Will removing planning controls crash the housing market?

Recent Twitter exchanges have helped me to understand a couple of additional confusions in the housing supply debates. Let me take them one at a time.

The housing supply mechanism

I dunno, man. There's a golf course just down the road from me where I live in SE London. That land would be worth 10-20x as much with permission-to-build.
You can argue that a massive increase in building wouldn't affect *prices* much but arguing nothing would happen is crazy

— no employers, don't google me (@sudonimbus) August 17, 2020

This Twitter statement contains some hidden assumptions and two main points; 1) that land is worth different market value depending on the rights attached to it, and 2) that massive amounts homebuilding will affect prices.

Points 1) and 2) are correct. But the hidden assumption that because land has a different value with a planning permit (or with different zoning) that overall homebuilding rates will rise if a plot is rezoned. This part of the mechanism is wrong, in my opinion.

It is not obvious to me that changing planning will greatly affect the rate of market supply. If you assume that planning is the reason new housing supply is not higher, then you are assuming the outcome. I don’t think it would do much at all.

This challenge was put to me.

Let's hypothetically suppose that a new regime grants permission to build literally anything up to 10 stories and compliant with building control on any site within 30 miles of Big Ben.

What happens, in your model?

— no employers, don't google me (@sudonimbus) August 17, 2020

I responded that not much would change.

Let us be clear. Many cities effectively have this type of planning system. Sydney councils, for example, allow tall towers in vast areas of the city and had record new housing construction for nearly a decade. That doesn’t stop people from saying these new apartments should be taller, or that supply isn’t a problem.

Sure a large scale planning change would be a shock to an equilibrium. It will probably stimulate a flurry of activity—site trades, new types of development proposed, and maybe extra buying of these new dwelling types. During this adjustment period, prices would probably rise rather than fall, as is usually the case. But this would quickly calm down until there is no sustained change to the rate of supply.

The effect will be like any other small shock to a dynamic system.

Developers slow their sales when prices fall, and increase them when prices rise. They build to order. I do not see what mechanism there it so sustain faster supply and falling prices with these economic dynamics at play. Would it make sense for any developer to sell out their apartments at lower and lower prices to sustain a faster sales rate?

The zoning and land value issue

Additionally, the fact that changing zoning, or permitting development, affects the price of a property seems to be evidence about supply constraints for many people.

Not sure the blog helps the author’s argument, as
1) land values and changes in value differ hugely depending on housing permission rights, that supports @s8mb point about interest rates
2) density of rental accom (people per flat and location rel to Work) have deteriorated

— Chris Giles (@ChrisGiles_) August 19, 2020

This exact argument was the second paragraph of a recent RBA paper about housing supply. 

There is a hidden assumption at play to make the leap from “different property rights have different values” to a supply shortage. Unless you want to argue that property rights should have no value, then this is a weird argument. 

No one would think it unreasonable that if you gave a landowner the rights to use adjacent public space to build extra housing that their property rights would have a higher value. Yet when we change the orientation of neighbouring rights from “beside” to “above” apparently these rights should be worth zero.



We know rights to airspace and higher density are valuable because they can be traded in some markets. They are a distinct property right. Planning is a tool to allocate them. 

There are no "true" property rights to land that go from earth to the heavens. With property rights, you get what you are given. 

Strangely Ed Glaeser’s approach to housing implies that property rights to land should be worth zero. He says, in essence, housing supply would be effectively unconstrained without planning and land values would fall to zero.

He is careful not to say it this way because it sounds stupid. He instead says that the cost of housing will be pushed down to construction cost. Hence, the land component of home prices will be zero.



This is unusual, to say the least. It implies that if you removed all planning controls (build anything anywhere) that land would become valueless. If this were true, announcing such as policy would crush land value to zero immediately as expectations get factored in. Who would want to own an asset whose value is rapidly trending towards zero?

How you can affect housing prices with “supply”

On the Jolly Swagman podcast I thought I understood you to be saying that housing supply is not the main issue. But then you also mentioned flooding the market with new stock would help and also that artificial drip feeding impacted prices?

— 𝙿𝚛𝚘𝚏𝚎𝚜𝚜𝚘𝚛 𝙳𝚎𝚖𝚘𝚐𝚛𝚊𝚙𝚑𝚢 (@PrDemography) August 19, 2020

The physical number of homes does not change prices much. It was, therefore, confusing to some when I said we could flood the market with supply to reduce prices. If we think about property price crashes, we can see what flooding the supply-side of the housing asset trading market can do. This effect has nothing to do with the total quantity of dwellings. In fact, such price declines are usually accompanied by crashing housing construction.

I also do not claim that developers artificially drip-feed new supply. There is nothing artificial about it. This is the normal market outcome. Another way of saying it is that there is a rate at which they must sell to maximise the value from their land. If the sold faster, they would undermine their own profitability, which would happen because these faster sales had an effect on price. When I looked at developer landbanks and sales data it was common for large approved (<200 lot) subdivisions to go a full year without a single sale. If they wanted to sell, say, 10 lots that year instead of zero, they would have had to drop the price substantially. 

"Flooding the market" can be thought of as mimicking the asset-trading dynamics that happen during a house price crash by adding many desperate sellers to the market. A public housing supplier could do this. The scale would have to be very large, but this is exactly the large scale change in supply many expect to happen automatically from rezoning. So why not guarantee that it happens with a public competitor to these private housing suppliers?

An improvement on this "flood the market" idea is to copy how the price of money, the interest rate, is regulated by central banks. They promise to supply reserves (and demand back reserves) at narrow price range around their target rate. Their promise to back these guard-rail prices with a supply of reserves is enough for private market participants to adopt that price. In effect, monetary policy is implemented by announcement. They rarely have to use the guard-rails because they are credible.

