand is highly elastic at -2.35, but quarter horse data suggests a combined elasticity of -0.98, which will be used here.

Now seems like a good time to talk about what we mean when we say “welfare.” Welfare consists of:

• Our total consumption (apples, sugar cubes, stablespace, silk ribbons),

• How long and hard we had to work to get that consumption (how many hours spent pulling a carriage or heavy iron plough, building a windmill),

• Our life expectancy, i.e. how long we have to enjoy the fruits of our labor.

We consider all of these factors when we say horse welfare in the 21st century is the highest it's ever been, for each individual horse (which makes sense, pasturing is much easier than pulling) but, surprisingly, if the culling of horses hadn’t happened (i.e. population had stayed the same from the early 20th century), aggregate welfare would be higher.

This is interesting because constructing this constant-population counterfactual would significantly reduce the wages and consumption of horses - but they still come out ahead.

Consumption

For the model, we assume that horse consumption is constant over time — we aren't getting any nicer food or stables etc. — which is very conservative. In fact, I do enjoy better feed than my ancestors — quality hay twice daily, the occasional bran mash, and actual veterinary care when I'm ill — luxuries my great-grandsire could never imagine while chewing on moldy oats after fourteen hours of pulling streetcars.

Unlike the real world, in our hypothetical world where, more analogous to humans, the population hadn't taken the “slack” for the loss of productivity (i.e. the marginal horse starved/was not worth keeping), the consumption of the horses did.

Wages

Labour and capital combine for output. Initially, horses were the only source of labour — we worked ~9 hours a day, up to ~1900. Our bodies are enhanced by capital, such as ploughs and carriages, but try putting a plough in a field without a horse! Output would be 0 if you did not have both us and your tools for the set of tasks that any respectable 19th century horse would perform.

Starting from the invention of the motor car, and beginning in earnest with that wretched Model T in 1909, those noisy machines began to partially substitute for horse labour. They can do some tasks much better (though I still maintain they're frightful on long journeys), some only slightly (have you ever seen a Model T prance elegantly for the Queen?), and some not at all. Not very many therapy cars out there, I see.

The idea is that wages are the product of the marginal return to labour, and the marginal returns to horse labour within labour. Initially, when you create a lot of cars, the marginal return to total labour will drop a lot.

After they figured out reliability, cars were strictly a better means of travel. Contemporaneous monitoring organizations like Mechanical Equine Transit Replacement (METR) projected the reliability over time.2 But eventually, as that the cars stopped encroaching on our task share, we will found our niche again - how many therapy cars have you ever encountered?

Life Expectancy and Work Hours

Our life expectancy has improved dramatically across America over the past 2 centuries. Consider this: where my great-granddam collapsed at age 7 after years of brutal city work, I can expect to live past 25. This matters tremendously—each additional year of life brings joy that doesn’t diminish like the pleasure of an extra apple or fancier blanket.

Meanwhile, our workload has virtually disappeared—from my ancestors’ backbreaking 9-hour plough days to my luxurious schedule of occasional light riding.3 To understand what this means for our welfare, economists try to calculate how much we horses value leisure versus work.

For humans, statistical value of life calculations 1 hour of work is worth about 0.88 hours of leisure—but let’s be honest, pulling a loaded coal cart uphill feels much worse than these figures based on air conditioned office jobs!4 Still, we’ll use conservative estimates: and assume we horses have a time preference discount rate of 2% (meaning we slightly prefer hay today over hay tomorrow), and our statistical value of life is 2.5. This means we highly value our longer, easier lives.

Welfare results by year are above. Horse welfare dropped by much less than population over the 1920-1960 period because it coincided with major growth in life expectancy. Today, the horse welfare index stands at 185, compared to 183 at its height in the 20th century in 1920. While any estimates here are necessarily quite imprecise, we can state with some confidence that the invention of the automobile was not catastrophic for our welfare.5

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Conclusion

You humans now stand where my kind once did—at the precipice of replacement. Your "artificial intelligence" gallops toward you much as the automobile once thundered toward us. We each had no property, had no other members of our species who owned assets we could rely on to purchase our labour and had no power in the political process. And still outcomes for us were far from terrible, with welfare only falling 26% from its peak and quickly recovering.

Unlike us horses, you own ourselves, and thus your wages, and you own tangible capital in the economy and control, somewhat, your own political process. By default, these may be sufficient to allow a rather better outcome for humanity than the reasonably good one we achieved for horses. With the development of superintelligence, you better hope that you can keep it that way.

Inference Magazine

How much economic growth from AI should we expect, how soon?

Is this the steam engine, electricity, computers, or something bigger…

Read more

a year ago · 12 likes · Jack Wiseman and Duncan McClements

Executive Summary

The view in San Francisco is that AI will far exceed the pace and depth of change in all previous technological revolutions. This is because of a belief that AI can automate the process of invention itself. Since Bacon, the march of science depended on the actions individual inventors and small groups of researchers; but perhaps in a few years, we can create AI systems that will be capable of performing research at the level of — or indeed, much better than — the best human researchers. We can put tech progress on autopilot.

How does this arise, according to this view? First, the AI labs create an AI system capable of performing AI research, on par with their top researchers. Next, millions of instances of the ‘digital AI researcher’ are run to make much faster research progress. These breakthroughs are applied to training the next generation of digital AI researchers, in a recursive self-improvement loop. This process leads to the creation of digital AI researchers which are much smarter than humans—this is ‘superintelligence’. In the dominant intellectual paradigm in San Francisco, this happens quickly. One important work on ‘takeoff speeds’ towards superintelligence argued that the time between AI systems capable of performing 20% of tasks humans do, and 100% of tasks humans do, was just four years.⁵

Superintelligence, as it is conceived, would have important implications for the economy: we could have an ‘explosion’ in R&D; and systems capable of performing 100% of the tasks that humans do could begin to automate the whole economy. (As the narrative goes, the superintelligence could figure out how to make robots which could perform as well as humans.) There is some academic work which investigates what happens to economic output when 100% of tasks are automatable, and many growth theory models show explosive economic growth (20% per year, or more).⁶ Under some conditions there is an economic singularity, which means growth models predict infinite output in finite time.⁷

On the contrary, most economists who study the impact of AI do not consider the prospect of recursive self-improvement. But most work on explosive economic growth does not deal with the microeconomic constraints of running an AI lab. This is a gap we hope to fill—providing a grounded view of what AI research automation will look like, and how this might come to affect R&D and cognitive labour automation in the near future.

AI research automation

The most important thing to understand about AI research automation is that the AI labs are constrained by computational power to run experiments, not by researchers. A researcher from the Gemini team at DeepMind has said, “I think the Gemini program would probably be maybe five times faster with 10 times more compute or something like that”. Whilst, the cloud providers are spending enormous amounts on compute—Microsoft just announced it would spend $80 billion this year on building AI datacentres, but most of this compute would be used to run inference for customers, and is unlikely to be for AI researchers to run experiments. The economics of inference for customers is very different from the economics of compute for R&D: compute for experiments and training needs to be amortised across all of the inference profit margins. As we shall see, there are strong headwinds to making money selling tokens!

One of the assumptions which proponents of the Explosive Growth view often make is that a digital AI researcher will be trained on a large compute cluster, and then millions of instances will be run on the same cluster. This seems irregular to us! If the point is to recursively self-improve the AI system, but the training compute is being used for inference, where is the next generation agent going to be trained? It seems much more reasonable to imagine that ~60% of the AI labs' compute goes on serving customers, ~30% goes on training the next model, and ~10% goes on experiments. (These numbers are extremely rough guesses.) If the AI lab wants to run instances of the digital AI researcher, they will need to trade this off against experimental compute; and remember, research output is bottlenecked by experimental compute. If the digital AI researcher has equivalently good or worse ideas to the best human researcher, it makes sense to run zero copies; for it make sense, the ideas have to be better.

AI research will be automated in the future. It is reasonable to imagine that, perhaps soon, we will create a ‘digital AI researcher’ whose research intuition—i.e. ability to predict which experiments will work—surpasses that of the best human researchers, but before then, digital AI researchers will have a bounded impact on research output, owing to the compute bottleneck. We discuss the practical challenges to increasing research output, as well as some reasons our mainline case could be wrong, in greater detail below.

R&D automation

Concurrent to our progress on AI research automation, we want to make progress in other fields of science and technology! The opportunity is enormous—for biomedical research, clean energy, materials, synthetic biology, nanotechnology, and robotics. As with AI research, the goal is to create systems which are capable of performing all steps of the research process—generating hypotheses, designing and running experiments, and interpreting results. There are a number of challenges to scientific automation, related to the availability of data, the necessity of real-world experimentation, and so forth. It also seems reasonable to believe that academia is poorly configured to take full advantage of the opportunity which AI automation is. We expand in greater detail on both points below.

We focus on three potential fields for automation—chip research because if we are compute bottlenecked, improving our chips would help to alleviate this; robotics as improvements here could begin to automate more physical labour, and biomedical research; for effects on human wellbeing. There are different challenges in each area to automation, though in general, experimental throughput is most likely to be rate-limiting.

Cognitive labour automation

Thus far, chatbots and ‘agents’ have struggled to meaningfully increase the productivity of human cognitive labour. Deploying systems is difficult right now—it requires specialised knowledge about how to build infrastructure for models. But as the models become increasingly capable of acting on long horizons, we expect most of the challenges to deployment to become diminished. We will still require people to have liability for AI systems, and in many professions, there are ‘embodied’ complements to cognitive tasks (e.g. when a doctor has a consultation, they are both doing the diagnosis, and tailoring their explanation to the patient, and expressing care and empathy, and so on) These factors together lead us to expect that people will be managing teams of agents in their jobs—it will look like ‘a promotion for everyone’—rather than a lot of job losses. However, there might be some areas where production is entirely substitutable, and so jobs might be lost. To estimate the increases to output from tasks being handed off to agents, we built a growth model that shows how many tasks might be automated, how much these tasks can replace other tasks, how cheap these AI systems are, and how concentrated this is within sectors. We find that growth will be quick by historical standards, but not explosive. We expect AI will provide a 3%-9% increase to economic growth per year in the near future, and we expect it will be in the lower end of this range due to bottlenecks we discuss further in the piece. This picture will seem conservative to some—but it is worth reiterating that we will develop intelligences greater than our own, and it will radically change almost all aspects of our lives, our analysis is limited to the near-term economic picture.

