## Tuesday, September 15, 2020

### Low interest rates will boost home prices, as designed

Interest rates are the main story for home prices in Australia. With our deregulated banking system, all demand for mortgages can be satisfied (conditional on servicing criteria). With an active and tax-advantaged investor market, this only adds to the tendency for the housing market to converge to the asset-pricing equilibrium, where mortgage interest on the home price substitutes equally for rent, along with some adjustment for ownership costs and expected capital gains.

Here’s the basic gist of the interest rate effect for a typical home that saw rising nominal rents until recently, but where rents are expected to see no nominal growth over the next decade.

Despite rents in this example rising only 47% in nominal terms over four decades, the equilibrium asset price (where mortgage interest substitutes for rent) increased by 338%.

Notice that the 2% point decline in interest rates has a larger effect when interest rates are lower. Halving interest rates should double prices, all else equal (and vice-versa). But that requires only a 2.5% point drop from 5%, but a 4.5% drop from 9%.

The latest bout of monetary policy that took mortgage interest rates from around 4.5% to 2.5% is nearly a halving, which implies scope for a near doubling of prices. Even if Sydney and Melbourne prices were far above the equilibrium due to a recent speculative period, this interest rate decline will bail out speculators and support those higher prices.

This is why I see mostly upside for home prices in Brisbane, Adelaide, and even Perth in the next few years. Gross yields for Sydney and Melbourne houses are around 2.6%. But they are 3.8% in Brisbane, 4.2% in Adelaide, and 3.8% in Perth. A 0.5% point decline in yields in Brisbane, would, for example, see a 15% price gain.

If you can borrow at 2.5% the maths looks like this for a home currently rented for about $400/wk ($20,000/yr).

Annual rent - $20,000 Price at 3.8% gross yield -$526,000
Interest on price (2.5%) - $13,150 Interest on price (2%) -$10,500

If you buy with a 2.5% mortgage instead of renting, you get nearly $7,000 year in your pocket to cover ownership costs and repay the mortgage. If you can get a mortgage interest rate closer to 2%, that gives you nearly$10,000 per year to cover these costs.

Even if you expect rents to fall 10%, this doesn't change the asset-pricing arithmetic much at all.

If you don’t expect prices to fall rapidly, buying makes good financial sense with low interest rates and high housing yields.

UPDATE: It is now cheaper to pay the interest on a mortgage than pay the rent in the major capitals on average (see blue line dipping below one). The below image is that ratio of the interest rate to the gross yield. It also shows the repayment for a 30-year mortgage as a ratio of the rent in orange.

## Friday, September 11, 2020

### Superannuation fees to rocket

These comments were reported in The Australian on 10 Sept 2020.
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At the current 9.5% compulsory contribution rate, Australia’s superannuation system is already an unbelievably expensive retirement income system. It employs 55,000 people and costs $34 billion in fees each year to deliver only$40 billion in retirement incomes (see the Scrap Superannuation report here). Increasing the compulsory super contributions rate to 12% of wages will do little to support retirement incomes while adding substantially to the economic cost of the superannuation system.

“The economic cost of super to members comes in the form of direct fees, which are around 1% of super balances on average, as well as the foregone investment returns from those fees,” says Dr Cameron Murray, economist and research fellow at The University of Sydney.

“For a typical earner with a 40-year work-life they can expect to have a real super balance of $743,000 at retirement, having paid about$108,000 in fees over their lifetime,” said Dr Murray [1].

“But those fees could have earnt an additional $74,000 in investment income, meaning the total economic loss is$182,000 over a lifetime.”

“Raising the compulsory super contribution rate to 12% will see funds charge this typical earner an extra $28,000 in fees over their lifetime, losing an addition$20,000 of investment income” concluded Dr Murray.

“Even if funds improve their performance and fees fall by half, the compulsory rate increase will see this typical worker lose an extra $16,000 to fees over their working life, and around$10,000 of investment income.”

“The super system is one of the most economically inefficient ways to support retirement incomes. Raising compulsory contributions will only add to these costs, creating even more jobs for blow-hard spreadsheet monkeys who pay themselves from our retirement savings.”

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[1] First ten years of work-life at 70% of average full-time wage, and last ten years at 30% above the average full-time wage, with middle twenty years at the \$90,000 average full-time wage. All returns and costs are in real terms. See Table 1 and 2 for a result summary.

## Tuesday, September 1, 2020

### A housing supply absorption rate equation

You are a housing developer with a large plot of land on the fringes of a major city with no planning constraints. How quickly should you sell these lots to supply them to the housing market?

This is the question I answer in a new working paper entitled A Housing Absorption Rate Equation (now published here). I sketched out some of my initial thinking on this topic in a blog post earlier this year. Here I want to explain this new approach more clearly and show why it is important for the housing debate.

