David Miles and Victoria Monro
Since the mid-1980s, the average real (RPI-adjusted) UK house price has more than doubled, rising around one and a half times as fast as incomes. Economists’ diagnoses of the root cause varies – from anaemic supply, to the consequences of financial deregulation, or even a bubble. In our recent paper, we explore the role of the long-run decline in the real risk-free rate in driving up house prices. Low interest rates push up asset prices and reduce borrowing costs. We find the decline in the real risk-free rate can account for all of the rise in house prices relative to incomes.
Chart 1: Mean house prices between 1985 and 2018, in real (RPI-adjusted) terms (2018 pounds)
Rapid house price growth over recent decades has provoked a wealth of academic literature on what drives house prices. The housing market has been subject to a raft of policy initiatives, focused typically on two issues: housing affordability (particularly for first-time buyers), and financial stability (banks’ vulnerability to house prices, and household indebtedness).
We contribute to this literature by taking a long-term view of what drives UK house prices. We find that the reduction in home-ownership costs implied by the decline in the real risk-free interest rate, added to the effect of rising incomes, more than explains the increase in house prices. Between 1985 and 2018, real house prices increased by about 160%. Our asset-pricing model estimates the expected real house price rise given the 5.5 percentage point decrease in 10 year index-linked gilt yields, changes in tax treatment, and income gains is around 170%; of this 170%, almost 110% is due to the change in the real risk-free rate.
In a pair of earlier BU posts (here and here), John Lewis and Fergus Cumming sketched out a framework for considering the relationship between the risk-free rate and house prices. Our model goes further, considering a time horizon twice as long (which includes the financial deregulation of the pre-2000 period and the financial crisis), and incorporating expected capital gains and other home-ownership costs – such as maintenance and taxes.
To assess the impact of the real risk-free rate on house prices, our framework outlines a key housing market equilibrium condition – namely that the rental yield (i.e. rents as a proportion of the house price) should equal to the costs of home ownership (also as a proportion of the house price).
What are the costs of home ownership? These include: (1) the opportunity cost of investing in a different asset (comprising the ‘risk-free’ interest rate, plus a risk adjustment reflecting the risk associated with housing as an asset class); (2) taxes (both transactions taxes, like stamp duty, and taxes on using housing services, such as council tax); and (3) the ongoing maintenance of the property. These costs are potentially offset by the household’s expectations of capital gains on the asset (i.e. expected increases in house prices). And they are also typically proportionate to the price of the home. Turning back to our housing market equilibrium, there are several implications. When the costs of home ownership (as a percentage of house prices) are constant, then the rental yield too must be constant; rents and house prices must be moving proportionately. We find that average rents typically grow with incomes/earnings (Chart 2) – suggesting a plausible hypothesis for the change in house prices in equilibrium (assuming interest rates, taxes and maintenance costs stay constant) is also income growth. But unanticipated changes in interest rates will mean that, as the market adjusts, house prices move in a sharply different way to incomes.
Chart 2: Average annual rents as a proportion of average disposable household income
An example may help here. Starting from rents:
Rent = house prices x [risk-free rate + maintenance + ownership taxes + risk premium on housing – expected capital gains]
…suppose the real risk-free rate is 2%, maintenance is 1%, ownership taxes are worth 1%, the risk premium is 3% and expected real capital gain is worth 2% (all as a proportion of house prices). House prices would be 20 times annual rent. If the real risk-free rate falls to 0% (the level seen at end-2018), holding all else equal house prices become 33 times annual rent (increasing by 67%).
In assessing the size of this adjustment, we account for the role of housing supply. In the short-run, supply cannot respond to a shock in home ownership costs, such as a change in the risk-free rate. This means that total housing demand (that is, the sum of demand for rental housing and demand for owner occupied housing) should also remain constant. This is true if rents and the user cost of housing (i.e. the cost of owning and maintaining a house for one period) do not change, leaving only the house price mechanism available to clear the market: house prices must increase sufficiently to offset the decrease in the risk-free rate.