There are a few variables across this whole analysis for which different assumptions would produce very different technological and economic outcomes. The most obvious is what is the inference cost of running digital researchers and cognitive labourers—if it is cheap to run both, we should expect faster research progress and we should expect greater economic growth from normal sectors of the economy. We note that it is important not to have too much confidence in a specific vision of the future; but rather see the direction of travel.

Read the rest of the piece:

Inference Magazine

How much economic growth from AI should we expect, how soon?

Is this the steam engine, electricity, computers, or something bigger…

Read more

a year ago · 12 likes · Jack Wiseman and Duncan McClements

1. Tyler Cowen argues that the way for them to show their sincerity would be to short the market, since they expect huge damages from AI eventually. (He further implies that their not shorting the market makes light of the x-risk view.)

2. Others argue that those worried about xrisk should go long on AI-related stocks – since actually, if AI is to be powerful enough to cause catastrophe, related stocks will have incredible gains for some period before that. It also buys insurance.

3. Another way of betting your beliefs would be to increase your current consumption (since you don't expect to be able to realise investment gains).

4. And another is to zero out your retirement contributions, since you think you won’t get to draw down.

So, does a lack of “endurance to collect on [your] insurance” imply shorting the market? Note that this is not investment advice.

Model

To answer which approach is the best, we need to model a portfolio that allows us to test each option. In our portfolio, there is three assets: first, a risk-free bond, which gives us the return r; second, a risky AI stock, with a mean return of μ₁ and a standard deviation σ₁₁; and third, a risky non-AI stock, with a mean return of μ₂ and standard deviation σ₂₂.

We want to maximise our return, while minimising our risk, and so we can represent returns as the annual returns for every year in the future, discounted back into the present, and our risk aversion with respect to income1

Finally, provided that the two stocks are not perfectly correlated, we should reduce our portfolio risk by owning some of both of them. The more uncorrelated the two stocks are (correlation is measured by σ₂₁), the more we would like to spread between them (holding returns constant). This means that the equation to calculate our optimal holdings and consumption looks like this:

Several things immediately appear. Firstly, the optimal portfolio is independent of discounting - so high estimates of doom do not suppress stock holdings. This is because as the mean return and standard deviation of stocks doesn’t change across time, the risk profile of any given allocation is time-invariant - so you don’t want to change your desired portfolio if you start valuing the future more or less vs the present.2

Secondly, if covariance is negative and both risky assets return more than bonds, optimal holdings of non-AI stock are always positive. This is because negative covariance means risk can be reduced by holding at least some of each stock, and the second condition means doing so is a better deal than bonds. 

Thirdly, although optimal consumption is increasing in both discounting and expected returns, η determines the relative degree of each - under low levels of risk aversion expected returns have no effect (η = 1), while under high levels mortality is greatly suppressed in importance.

Parameter estimation

High estimates of doom are theoretically compatible with high estimates of covariance though - so we need to establish upper bounds of individual’s beliefs on this to check whether any set of beliefs could justify shorting the market.  

μ₁: The mean return of AI stock. Under Manifold’s, a prediction market, estimates for when OpenAI firms reaches a $1trn valuation (current valuation: $150bn), expected returns would be 52%/year if valuation growth was monotonic and the firm was worthless if it never reached $1trn. However, Manifold also estimates a 62% chance at least one of OpenAI and Anthropic drop below their current value by 2030 and 34% OpenAI no longer exists by 2030. Many of these trades are on very low volume markets, but if Anthropic and OpenAI are equally likely to no longer exist and have reached a valuation of $1trn at one point in half of those worlds, then this implies a 44% mean return.3

Of course, OpenAI and Anthropic aren’t available to buy in public markets. What is the maximum the heavy-AI public portfolio could return?

If Deepmind was valued at $100bn, given Alphabet’s $2.1trn valuation this only raises returns by 5.6% to 2035. If chip manufacturers can capture 10% of additional value created - noting that this would be 4x the AI firms themselves - this would given Nvidia, TSMC and ASML’s combined valuation of $4.42trn boost their returns by 14.7% to 2030. If they capture as much, this again falls down to 5.5%. The 5.5% excess return (so 15.5% total return) will be used here.4

σ₁₁: Standard deviation of AI stock return. In each of the above cases the standard deviation was 1.02 and 0.46 respectively.5

μ₂: Non-AI stock return. 10%. 

σ₂₂: Non-AI stock standard deviation. 15%.

σ₂₁: Covariance. This could be negative due to direct AI damage (including existential risk), or automation or similar effects increasing output but displacing existing firms. As noted above, to the extent that this is true optimal stock holdings are positive. Positive covariance could be driven by positive innovation spillovers to the rest of the market. Firms in general capture 2.2% of the value they create, boosting average returns over the next 10 years by 12.4% in the narrow specification, or by 0.6% in the broad specification.6

r : Risk free rate. 5%.

ρ: Pure time preference discount rate. 2%. 

η: Relative risk aversion. 2.

Results

Most importantly, non-AI stock holdings are always positive, and increase as covariance declines - so higher estimates of damages do not imply shorting the market. This is because if the stocks have negative covariance, they serve as a hedge against each other - a hedge which is more valuable the greater the expected return from AI.

The differences in consumption suggested in the table above are very small. This is because wealth growth rates don’t differ much across scenarios - in the optimal allocation, the additional income from access to very high-return AI stocks is used mostly to buy safe returns rather than increasing income. Higher wealth growth rates are then cancelled out by higher portfolio variance, which makes wealth more important as a risk-hedging tool.

What about existential risk pushing up discounting and thus consumption?

Optimal consumption is high enough in all these models any such effect to be undetectable for most individuals. For someone with 40 years of working life remaining discounting at 3% (5% less 2% income growth), their income flow is already only 4.2% of lifetime wealth - so they are credit constrained, desiring to borrow more at the risk free rate but unable to do so. Income only crosses 5.7% of remaining lifetime wealth 24 years before work concludes, so in an individual’s early 40s.7

Discussion

There are several issues in general with applying this kind of portfolio model - most wealth for most individuals are in future wages not assets lowering optimal leverage, investment returns do not follow a normal distribution raising optimal lecture, etc. In this setting several other effects manifest.

If existential risk is high, AI stocks are a better deal than modelled here - bankruptcy options are much more valuable with high variance assets. However, if nationalisation or political risk is higher if returns are high then returns are overestimated. Also, AI-induced technology could also introduce new goods, lowering effective η- if air conditioning is invented, you have something else valuable to spend higher levels of income on, so marginal utility declines less as you become richer - scaling investment choices proportionately. 

Discount rates are probably correlated with AI returns, as mortality risk may be higher if the technology is coming along more quickly; discounting doesn’t affect optimal portfolios, but consumption could change. Very rapid increases in wealth could also increase asset holdings amongst the old (who have converted more of their human to financial capital), or increase asset holdings for those with lower discount rates so have saved more historically, and so could have systemic effects on future premia. 

Lastly, these estimates don’t account for transition dynamics. To upper bound this, if (unpriced) mortality is 50% over the next 30 years, then annual mortality is 2.3%, implying a 30% price reduction. If society realised this over 10 years, returns fall by 4.8% - falling to close to bond levels. If covariance is negative, then optimal non-AI stock holdings will certainly remain positive; in the baseline broad specification stock holdings remain positive at 7.1%. Hoping to profit off of transition dynamics thus cannot justify shorting the market overall.  

Conclusion

As Tyler Cowen argued in a later Marginal Revolution post, finance theory is indeed non-obvious, and there are returns to doing the sums. Those with higher appraisals of AI risk want to hold more non-AI stocks, not fewer, as non-AI stocks then provide a more effective hedge against the failure of the high-return AI firms - and in no cases modelled here do individuals wish to short the market. Higher discounting could justify higher consumption - but the faster rate of economic growth AI could enable does not, over the short term. Forseeing any potential apocalypse generally cannot make you much money in a way that you care about.

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Historically, governments often employed a simple solution to these problems - they paved over rivers and then sold the additional land to reduce pressure on housing prices and improve their own financial position. Hence the disappearance of the Tyburn, Fleet and Walbrook. 

We can employ the same solution today. 

We estimate a total cost to reclaim the relevant land with matching sewer capacity within London of £3.13bn. The underlying land value plus a subset of agglomeration, less reductions in amenities, is worth £48bn, resulting in a cost benefit ratio of 6.5:1.1 The river’s pre-existing volume before entering London is relatively small (it increases in width by a factor of 10 while flowing through), and South East England has been in need of a new reservoir for some time, so the reservoir could just be positioned to capture the existing flow. Any environmental issues would be small, and relatively easy to mitigate. Although the calculations will be undertaken for London, we expect that a roughly similar logic should hold for most large cities around the world.  

Reclaiming the river

We’ll follow a similar strategy as we previously modeled for Dogger Bank: build a breakwater at the points where we wish to interrupt the river’s flow, pump the necessary water out, replace the sewage and drainage with tunnels then re-fill in. Thankfully, the scale will be vastly smaller. The Thames is only 70m wide and 6m deep when it enters London; even when it leaves it barely exceeds 750m with a depth of 17.5m. Assuming that the cost per unit distance of a wall goes as the square of depth - as deeper walls must also be made thicker - this gives a cost of £150,000 for the wall at the upper end of the Thames and £14.1mn at the lower end. Pumping the water out would cost £4.8m. 