### Why is this important?

Economic analysis of housing supply is usually based on a one-shot static density model. In this model, landowners choose a housing density that maximises the value of their site. The density that achieves this is where the marginal development cost of extra density equals the marginal dwelling price. Every landowner does this instantly. There is no time in the model. It just happens.

But optimal density (dwellings per unit of land) is not optimal supply (new dwellings per period of time).

Despite this conceptual confusion, radical town planning policy changes have been proposed around the world. By allowing higher-density housing, proponents of these policies expect that the rate of new housing supply will increase enormously, reducing housing prices.

I wouldn’t be that confident. It is not clear that the economic factors that influence the optimal density are the same ones that affect the rate of new supply, or what is known as the absorption rate.

### What factors influence the optimal rate of supply?

To answer this, we break apart the time dimension of the development problem. In a dynamic setting, the economic value from a sequence of dwelling lot sales is maximised when delaying the marginal sale into the next period makes you equally as well off as selling that dwelling today.

The economic factors that influence the absorption rate are those that change the relative gains from selling now rather than delaying and selling later. Let us think about the motivating puzzle of a housing developer selling new lots.

From the perspective of the second period, if you sell a lot today, you get the interest rate on the lot value, plus you avoid any taxes on that lot value.

If you sell on that later period, you got the value gain of the lot. This value gain comes from the market at large (i.e. the trade of existing dwellings) but is also affected by your own sales in the first period. Sell more now, get lower price growth and hence a lower price in the next period. The net price gain is, therefore, market demand growth minus your own-price effect on that price growth.

The optimal point is where you are equally well off making the same number of sales in the current period and the next period.

The result of the dynamic supply problem is this equation.

Let's walk through this one parameter at a time.

#### Price growth sensitivity to own-supply, a

The first parameter of interest is the own-price effect, a. A higher a means that each sale today has a larger effect on price growth. It’s a measure of the “thinness” of the demand side of the market. Since a is the denominator, it means that the thinner the market, the lower the optimal rate of sales.

#### Market demand growth rate, d

When demand growth is high, you sell more. This makes sense. You sell into a boom and withhold sales during a bust. This is important because one argument for relaxing density restrictions is that new supply would occur at such a rapid rate that prices would fall. But falling prices reduce supply. There is hence a built-in ratchet effect in housing supply dynamics.

#### Interest and land tax rates, i and 𝜏

These two rates work in combination. The interest rate is the gain you get on the cash from selling a lot today, and the land tax rate is a cost you avoid from selling today. The gain from not owning land (i.e. selling it) is the interest rate and the land tax rate, which is positively related to the optimal absorption rate.

#### The efficiency of higher density, ω

The final piece of the puzzle is the ω parameter. This parameter captures the idea that if you delay selling a lot you can change the density of development in response to rising prices. Remember that static density model? This is where it is useful. It shows that if prices rise, undeveloped sites rise in value more than the dwelling price because the higher price justifies denser housing development.

I show this in the below diagram. At price Pt the optimal density is Dt, and the site value is the orange shaded area (the dwelling price minus the average development cost times the number of dwellings).

If prices rise to Pt+1, then the optimal density is now Dt+1. The value gain for the site is not just the area marked A, which it would be if density was fixed. It is the area A plus the area B, minus the area C. Since B > C this means the site value rises more than the dwelling price change. The ω term captures how much bigger A + B - C is than A. When ω is 1, it means that density is constrained to Dt and site value rises only by the dwelling price change. Flatter cost curves create a larger ω.

The important thing to remember is that constraining density makes ω smaller (holds it at 1). This increases the optimal absorption rate because it reduces the gain to delay that comes in the form of the ability to vary housing density.

### Where does this model leave us?

Having a simple absorption rate model allows housing researchers to think more clearly about the economic incentives at play for housing suppliers. It allows us to break away from the “density = supply” confusion. Instead, it focusses attention on the key issue of the relative returns to delaying housing development.

Any policy that increases the cost to landowners from delaying housing development will increase the rate of new housing supply. For example, higher land taxes and interest rates.

Another way to increase the cost (reduce the benefit) of delay is restricting density. This goes against the intuition of most housing researchers, but the economic effect is real.

Think about it this way. You announce a policy that will limit density in an area to half of what is currently allowed in five years time. What happens? You get a housing development boom as projects are brought forward in time. You massively increased the cost of delay.

It is obvious that planning controls change the shape of cities. They reduce housing density in some areas and restrict certain uses in others. That’s what planning does. But how this translates into an effect on the rate of new housing supply across a city is far more difficult to ascertain. This model goes some way to helping housing researchers clarify their thinking about the economic incentives at play in housing supply, instead of relying on intuition and inappropriate static models.