Missing middle housing? Blame economics, not planning

A common objective of town planning schemes is the densification of existing suburbs to create “missing middle” density. This is usually enacted by allowing areas previously developed for detached housing to be redeveloped into incrementally more dense uses, such as townhouses and walk-up apartments.

But economic constraints, not planning constraints, are the main reason that this middle-density housing is missing.

First, in low-price areas, the per-unit cost of building higher-density dwellings may exceed the market value of a dwelling. Higher density dwellings are more expensive per unit to build (there are rising marginal costs to density), and they have a lower market value per unit. That is why you won’t see high-rise residential towers at the city fringe, or in small towns, even if they are allowed. Middle-density housing is also relatively more expensive per unit than detached housing.

Second, in high-price areas, if a site is worth redeveloping, it is probably much more profitable to redevelop to higher densities than the desired middle-density.

The diagram below shows the basic economics of this problem. If a single dwelling is built when the price hits P1, the existence of this dwelling makes the site much more expensive to purchase for redevelopment than a vacant site. You now have to bid against potential occupants of the existing detached dwelling to buy the site—effectively buying an extra house you don't want.

This additional cost adds to the redevelopment cost. In the diagram above, this shifts the average cost curve up from the orange line (the cost of developing a vacant site) to the blue line (the cost of developing from a site with an existing dwelling).

Between prices P1 and P2 the “missing middle” density is optimal (the marginal development cost per dwelling equals the price). But in this same price range, the average cost is above the price because of having to purchase the existing dwelling.

Thus, the existing detached dwelling “quarantines” a site from incrementally more dense uses. For example, demolishing multiple detached dwellings to rebuild a slightly more dense townhouse development is usually going to be uneconomical.

When prices are high enough to make redevelopment of detached housing into “missing middle” housing viable, these high prices are also going to make much more dense apartment towers even more profitable. In the above diagram, a price above P2 makes a tower apartment building the most profitable density.

The most economically viable locations to get “missing middle” density are actually in new fringe areas where low-value agricultural or industrial uses are being converted into residential uses. Perversely, it is the outer fringe where the “missing middle” is going to be most viable.

We can see this economic incentive at play in many large housing developments in fringe suburbs of Australian cities—these new suburbs now offer a mix of townhouses, small apartment blocks, and detached homes. In the inner suburbs, “missing middle” housing typically exists in places that were on the fringe of transit-constrained cities when they were built many decades ago.

Rather than fight against economic constraints, higher density in existing areas can be achieved with granny flats and other subdivision types that do not require demolishing existing dwellings. It is these alternatives that can be encouraged in the planning system.

A housing absorption rate formula—first cut

Housing supply is one of the most misunderstood processes in economics. The reason for this is that the core standard theory of economics is a static one-period model of production with a fixed capital endowment. They confuse the optimal density of dwellings, given the fixed capital of one unit of land, with the optimal rate of supply of new dwellings per period of time.

To be clear, the decision to supply existing housing to the rental market at any point in time is short-run production decision given a fixed stock of homes. That is why most homes that exist are not vacant. The marginal cost of renting (compared to keeping vacant) for a dwelling owner is typically far below the marginal revenue.

Building new homes is instead a capital allocation decision. Land and cash assets must be given up to build new homes. These assets earn a return over time and can be used in future periods instead of the current period. Building too many homes today depresses prices and rents, thereby reducing the return to both existing homes and homes you can build in the future.

So how is the optimal rate of new housing determined?

It is clearly not determined by the optimal density, as static models assume. Take a look at the figure below showing a housing subdivision in a street. The static theory says that if you approve a subdivision of five housing lots, you increase the rate of supply per period by five dwellings. They all sell in period one.

In reality, these dwellings do not sell all in period one (i.e. all in one day). They are drip-fed to the market over time, with one possible series of sales shown in the figure below. When I looked at the land banks of Australia’s top eight listed housing developers, the average age of their housing subdivisions and apartment blocks since their first sale, was ten years. The oldest was 25 years! They were still selling housing subdivisions approved in the last millennium. 

This slow rate is optimal because housing developers are rational. Selling faster reduces both the value of the rest of their subdivision and the growth rate of the prices they receive over time. They are giving up future returns if they flood the market today.

What do those future costs look like?