Of course, the river currently serves a role both for sewerage and storm drainage - so replacement drainage capacity would have to be built. The river is currently sufficient for this purpose despite also carrying normal flow, so would also be sufficient with strictly less volume. How much? The wettest day in London in the past 25 years involved 42mm of rain; if 70% of water is ultimately diverted to the Thames, this would require 46m m³ of storage plus throughput in a day.2 Low-grit water generally shouldn’t move faster than 5.5m/s; a desired maximum system capacity of 80mm of rain in a day gives a required tunnel radius of 7.7m. 

Table 1 (first two columns adapted from Lin and Tsai 2009. Ouyang (2003) was omitted as it modelled no diameter or depth relevant to our calculations)

From here, we can then use existing estimates for the cost of cut and cover sewers. As no digging will be necessary, this does of course strictly overstate total costs. Construction inflation has been roughly double general inflation, and this correction will be applied. This gives a median cost estimate for sewerage capacity of £2.72bn.

In order for the construction to be practical - due to the need to continue potential storm drainage during construction - it would likely in practice be necessary to do a scheme similar to separately draining each half of the river and constructing there. Again assuming wall costs go as the square of depth, this leads to an additional expense of £389mn.3 This gives a total cost to the project of £3.13bn. 

Benefits

We find a £48bn gain from new real estate generation and agglomeration externalities. First, direct land gains. Given the dimensions discussed above, the river will have an area of 21km² within London, assuming a power-law function of river width to distance. The average London residential land valuation is £21mn/hectare (inflation-adjusted). This land will be disproportionately in the lower-average-value east of the city, and on the outskirts, relative to its course; however, other geometric considerations raise the value substantially.4

However, riverside properties do command price premiums that would presumably vanish. A home in the South East commands a 46% higher valuation in general if on a waterfront; riverside properties command an average 76% gain vs an average 80% across the entire country, suggesting a 44% gain. Assuming that the valuation premium declines by 50% per property from the waterside, this gives a total 88% gain in neighbouring property values. Under an average property depth of 20m (typical for homes), this gives a total loss of value equivalent to the loss of 2.4km² of land, giving an overall land value of £39bn.

This will also, in addition to releasing a large amount of land, enable substantial agglomeration by reducing inter-city transportation distances. Transiting the river is costly, both leading to a Tube network that connects north and south of the river infrequently and less foot traffic than would otherwise be the case. We won’t model this, but this would also raise the overall benefits substantially. 

We can, however, model the benefits from increasing population density this way. If this land has equal population density to the remainder of the city, then this yields a 1.1% increase in total population, which under an agglomeration elasticity of 0.046 and a 3.5% discount rate yields present value benefits of £9.0bn given London’s GDP of £520bn. 

Are there going to be any other economic costs from shutting down the river? The portions within London haven’t been used for unloading shipping since the Docklands were turned into the city’s premier financial district in the 1980s; commuters and tourists only take 10,000 journeys per day on the city’s public riverbuses, which even if it generates full surplus equal to the £10 ticket/journey (unlikely given the city’s excellent transport networks) is only a cost of £37mn. Some other economic benefits from the river do exist (such as a pub whose main marketing point is being on an island), but these are likely  to be comparable in size.

This gives net economic benefits of £48bn, or about 2% of UK GDP.

Environmental costs

We’ve already accounted for any local externalities: these will be reflected in property value differences of properties closer versus further from the river. However, some benefits the Thames provides apply across the whole city, or even globally - sequestering carbon directly, alleviating air pollution, providing a space for wildlife, reducing erosion and providing cooling - and so would have been ignored by the above methodology. Will the cost of removing any of these be substantial? No. Direct carbon losses will be small, at 472kg CO2/annum (worth £2500 present value), assuming an intensity of 242g CO2/hectare, as for grassland. Any air pollution effects can be mitigated by ensuring a sufficient fraction of the new land is designated as parks. Biodiversity losses can be easily mitigated by purchasing and rewilding farmland elsewhere; the price of pasture in the North East is only 0.08% of London average land prices above. Although a reservoir might be necessary upstream to catch the Thames’ pre-existing throughput, South East England has been in need of a new reservoir for some time regardless, so this adds no additional required infrastructure on what current population trajectories would regardless suggest. 

Might this cause substantial land losses elsewhere by increasing erosion downstream? The 46% of soft shorelines that erode do so at 0.43m/year - and around 17% of overall UK shorelines are eroding currently. Assuming that the Thames estuary is entirely soft, and using a 100km size, implies that even if this scheme would cause erosion to double and if exclusively arable land was eroded (rather than less valuable pasture, or land unsuitable for agriculture) only 0.02km² of land would be lost per year - worth present value only £1.4mn. 

The cooling effect of rivers is large near a river but dissipates very quickly, entirely vanishing after 500-700m - using the lower end to account for the river’s bends gives an area of 68km², or 3.9% of the city, being raised in temperature by 1 degree during summer. Cooling is just below 10% of UK electricity consumption, and per capita varies very little across the UK. A 1.6-degree average rise in Europe boosts cooling demand by 4.4% - but only 5% of households have air conditioning. To upper bound the total welfare loss, if all buildings affected used air conditioning, electricity is 11.5% of UK carbon emissions, so this would only increase UK aggregate emissions by 0.0037% - under a carbon price of $240 only equivalent to £75m of damages present value. 

Conclusion

The intuitive case for covering rivers follows from the reversibility test - few would suggest returning the now-buried rivers to the surface - and it also seems unlikely that, once the Thames was filled in, there would be any suggestion of excavating and flooding the land again, suggesting that if transition costs are small (which we estimate they are) the transition is worthwhile. General aesthetic benefits barely vary our results also - even if the average Londoner valued the river at £100, this would be worth less than £1bn - in the context of £48bn worth of net land gains. The benefits could also be much larger than we estimate - costs per unit space only increase fairly slowly with building height, and when public authorities capture all of the upside they have often historically been more willing to zone for high density (as with the conversion of the Docklands). This could bring benefits equivalent to much more land reclamation, and enable greatly more agglomeration.

Filling in the Thames would thus have a cost benefit ratio of 6.5:1, even ignoring much of the substantial agglomeration boosts. Environmental costs are very small in comparison to the size of the gains, and so are straightforward to offset. We thus have the opportunity to substantially increase the benefit to society from what are today the least-utilised pieces of land in our most expensive cities.

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What can we do? In the short term, countries will try to encourage immigration – see Japan’s recent liberalisation of immigration rules. But, fertility is falling everywhere. We might then try relying on the traditional driver of population growth over the past century, namely the lower mortality rates from economic growth and medical advancements. However, the gains from this approach have been exhausted. People rarely die before reaching the age at which they would have stopped having children.1

So, we’re left with trying to encourage more births, or removing barriers that exist currently. More people are good. Not only are they capable of leading happy lives (a philosophical position), but they have ideas, and innovate. However, it is not immediately clear if we, like good economists, should subsidise this positive externality. This is because, bar some sophisticated (and politically difficult) targeting, we’ll have to subsidise all births, including those that would’ve happened anyway. 

In this post, we show that under the median estimated elasticity the socially optimal fertility rate is 2.4 in the US, well above today’s 1.7, given that the US should place a value of 14.28x GDP/capita per additional birth ($1.17mn per birth). Furthermore, to achieve this, the US should be willing to spend the equivalent of 3.8% of its GDP ($290K per birth) on fertility subsidies. For context, the existing child tax credit is worth $2000/year, or $26K present value. We’d like to stress that these figures are highly uncertain, because of both the varying welfare gain from more births, and also varying estimates of how effective subsidising births are. Even still, in the main case, the US government should seriously consider greatly increasing its child tax credits, and explore more creative and ambitious solutions to address this looming demographic crisis. 

How much should we be willing to pay for an additional birth? 

There are probably four reasons why you should care about increasing fertility rates: public goods (the fixed cost for public goods are spread across more productive people), externalities from research (more people, more ideas!), life cycle effects (the young can help the old) and altruism (we care about the happiness of future generations).

Firstly, more people, more ideas. Ideas have been the driver of economic growth, and people are the driver of ideas. And ideas are ‘non-rival’ - if we invent a better way to grow wheat, it doesn’t matter whether the technique is used by 100 people, or a million. To figure out how valuable these new people and their ideas are, we work out the value of the worlds where they did and did not exist. There are a couple of considerations we need to make these calculations. However, the quality and quantity of ideas (as measured by their economic contribution) does not increase in direct proportion to the number of people. They suffer from diminishing returns which means we should multiply each additional person’s output by 0.75. Because we’re only concerned with the US, using the contributions of scientists to published research as a proxy for total contribution to scientific output, the US accounts for only 26% of global science output.2  We must also remember that the new births are children, and so we should apply a discount factor of 0.82.3 The Economist, arguing against the subsidies we model, noted that only 8% of children of parents without college education will get a college degree, compared to 62% of all parents. However, even if we fully account for this, this still yields a $1.03m (around 12.67xGDP/capita) willingness to pay for any given birth from just their research contributions.4

Now we also should add the additional benefit from spreading the fixed cost for public goods, eg. on defence or public debt, across more people. Such public goods are “non-rival”, which means that they don’t get worse for existing users if more people use them. As a result, if we increase births, we increase the number of people who can pay for them, and hence reduce costs for existing users. For the US, we model just the military and public debt, subtracting climate change. The US devotes 3.4% GDP to the military and has debt worth 122% of GDP. And, how about increasing birth’s effects on climate change? Well, though the aggregate costs of climate change increase faster than the population, it’s not by much, with an elasticity of 1.18.5 When we consider this with a 3.5% discount rate the present value decarbonisation expenses are equivalent to 23% GDP for purposes here, overall resulting in the 1.96xGDP gains from the other public good effects, which we also discount by 0.82. 