Imagine a Central Housing Bank (CHB) with a promise to buy any dwelling at a $300,000 price and sell as many dwellings as desired at $310,000. Obviously, it would be more sophisticated than this with price schedules for different locations and dwelling types. But regardless, it sets a price corridor with a price promise backed up with an ability to supply housing.

If this institution demonstrated its ability to back up its sales with new housing, this credibility would lead the market to accept that price and operate within the corridor. It would realign market expectations on prices and capital gains.

How many new dwellings would need to be built to back up that promise and demonstrate its credibility? Probably not as many as you would think. Yes, there would be waiting lists at first as home production ramped up to back up those sales. But even then there would still be an effect. Pay $500,000 or wait a while on the waiting list and pay $310,000?

I would guess that building about 30,000 thousand dwellings per year for the first few years in Australia would make the CHB credible. Maybe 60,000 per year in the UK.

Now, I do not think this is the best “solution” to high housing prices. I think the best affordable housing system is Singapore's proven model.

What thinking about this option does is show that we do intervene in important asset markets, like money, when we think a different price would be socially more desirable. It also shows how difficult it would be to get prices down via supply-side interventions. 

It also puzzles me that those who want low home prices and think homebuilding will get us there usually do not advocate for such systems. Why not advocate to copy Singapore’s model to build every citizen a new home at construction cost? Why not propose to flood the market via a non-market housing developer who will meet their supply targets regardless of how low they have to drop prices? 

This report, entitled Help to Build, is apparently a plan to support housing supply, yet it proposes only demand-side interventions. In effect, it concedes that housing supply responds to demand and that we just need more demand to get the supply. If this is true, then it cannot be true that planning changes will result in voluntarily faster supply at the same level of demand.

Likewise, suppliers are unwilling to ramp up output unless they think there will be a prolonged period of high demand since they do not want to start up only to have to switch off shortly after.

This is a long post, so I will stop. Post your questions in the comments.

Sam Bowman's 9-points on housing supply

Sam Bowman thinks that a lack of supply is the primary reason for high home prices. I just released a podcast with Ian Mulheirn going into detail about why I think this is not the case.

Sam is right about some things but wrong on most. So let’s try and pin down our disagreements.

Let me first disclose my professional background. I have worked for listed and private residential and industrial developers and worked for the state regulator on infrastructure charging regimes. My first degree was in what was a then niche area of property economics, covering a range of topics involving construction management, design, town planning, feasibility methods. My PhD included extensive analysis of planning decisions, and I have published many academic papers on housing, planning, and supply dynamics. I have also been an expert witness in corruption cases involving town planning decisions.

I can assure you that if there were an issue with the planning system constraining the rate of new housing supply, at least in Australia, then I would be spending my days arguing that case.

Let me also say that I am not anti-supply. I do think the planning system is more cumbersome and costly than it needs to be, even in most jurisdictions in Australia. But I don’t think that changing the planning system is going to do anything about the overall price level of housing. I support public housing supply programs that have clear objectives and penalties for missing targets.

I like to preface any housing supply discussion with a thought experiment to help disentangle whether housing issues are mainly about distribution or supply. If every mortgage was written off, and every renter was given the home they currently live in for free, so that 100% of households lived rent- and mortgage-free in their current homes, would there be a housing affordability crisis?

I’ll leave that with you.

Sam makes nine arguments against certain claims of "shortage deniers". Please go and read them in full.

1. “House prices are high because of interest rates, not a lack of supply.” 
2. “Rents haven’t been rising as a share of income, so there is no shortage.” 
3. “The elasticity of house prices to new supply is low, so building more houses won’t do much to lower prices.” 
4. “Nine out of ten planning applications are granted, so the problem isn’t the planning system.” 
5. “Land banking is the cause of housing shortages.” 
6. “Empty properties make the housing shortage worse.” 
7. “The private sector cannot build enough houses to meet demand.” 
8. “It is impossible to make housing “affordable” without council housing / affordable housing.” 
9. “We risk speculative development after building booms which leaves us with ghost towns.” 

These are my responses. 

Low interest rates

On this issue, I think we mostly agree. Low interest rates increase the price of assets by reducing the capitalisation rate. 

We differ on this part of Sam’s explanation. 

"Falling interest rates do not increase the price of other durable goods like airplanes or ships, or of housing in places where there is not a supply constraint, like in the North of England or Houston (which has a liberalised planning system)."

The missing distinction here is that housing is a durable good attached to a property right to a piece of the three-dimensional space that has been carved up with a land titles system. Home construction has not inflated in price, just like other durable goods. But the cost of buying a share of the property rights system from the system’s existing owners has inflated. Without that, you have nowhere to put your dwelling.

We can, therefore, agree that the problem has something to do with property rights having perverse effects. Sam thinks it is the permitting part of the property rights system. I think it is the property titles system itself.

We also disagree on this point.

“If interest rates were the only factor, we would expect to see houses everywhere rise and fall in line with them.”

No. We would expect to see the interest rate effect on the capitalisation of rents the same everywhere, but with prices still diverging due to non-interest rate factors. Different cities have housing price booms at different times for different reasons. Houston’s 1980s price boom is a classic example of a price boom that far exceeded that scale of price growth in other cities at the time. There were other factors at play, including plain old expectations and speculation. 

Sam's own chart seems to show that most variation in prices is common between London and the rest of England. 

Rents as a share of income

I think we agree here that rent is the appropriate measure of the economic price of housing, which is good.