In the long-run, however, supply can increase in response to a decline in the cost of owner-occupied housing. The return to equilibrium therefore requires a corresponding demand response. We model the housing market, applying parameters for supply elasticities consistent with the empirical literature (which suggests they are very low), and estimate that the medium term sensitivity of house prices to unanticipated changes in real interest rates is about 90% of the short-run effect.
The critical assumption
The model relies on one critical assumption: that the decline in the real risk-free rate was both not anticipated by the market, and expected to persist. If market participants anticipated the 30 year decline in the real risk-free rate, then that expectation would have been factored into house prices from the beginning. And, if the market thought that lower rates would not persist, then for an asset class like housing – held over the medium/long term – there would be limited price impact.
The evidence overwhelmingly supports this assumption. Chart 3 compares the 10 year index-linked yield in each period with the expected 10 year index-linked yield in 10 years’ time. The two series are very similar – in other words, people’s expectations of the 10 year risk-free rate in 10 years’ time was pretty much the same as the 10 year rate at that time. Movements in the risk-free rate were therefore expected to persist – but the 30 year decline was not anticipated.
Chart 3: A comparison of the interest rate on 10 year index-linked gilts to the expected interest rate on the same gilt in 10 years’ time
Our model uses the short-run and long-run equilibrium conditions to show how house prices would have responded to changes in real interest rates and in rents (which are assumed to follow incomes – as Chart 2 strongly suggests).
In the short-run, we allow only the risk-free rate (as approximated by the 10 year index-linked gilt) to vary, holding income and other costs fixed. Our model estimates that an unexpected, but persistent, 1 percentage point increase in the risk-free rate could reduce real house prices by 18% in the long-run. If the risk-free rate were to now increase from its end-2018 level (around -2%) to 0% (levels last seen in 2011), real house prices could fall by 31% across many years.
In the long-run, we account for movements in the risk-free rate, tax changes and income. Between 1985 and 2018, the 10 year index-linked yield fell from around 3.5% to -2%. Across the same period, taxes on housing transactions (stamp duty) increased whilst subsidies (such as mortgage interest relief) were gradually phased out. Therefore, the net tax due to home ownership increased over this period. Data on stamp duty is limited: our best estimate is that the net effect of these changes is worth around 0.7% of house prices. Finally, the UK household sector’s income increased by around 80%.
Combining these factors, we estimate that the long-run effect of the decline in the risk-free rate increased real house prices by about 108%; the increase in household income increased house prices by around 80%; whilst the increased net tax obligations pushed house prices down by around 15% (see Chart 4). In total, the model estimates house prices would have increased by 173% – the observed increase was 156%. One reason for this over-prediction might owe to the slight rise in mortgage spreads. An extra 20-30 basis points in the mortgage spread to the risk-free rate on the stocks of mortgage debt might reduce the predicted house price growth over the period to between 161% and 164% – very close to what happened.
Chart 4: Decomposition of our model’s estimates of real house price growth, and actual house price growth (1985-2018)
There has been a substantial decline in a key component of the user costs of housing over the last 30 years, driven by the decline in global risk-free rates. Given the responsiveness of demand (strong) and supply (weak) to these costs, this has pushed up real house prices substantially. Our model can explain all of the observed rise in terms of lower rates and higher real incomes: it suggests prices are not currently over-valued.
Were the trend to reverse, in the long-run (and absent any other structural changes) we might expect the real house price to fall. Our results indicate that if the risk-free rate moves by just 1%, this can result in real house prices ultimately moving by roughly 18% in the opposite direction in the long-run.
David Miles is a Professor of Financial Economics at Imperial College Business School and a senior advisor in the Bank’s Financial Stability, Strategy and Risk Directorate. Victoria Monro works in the Bank’s Macrofinancial Risks Division.
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