Next, higher fertility means younger people. In the medium term, this results in higher taxes per capita. Unfortunately, we don’t have good figures of the marginal government spending over a lifetime by age. Both caring for the elderly and educating children are expensive - so we don’t know what the net effect will be, because the elderly are much more expensive per person, but their costs are also far in the future. We’ll leave this out of our calculations for now. 

Finally, we’ll briefly consider the “full altruism” case, ie. one where we also value the raw happiness enjoyed by these new people. A life is worth much more than a total lifetime income.6 We get this from considering the statistical value of life, currently $13m, which is much higher than expected lifetime income. This yields a 164x GDP in the US. We don’t include this number for our baseline estimates – whether or not to do so philosophically controversial - but do present results if this utilised.

Model

Now that we have society’s “willingness to pay” for an additional birth, we need to estimate how responsive fertility is to a subsidy. 

Suppose that fertility, n, has a constant elasticity to the private value of having a child, so takes the form:

Given that the policymaker places social externality k (calculated above) and private value v on each birth, they will try to maximise:

This solves to

Which means that, with the optimal subsidy, fertility will increase to:

We can therefore see that the condition for this subsidy being greater than zero is that the elasticity needs to be greater than the private value over the social value, or: 

Quickly estimating the rest of the parameters:

• v is the perceived value of raising a child. On the margin, this will equal the perceived cost of raising a child. In the US, this was $233,000 in 2017, or 3.88. 

• mu is the elasticity. This literature review estimates that the elasticity of fertility to a payment equivalent to 1% of income is between 0.04-0.3. We then need to multiply this by 3.88, because we’re interested in the elasticity to the private valuation v, getting 0.15 to 1.16, with median estimate 0.51.

Results and discussion

We find that, for any intervention, the elasticity for fertility needs to exceed 0.27 – if you only care about the research and public goods externalities. This means that most existing interventions would be well worth the money if implemented in the US.78 While the recommended payments are substantial, if US borrowing isn’t too large a share of overall capital markets then the large size of these payments won’t pose a problem.9

We should also note that our estimates are a static, not dynamic model, meaning that our estimates are conservative. If we consider the world where, as a result of this policy, the population itself increases – and this causes many of the effects we model (both positive and negative) to change as well. Because, under our estimates, the positive effects likely increase by much more than the negative, a dynamic model of this policy means that we should be even more willing to pay for more births.10

The other effect that we do not include is the welfare gains from the non-marginal parent who now gets a free subsidy for children they would’ve had anyway, and are now strictly better off. We treat their welfare gain from this as zero, and so overestimate the costs.

One billion Americans

We conclude that the US government should be willing to pay up to $290,000, overall, to each parent who gives birth. This is a result of our model that shows that any new child born, that wouldn’t otherwise have been born without the subsidy, has a $1.17mn value to the US. In practice, suggestions for additional child tax credits from across the aisle should be implemented, and perhaps even greatly increased. 

Because there is a huge range of elasticity estimates in the literature, there is only so much confidence we can ascribe to any policy implications. Existing interventions aren’t well studied. And we’re interested in the best interventions, not the average ones. Society should invest more resources in studying fertility interventions worldwide, and coming up with new ones: subsidising fertility treatment, reforming child care regulation, changing cultural norms. 

For this post, though, in many senses, we’ve modelled the worst case. That these subsidies are non-targeted, while in practice, we can do much better. That more young people won’t improve the demographic structure of the economy, while in practice, it will. That society doesn’t account for the happiness of the new children themselves, while in practice, we do. 

Humanity has a fertility problem. But it’s a solvable one.

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As many note, this is overwhelmingly due to Britain’s bloated planning restrictions. For example, in London, these restrictions essentially ban building in an area three times larger than the city itself, while very heavily restricting construction within its borders. We have previously estimated, conservatively, such restrictions cost 6% of GDP a year. Yet, they have endured largely because existing residents don’t want the inconvenience of housing construction and increased population density more broadly.

Well, if the difficulty is existing residents, we have a Wales-sized solution. Dogger Bank. 

Dogger Bank has a perimeter of 720 km and area of 17,600 km², compared to Wales’ 20,600km². It’s almost entirely within Britain’s territorial waters (sorry Germany). And it's only 15-40 m below sea level to boot - so at depths humanity has constructed large engineering projects before. 

Headline results: we estimate raising Dogger Bank would cost £97.5bn, but would bring present value benefits of £622bn. Under the government’s standard method of cost-benefit analysis, this project would get a go-ahead, with a cost-benefit ratio of 6.2.

Methodology

What exactly is involved in reclaiming land?

Well, a layman’s guide to land reclamation:

1. Build a wall around the area you want to reclaim.

2. Pump out the water.1

3. Fill it up with your desired material. 2

4. Develop.

To estimate the costs for Dogger Bank, we’ll simply add up the costs for each section.

Build A Wall 

There are only two comparable projects of this scale, the Dutch “Oosterscheldekering” and South Korean “Saemangeum.” The Oosterscheldekering is a series of 65 concrete walls each 40m tall that form 9km of the Dutch Coastline. The project was completed in 10 years, from 1976-1986 at a cost of £6bn. The Saemangeum was much cheaper, a 33km seawall built in 2010, at an average height of 36m, at the cost of £1.94bn. 

Using the South Korean numbers, which are both more modern and closer to the size of our project, we calculate that building a 720km seawall will cost £76.1bn. This, conservatively, considers that all costs, such as transportation and labour, scale at a similar rate to UK wages compared to 1998 Korean ones - increasing by 86%. We also adjust downwards to account for economies of scale, additional efficiencies gained from this large project size, adapting our figures from the equivalent measures in homebuilding, where a 100-fold increase in project size reduces price per unit by 20.5%. 

To check our work, we compared this seawall cost to the proposed 700km North European Enclosure Dam (NEED), which the literature estimates will be in the range of £250bn-500bn.3 This corresponds with our results, because for comparable lengths, NEED requires construction at much greater depths, up to 300m in the deepest parts, compared to a maximum depth of 40m for DoggerBank.

Pump Out The Water

Delightfully, the Pump Express company publishes the costs to pump water using centrifugal pumps. For us, we calculate that we’re going need around 7.16mn CP230, their most cost-efficient model that can pump water high enough, which will cost £1150 per machine. 

Unfortunately, the ground is leaky. This makes for a fun optimisation problem. If we assume that water seeps back into the area of ~1% a day, it turns out the cost-minimising solution involves keeping those 7.16mn of those machines on for 107 days, assuming an electricity cost of 9p/kwh, at 50% efficiency. This yields a total cost for this step of £12.1bn. 

Fill It In

We’ll need to fill 634 cubic kilometers, meaning that we’ll need 2 gigatons of rock – this accounts for the 10-30% increase in volume required because the rock must be compacted. Using open quarries at a typical rate of $5/tonne, this will cost £7.9bn (or perhaps a great volume of dynamite and some less picturesque Welsh mountains). To transport these 2 gigatons, we’ll use commercial shipping and trucking rates of £1.22/tonne/1000km and £4.77/tonne/1000km respectively. This gives us a total to fill in Dogger Bank of £9.3bn. 

Dogger Bank Reclaimed

Concluding, this gives a total construction cost of £97.5bn across the three steps, or 4.3% of UK GDP.4 That’s about as much as the full HS2. 

Development

At the moment, DoggerBank is a barren piece of land in the North Sea, even wetter and windier than the mainland. We’re going to need some infrastructure.

We can split this calculation into two parts:

1. Infrastructure paid for by the end user, such as ports, reservoirs, power generation and telecommunications – which we don’t calculate because will be covered privately

2. And infrastructure provided by the government, think schools, hospitals and roads. 

Based on our prior estimates, schools and hospitals cost £2277 and £2588 per capita, respectively. Underground lines in London cost £9100 per capita, but using Madrid's cut-and-cover method before house construction, costs can be reduced to less than a tenth per kilometer. Fares at London levels should drive net costs to zero.

Per capita costs will be factored into house prices. Roads cost £1194/capita (based on a £4bn maintenance budget, 5% discount rate). Courthouses and prisons have capital expenditure totaling £567/capita (assuming all capital spending is for building maintenance). Police and fire stations, managed locally, cost £19/capita and £51/capita respectively (based on Essex Police and North Yorkshire figures, including all capital expenditure).

The total budget is £6129 per capita, which translates to an implied cost of £14,464 per household (average size: 2.36 people). 

Benefits

We’ll use our adaptation of Hsieh and Moretti 2019 to estimate the implied benefits. See our housing paper for all parameter estimates not undertaken here, and for a more detailed exposition of the model used. 

We'll make several improvements to our previous calibration.

1. We remove the variation in construction project size, as this will be a new city that can be constructed in larger chunks, assuming each is £100mn in size (the limit of the data).

2. We now allow increases in buildable envelope, considering that in London today, 2.27x as much space is used on residential gardens as on residential buildings, and more space is used on private gardens than residential buildings in all but 5 of the 33 boroughs. These gardens add relatively little value to properties, so they would be removed by a free market.

3. Price index convergence is no longer relevant as all possible houses are built in the same region – we instead assume that all homes will be built at the combined London index.

4. As construction will occur upon a completely flat area the size of Wales over a 40-year period (the length under which the mobility assumptions are computed), there is little reason to expect prices to vary with quantity. Therefore, the Price Elasticity of Supply (PES) will be assumed to be infinite in all cases.

5. Levies are lower for reasons explained later, albeit calculated more comprehensively.

6. We retain the 8-storey assumption as this minimizes prices under our estimated price levels.

7. Project construction time will also vary, as this affects the present discounted value of undertaking it. The envisioned construction techniques should scale roughly linearly to time spent, making a 5-year construction schedule plausible. However, 20 and 40 years will be assumed for the central and conservative cases, respectively.

The most important change compared to the previous model is the inclusion of land prices, which is necessary to model cases other than merely increasing density. In the conservative case, we copy existing land prices wholesale, albeit under the retained assumption from the previous model of average building heights of 8 storeys, up from a presumed average height of 3 storeys in London and 2 storeys in the rest of the country.