Sam’s view here mainly deals with UK rental statistics. I would defer to Ian Mulheirn who has two detailed pieces about that issue (one and two). 

But we differ on this point.

“Suppose everything we spent money on changed in the same way, rising in real-terms as we got richer – groceries, electricity, clothes – without getting any better in quality. Economic growth would be meaningless, because any overall income growth we experienced would simply be eaten up by these rising costs.”

Remember my earlier point. Housing products have not increased in value in line with incomes. The combined cost of renting houses and that location in the property titles system has grown in line with incomes. Remember also that this location rental is also someone’s income.

What makes property different? When you rent a dwelling you also rent the location, essentially buying out your transport costs by paying the owner of a better location. If we had an equilibrium where people spent 5% of their income on rent, some people might start deciding to spend 7% of income on rent (40% more rent) to live in better locations rather than spending that money and time on commuting. Those with higher incomes will find that the time-cost of commuting is relatively higher, with the equilibrium process sorting the location of households by income or wealth at their maximum willingness to pay (taking into account the cost of transport).

Compared with tradable and transportable consumer goods, it is the finite nature of locations and their relative advantages that ensure we end up in a fixed-share-of-income equilibrium.

The way to use rent-to-income as a supply metric is to see whether the number of people per dwelling is increasing compared to the average size of dwellings. A shortage would be indicated by more people in smaller dwellings paying the same share of income on rent.

It may be the case that this exists in some locations but not others. The question would then arise, how does this situation persist if there are alternatives in different locations — just pay the lower rent plus higher transport costs and get more space.

These are the types of questions and the evidence we should be looking about when talking about the adequacy of housing supply.

Elasticity

It is also good that we agree that the price elasticity of housing supply is low.

Sam says the following

“Imagine a similar argument being made during a famine where the price of food was very high: if an additional food shipment did not make a big dent in overall prices, would we conclude that the solution wasn’t more food?”

Yes. That’s right. This evidence would force you to conclude that although more food would be beneficial, the distribution of food is mainly causing the famine because adding more total food to the system is not helping much. This very point is the subject of many debates about famines and food prices. It is also why I prefaced this piece with a thought experiment about the distribution of dwellings.

Regardless, saying that more dwellings won’t decrease prices is wrong. What Ian Mulheirn and I are saying is that because housing supply matched population growth, and in many places far exceeded it, that supply is not the cause of the price growth observed. Adding more supply will decrease prices, (putting aside whether changing planning rules actually will change the rate of supply). But it happens in a slow and expensive way. 

In Australia, around 8% of the labour force and 6% of GDP is spent on building new homes. When someone says “let’s double housing construction” from 1-2% of the stock per year to 2-4% of the stock, they are really saying “let’s take 8% of the workforce away from what they are doing to build more housing for a 1% rental price decline each year”. Maybe that trade-off is worth it (assuming supply would increase this much by removing planning regulations). Maybe not. But this is where you should end up when talking about elasticity and the size of the price effect of the investment in new housing.

High approvals rates

I agree that this metric cannot show the effect of deterred planning applications.

But does that make it meaningless? I don’t think so.

In a radical supply shortage situation, with so much profit to be made from getting into the housing game, even low probability applications would be made. People buy lottery tickets all the time. Large organisations often invest billions in activities with low probability outcomes when there is a large potential payoff.

Shouldn’t we see the planning system swamped with low probability applications and observe them being rejected? 

Then there is the issue of one million excess planning permissions granted in the past decade. Very hard to explain this as a planning constraint.    

I also have a gripe about planning applications and their apparent slowness. While the situation is different in the UK and Australia, slow approvals usually happen because the applicant has sought approval for a development that is far outside the scope of the plan. They bought land that was not designated for what they wanted to build, then chose a slower route through the planning system rather than a faster one. I'm surprised that these developers have the confidence to blame someone else for their self-inflicted problems!

Land banking

Sam writes that land banks are an inventory necessary to smooth out supply and ensure workers are not idle after selling stock.

I agree that land banking smooths out supply.

I disagree that land banks are inventories. I even have an academic paper on this topic where I looked at the annual reports of listed housing developers to see what they say to investors about planning when they are obliged to be honest (here's a free working paper version). Australian developers never seem to tell investors that planning is delaying them.

We are now getting to a key issue on housing supply. How does a developer choose the rate per period to sell their subdivision?

They need to be careful not to sell too fast. Faster sales might require lower prices, or raising them more slowly, reducing the present value of the return from that project. But if they wait too long, they might also miss out. As I often say, what kind of crazy property developer floods the market because they can?

I also don’t see how land banking is a symptom of a shortage. In any other product market, even large durable goods like ships or trains, large inventories don’t happen when there is a shortage. Do these firms “buffer” and keep large inventories to smooth out their production? Most large capital goods production is on a “build to order” model where the process schedules buyer orders, matching supply to demand.

Empty properties

I have no idea how many empty homes there are in London. Sam seems to have the data. I can attest to the fact that Australia has more empty homes as a proportion of total dwellings now than at any point in history, along with larger homes and fewer people in each one.

The private sector cannot build enough / need council housing

I agree with Sam that the private sector can build enough homes. I disagree that they would just because they could. 

 

I love how all the housing supply people bang on about planning, but almost never propose that the government should build so many houses that prices collapse.

You know, just in case private developers choose not to collapse the housing market by flooding it with new supply.

— Cameron Murray (@DrCameronMurray) July 30, 2020

I am quite often puzzled that using the power of government to flood the market with housing is never proposed. We just cross our fingers and hope that the private sector will crush the price of their assets. 

