# Houses are assets not goods: taking the theory to the UK data

John Lewis and Fergus Cumming

In yesterday’s post we argued that housing is an asset, whose value should be determined by the expected future value of rents, rather than a textbook demand and supply for physical dwellings. In this post we develop a simple asset-pricing model, and combine it with data for England and Wales. We find that the rise in real house prices since 2000 can be explained almost entirely by lower interest rates. Increasing scarcity of housing, evidenced by real rental prices and their expected growth, has played a negligible role at the national level.

To infinity and beyond…

A standard framework for pricing assets is the “Dividend Discount Model”. Just as the equilibrium value of a tulip bulb should be the (net present discounted) value of the future flowers it produces, for a houses the value is given by rents. More formally:

$P_t=R_t+\sum\limits_{\tau=1}^{\infty}\frac{E_t (R_{t+\tau})}{\prod_{T=t+1}^{t+\tau}(1+\rho_T)}$

We observe current rents (the first term on the right-hand side) and the path of expected rents (the numerator). For the denominator, the discount rate is the expected future interest rate (observed from yield curves) plus an estimated constant risk premium. Given all this, we can compute what the model says prices should be. Sure, this misses many other things (credit constraints, tax changes etc), but it’s just meant to be a simple model to illustrate the magnitudes of some of these channels rather than a definitive assessment of over/under valuation, or capturing all relevant factors. And it isn’t a forecasting tool.

Lower interest rates raise asset prices by increasing the present value of future cash flows. These effects can be powerful, especially when interest rates are already very low. To see this, suppose a contract pays you a pound coin every year forever. The first 20 pound coins are discounted by the prevailing expectations of future interest rates at the appropriate points on the yield curve, and then assume the discount rate is constant at some other value after that. How much would this contract be worth at different points in time?

The powerful role of discounting rates….

The purple lines on the chart below show the UK forward yield curve each month from January 1999 (darkest) to the present (lightest). Loosely, each curve is the expected annual rate of return on benchmark assets over each of the next 20 years. July 2019’s is red; August 2008’s is in green and May 1997, the beginning of the inflation-targeting era, is in blue.

The dots on the charts below decompose the valuations of the coins using these three yield curves, assuming the interest rate in year 20 persists for all future years, and no risk premium. The darker bars show the value contributed by the first 20 coins, the lighter ones the value of the rest.

As rates fall, the value of the coin stream increases from £14.20 in May 1997 to £21.40 in August 2008. The subsequent fall in interest rates to the July 2019 yield curve generates a further near-quadrupling in value to almost £80. The bulk of this rise occurs via dramatic increases in the value of the coins that arrive in more than 20 years’ time.

The chart below explores that sensitivity further. Each line shows the value of the coins assuming a given yield curve for the first 20 years, and then a range of values for the rate after that. The actual value of the 20-year rate at each point is shown by the dots (i.e. the rate used for the light bars above).

In May 1997, coins arriving in the far future are not worth very much because 20+ years of discounting at 7% erodes most of their value. So the blue line is fairly flat: shift your assumption about long rates and the value of the coin flow is virtually unchanged.

In August 2008, it’s a similar story. But fast forward to the July 2019 yield curve and a 1pp change in discount rates beyond 20 years can make an enormous difference to prices.

This is a problem because ultra-long run interest rate expectations are difficult to measure and not easily captured by financial market instruments. And over the decades very long yields can move around a lot. So in our model below, we switch off the ultra-long run interest rate channel completely by fixing the long-run discount rate to a constant rate of 3.8% (the 2000-2018 sample average) beyond 20 years. That means changes in expected future interest rates up to 20 years ahead (but no further out than that) can affect prices. It’s simple, but captures the belief that investors don’t make large revisions to their ultra-long run interest rate expectations.

What does the model say about house prices in England & Wales?

The black line is the model’s estimated value of average house prices assuming the annual discount rate reverts to its sample average after 20 years. For comparison, the gold line shows the case if the prevailing 20-year rate is extrapolated forward for the rest of time. The gap between the two is fairly small until 2014, when 10+ year rates really started to fall. The red line shows how actual prices evolved, re-based to the same units as the other lines. The red line is 70 at the start, indicating that actual prices were about 30% lower than the model’s benchmark in January 2000. Overall, the cumulative price growth between 2000 and 2018 matches the model quite closely. Though in individual years actual prices do sometimes diverge significantly from the model.

The drivers of change

The coloured bars below decompose the predicted nominal growth of the black line above into the different components (details in the appendix).

First up, the grey bars show the role of CPI inflation. If house prices rose at the same rate as goods in general, they’d have risen by 50% since 2000. So what explains the remaining 60pp of real house price growth?

Rising real rents (pink bars) only account for a very small amount. Yesterday’s post argued that scarcity of housing should show up in rising rents, so this suggests lack of supply has had very little role to play (similar to Ian Mulheirn’s recent paper). That doesn’t say anything about scarcity relative to other countries, but it does imply that housing hasn’t really got significantly scarcer over the past two decades.

The tiny maroon bars show that the role of expected future rental growth has been negligible. Admittedly, our model takes survey expectations rental growth 6 months ahead and then assumes it reverts to long-run averages after two years, so it’s hard for this channel to show up much. But we can also cross-check this against actual rents – if rising prices were driven by the belief that rental growth would be permanently stronger than in the past, those expectations weren’t borne out over the sample period.

By far the largest contributor is the lower discount rate (green bars), which accounts for almost all real house price rises since 2000. We completely shut down any role of interest rates beyond 20 years. That’s probably an overly harsh assumption( it’s probably unrealistic to think rates suddenly ping back to our 3.8% constant), but even with this crude way shutting down discounting effects at long horizons, you can still generate effects that match the observed 60% rise in real house prices.

Even if the aggregate model suggests it’s mainly about lower interest rates, this cannot explain any geographical variation: risk-free rates are the same across the whole country. But all the other variables in our model are available at regional level. So we did the same exercise for the nine English regions and Wales. We group them into four geographical blocs based on similarity of results.

In “The North” (North East + North West + Yorkshire and the Humber), real rents have been declining, pulling down on house prices by about 20% over the sample period.

In “The Middle” (East Midlands + West Midlands + East of England + Wales), real rents have exerted less a smaller pull, tapering to near zero by the end.

By contrast, in “The South” (South East + South West), real rents have pushed up on prices, by around 8pp by 2018.

And in London has seen a similar but smaller contribution from real rents, though the overall magnitude of actual prices rises is higher.

So the role of rents in explaining house prices is relatively small in all regions, and the apparent greater scarcity in the “South” has in aggregate terms been offset by less scarcity elsewhere, with little effect on aggregate prices.

Conclusions

In levels terms, house prices are about in line with our model’s estimates, as is the overall rise seen since 2000. It attributes this primarily to CPI inflation and lower interest rates, even though our approach shuts this channel down after 20 years. The model says that relative scarcity of housing has played almost no role at the national level since 2000, though it has pushed in opposite directions in different regions.

John Lewis works in the Bank’s Research Hub and Fergus Cumming works in the Bank’s Monetary Policy Outlook Division.