For the central and stretch cases, we consider two additional effects from a possible increase in buildable envelope:

1. A direct effect of spreading land price over a greater number of homes, reducing unit costs.

2. An indirect effect of reducing prices through demand-curve effects.

Findlay and Gibb (1994) report that estimates of housing's price demand elasticity vary in the literature from -0.5 to -0.8. Assuming this maps onto land, we'll use the implied estimates of changes in land price.

An area the size of Wales could generate economic activity beyond the cities located nearby. While potential mining or energy industries will be ignored, changes in territorial waters related to North Sea oil and gas could lead to substantial effects in the energy sector.

Agriculture, however, could produce more significant effects. Arable land is valued at £9,272/acre, or £2.3 million/km². The proposed city would have population densities 2.7 to 5.3 times higher than present-day London, so even with the size of London it would only operate 3.3% of the island. The remaining agricultural land would then generate £38.97 billion worth of agricultural land as a one-time benefit, equal to 1.7% of GDP.

To calculate the value of these changes, we will adopt the British government's approach of using a 1% real long-run discount rate. For the sake of brevity, only imperfect mobility results will be reported, as perfect mobility results would be higher. It will be assumed that housing benefits from migration accumulate linearly over the 40-year period corresponding to the imperfect mobility coefficient.

We present the results for London and Reading and Bracknell, the two most productive Travel To Work Areas (TTWAs) in the UK. The results for all cities more productive than Birmingham are roughly similar, within a range of approximately ±25%, to those of Reading and Bracknell. However, for cities less productive than Birmingham, the model yields much lower values that typically do not pass a cost-benefit ratio.5

The results in this analysis vary much less across specifications compared to our earlier work. This is because the rent variation across different scenarios is much smaller, and the price elasticity of supply is no longer relevant for topographical reasons, leading to smaller changes in migration as well. However, the estimated GDP gains under imperfect mobility are much larger; this occurs because the model assumes decreasing returns to scale due to land constraints, so creating a new London with relaxed restrictions is considerably more valuable than relaxing restrictions in present London. It is important to note that the results are applicable for a wide range of plausible productivities that are high enough to justify the scheme. 

Discussion

We present the costs of complete reclamation for Doggerbank for illustrative purposes only. An area much smaller than the size of Wales would be initially needed for any likely city construction program. London's current size is 8.9% of the proposed reclaimed area, and Singapore's is 4.2%. As costs for the wall decline with the square root of size, the cost-benefit ratio could be substantially improved compared to the value presented here, with agricultural benefits constituting only a small fraction of the total.

However, the project's success is based on the ability to continually grow a city to a size comparable to current cities. If the same British residents who currently oppose housing construction in existing cities move in, they may force the city to stagnate at a much lower size.

The project would be at little risk from sea level rises, as above-ground sea walls are generally inexpensive, costing only £700-£5400/m² with low maintenance costs. Building a sea wall around the entire project would thus add at most 4% to the capital cost.

There is a possibility that this project could damage marine ecosystems, but it is likely less than any land-based construction. Oceans contain around 200 times less biomass than land per unit area on average, although this figure is likely higher for the North Sea compared to most oceans due to closer proximity to coastlines. Additionally, the project avoids the usual costs associated with land reclamation proposals, as it does not require large quantities of sand. It will only disrupt extant marine ecosystems in the quantity of seawater now occupied by the newest constituent nation of the UK, not elsewhere.

Conclusion

As with Mankiw and Weinzierl 2009’s famous study of optimal height taxation, there are two possible ways to interpret this post. The first is a simple reductio ad absurdum argument against current land use regulations - the planning system means that the British government would receive a greater than 6-fold return from reclaiming an area the size of Wales from the North Sea. The second is that it is a perfectly sensible suggestion similar to existing policies to circumvent NIMBYs in other areas - just as we escape the planning system’s strictures on wind farms by building them offshore, we can do the same for cities. We leave the correct choice as an exercise for the reader. 

Further details can be found here: https://txp.fyi/progress-prize

Regulators are easy targets. Before 2009, EU Regulation No. 1677/88 required “Class I cucumbers must not bend more than 10mm per 10cm of length.” Colorado’s child care regulators dictated everything, from handwashing to block-sets (“a minimum of ten blocks per set.”) In Britain, this detailed, prescriptive regulation controls everything, fire-safety to financial services.

Us progress-types pay much attention to zoning laws (which should be scrapped), limits on high-skilled immigration (which should be loosened), or certain tax reforms (which should be implemented). However, “process-based regulation”,  is an often-overlooked cause of Britain’s stagnation. 

Instead, we propose replacing these process-based regulations with outcome-based regulation, and, for some sectors, introducing a Mandatory Insurance Scheme (MIS). Our analysis will focus on three sectors – childcare, energy, housing – where, if implemented, we expect our proposal to most boost British growth.

Outcome-based Regulation

Instead of prescribing a specific process, regulators would instead specify some overall objective, and leave the regulated entity to find the most efficient way to achieve this.

For example, for child-resistant packaging, the CPSC, the US’ consumer safety watchdog, doesn’t specify how to make bottle-caps. Instead, it requires that all manufacturers test any new child-resistant packaging with a sample of four-year-old children, 85% of whom mustn't be able to open the package within five minutes. 

Regulators can achieve regulatory outcomes, while allowing businesses and individuals to decide how. Businesses have many ways to produce their product: regulators with imperfect information will struggle to discern which way is the best. If regulators fine businesses with the social costs of various actions, businesses can optimise accordingly. 

Mandatory Insurance Schemes

One difficulty of simple outcome-based regulation is that, in many industries, regulations are not for definite harms, like dumping chemicals into water sources after usage. Instead, they aim to prevent low-probability, high-downside events, like nursery accidents, nuclear meltdowns, or property fires. 

In these cases, we further propose the adoption of a Mandatory Insurance Scheme. 

In limited cases, we do this already. For example, instead of requiring specific worker-safety standards, British firms must buy workplace injury insurance. If there is an accident, the insurer will pay the workers compensation, and, when necessary, a fine. Mandating insurance means firms will price in the risk, and cannot hide behind limited liability. And ensures victims get compensated. 

This simple change can transform British growth. We’ll now look at three sectors where Britain is stuck and, through implementing our proposal, we can get it moving again.

Childcare

Britain has the second-highest childcare costs in the OECD.1 On average, a two-earner household with two young children will spend one-third of their disposable income on childcare. No wonder fewer than 15% of mothers return to full-time employment five years after giving birth. These costs may be one factor behind lower birth-rates.

Britain’s crippling childcare costs come from UK regulation on staff-to-child ratios. For under-threes, they are the strictest in Europe. If Britain relaxed ratios to Norway’s, this would halve costs, with almost no effects on child safety. One 2015 study shows that this may even increase the quality of childcare, because the nurseries’ fewer staff have increased training. 

While we could (and should!) implement this specific change to staff-to-child ratios, switching to outcome-based regulation would solve this problem, and future ones. Regulators would simply decide the fines and compensation for an accident, and implement a mandatory insurance scheme. Insurers are incentivised to verify safety compliance, and punish unsafe practices. The resulting price decrease might alone increase British birth-rates by 3-4%.2

Nuclear energy

British electricity consumption is set to double by 2050. As global electricity prices have fallen, British electricity prices have doubled in real terms since 2008. Beyond increasing our electricity bills, higher costs have led to significant lost industrial capacity.3 While Britain’s energy sector as a whole needs reform, nuclear power plants are a missed opportunity. They are reliable, safe and environmentally-friendly. Yet the most recent finished British reactor was finished 28 years ago.

This is because British regulation previously only permitted large, pressurised water reactors. These reactors were optimised to keep submarines underwater for as long as possible, not to minimise costs. Hinkley Point C, currently under construction, will likely cost $42bn.

Here, we can see another benefit of our proposal: increasing innovation. Under these changes, if a firm could demonstrate its safety to insurers, it could build a new design.4 This would allow: safer molten-salt reactors that don’t melt-down, thorium reactors that don’t produce weapons-grade plutonium, cheaper highly-scalable small-modular reactors. By allowing firms flexibility, regulators can achieve their desired outcomes – safer nuclear power and greener energy – by allowing for innovation.

Housing

Housing prices across Britain have grown astronomically. Indeed, if inflation since 1971 had matched the rate of house prices increases, a chicken today would cost £82. 26% of median British family income is spent on rent, and 35% in London. 

This is a result of the “Green Belt.” Infamously, this is region around Britain’s most productive cities where regulators have made new development practically impossible, and responsible for much of today’s prices. This zoning, and housing generally, has been the target of specific policy reforms by progress-types for decades (which we support): street votes, deregulation of the green-belt around railway stations, mandatory home-building targets for councils. However, some process-based reforms are vulnerable to motivated adversarial actors, like “NIMBYs”, who can find loopholes in a new process.

Outcome-based regulation changes the incentives, leading to more resilient change. Regulators would simply have to specify desired environmental results and food production, and allow firms to develop accordingly. Following, firms may purchase and provide protection to land elsewhere in the country, achieving desired environmental benefits at the lowest cost.5 Developers would find the most effective solutions.

Implications

This isn’t (only) a list of specific changes to boost British growth: decrease staff-to-child ratios, approve innovative nuclear designs, reform land-use. We highlight a general procedure on how to achieve those changes. Regulators should optimise for the outcome they care about, not dictate the process to achieve this. Whether that be accident-free nurseries, safe nuclear reactors, protected natural beauty, or any regulatory outcome: safer construction, cleaner air, non-toxic medical drugs. 6

We emphasise childcare, electricity and construction because implementing this proposal in these sectors could boost workforce participation and birth-rates, lower energy costs and attract businesses, decrease house prices and increase worker mobility. Those industries neatly illustrate the three, central benefits of outcome-based regulation: cost-effective safety procedures, technological innovation, and resilient policy reforms.

