I was going to title this blog ‘house prices, supply, rents, incomes and interest rates‘, but then wondered if any would be readers would still be awake.
The background is the discussion which has been going on for a while about whether UK house prices so high because of a lack of supply, but it also leads me to some thoughts about the linguistics of ‘rent’
Here’s an example of the current debate:
In which @RobinBHarding misses core point of the ‘no shortage’ evidence: it’s *not* about counting houses, it’s about the price of housing services. Let’s debate the actual case made – is it economic theory or ONS data that’s wrong? https://t.co/3JqsTfxnDJ https://t.co/hSi8je4cyv
— Ian Mulheirn (@ianmulheirn) August 14, 2018
As a former bond analyst, I have thought about house prices as the net present value of actual or imputed rents, so expecting them to move in line with long term interest rates. It’s a view implied – with the refinement of depreciation – by Ian Mulheirn’s formulation:
Rent = House price x (interest rate + depreciation rate)
Against that, the view of what here I’ll call supply-siders, for example Robert Harding in the FT, is that:
the cause of those high costs has become more widely understood: restrictive planning and zoning rules lead to a chronic lack of supply in the places where people want to live.
Again as a former bond analyst, I look for the arb (arbitrage opportunity). If house prices are so high, why aren’t people building more, and bringing the price down? Thinking like that makes me more of a supply-sider.
To reconcile the two, here’s a model, and some thoughts about how to test it.
My starting point is to think of housing as a consumer durable, where there is a cost of production, and a series of net benefits to the owner over its life. Where the market is competitive, the amount produced will increase to the point where the value of these net benefits is the cost of production, plus some reasonable profit margin, and this total will be the price. Where the market is not competitive, because supply is restricted, the price include a premium above this amount. The costs of production – henceforth taken to include a reasonable profit margin – will depend on the cost of supplies, including to a large extent labour, so will depend on incomes, but given the mobility of construction workers, and national / international supply networks, this cost will not vary that much by region. It will also not vary with interest rates any more than the price of any other consumer durable – cars immediately come to mind.
The value of the premium will depend on how much people will pay in rent, and how long a premium will last. The first, the demand, will be very local, linked to incomes, and quite responsive. The second depends on how the elasticity of supply, which will be low in the short term, increases with time to the long term. I don’t know if there is a name for this, but we can suppose a factor, λ, the annual percent increase in net supply as a proportion of stock divided by the housing price premium as a percentage of the cost of housing supply. This factor will be a measure (inverted) of the tightness of a local housing market.
The value of the premium, ceteris paribus, then becomes the NPV of a series of actual or imputed cash flows to the landlord / owner occupier, exponentially declining annually at a rate λ, but also varying with local incomes. The NPV will then depend on these, and also long term interest rates, making the price of housing a function of:
- underlying costs, for which national nominal GDP will be a first approximation
- local incomes
- local housing market conditions, λ, and
- long term interest rates, r
I could try formulating that with a more specific form than
Prices = f(nom GDP, local income, λ, r)
e.g. with the summation involved in that NPV calculation, but I’m not entirely comfortable with how I’ve formulated λ, and I suspect others will have thought about this already, so for the sake of not reinventing wheels, I’m leaving it at that. In any case, it would be useful to know what empirical data was available to test the model. I would expect there is a reasonable amount, but that again is something to ask about.
Trouble with ‘Rent’
Slightly peripherally, I wonder if the linguistics of the word ‘rent’ interferes with clear thinking in this debate. From the era of classical economics, e.g. Ricardo, rent has been understood as income received by the fortunate owner of an asset which is not only in demand, but whose supply cannot be increased. In his day, most rents were like this, because agricultural rents were what mattered most, and most land under cultivation was not merely marginal, and so most rents were payments to the lucky owners of landed estates. In the politics of the day, and adopted by 19th century Liberalism, it became a stick with which to beat the landed interest.
Since then, rents have become much more payments for accommodation in cities, but thanks to the same legal language, they are still called rents, and landlords are still unpopular. Later in the 19th century, Henry George pointed out a comparable stroke of luck for urban landlords, who could also demand premium rents in cities benefiting from what we now call the economics of agglomeration, and his followers became a powerful new force in political Liberalism.
George’s arguments didn’t become mainstream because the supply of urban properties is not quite fixed as prime agricultural land – it is possible to densify urban development. Instead, they were absorbed by the still Liberal precursors of neo-classical economics, such as Alfred Marshall, who took spatial economics seriously. However, he also gave ‘rent’ a new economic, non legal meaning, as whatever income accrued to someone thanks to the ownership of an in demand asset in tight supply. Rents paid to a landlord which reflect the costs of maintaining property and its depreciation may indeed be called rents, but they are not economic rent. In areas of low housing demand, such rents will constitute most of actual rents.
Since Marshall, economist have reasonably enough castigated ‘rent seeking behaviour’, of which there will be a fair share in housing, but the rent seekers may be as much those looking to restrict supply as landlords. There will be a big overlap between the sectors, especially among more speculative landlords in areas of high demand, but the sectors are not the same.