A New Atlantis

An outlandish proposal to solve the housing crisis

Housing in Britain is unaffordable. The average British home costs 9.1 times median earnings to purchase - the highest since the unification of Germany - and rents are 27% of pre-tax monthly income in England as a whole, and 35% in London. For all this, Britons get homes that are smaller than in New York and demolished so infrequently that equilibrium entails an average house age over 1350 years old.

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. 

A new green and pleasant land (adapted from Wikipedia)

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 

Dutch Wall: (and keep the foreign water out)

They say God created the world but the Dutch created the Netherlands

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. 

Table 1: Assumptions by calculation. *Without buildable envelope changes changes in PED have no effect in this model.

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.

Table 2: Estimated rents for the new city by assumptions - “recreating Birmingham” in this model means both having West Midlands housing construction prices estimated here and current wages. The North East shows no variation due to actual house prices being below predicted construction prices, with this being a result of falling populations causing a temporary disequilibrium.

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.

Table 3: GDP gains under imperfect mobility, new city has productivity of London

Table 4: GDP gains under imperfect mobility, new city has productivity of Bracknell

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. 

1. Due to backflow, you need to pump more than you think, because water will seep back underground.

2. 1.1-1.3x, because you need to compact it.

3. Cowen’s Second Law!

4. These estimated costs per unit area are around 100x smaller than the average figure for Singaporean land reclamation - this likely mostly derives from most of the cost in this model coming from the sea wall, which has a price per unit area directly proportional to the square root of project size, so the much smaller scale Singaporean efforts are enormously more costly. Additionally, by employing very expensive sand rather than crushed rock their costs rise further.

5. Specifically, the other sufficiently productive cities are Cambridge, Oxford, Wycombe & Slough, Guildford & Aldershot, Stevenage and Bristol.