In short, these sectors epitomise why Britain is stuck. Changing burdensome process-based regulations to outcome-based ones can get it moving again. 

Looking forward, the most exciting application of our proposal may be in regulating new, rapidly-evolving technologies, which have massive potential benefits, but also the potential for widespread harm. Think biotechnology, nuclear fusion, artificial intelligence. British regulators today face an impossible dilemma. They must try to regulate an exponentially-changing technology without limiting innovation or scaring away companies, and simultaneously protect public safety, all while lacking resources and technical expertise. 

However, by mandating outcomes and insurance schemes, regulators need not design and redesign standards as technology advances. Instead, regulators can set their desired outcomes - letting developers, and insurers, find the most cost-effective way to achieve and monitor them.7 Only this way might Britain stay moving.

with c as consumption, alpha as intergenerational altruism, n as the number of children and sigma and epsilon reflecting diminishing marginal returns to material consumption and children respectively. Alexandrie and Eden 2023 find that alpha would need to be 0.09 for a steady state solution i.e. individuals must value the welfare of their first child at merely 9% of their own, given other commonly accepted parameter values.1 This value seems paradoxical considering that the average child's consumption level is far above 9% of their parent's, while under log utility functions under altruism of 0.09 the child’s consumption would be 9% of the parent’s. Indeed, an infant's market consumption could feasibly surpass £100,000 under some definitions given that their demand for attention equates to about four full-time equivalent (FTE) units per year. So, what could possibly account for this discrepancy?

One possible explanation could lie in the scale economies in household production, allowing parents to provide certain services much below market prices. This theory holds water in scenarios like caring for infants, where a parent promising to feed a baby whenever they wake has a much lower utility cost than paying someone else to do so - except for the very wealthiest individuals. However, this doesn't fully elucidate many parental behaviours, such as the allocation of extensive resources towards toys and children-specific activities, where such household-generated economies of scale are non-existent - and it regardless appears that the marginal toy contributes significantly less than 11.1 times the utility than the same consumption would confer to a parent.

Another theory posits that children are utility monsters, an idea that, while unprovable due to its unobservable nature, could hold some merit. Children may exhibit a higher value of nu than the average adult, appearing more content with and attached to a single toy than adults are with comparable levels of wealth. This assertion seems paradoxical, as children have abundant leisure time, and if consumption returns per unit of leisure time diminish, children should have a lower value of nu. The quantification of this distinction would be intriguing, possibly using children’s risk preferences with differing amounts of sweets, although this could be complicated by the potential misunderstanding of probabilities on the children’s part due to internal computational constraints.

Yet another explanation suggests that parents view their children as a prestige good. Accordingly, children partaking in various activities becomes a costly signal, trapping us in an inefficient equilibrium. In this case, a government might - in a way similar to the optimal response if education is primarily signalling - reduce the current subsidies currently allocated to children’s consumption, for example via tax exemptions on many goods primarily intended for children, or could even tax their consumption once all existing net subsidies are removed.

A more plausible answer, perhaps, is that most individuals are hold some person-affecting adjacent view—they don’t value the potential utility of a person who could exist but does not as equal to the utility of an existing person. This belief seems quite plausible given typical responses to philosophical questions. Such responses are generally only partially total utilitarian in nature; otherwise, many more beliefs beyond those currently expressed would follow. This would imply that consistent consequentialists would have more children than deontologists, ceteris paribus - which would be fascinating to investigate. 

Russia’s invasion of Ukraine has caused the loss of countless lives, hundreds of billions in damage and about $150bn financial and military aid from allies, primarily the United States and the Europe Union (EU).

One potential idea to end the conflict is to pay Russian soldiers, often unwilling combatants, to surrender. Indeed, the Ukrainian government, shortly after the invasion began, offered Russian soldiers 5 million roubles ($48,000), or four years' salary for the average Russian, to do so. 

More than a year later, the scheme has received very little public attention. At the time, Bryan Caplan, an economist at George Mason University, said the scheme would have limited effect because Russian soldiers considering it had to weigh it against three large costs, namely the risks of: 

1. Being shot for desertion by the Russian army 

2. Ukrainian soldiers disobeying international law and shooting any captured prisoners 

3. Them being returned to Russia in a peace deal where they would most likely face death or imprisonment for defecting.1

Caplan suggests an improvement: offering not only payment but also EU citizenship for Russian soldiers and their families. This means that defecting soldiers and their families can both establish themselves and permanently enjoy an income several times higher than their previous life while facing little risk of forced repatriation. Although this scheme has attracted some interest elsewhere, no attempt has yet been made to model its impact.

In this post, we provide a simple model of the effect of such a policy. Conservatively, we conclude that if there is a <17% chance of death while trying to defect, a $100,000 payment is sufficient to incentivise the average Russian soldier to do so – meaning that it might cost as little as $20bn to end the war entirely.

The Model

We’ll assume a rational choice model for any individual soldier. Therefore, if they receive greater utility from defecting than they do continue to fight, they will do so.

We first compute how much utility soldiers get from continuing to fight. We do this by taking the amount they value living in Russia (after the war) and multiplying that by the probability they survive the war, should they continue fighting, added to a constant term to account for whether they believe in the cause they are fighting for.2 See the equation below.

Then, we compute how much utility soldiers gain from defecting. We adapt the same model, adding a lump-sum payment, adjusting for EU incomes and replacing the probability of death by the probability of being killed during defection and the belief term with the utility cost of moving to a new country to live. See the equation below:3

Parameter Estimation

We now estimate the relevant parameters. We'll start with some key values:

1. Yhome: The per capita income in Russia is $32,862.60. Yforeign: Meanwhile, the highest per capita income (PPP) value in the EU is Luxembourg's at $115,683.49. Since Russians could choose any EU member state, selecting any other country means that they derive a strict increase in utility from their choice, rendering this a lower bound.

2. r: Based on the research by Matousek, Havranek, and Irsova 2019, the corrected discount rate is found to be between 0.15 and 0.33. We'll use the geometric mean, which gives us a value for 1-r of 0.76.

3. alpha: The current birth rate per capita in Russia is 0.75, and the alpha value for a steady-state population is 0.09, from Alexandrie and Eden forthcoming.

4. ghome: PWC predicts global economic growth at 2.7% per year for this decade. We'll assume Russia's growth (ghome) equals this, as its GDP per capita is around the world average. gforeignMeanwhile, average EU growth during the 2010s was 1.58%, which we'll use for the foreign growth rate (gforeign).

In terms of the war-related parameters:

1. D: Over the past year, Russia has seen around 50,000 deaths in the war from more than 750,000 deployed soldiers. Assuming the war lasts for another 2 years, we'll use a conservative death rate estimate (D) of 0.2.

2. H: The risks that Ukrainian soldiers shoot those attempting to surrender are rendered minimal by providing financial rewards to Ukrainian soldiers for capturing Russian soldiers.

3. B: We can estimate the utility of joining the military (B) by examining the large salary increases for potential Russian recruits in mid-2022 and the actual number of soldiers recruited. Despite significant financial incentives (up to 10 times regular military salaries) and reduced wages in other sectors, military recruitment declined after the war began. By comparing the current utility without B assuming a 3-fold increase in wages (41.4 utils) to the utility before B (46.4 utils), we conservatively estimate B at 5.0 utils.4

4. gamma: Based on a forthcoming study by McClements and Cheang, the cost of relocating is bounded by $62,000 for individuals with slightly above-average global income. This translates to 1.82 utils if consumed immediately, or more if consumed optimally, which it will be here.

The Results

Even if the probability of successfully surrendering appears high at 80% with a $1,000,000 payment, it's important to consider that soldiers can choose the timing of their surrender. With many opportunities to surrender, they can perform better than randomly sampling across these chances would suggest.

At a more reasonable payment of $100,000, a combined value of 0.17 for the cost of human lives and the difficulty of surrender (H+T) would be sufficient. This scenario becomes more plausible if the Ukrainian army adapts to make surrendering as easy as possible for Russian soldiers. If all but 200,000 soldiers were to defect under these conditions, the Russian war effort north of Crimea could be all but defeated, costing only $20bn. This is a relatively small price compared to the $150 billion spent on the war so far, with no end in sight.

Estimating The Impact

To estimate the potential gains of the scheme implemented successfully, we can use a modified version of Lancaster's Laws, as presented in Taylor 1981, a set of mathematical models used to describe the relationships between various factors in war, such as force size, attrition rates, and the duration of a conflict.

As there is currently insufficient or unreliable data on army sizes over time or casualty figures for individual battles, we make the following assumptions for the purposes of calculating a ballpark guess:

1. Wounded soldiers are permanently taken out of action.

2. The Russian army has a constant strength of 500,000, while the Ukrainian army has 700,000 soldiers.

3. Both armies maintained these numbers throughout the war.

4. Russia has suffered 200,000 casualties (dead and wounded) to date, while Ukraine has experienced 120,000 casualties.

5. Russia or Ukraine would each surrender if they suffer over 50% of their current strength as casualties.

Feeding these into a model produces the following results.

Even if there were only several hundred defecting a day, these results imply the war could be shortened by over a year, saving many billions of dollars and tens of thousands of Ukrainian lives.

Possible Variations

If actually implemented, policymakers might want to consider a number of variations to the policy to make this more effective, such as:

1. Pay higher-ranked or better-trained Russian soldiers more to defect, and to bring their subordinates with them,

2. Paying Russian soldiers for bringing equipment with them,

3. Pay Ukrainian soldiers for prisoners they captured to ensure the Hague Conventions are obeyed,

4. As Caplan initially proposed, offering a higher initial payment to soldiers who initially defect incentivises faster adoption and increases the credibility of the scheme.

Discussion and Conclusion

In the worst case, even if Russia manages to significantly increase surveillance on its troops, maintaining desertion at current levels and closing its borders to prevent the families of defecting soldiers from leaving under the scheme. Despite these countermeasures, both actions would come at a high cost for Russia. Increased surveillance would likely further diminish the already low morale among soldiers while closing the borders would destabilize the existing regime and increase trade costs.