In the figure below we can see the effect of new dwellings sales on market prices and growth. The top line is the counterfactual price path if no new dwellings were supplied. Each additional dwelling when it is sold goes to the highest bidding buyer at that point in time, taking them out of the market and reducing the price to the second bid. This gap between the highest bid and next bid is labelled as alpha, and represents the “thickness” of the market in terms of how many people have bids clustered at the top of the curve. If you rank bidders from highest to lowest and get prices of 1.0, then 0.9, then 0.8, then alpha is -0.1 (the slope of this bid curve when buyers are ranked). If the market is “thicker” the bids might be 1.0, 0.95, 0.9, meaning alpha is -0.05.

Each sale at any point in time takes out a buyer and reduces the maximum price. Meanwhile, the other bids grow over time (or not) depending on macro and market factors. The next sale has the same effect, wiping off the next highest bidder and reducing the price, and so on.

So each sale has a pure price effect in terms of alpha. We can add these up on the above figure, and with a rate of sales of three per period, the price effect—the difference between the end of period price on the counterfactual end of period price is three times alpha.

This is standard economic theory, whereby increasing supply per period has a price effect. No surprise there.

But notice something else. The result of this pure price effect is that the price path is flattened compared to the counterfactual. Not only are end of period prices lower, but seen as a path, prices are growing more slowly.

The faster the rate of sales today, the lower future prices tomorrow. In essence, the pure price effect can be reinterpreted as a reduction in the growth rate of prices over time rather than a static price effect.

We can see this in the figure below where we reduce the rate of sales from three per period. Notice that the first lot is sold at a higher price because it is sold later, as is the next lot, with the third lot still to be sold at the end of the chart at an even higher price.

Somewhere between selling zero new dwellings, and selling enough to ensure that prices never rise above costs, is an optimal rate—an absorption rate that maximises returns to landowners from converting their sites to cash by selling lots to residents.

How should we think about what is optimal? Sticking with the basics, we can choose a rate of supply maximises the expected present value of the flow of lots into cash.

It is tricky to think of supply as a rate. But a simple logic can be used here to understand what is optimal. You want to at a rate that maximises the revenue this period and the value of the flow of revenue from all future periods, based on expectations and discounting. At this optimal point there is no gain from increasing the rate, since increase the rate comes at a cost of future price growth (and vice-versa).

The immediate revenue from the rate of sales is simply the price times the rate of sales. We can ignore the price effect in this because we capture it in the growth term which affects the value of future revenues (you can imagine supply as a sequence of sales, with any individual sale not having a price effect as it is the price setter at the margin at that point, but it reduces the price of the next sale in the sequence).

The value of the flow of future sales is the capitalised value of the end of period price, which is now lower because the rate of current sales has lower the growth rate.

As a mathematical approximation, we have the following equation to maximise (where I use f() to as a shorthand way to say this is some function of this term, but I’m not going to specify that function).

The maximisation happens when the marginal benefits from higher rates of supply today (the derivative of current revenue with respect to the rate of sales) equals the marginal cost in terms of lower value of future revenues (the derivative of the present value of future revenue).[1]

The rate of sales that maximises this value is

What is the intuition here behind the direction of the relationship between each market parameter and the rate of sales?

First, if the growth rate is higher, you need to increase the rate of sales in the next period to capture more of that value of that growth, which, because we are dealing with an instantaneous rate of sales, means increasing sales this period into the next period.

Second, a higher interest rate increases the rate of sales. This is because the future cost of lowering price growth by increasing sales is worth less today with a higher interest rate. A low interest rate means that the price effect on the future is more valuable today.

Third, the alpha term is negatively related to the optimal rate of sales. This makes sense. The thinner the market (the higher the alpha) the fewer sales can be made with the same price effect.

Notice how different this “optimal rate” thinking is to the usual economic analysis housing supply. This equation does not care how big your subdivision is—approving a larger subdivision won’t force anyone to sell or develop more quickly.

There is a lot more to this story. We actually don’t yet have an answer for how fast our five lot subdivision above should sell to be optimal. We know that if price growth and interest rates are low that they will sell lower than otherwise. We know if the market is thin they will sell slower than otherwise (say if they are in a small town compared to a large city).

I am working on a neat way to show the present-future trade-off, but it is not that simple. This might explain why theories of optimal rates of housing supply don’t really exist yet. There is a lot more to this mathematical story and if there are economic theorists out there who would like to help me ensure that my next “absorption rate formula” is consistent, please get in touch. 