Sam has stumbled across the “absorption rate question”. How fast should developers build to maximise the present value of the flow of their economic returns from development?

Clearly, it is not so fast that the final sales of a subdivision are at a far lower price than the first sales. This would also see problems with buyers pulling out of contracts and purchasing at the lower later price. 

If we look historically, periods of rising homeownership and rapidly expanding supply are usually associated with government programs—housing for returned soldiers, giving public housing to tenants, Singapore's subsidised housing model, and so forth. My view is that we should expand these programs just in case the private market doesn't deliver what it promised. Think of it as insurance.

We risk ghost towns

I don’t think already large cities are going to risk this, so I agree with Sam that this is a silly argument.

I would only note that this happens in places like mining towns where they really do see rapid demand growth—expressed in rents—along with high and unconstrained rates of new home building. Of course, despite the lack of supply constraints, mining towns always seem to still get a boom and bust rent and price cycle. I wonder how Sam would explain this.

Are NIMBYs financially motivated or are property developers?

A puzzle came via twitter following the crazy story of RBA research claiming that if you remove planning controls, apartment prices will fall 42%.

I argued that it would be weird for property developers to lobby for policies that eroded the value of their products and sent their housing projects broke.

Andrew responded as follows:

Equally, do you think that NIMBYS aren't arguing for restrictions that increase the value of their land?

It seems pretty obvious to them that if they restrict higher density in their area and force it on other areas the value of their land will increase.

— Andrew Paul (@ASPaul85) August 6, 2020

So we have two groups who apparently stand to benefit from tight planning controls if they do in fact increase prices, yet they are arguing opposite cases.

This is a genuine problem. How do I make sense of it?

The first thing I would do is break it down further. Homeowners are an investor-renter hybrid—landlord and tenant of the same property. Maybe we can break out renters and landlords separately and see if they lobby for different planning outcomes. The position of homeowners would then reflect them acting as their “renter” or “landlord” selves.

Survey research has shown that renters are just as likely to oppose rapid development in their neighbourhood as homeowners, perhaps even more so if we believe this survey.

“If a similar ban were proposed for your neighborhood, how would you vote?”

Given the consistent NIMBYism found among homeowners nationally, I expected homeowners to show stronger support for a ban on new development within their own neighborhood. Instead, only 40 percent of homeowners chose to support this ban compared to 62 percent of renters. In other words, 30 percent more renters supported the NIMBY ban than homeowners.

This gels with my experience in community groups. Renters play a large role. Investors/landlords not at all.

If tight planning controls increase prices, renters will be the worst off, having to pay higher rents. Yet they lobby in favour of these tight controls.

Landlords will be better off, but they do not lobby in favour of tight controls.

So if homeowner NIMBYism matches the behaviour of renters, not landlords, then we can say that NIMBYism is not financially motivated by homeowners looking to increase the value of their homes.

This goes against the conventional wisdom [1]

NIMBYism is part of what drives property prices so high. When opposition to local development means that homes can’t be built in useful areas, the remaining homes become scarce and extremely valuable.

So what’s the deal?

One way to reconcile this behaviour is to question whether in fact tight planning controls increase local rents and prices. My experience as a property developer is that areas undergoing rapid densification become more attractive and, if anything, increasing in value.

Some have argued that it is the risk, or variation of the outcomes, from densification that homeowners don’t like, hence their conservative status quo bias. Will the benefit of more local retail services outweigh the cost of extra traffic or not? This risk issue could certainly be part of the story.

Another resolution to the puzzle recognises that densification typically does increase local rents and prices but, unlike investor landlords, homeowners can’t realise any financial gains without selling and relocating.

Since they chose to buy and live in their suburb rather than an alternative area, they have a preference for the current density/amenity. Had they known they were buying into a high-density area that was not yet built, they may have chosen to buy elsewhere instead. The same logic applies to renters.

It would be a bit like someone coming along and offering to paint your car pink. Sure, maybe pink cars sell for more, but if I wanted a pink car, I would have bought one in the first place. 

If NIMBY psychology is more like this, we would expect that development that complies with zoning codes to see little push back, as homeowners have reasonable expectations about what sort of development is planned for their area. But we would expect a lot of push back against development proposals that fall far outside planning codes. This is consistent with my experience. 

In the end, I don’t think I am fully satisfied with any of these ways to reconcile the NIMBY and developer puzzle.

What is clear is that the story is not a simple one of NIMBYs preventing some local developments in order to increase the value of their home.

What are your thoughts?

fn. [1] The conventional wisdom is often wrong when it comes to property markets and planning.

NSW Federal Financial Relations submission

Read my full submission here.

The NSW government has been conducting a review of taxes and federal financial relations. One of the main proposals to come out of the review has been to replace stamp duty on property transactions with a broad-based land value tax, or what I have called SD4LVT. 

There are many reasons to be sceptical of the political motivations of these types of reviews. Typically, you only undertake this type of drawn-out review process if you a) already know what you plan to do, or b) plan to do nothing but use the process to keep all the interested parties busy talking about something that will never happen while appearing to do something. 

I think this is a case of a). I say this because although the review proposes SD4LVT, the NSW government recently announced that it will be reducing land taxes by 50% for 20 years for corporate landlords. The reason given is to promote a corporate build-to-rent housing sector [1] which is currently disadvantaged because there are threshold values above which land taxes apply, giving a tax advantage to landlords that own few properties. 

But if the NSW government wants to expand land value taxes, why offer additional exemptions and reductions to fix the imbalance rather than remove the current exemptions to level the playing field?  

So I'm a sceptic. 