Furthermore, it might at first seem morally unjust that attacking Russian soldiers would be offered EU citizenship when this is not available to Ukrainian soldiers defending their homes. We hope that, if this scheme is implemented, the expedited end of the war opens the door for Ukrainian EU membership, affording all Ukrainians such a right. 

Considering these factors, this scheme represents a highly cost-effective way to gain an advantage in the war if it works as intended. Even in the worst-case scenario, the strategy could still yield considerable benefits without incurring any costs beyond the paper on which the announcement was written.

For the purposes of this blog post, they will be compared to a system with equal deterrence, no incapacitation, no rehabilitation and no criminogenic component and no financial cost excess of court and policing expenses. The no incapacitation assumption is highly conservative due to the low costs and high incapacitation potential of employing say electronic tagging coupled with a curfew for convicted individuals, and the no rehabilitation component would also likely be highly conservative due to the likely public desire for governments to provide such a service. A criminal justice system with zero financial costs beyond the courts and police could be achieved by a massive expansion of community service to allow prisoners to replace existing workers employed by the government for some tasks such as removing litter, plausibly even saving funds on net, or by similar means. The no criminogenic aspect simply relies on the proposed alternative system not forcing individuals convicted of previous offences to live with each other and only each other for years on end, and seems highly plausible. Equal deterrence seems very easy to achieve by frontloading costs, as criminals have much higher discount rates than the already astonishing 20-35% for the general population.1

Cullen, Jonson and Nagin (2011) reviewed several studies on the effect of prisons on recidivism, with the criminogenic effect dominating the rehabilitative effect. Of the meta-analyses which provided the quantitative estimates necessary for this model, Gendreau, Goggin, Cullen, and Andrews (2000) found a 7% increase; Smith, Goggin, and Gendreau (2002) found an 8% increase, rising to 11% on the highest quality studies; and Jonson (2010) found a 14% increase, falling to 5% on the highest quality studies. An 8.7% effect size will be used here. Implicitly this blog post’s methodology ignores the large numbers of crimes committed within prison or not reported, rendering the benefit estimate conservative. Canada provides a breakdown of recidivism rates by age at release for the 2007-2012 period, which will be used here to estimate total costs of crime over a lifetime for someone convicted of a crime at a given age by punishment system.2

The resultant cost ratios for a 20-year-old can be seen above.3 The alternative system is better for all crimes and crime costs excluding the very highest sentences for the most costly of crimes - indeed, if interpretted literally the results above imply that only murderers would optimally go to prison as very few crimes even have costs of the minimum $500,000 modelled, let alone the near $10,000,000 required for prison sentences to be better than the alternative.

This method does however have a number of shortcomings. By using data for the average prisoner, this result does not imply the replacement of prison for all offenders, and as recidivism rates may vary by crime does not even necessarily imply that prison is worse than the alternative above for the majority of people in prison for every crime. Additionally, some would argue that the suffering of those who have harmed others is inherently good, which if prisons were worse than the conditions in the alternative could mean that those who held such a belief would place a higher value on prisons relative to the alternatives than the results above. Finally, individuals can commit more than one type of crime over their lifetimes, while the model above only allows individuals to commit crimes of a single cost, albeit permitting them to do so multiple times. This may be problematic because the government could today use the fact that individuals are committing more minor crimes today as a signal that more severe ones will be committted in future, reducing total crime costs, although to the extent that this is a boost in the reoffending rate following crimes this effect will boost both costs and thus have only a small effect on optimal behaviour. These shortcomings will be addressed in a future post.

A Cobb-Douglas production, shown above, takes productivity, A, labour, L, and capital, K, as inputs, and outputs income, Y. In this case, labour is the number of individuals currently serving under arms and capital is the sum of military expenditure in this year and all prior (somewhat depreciated) expenditures. The theoretical capital capacity of Ukraine is far greater, as the combined GDP of NATO is $32.4 trillion in comparison to Russia’s $1.78 trillion, but this advantage is lower than first appeared as absent the recruitment of foreign mercenaries (which may be undesirable for political reasons) the Ukrainian labour component is fixed while Russia has considerable capacity to expand labour allocated to the war through conscription due to the large divergence in population between the two states, although whether Russia has the political ability to mobilise such a fraction of its population is another question.

Since independence in 1991, Ukraine has spent the equivalent of $70 billion on its military. However, this steeply overestimates the capital that was accessible to Ukraine upon the outbreak of the war due to not accounting for the Ukrainian army consisting of humans rather than entirely robots and capital depreciation over time.1 Assuming Ukrainian capital and labour expenditure proportions are identical to those of the British military accounts, personnel costs account for about 41% of the budget (modelled as 0.3 to 0.5 normal) and depreciation is (less £700 million to account for impairment expenditure) roughly 28% annually.23 However, not the entirety of Russian capital could be deployed, due to Russia’s possessing borders with the Baltic States, Poland and Finland: this effect will be modelled as 0.6 to 0.85 normal. 4

Russia does not publish breakdowns of its military budget by service, and although only 20% of active duty Russian army personnel were directly deployed in Ukraine before the mobilisation three months ago a considerably greater proportion of total capital would have been allocated to the war. The US spends 49% of the military budget on the services which Russia would have been able to deploy at a large scale during the war (army and air force), but as Russia is primarily a land power this ratio would be expected to be rather higher: however, Russia has regions (Kaliningrad, St Petersburg and shortly the entire Finnish border) that border NATO, so would not be able to deploy all land and air force based capital. Additionally, as naval, air force and nuclear services all have higher capital-to-labour ratios than land forces, they will all likely occupy a lower proportion of the military budgets of countries with lower GDPs per capita: this effect would probably be larger with Ukraine than Russia due to Ukrainian pre-war GDP per capita being $4800 per capita compared to Russia’s $12000. This will be modelled as 70-90% of Ukrainian military spending being on land and air forces and 50-75% of Russian military spending being on land and air forces, with 80-100% of Ukrainian land and air forces being deployed and 65-85% of Russian relevant capital being deployed, all distributed normally.

Lastly, the value of A can in this case be interpreted as the relative institutional quality of the Russian and Ukrainian armies. To avoid needing to compute the exact path of Ukrainian familiarity with NATO technology and other effects, the opening of the war provides some data, although of potentially limited use due to the substantial expansion in both Russian and Ukrainian forces since then. A complicating factor is that warfare success likely depends on both the absolute level of capital and willingness to expend capital - tanks matter in relation to their number rather than casualty figures, while tank ammunition matters only insofar as it is in fact expended. However, without access to data on the exact rates of ammunition consumption of both powers such considerations will be neglected. At the beginning of the invasion, Russia had about 180,000 regular military and 34,000 Donbas militia, while Ukraine fielded around 200,000 regular military and 100,000 paramilitary troops. Including paramilitaries, weighting Ukrainian (0.6 to 0.85) more highly than Russian (0.2 to 0.5) due to the much higher performance of Ukrainian paramilitaries than the forces of the LPR and DPR, thus provides a relative estimate for Aa, with a as the ratio of Russo-Ukrainian military power in the opening days of the war and A as the ratio of Ukrainian-Russian efficiency, of 7.9 (90% 3.2 to 17). a is also chosen with very high uncertainty, but is modelled as lognormal 1.2 to 3.7. This gives an implied value of A of 5.6 (90% 1.1 to 21, implying that the Ukrainian military utilised the resources it had access to 5.6 times more efficiently than the Russian military did.

Given the value A, three separate groups of estimates need to be made: possible maximum Russian mobilisation, the state of both sides’ militaries in 2023 and the required ratios the Ukrainians would need to achieve various possible goals. For the first, Russia has a GDP of $1.78 trillion, and during WW2 the military of the Soviet Union peaked at 7 million in size, with the USSR’s population then around a third higher than the current Russian population. During WW2, Britain’s defence spending peaked at 52% of GDP and America’s defence spending peaked at 43%: both these population and GDP figures likely represent upper bounds on plausible expenditure, but as defence spending occasionally exceeded 15% of GDP even in 18th century Britain a 90% confidence interval of 20% to 40% will be used for defence spending as a proportion of GDP and a military size of 3 million to 5 million.

The position of both sides’ militaries currently depends on the rate of extant capital depreciation, the current size of the Ukrainian army and the capital transfer that has occurred to date. As financial backing pledged thus far by the European Union alone is only slightly less than the entire Ukrainian military budget scheduled for 2023, Ukrainian military expenditure will be assumed to effectively be a subset of capital transfers from NATO (which is an assumption with no impact if Ukrainian labour is fixed, which it is believed to be for reasons mentioned above). The Ukrainian army currently stands at 700,000 and has received just over $40 billion in external military funding. For extant capital depreciation rates, Russia in 2021 had over 10,000 tanks in storage, of which 1500 have been confirmed captured or destroyed: however, as Russia likely deployed the more modern tanks first and many remaining tanks have been cannibalised for spare parts, and the 1500 figure only refers to losses photographically confirmed, the actual depreciation rate will be much higher. As Russia appears to be deploying tanks mostly seen in museums elsewhere, very high depreciation rates for usable capital seem reasonable and a lognormal estimate of 0.4 to 0.7 will be used.

A final estimate needed is the Solow ratios required for various objectives: these are modelled here as a stalemate at current front lines, a return to 2014-2022 boundaries or restoration of pre-2014 boundaries, respectively. Due to a lack of previous study of this approach to modelling warfare, these estimates, as those of relative effectiveness were above, are necessarily rather arbitrary: quantitative work on this model would be extremely helpful. However, the rough intuition is: defence is possible even if a military is rather weaker than its opponent, so a ratio between 0.3 and 0.8 normally distributed would be sufficient: a return to pre-war lines would require a much higher ratio, as it would require taking territory currently occupied by Russia, so a ratio of 1.4 to 3.9 lognormally distributed would be required: and a full return to pre-2014 frontiers including the reintegration of Crimea would be rather more difficult and would require a ratio between 2.2 and 4.5 distributed lognormally.