_____________________
Fn. [1] I have taken a bit of liberty here to simplify the equation. Strictly speaking, the problem is a recursive one, in which the value of future revenue itself depends on future values. Also, strictly speaking, you could capitalise future incomes by the interest rate minus the expected growth rate, but this has problems. And, there are issues about the representative agent owning all the land, and whether you should account for the value of current housing or the value of the options for development in the price effect. The above equation is the simplest version that captures the direction of all effects and is the clearest way to show the future cost of faster supply.

Economic tide reveals naked policies

Superannuation

It seems that when people want to withdraw their money from super, the money is not there, and it requires asset selling that reduces asset prices across the board. This same effect happens ALL THE TIME. That is why a scheme that requires nearly 10% of wages to be spent on asset purchases is a bad idea, as it boosts asset prices. When the super system needs to pay out more than it gets in, asset prices are squeezed, and the value of what we thought we had saved begins to fall.

If only someone had warned about this.

Valuing life and the cost of lockdowns

Every policy involves trade-offs that can not only be measured in the monetary value of resources, but in blood. It is very standard to think of gains from health policy in terms of Quality-Adjusted Life Years (QALYs) as a metric of performance. Every public policy—from road rules to medical funding, to retirement, to workplace safety, to minimum standards—has an implicit trade-off of resources for lives.

Yet everyone has lost their shit about coronavirus as if lives lost this way are worth orders of magnitude more than lives lost any other way. In two to three weeks time the reality will set in that there are real costs of locking down society that can be measured both in value of resources wasted and in blood. All perspective has been lost at present.

Money was never an issue

Perhaps the greatest change from the crisis is that money was never a constraint. Politicians spend on things they like and don't spend on things they don't like. The budget was always an excuse.

I have often told policy advocates to stop arguing to politicians how cheap their solutions are to homelessness, or environmental losses, and other issues. They should instead argue how large of an investment is required to fix them! At the moment we are in a political vortex of one-upping each other in the ‘tough on the virus’ stakes, and this is coming with ever bigger cash splash promises.

But this is actually how things work all the time. Useless “ego-infrastructure” projects that give politicians a plaque and a ribbon-cutting photo-op are the norm. Big spending decisions are driven by political egos, not logical resources trade-offs. 

Housing was always a macro issue

I have heard for years from experts in my field of housing economics that zoning was constraining supply and rezoning would see a construction boom like never before. In fact, according to their numbers, we could double, or triple, the rate of construction by changing just a few words in a few town plans to allow higher densities.

But I have yet to hear rezoning proposed as the solution to the inevitable construction crash. Why not? Could it be that the argument was always bullshit and that housing supply is (you will never guess) constrained not by regulations, but by demand from new buyers? When buyers leave, construction falls.

This is not some radical “crisis-only” situation. This is always the case.

A "Central Housing Bank" proposal for a crisis and beyond

Cameron Murray
Henry Halloran Trust, The University of Sydney
20 March 2020

Download proposal as a PDF

• We propose that State governments (or Federal) create a “Central Housing Bank” (CHB) that stabilises the housing construction sector by swapping assets, in this case, cash, for new dwellings. Just as the Central Bank swaps cash for other financial assets to solve liquidity problems in financial markets, the CHB would do the same for one of the nation’s largest economic sectors. 

• As a national program, a dwelling target for the first year could be 30,000 dwellings across the 20 largest towns and cities in the country (around 0.5% of the number of dwellings in these towns). This is roughly 15% of the new dwelling completions in 2019, a significant demand buffer for the housing construction industry, supporting an estimated 150,000 highly productive jobs. 

• In balance sheet terms, these actions are costless for any government that undertakes them, as they receive a dwelling of equal (or perhaps higher) value to the cash they give up. Margins on housing development are typically above 25%, so this would be an opportunity for a public agency to engage in discounted counter-cyclical asset purchases to support jobs in the construction sector. 

• The CHB can then use those acquired dwellings in a number of ways to support policy objectives, such as 

1. renting in the private market to help stabilise rents, 
2. using them for public housing at discounted rents, 
3. selling to social housing providers at discounted prices, 
4. or selling to the private market in future periods when prices are rising to dampen the housing cycle. 

• Housing construction investment is a volatile, but productive, part of the economy, currently accounting for around 5% of GDP and 7% of Australia’s workforce (including housing construction and ancillary industries).

• Ensuring continuity and utilisation of productive organisations, such as builders, manufacturers of construction materials, and the design and management professions, can help ensure productive capacity is maintained during the crisis, and in the post-crisis period.