Regardless, the SD4LVT proposal has been justified with a lot of dodgy economics. I outline in my submission four main areas where the economic reasoning is flawed. 

1. The economic efficiency costs of stamp duty are low, not high.
2. Removing stamp duties may increase the price of housing.
3. Lower churn of housing assets is an economic benefit of stamp duty. 
4. Stamp duty revenue volatility helps stabilise the macroeconomy.

Please read the whole submission. Here's an excerpt about the nonsense economics that is behind the conventional wisdom about the high efficiency costs of stamp duty. 

_______________________________

The metrics of economic disaster caused by stamp duties are derived from economic analysis using computational general equilibrium (CGE) models of the macroeconomy. The below table from the Draft Report shows that multiple assessments conclude that there are high economic costs to raising revenue from stamp duty.

However, these studies all use CGE models that assess the effect of transaction taxes because there are no transactions in the models. Instead of using a better tool for the job, or admitting the limits to knowledge, modellers have simply pretended that stamp duties are a different tax that applies to a tax-base that is in their model.

There are two main approaches to this. First, in the KPMG models, rather than stamp duty being a transaction tax that is incident on the seller (and therefore incident on land values), as it is in reality, they assume this instead.

...conveyancing stamp duties are modelled as a tax on investment in residential and commercial structures (p.125)

They assume that stamp duty is not a tax on transaction where the economic incidence is on land. Instead, they assume that stamp duties raise the cost of housing to all buyers and renters because it is a modelled as a tax on construction. The model assumption requires that stamp duties raise the cost of building new houses without affecting land prices, leading to reduced new housing construction in general. This is a classic example of garbage in, garbage out.

A second approach is in the COPS model is to pretend that stamp duty is a tax real estate agent fees and legal services used in housing transactions.

Stamp duty on conveyancing or property transfers in Australia are taxes that apply to the transfer of ownership of most properties. While the duty base is the sale value of the property purchased, the resources used in transferring property ownership is usually only a fraction of the value of the property transferred. To model transfer duties on residential property ownership in this way, we introduce a new bundle of goods into the household decision problem in VURMTAX, called Moving Services. This bundle consists of goods produced by the Real Estate Services, Other Business Services and Public Administration industries, and represent the real estate agent, legal and public administration goods demanded by households when transferring property. (p17)

...we have $8,367 million of stamp duty being levied on an activity with a resource cost of only $1,881 million. This implies a tax rate on the activity of transferring property of 445 per cent (=8367/1881). (p.804)

This means that instead of the tax being a small percentage of a large base (property turnover value) they are instead suggested that the tax is a 445% tax on real estate agents and conveyancing.

If that sounds crazy, that’s because it is. Any tax at this rate is going to look costly and inefficient in a CGE model. The more bizarre part of it is that if you believe this modelling approach is an accurate representation of stamp duties, then the cheaper real estate agents and lawyers become, the more economically inefficient stamp duties are.

The claims about the economic inefficiency of stamp duty that are relied upon to justify its removal have no plausible economic basis.

_____________________________

[1] I've never understood what is supposed to be achieved by this. We currently have a rental market ownership structure of "investor owns dwelling." What is achieved with a structure of "investor owns shares of a company that owns dwellings?" On net its the same. I could be convinced that landlord professionalism could be improved. But again, most landlords employ profession property management services anyway. 

What is Gigi actually saying about COVID?

* Read Gigi's piece at The Conversation

Twitter is a mob, and the mob has a new enemy. Professor Gigi Foster has been on a few television shows lately trying to make the case that economic lockdowns cost lives, just as COVID does, and therefore we want to make sure that we aren’t inadvertently killing more people over the long-term by crushing economic activity and livelihoods.

After all, a functioning economic system is what delivers high-quality healthcare, safe roads and workplaces, investment in public works, the ability to devote resources to research medical treatments and new drugs, and more. It delivers livelihoods and careers, leisure and happiness. It delivers quality of life as much as it delivers quantity.

However, I don’t think gotcha television and infotainment current-affairs shows are the best venues for this discussion. From what I saw, these outlets were actively avoiding putting a number on the trade-off, or even acknowledging it. A cabal of social media economists avoided acknowledging this trade-off a few months back. They then back-peddled, said there was a trade-off, and botched their attempts to quantify it.

The puzzle to me is that everyone seems to want to say Gigi is trading off lives for the economy. Her point is that a functioning economy delivers health and welfare outcomes, and hence the trade-off is about lives for lives.

For some reason, saying this is a new taboo.

Policy decisions that explicitly make this trade-off occur all the time. Should we fund more medical research? Should we install traffic lights? Should we make people wear seat belts? Should we ban alcohol and cigarettes? Should we legalise recreational drugs?

Policy analysts, particularly economists, spend careers looking at these welfare and livelihood trade-offs in all sorts of policy domains.

When she says "man up" she means that we need to face up to the fact that we cannot create a pre-COVID world. There are going to be losses of life quality and quantity, either from the virus or our response to it.

I want to go through some of the strange things I see when talking about our COVID policy response, and some of the things people say to avoid facing the reality of this trade-off. My personal view is that the reasonable thing to do is to make sure our policy response does not shorten lives and reduce their quality more than COVID would. I hope that this helps people to understand where Gigi is coming from.

1. The exponential growth and tail risk story
One of the big claims early on was that those talking down the risk didn’t understand exponential growth. Strangely, exponential growth doesn’t usually apply to virus propagation. The pattern is well-understood to be logistic growth, which is going to saturate the population at some point. The unknown was merely where that point would be. An upper bound for that point was pretty clear early on based on evidence from China, Italy and the Diamond Princess cruise ship.