Table 1 shows the results. As the annual NATO military budget is well in excess of $1 trillion, this implies that even in the case of complete Russian mobilisation NATO could likely still provide sufficient funding for a Ukrainian victory and would certainly be able to provide sufficient funding to allow a stalemate at Russian front lines. Russian victory, absent the use of nuclear weapons or similar, is thus extremely unlikely assuming NATO will continue financing Ukraine.

However, this model also allows us to investigate a different question. Ukraine retains complete victory as a goal, which would maximise the incentive against future state-on-state aggression worldwide and minimise the increase in the incentive to possess nuclear weapons, while many of its NATO allies are concerned about the potential for nuclear escalation during any battle for Crimea due to current opinion polls indicating strong support within Russia for defending the peninsula. What probabilities does this model give existing Western aid of victory or a draw for Ukraine? The model predicts that if Russia were to double both the number of soldiers allocated to Ukraine and the military budget existing Western transfers would have been sufficient to ensure the probability of Ukrainian victory would be at around 11% while the probability of at least a stalemate at current front lines would be 95%.5 This provides some evidence towards this being the strategy that NATO states are employing: the much slower delivery of offensive weapons such as tanks and APCs compared to more defensive infantry equipment and missile systems provides qualitative evidence.

What principle shortcomings are there of this model? A key problem is that military production, unlike industrial production, uses single-use inputs - ammunition - to create output, but this output cannot be sold to create new inputs.6 This means that actual combat power is probably a function of capital stock, rate of ammunition expenditure, and manpower, which would be a useful development of the model here. Another issue is that the Solow ratios and effectiveness ratios are all parameters chosen with very low confidence, due to a lack of previous studies on them. Finally, implicitly the model has assumed that A - relative Ukrainian to Russian efficiency of converting inputs into combat power - has stayed fixed during the war, while, in reality, the number of trained officers, quality of weaponry and level of corruption may have varied considerably as the war progressed.

This post thus implies that Russian victory in Ukraine is effectively impossible given Western willingness to continue financing Ukraine merely out of current defence budgets - which given that Ukrainian military spending per soldier remains much below Western levels remains considerably cheaper than financing comparable NATO militaries. However, the model lacks empirical verification elsewhere and does not incorporate ammunition expenditure: key shortcomings which will be rectified in a future post.

For the purposes of this post, the dataset that will be used is the Code of Federal Regulations, which has the advantage of running continuously since 1949 (with annual supplements listing changes published from 1938 to 1949). It is also the focus of the academic literature that is relevant to our purposes by estimating the effect of regulatory changes of countries on the productivity frontier. It likely represents a decent proxy for regulation as longer regulatory codes should be expected to be more burdensome to comply with, and thus bring greater costs.

Several studies make estimates relevant to our purposes of the effects of regulation on economic growth. Dawson and Seater 2013 adapt a model of taxation’s impacts on the economy to measure the effects of the increase in regulation from 1949 to 2005, although difficulties in classification and measurement mean that they neither differentiate regulations by type nor include the effects of state-level regulations. They find that regulation has effects on the trend level of output, but some of these are lagged, with the result that they measure a net reduction in trend output growth of 1.9% over the period while the average long-run effect is a reduction in 2.2%. Loayza et al 2005 find that a one-standard-deviation increase in regulation reduced GDP growth per year by 0.4%, which given the 500% increase in the regulatory level above is equivalent to a 2.4% reduction in the annual growth rate. Bourles et al 2013 find the aggregate effect of all regulation to be a reduction of annual growth of 1%: however, this may be of more limited use than the above studies as under a model whereby the regulations with the positive or least deleterious effects on economic growth are implemented first this does not provide an estimate of the marginal effect. However, it has the advantage of finding that the costs of regulation increase the closer to the technological frontier a country is, implying that the results are primarily due to suppressing innovation rather than one-off growth boosts. Due to concerns with the possible one-off nature of gains, this blog will use the average of Bourles et al 2013 and half of each of Loayza et al 2005 and Dawson and Seater 2013 of 1.1%.

Importantly, it must be stressed before any further discussion that even very small effects on trend growth rates have titanic welfare implications - Robert Lucas argued that once you start thinking about economic growth it is hard to think about anything else1. A 2% difference in growth rates multiplies per capita incomes by a factor of 7.2 if maintained over a century: undoing growth in Britain by this factor would reduce incomes to the level they were at slightly before the formation of Germany. As utility is natural log of consumption in economics, the entire increase in living standards from the days of 5 year old chimney sweepers to today would be replicated by such a change.

Before it is possible to determine the impact on the optimal aggregate quality of regulation, two further factors need quantifying: the lag between innovation in one country and implementation of the technology in another, and the discount rate to determine the value of such lags. The lags between an innovation being discovered and its adoption by the entirety of the world feels very large, given that living standards in Europe during the 19th century were considerably higher than living standards in much of Africa or India today, but also likely decreasing over time. Conversely, however, as countries benefit from trade with each other an increase in the productive capacity of one country will benefit all others through comparative advantage, and some sectors in developing countries, such as the Indian IT sector, may be able to rapidly absorb productivity improvements abroad. For the purposes of this post, a discount rate of 5% and a lag to reach 30%2 of the world’s population of 10 years, and an infinite lag to reach the remainder, will be conservatively assumed, which is equivalent to a valuation discount factor of about 0.6.

The numbers above imply that global income per capita would be 27.8% higher had the increase in US regulations since 1949 not occurred, which assuming the increase would have been spread evenly across the 30% of the global population that otherwise would have experienced it represents an annual loss of 1.56 billion utils (value of an increase in income of a factor of e) or 78.7 trillion Open Phil dollars (marginal value of a dollar to someone on an income of $50,000), or under a 5% discount rate a loss to infinity of 40.0 billion utils and 1.99 quadrillion Open Phil dollars assuming regulation increases at the same rate to infinity. Assuming that both the benefits and costs of regulation have unitary elasticities with respect to the total quantity of regulation, if native welfare is as valuable as foreign welfare the optimal value of regulation for the United States decreases by about 78% if the current level of regulation is privately optimal3.

This result is rather stark: taken at face value it implies the removal of almost the entirety of the increase in the period covered if foreign and domestic welfare are equally valuable - and renders this regulatory innovation externality of comparable, and soon to be greater, size than the entirety of climate change on a GDP-effect basis, merely from the actions of the United States alone4. It is on another level unsurprising though: any reduction in trend output necessarily causes long-run output over the span of decades to plummet, and the evidence surveyed above indicates that the effects of regulation on trend growth are large indeed.

One potential limitation with this result it that due to cost-benefit analysises usually not being carried out with new regulations, and those that exist often being decades out of date it may be unclear which regulations to abolish, without the perfect rank-order information of their harm that the 78% figure would imply. If we instead have to choose to rip out pages at random from the codebook, we may end up abolishing some of the most beneficial regulations as well as those that are negative once the external effects are included. However, as the above externality is so large in the case where we have no knowledge and are not risk averse the optimal policy is to abolish the entire codebook, bringing a net annual gain relative to the present of 230 million utils or 11.5 trillion OpenPhil dollars. We can reverse the calculations above to calculate the growth difference that makes us indifferent between abolishing the entire codebook, reaching a figure of 0.4%: if regulation reduces GDP growth due to innovation by less than this every year, then in the case of zero knowledge we should not abolish the entire codebook.

How could this result be overturned? If the regulatory innovation elasticity was overestimated, the claim could fail: however it was shown above that it would need to be out by in excess of a factor of 3. Alternatively, the current amount of regulation could be vastly suboptimally low, meaning that the additional of the effect on citizens of foreign countries still implied that roughly the current or a higher level of regulation would be optimal. Lastly, the elasticities of the regulatory benefits and costs could be incorrect, with the result changing if the benefit elasticity is substantially lower or the cost elasticity substantially higher. These will all be explored in more detail in a future post.

Comparative advantage can be visualised on a production possibility frontier (PPF) such as Figure 1. This represents the ability of society to produce two consumer goods X and Y, and any point along the PPF is Pareto Optimal - production of one good can only be increased by decreasing that of another - while only a single point is allocatively efficient - the optimal ratio of each good to produce. If consumers utility functions are log in all goods differing by constants, then all individuals will buy the same ratio of X and Y as society does. Let X’ and Y’ represent the maximum possible production of X and Y respectively.

Diminishing marginal returns to all inputs mean that the worst possible structure to the diagram would be a straight line from X’ to Y’, and the best possible a square with X’ and Y’ as vertices. Comparative advantage as opposed to specialisation, scale or innovation is unable to increase X’ and Y’, but merely able to increase the ability of society to realise consumption levels of X and Y where both have substantial value. This, in a manner unlike innovation, thus necessarily caps the per-capita benefit - no gain beyond a doubling in consumption of all goods can occur from comparative advantage alone.

The results from using individual ability distributions under a Pareto distribution with a value for alpha of 1.75 are shown above. As can be seen, the space for gains is limited, and the gains from even very large proportional increases in the population become very small, with the gain from even moving from a population of 10,000 to 100,000 representing but 0.6% of total production in that year at most, in the case where the goods should be produced in constant proportions. The benefits from higher population in the effects on technology and public goods provision remain substantial: additionally, by allowing more firms to access the minimum efficient scale, the promotion of competition - but comparative advantage is far less important.

This suggests that comparative advantage effects are near-insignificant when determining optimal populations in the two-good case. However, the economy of the real world contains more than two goods, and in cases with larger numbers of goods the effects could remain substantial even at current levels of population due to the higher degrees of freedom. Additionally, free trade does not only bring benefits due to comparative advantage but due to the accessibility of increased returns to scale, which are entirely absent in the above model. Quantifying these effects will be done in a future post.