• The basic implementation of a CHB would be as follows:

1. Employ a small group of senior construction and project management experts to manage the CHB, ideally from the non-housing construction sector, such as mining and oil (to avoid conflicts of interest). 
2. This CHB team would request tenders from private housing developers or landowners to supply new apartments at an agreed price. The objective is to utilise the pipeline of already approved housing developments to speed up the process. In Sydney alone, there are an estimated 20,000 approved yet not-yet-commenced dwellings. Nationally, the top eight housing developers have a landbank of over 200,000 apartments and houses. There is a massive pipeline of sites that the private sector has queued up for housing that they will be looking to sell to reduce exposure to falling land prices. 
3. They could also shop for development sites as a market participant. 
4. The CHB management team would be incentivised to meet dwelling supply targets both in terms of the quantity delivered, and the location-adjusted average price paid. Independent assessment by State Valuers, in conjunction with State or Federal Treasury, can determine the value for money and hence the performance bonuses of the management team. 
5. Rough annual new dwelling purchase targets for the CHB could be set as a schedule across major towns and cities in proportion to their population, for example, 0.2% of the population in every town or city above 100,000 residents (of which there are 20 towns and cities nationally). Expansion to smaller towns can be conditional upon the success in the first three years of the CHB. This would be roughly 30,000 dwellings in the first year. 

• There are enormous macroeconomic stabilisation benefits of this system. The accumulated stock of rental housing owned by the CHB can be used to dampen housing price upswings by introducing a selling rule. For example, if dwelling prices begin to rise above a set rate, of say 5% per year, this would trigger sales of the stock of dwellings held in that region to private sector buyers at the rate necessary to keep growth below the target rate (again, like Central bank intervention to stabilise interest rates), absorbing speculative demand and stabilising housing prices.
• This system is not dissimilar to housing systems in Singapore, and public housing systems in Europe, and previous housing systems in Australia and North America.

Economic crisis? How about ‘equity mate’?

During 2009 farmers were paid $61million per month in drought assistance as part of Exceptional Circumstances Subsidies. But the public got nothing for it.

I have often said that public subsidies, even in a crisis, should always come with obligations. The simplest of all is to make the subsidy an asset swap rather than a gift—provide the cash, but take an equity stake in exchange, diluting ownership. This 'equity mate' public policy can help ensure the continuity of productive capacity during crisis periods.

Central banks provide liquidity via asset swaps to financial institutions in exceptional times. 'Equity mate' is just a way to provide cash via asset swaps to the companies that do the actual production in the economy. 

But in practice, this is not easy.

In a crisis, the value of equity falls. By taking a new equity stake when the value is low, you are providing much less cash per share while diluting an already lower equity value.

How this could work in practice is to have a “standing facility” whereby a rule about the value of equity the Treasury or Central Bank would pay is set in advance, and businesses can choose to use it up to a maximum share, of say 10% of the business value. As an example the rule could be:

For listed companies, equity comes at a price of the lower of—

1. The middle of the price range of the two prior years, or
2. The middle of the price range of the prior year, or
3. The current price plus 15%.

For unlisted businesses, equity comes at a price of—

1. The average of the marked-to-market balance sheet from the two prior years.

These rules would have to be broadly considered, but you get the idea. When equity values are rising, the price paid would be too low compared to the option of expanding cash for investment by issuing equity to private investors. Only during downturns would this kick in, when sudden declines in economic activity spook the market as a whole. Having this option in place might also dampen selling during a crisis, just like the government guarantee on bank deposits deters bank runs. 

This ‘equity mate’ injection of funds is a way to provide liquidity insurance to our productive enterprises without massively changing their incentives. A problem with drought assistance, for example, is that the expectation of future subsidies gets capitalised into the value of farmland. The insurance is free, and the incentives to invest in a way to mitigate loses from predictable rain variation are reduced. 

Buying up the nation's companies in a downturn is also just a smart investment. Buy low, sell high, make money. In the 2008-09 financial crisis, the Reserve Bank of Australia used counter-cyclical investment in currency to stabilise the dollar. It bought a lot of AUD using its USD reserves when the AUD fell to below USD0.60. In the following years, the AUD increase to above USD1, making a large profit for the Bank, which is an income for the public sector. Like this example, counter-cyclical purchases of a small public stake in a wide range of companies will provide future public revenues. 

What are your thoughts?