2. Virus prevalence estimates
How much of the population has been exposed to the virus? This is another area where the worst-case scenarios got all the airplay, and where more sensible estimates were ignored. The more prevalent the virus was, the lower the overall mortality. You can see the media incentive for publicising the high mortality estimates, even though it was known quite early on what the realistic estimates were.

3. Infection and case fatality rates
Initially, the highest estimates were promoted, but the reality is that the range of 0.25-0.65% for infection fatality is the current view. If two-thirds of the population is infected overall, that is a worst-case scenario of about 0.16-0.4% of the population dying from COVID, or a few months of normal deaths brought forward in time. This is a generous worst case. The "Swedish disaster" has seen a crude COVID death rate of just 0.05% of the population, under a third of my lowest estimate. 

4. Getting the orders of magnitude right
I asked my Mum when she was panicking about the COVID outbreak how many people she thought had died. She said 5.

When people tell me about the shocking number of COVID deaths I like to ask them how many people die each day in normal times. No one seems to know, or care.

Nearly 8,000 people die every day in the US. Fear does not care for statistics.

The 6,000 coronavirus deaths likely to come from the virus in Sweden are equal to around 24 days of normal expected deaths, and many of these COVID deaths are not in excess of normal deaths. 

A good rule of thumb is that 8 in 1,000 people die every year (0.8%), or about 60 million globally.

For perspective, the seasonal flu in Australia kills 1,500 to 3,000 people, with about 18,000 hospitalisations.

In Queensland alone last year 285 people ended up in ICU due to flu. 

5. Getting the cost of life right
Everyone dies, so dying of one thing today simply stops you dying from something else later. Deaths are life-shortening. In the trade-off I described above, economic recessions and lower future output are also life-shortening. There is no point talking about “prevented deaths”, only shorter lives (that whole quality/quantity thing). If people die a year to two younger than otherwise from COVID, then that’s not too bad. If they die 30 years younger than otherwise, the loss is fifteen times worse per death.

6. But what about transmission!
Another argument is that coronavirus can have lasting effects on some people. Yes. And? Others say that you might feel bad transmitting the disease to others. Yes. And? These issues are true of all viruses. They were true of last year’s record 1,300 flu deaths. There are hundreds of people out there who transmitted the flu virus to someone last year and it killed them. Where was the outrage then?

7. Or do recessions save lives?
I’ve heard the argument that recessions decrease traffic and workplace fatalities, reducing crude death rates. I can’t make a judgement about whether this is true, but it makes perfect sense and could be. But it only raises another question—if recessions save lives as a general matter, why aren’t we trying to orchestrate recessions all the time? If it is logical to do it for coronavirus, then it is logical to do it for traffic fatalities, workplace deaths, or whatever other indirect mechanisms of death are at play during economic expansions. 

8. The poorest countries suffer the most
There are global costs to lives from large scale lockdowns. Global vaccination programs for preventable diseases are being delayed, costing lives right now. Construction of health facilities is being delayed, costing lives in the future. Their general development and progress are hampered. Worse still, with very young populations, most poor countries have relatively few people at risk of COVID. 

9. The endgame. What endgame?
After a month of “flatten the curve” rhetoric, which basically had the right intention, there was a silent shift towards “crush and eliminate”. How does this make sense in a globalised world where the virus is going to saturate the rest of the world population? What endgame does that entail?

Being a national bubble with no international travel for years until a vaccine adds to the human cost of our policy response. If (or when?) the bubble is breached we get outbreaks anyway. New Zealand is hailed as a success on this front. But until when? The first person who arrives with COVID will simply take NZ back to square one. 

10. The counterfactual
This is tricky to consider. Is there a “no panic” counterfactual where the media doesn’t whip up society into a frenzy? I think there is, and this means that the “people would voluntarily lockdown” argument doesn’t fly. Why would they voluntarily lockdown?

The 2017 flu season was nearly 4x worse than the 2016 flu season, with 1,255 deaths compared to 464 the prior year.

In relative terms, the 2017 flu season was huge. It also had the risk of being multiple times bigger given the state of knowledge in the early stages. Yet no one panicked and shut down society.

If people don’t notice a 4x jump in flu deaths, would they notice a 10x jump from coronavirus deaths and voluntarily lock down? I argue they wouldn’t.

The “don’t panic, don’t lock down, invest in health resources” counterfactual is a plausible one. 

11. The un-science cancel culture
The Twitter mob has decided it can decide what is science and what is not, while at the same time attributing all variation in the COVID outbreaks across different countries or states to the policy response, leaving no space for randomness or luck.

This is “un-science”.

There is also nothing the un-science mob loves more than cancel culture. If my Twitter searches are anything to go by, plenty of people now want Gigi to be fired from her job. Yes, for raising the point that we should try and save the most lives possible by accounting for the cost to lives from our response to COVID, she is apparently now someone who can justifiably be cancelled.

12. A final thought
One thing I have learned to do to help maintain perspective is to turn a problem around and ask the reverse question. How many early deaths would we tolerate to avoid a large recession? Is your answer really zero? Even a global one?

How many early deaths do we tolerate by not spending more on the public health system? Where is the outcry?

[UPDATE]: After being hailed as a success story, on August 13 New Zealand went into a second lockdown after a new COVID outbreak—just as predicted would happen sooner or later. 

Submission to NSW Housing Strategy

The New South Wales government is creating a long-term housing strategy. Hooray!

You can read my submission here.

What's the strategy all about? It's always hard to know with these jargon-filled government documents. To avoid accountability for specific outcomes these documents 1) never make direct, clear, points and 2) always use coded language.

