Harvesting housing supply

There is a common thread between the boom in lumber prices in the U.S. and dynamic models of housing supply. 

That common element is that lower interest rates make it optimal to both harvest trees slower and to build new homes slower. Let me explain.

Take a look at the diagram below representing a forest with trees at different stages of growth.

The stock of potential timber from trees at different stages of growth is marked as Q. So 10 tonnes of large trees, 7 tonnes or medium trees, and 3 tonnes of small young trees. A total of 20 tonnes of timber there. 

But each stand of trees with a different maturity has a different rate it grows per year. Young trees accumulate timber faster (proportionally) than older trees. The growth rates for the trees in each stand are marked—the oldest grow at near enough to 0%, the next at 5%, and the youngest at 10% per year.  

Given this forest with a stock of 20 tonnes of timber, how much is optimal to harvest each year?

The trick to thinking about this question is to realise that the trees are assets, quite literally growing in value each year. When you harvest a tree you are swapping a "tree asset" for a "cash asset". The way to tell what is optimal is to compare the return from the tree asset that you give up to get the return from the cash asset.  For example, if you can earn a 7% return from cash, you won't harvest a tree that is growing in size, and hence value, by 10% per year. It's a losing trade to give up 10% to get 7%. 

In this forest, we harvest 10 tonnes this year if the interest rate is below 5%, and 17 tonnes if it is above 5%. 

When it comes to forest management, lower interest rates mean slower harvesting of timber. If interest rates fall from 7% to 3%, then all the trees growing at a rate between 3% and 7% per year should be left to grow rather than be harvested and replaced with saplings. This is well understood when it comes to harvesting forests. 

But it is not well understood when it comes to "harvesting housing development opportunities". 

Undeveloped urban land is a lot like a tree—it grows in value without being developed (harvested). Like our forest, we don't just develop all land as soon as the revenue exceeds the cost. We optimise the rate per period to maximise value from the site (or set of sites). This is why developers stage housing subdivisions as much as possible. 

A lower interest rate changes the trade-off between owning undeveloped land and getting cash from development. It makes a slower pace of housing development optimal, all else equal. 

Not all else is equal, obviously. The price adjustment to lower interest rates generates demand that new housing supply responds to—interest rates are not the only factor. In the last 20 years we have relied on this temporary demand-boosting effect of interest rate reductions to generate supply, but this has led to structural low-interest-rate conditions that will not encourage supply when demand falls. 

In housing, optimal harvesting is called the "housing supply absorption rate". I explain it here. 

Stamp duty for land value tax

The NSW government is proposing to give homebuyers the option to not pay stamp duty on their housing purchase and instead opt to pay an ongoing land value tax. I have labelled such policies SD4LVT.

SD4LVT seems to be motivated by "bad economics". All the efficiency gains that economic analysts claim will occur are merely assumptions and not very realistic ones at that. 

A major consideration for SD4LVT is its effect on housing prices. While SD4LVT is often marketed as "saving buyers" thousands on their purchase, this ignores the well-known issue that stamp duty is economically incident on the seller. 

What that means is that buyers have a willingness to pay for a home that includes the cost of stamp duty. If the market price of a home is $500,000 and stamp duty is 3%, then the purchaser must have been willing to pay $515,000 to buy the home. If stamp duty is removed, then this purchaser who was willing to pay $515,000 to buy the house can spend that $15,000 saved on stamp duty bidding up the market price. Instead of the government getting $15,000, the seller gets it. 

This is why a stamp duty holiday on housing purchases was enacted in the UK last year to "kickstart the stalled housing market".

So we know that reducing stamp duty alone will increase prices. But won't a land value tax decrease prices because it adds an additional cost for the buyer?

Yes.

And we are now at the crux of the issue. Neither tax will, in the short run, reduce the cost of housing. Homebuyers are paying the maximum they are willing. Whether that payment is directed to home sellers, or the government via stamp duty or land value taxes, has no effect on the underlying property market dynamics of rationing via prices and the costs buyers will need to pay.

In a presentation I made to Victorian Treasury a few years back, I explained this point with reference to the ACT's ten-year SD4LVT transition. I showed the below graph which makes the point that if the present value of the flow of future land value tax liabilities equals the stamp duty, the same willingness to pay for housing is just distributed differently under a land tax regime.

I also explained how to calculate the likely market price effect for a government replacing the same average stamp duty revenue stream with a land tax revenue stream.

The rule is

1. If turnover rate < capitalisation rate, price increases
2. If turnover rate > capitalisation rate, price decreases

Let's work through an example with some round numbers to demonstrate. The average housing sale is priced at $700,000 with a $37,000 stamp duty (5.3%). Without stamp duty, the price would be $737,000.

Assume that turnover is 100,000, or 4% of stock per year. This provides $3.7 billion in stamp duty revenue.

For a land value tax to raise $3.7 billion, it would need to raise $1,480 per dwelling, since in this example there are 2.5 million total dwellings. A land value tax rate in the dollar can be worked out in order to raise this amount based on the land value share of the average home. Say land value is 60% of the average home value, or $420,000, then the land value tax rate on the dollar is 0.35% per year.

Whether the market price rises or falls depends on whether the present value of a perpetual stream of $1,480 annual payments is worth less or more than $37,000 upfront stamp duty. 

If the capitalisation rate is 5% (the rate at which a flow of income is converted to a present value), then the present value of the land value tax is only $29,600. In this scenario, the market price would rise to $707,400 because a $37,000 stamp duty liability has been replaced with a $29,600 land value tax liability. Notice that the capitalisation rate here is above the housing turnover rate (5%>4%). 

If the capitalisation rate is 3%, then the present value of the $1,480 land value tax payment stream is $49,300. In this scenario, a $37,000 stamp duty liability is replaced with a $49,300 land value tax liability, and hence the house market price will fall by $12,300 to $687,700.

The question of whether SD4LVT is a good policy change depends not on the price effects—it merely redistributes who gets what payment and when—but on efficiency effects from making housing turnover cheaper. On that note, I refer you to my previous analysis showing that these claims are overblown and that the revenue volatility of stamp duty is a good thing because it stabilises the economy. 

In general, if you want to reallocate the economic rents that have accumulated to landowners, then a land value tax is a good way to go. But you do not need to remove another tax that achieves the same thing. Both taxes can work well together to divert economic rents from landowner to the public.