To get a feel for what the priorities are in this strategy I did a word count of key terms that seem relevant to me when it comes to housing. If word frequency is any guide, the strategy is all about population, planning and supply.

Notably, it is not about prices.

This is weird. The Housing Strategy discussion paper notes that rents are the best metric for determining the adequacy of supply and that by this metric supply has been sufficient to meet the record population growth of recent years.

Given the large amount of housing supply currently being delivered, the vacancy rate has risen in Sydney and rent increases have moderated.

So we have a whole housing strategy being created on the basis that housing supply is not responding to population growth because of planning. Yet at the same time, there is a hidden admission that this is definitely not a big issue.

The only logical conclusion is that the government needs to be seen to be doing something about housing because of declining homeownership and enormous wealth gaps the housing market is creating. But it cannot actually enact policy to make housing cheaper.

The fact that community concern about rising prices is not the focus of the discussion paper is quite clear evidence of a political balancing act being played out. Housing is desired to be more “affordable”, but policies that actually lower home prices are political suicide and also come with macro-economic risks.
...current renters and future buyers are the main beneficiaries of lower prices. But they are few in number, and low in wealth, compared to the homeowners and housing investors who gain from higher prices and rents.
This is the heart of the NSW and national housing dilemma that should be the focus of any housing strategy at any level of government. A realpolitik view is that this dilemma is behind the promotion of supply-focussed policy—it can plausibly be claimed to be helping reduce prices while in practice not having any price effects, keeping homeowners and investors happy. In addition, it provides a justification for using the planning system to deliver windfall gains to politically connected landowner ‘mates’

There you have it. Expect a lot of talk and debate about housing during the development of this strategy. Expect no substantial changes except for a few more giveaways from the planning system to well-connected developer mates. 

JG advocates want a UBI, they just won't say it

Let’s retire this debate and the endless word-games.

A Job Guarantee (JG) is a way to guarantee a certain income level to anyone willing to do tasks that some administrator decides are good.

A Universal Basic Income (UBI) is a way to guarantee a certain income level to anyone willing to do any task they decide is good.

We know that many JG advocates simply want to give people money for doing what they would do anyway if their income was guaranteed. They just have dogmatic beliefs about the dignity of work and the word "job."

Here’s Bill Mitchell saying that you would eventually do whatever you liked in the JG (my emphasis).

The Job Guarantee in fact provides a vehicle to establish a new employment paradigm where community development jobs become valued. Over time and within this new Job Guarantee employment paradigm, public debate and education can help broaden the concept of valuable work until activities which we might construe today as being “leisure” would become considered to be “gainful” employment.

So I would allow struggling musicians, artists, surfers, Thespians, etc to be working within the Job Guarantee. In return for the income security, the surfer might be required to conduct water safety awareness for school children; and musicians might be required to rehearse some days a week in school and thus impart knowledge about band dynamics and increase the appreciation of music etc.

Further, relating to my earlier remarks – community activism could become a Job Guarantee job. For example, organising and managing a community garden to provide food for the poor could be a paid job. We would see more of that activity if it was rewarded in this way. Start to get the picture – we can re-define the concept of productive work well beyond the realms of “gainful work” which specifically related to activities that generated private profits for firms. My conception of productivity is social, shared, public … and only limited by one’s imagination.

In this way, the Job Guarantee becomes an evolutionary force – providing income security to those who want it but also the platform for wider definitions of what we mean by work!

If we are going to be this lenient and generous with the definitions of a job, why bother at all? How about being a parent, carer, child, or just a citizen? Why aren’t these “jobs”? And if they are, aren't you just advocating for a guaranteed basic income of sorts?

The inflation concerns that JG advocates claim to have with a UBI are nonsense. They are just backfilling excuses. Obviously, most JG jobs wouldn’t in be sectors where output is priced, so wouldn’t enter inflation calculations anyway. Just like my housework isn’t priced, but could be if supplied by the market, a JG that includes my own housework would have no effect on reducing inflationary pressures.

Further, isn’t the insight of MMT that you might have to tax to reduce demand sometimes? In which case, a UBI can be easily designed to include taxes so that it redistributes in a way that doesn’t create demand-pull inflation.

Oh, and then there are people wouldn't participate in the JG anyway, like children, the elderly and the disabled. They would have to just get money anyway.

So let’s retire the debate. Yes, the government can be a money-creator if it wants. There are only real constraints. So let’s now talk about funding things that we think are important for society over things that are not. Let's talk about practical ways to redistribute income and wealth. Let’s get our priorities right and forget the word-games.

UPDATE: Despite all these nice words that have attracted many supporters to MMT, it turns out Bill Mitchell would like to scrap unemployment insurance from the welfare state and force people to take a JG job. He definitely does not want to give people money without workfare. 

Submission to NSW Productivity Commissioner

Review of Infrastructure Contributions

Dr Cameron K. Murray

Henry Halloran Trust, The University of Sydney
May 2020

Download this submission as a pdf here.

Summary:

I argue that betterment is a more transparent, efficient, and certain tax base for raising council revenue for infrastructure or any other expenses. Compared to fixed-rate infrastructure contributions levied on a per-new-dwelling or per-new-building-area basis, a tax on betterment automatically adjusts to local economic circumstances, boosting efficiency.

I recommend the following:
a. Infrastructure contributions be scrapped in NSW.

b. Betterment from the planning system should be called “Community Development Rights” and a betterment tax should be implemented and called a “Sale of Community Development Rights”, or SCDR.

c. An SCDR be required at the time of planning approval.

d. The amount of to be paid for SCDR be calculated at 75% of the difference in site value when valued “at current use” compared to “at approved use”.

e. These valuations should be undertaken by a third party, rather than councils, such as by NSW Revenue using valuation expertise from within the State government.

f. Payment of the SCDR will be via
i. a 10% deposit of the assessed tax when planning approval is issued and,
ii. the balance on development completion (prior to registering the new plan).

g. For simplicity, in high-growth areas a schedule of pre-calculated betterment tax amounts on a per-dwelling or per-building-area basis can be published. These schedules will be produced by valuers based on local market conditions, borrowing from a process used in the ACT in 2012. 

Key points

1. The Terms of Reference for this Review are focussed on economic issues such as improved transparency, efficiency, and certainty of infrastructure contributions. These are desirable features of an infrastructure contribution system.

However, these are not the features of a system desired by those who pay them. If contributions are raised, even if levied in a more transparent, efficient, and certain way, I expect these economic objectives to suddenly become irrelevant to the development industry. This needs to be acknowledged up front.

The development industry mostly wants lower infrastructure contributions.

For example, Queensland implemented changes to tighten up and clarify its infrastructure charging regime in the 2009 Sustainable Planning Act. These changes ensured a tight nexus between the forecast costs of identified trunk infrastructure and the rate of the charge. These infrastructure charges were published in a simple schedule (an Infrastructure Charges Schedule) linked to a supporting document that identified the infrastructure upgrade and investments planned by councils (the Priority Infrastructure Plan). It was transparent, efficient and certain.

However, because many of these charges increased, rather than decreased as expected by developers, they then lobbied to have them capped, which was swiftly done by the Bligh government in 2011.[1]

2. There is a conceptual conflict between the idea that contributions reflect efficient costs while also complying with the principle of beneficiary pays. Benefits of infrastructure investment, as reflected in the value gains to nearby property, may be less or more than the cost of new infrastructure.

3. Betterment is the name for the value gain arising from increases in property value due to external factors, such as local infrastructure or new property rights granted to landowners through the planning system.

4. For property redevelopment, betterment is the value of the new property rights that allow for that development to take place, which are, until then “owned” by the community. We know this because redevelopment rights can be sold to property owners by councils, rather than given for free.

For example, in São Paulo, Brazil, auctions are held periodically to sell to landowners the rights to construct additional density, called Certificates of Additional Construction Potential (CEPACS), raising around $USD 200 million/year in revenue.[2]

Using betterment as a tax base can help side-step many of the technical arguments used against infrastructure charges on economic grounds. Just as property rights are sold at market prices from the public when disposing of land, property rights granted through the planning system can be sold at market prices.

5. Since 1971 the ACT has taxed betterment at 75% of its market value to fund territory government activities. Their system is known as a Lease Variation Charge (formerly a change of use charge). In addition, by being the monopoly developer of land subdivisions they gain 100% of the betterment in converting rural to urban uses.[3]

The below table scales up the revenue from these sources in the ACT for the difference in housing prices and new housing development in the other states, showing that if a similar scheme was enacted, over $18 billion could be gained by councils in other states using this mechanism.

In NSW alone, there was $8.2 billion of potential revenue in 2018-19.[4] Many other methods for capturing betterment for the public have been implements in Australian and abroad.[5]

6. This implies that over $12 billion worth of redevelopment rights, accrued to landowners in NSW at no cost through the planning system, were utilised in 2018-19.

7. From 1970 to 1975 NSW had a betterment levy of 30% of the value gain from the conversion of rural land to urban uses, raising $17 million in that time with $2 million in total administrative costs. This was used to finance the infrastructure necessary for expansion of the metropolitan region.[6]

However, political lobbying by wealthy landowners on Sydney’s fringe led to the demise of this funding mechanism.

In November 2007 the NSW Government foreshadowed a ‘Rezoning Infrastructure Contribution’ (also known as a ‘Staged State contribution’) to be paid either at the time of rezoning or at the time of sale. However, this approach was abandoned in the final package of reforms to developer contributions in NSW.

8. The beauty of using betterment as a tax base is that it prices property rights that are given away by the public that should be instead sold. The ACT system is equivalent to a 25% discount on the market price of the right to redevelop to higher intensity uses.

9. Additionally, like infrastructure contributions, the costs of a betterment tax or levy cannot be added to new housing prices. Instead, these costs are subtracted from the value of land prior to its development. On net, it is an economic transfer from current landowners to the community at large (via the council) that confers these new rights.

This is why the abolition of the Sydney Betterment Levy was such a political issue in city-fringe electorates—the value of the levy came off the value of the land with development potential.

10. Un-priced betterment is also the honeypot around which corruption emerges at both state and local levels. In most states, local councils have a history of corruption involving favourable rezoning and planning decisions. It is the fact that these decisions grant valuable new property rights for free to the recipients that fuels the corruption cycle. A recent example involves Casey Council in Victoria.[7]

A study I co-authored in 2016 showed that landowners in Queensland who were politically connected or employed profession lobbyists were much more likely to find their land within a rezoned area compared to near-identical neighbouring land, and in the process, these connected landowners gained $410m out of the $710m worth of development rights given to all landowners from these rezoning decisions.

UPDATE:
Certainty is greatly increased for the development industry by using betterment as a base for raising revenue as it solves the land purchase price dilemma. If planning outcomes are uncertain, the developer who is the most confident of a generous planning outcome will win any bid for the purchase of a development site. They will then require a generous planning outcome to justify the price they paid for the site. With a tax on betterment, they can pay only slightly above the value at its current use for the site. If they fail to get a generous planning approval then they pay less for the betterment tax. If they get a favourable approval, they pay more. 

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.