Real house prices in the UK.

Barrell, Ray ; Kirby, Simon ; Whitworth, Rachel 等

Introduction

The housing market plays a fundamental role in the economy, and its functioning affects both consumer welfare and economic stability, as the recent crisis has made clear. Research by Barrell et al. (2010) shows that house prices are a key determinant of financial crisis probabilities in OECD economies, and contribute significantly towards systemic banking risk. This must lead the regulator to assess carefully the role of the housing market in this relationship, and if necessary impose regulatory restrictions on the market so as to ensure it functions in a way that reflects the best interests of the economy. In this note we look at the evolution of real house prices in the UK, noting that they have a strong cyclical pattern, we then look at the factors that might affect the evolution of real house prices, and we estimate a dynamic equation describing those prices. After considering a wide set of factors, we demonstrate that there is little role for the supply of housing relative to the number of households. This may be because the ratio of these two variables has been relatively constant over the past thirty years. We show that real borrowing costs, real incomes and the loan-to-income ratio are significant factors determining the long-run path of real house prices, and that front loading problems from high short-term nominal interest rates affect the path of adjustment. Overvaluations can persist for years, and we would judge that real house prices are currently fundamentally overvalued by around 10 per cent. If loan-to-income ratios are reduced then the fundamental overvaluation will increase, and such a policy will put further downward pressure on real house prices.

House prices in the UK

Figure 1 illustrates real house prices since 1964, using a seasonally-adjusted version of the Department for Communities and Local Government (DCLG) mix-adjusted house price index (deflated using the National Accounts consumption expenditure deflator). The series has clearly been following an upward trajectory throughout the period illustrated, and this trajectory has steepened notably since the start of 1996 but has seen a steep correction following the crisis. House prices have fluctuated a great deal around what might be described as an upward trend.

One possible explanation for much of these dynamics could be movements in the general rate of inflation of all goods and assets prices, which is used in the calculation of real house prices. Figure 2 plots the quarterly annualised percentage change in real and nominal house prices and the consumer expenditure deflator separately.

[FIGURE 1 OMITTED]

The chart illustrates that, historically, spikes in the growth rates of real and nominal house prices have been followed by periods of readjustment, often necessitating declining real house prices for several years. The most notable readjustment took place following the 1973 oil price shock which induced a period of high inflation and negative real interest rates. However, in the recent period (aside from the crisis) real house prices have tracked nominal prices more closely and the volatile dynamics seen in the history of both series have been replaced by a period of more persistent and accelerating growth. Over this more recent phase, inflation has been markedly lower and more stable than previously; the Consumer Price Index (CPI) inflation rate has largely remained in the region around the 2 per cent target following the independence of the central bank in 1997. This reveals that in the presence of nominal rigidity; high inflation is needed to induce a readjustment in real house prices, and it is therefore more difficult to achieve an adjustment to equilibrium in periods of low inflation. The remit of the Bank of England is to keep the rate of inflation at the 2 per cent target rate. In the absence of an adjustment to the remit to 'lean against the wind', some additional policy instrument is needed to induce these necessary readjustments.

The two relevant policy questions are (i) whether actual real house prices reflect their equilibrium values, and (ii) if not, what policy instrument could be used (besides monetary policy) to mitigate problems caused by a disequilibrium growth path? We address both these questions. First, we consider which variables drive house prices. Given a set of possible components, we then proceed to estimate a structural error correction house price equation. We use the long-run properties of our estimated equation to derive the equilibrium trend, which in turn permits calculation of the extent of disequilibrium in the housing market. Second, among the components we tested, we consider contenders for policy instruments, namely the loan-to-value and loan-to-income ratios. We find that the loan-to-income ratio is a significant driver of house prices, and use our estimated model to show that this could be an effective policy instrument for regulating house prices and therefore addressing the role of the housing market in contributing to systemic banking risk.

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Driving factors

We consider several demand-side variables as factors that may have driven the recent house price dynamics: firstly, the long-run borrowing rate and the short-run nominal interest rate, which have both been steadily falling since the 1980s reflecting the process of financial liberalisation that took place since this period. Both series are plotted in figure 3. The borrowing rate equals the sum of the Bank of England's policy rate and the spread between household borrowing and deposit rates adjusted for the rate of inflation. This reflects mortgage interest rates, and as such proxies the real cost of borrowing that would be used in a net present value calculation based on the expected future (implicit) rental value of the house. The other series plotted is the 3-month nominal interest rate, as defined by the interbank rate, which feeds into mortgage contracts and therefore represents front-loading of mortgage costs. That is, it will determine the timing of housing purchase decisions in the short run, as a rise in short-term rates will raise mortgage repayments as a per cent of total incomes, even when the real interest rate is constant. Both have an inverse relationship with demand for houses and thus as both series have been falling, they would theoretically cause upward movements in house prices.

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In previous literature, real income has been found to affect demand for housing significantly; Holly and Jones (1997) found this to be the single most important determinant of real house prices, using a dataset that extended back to 1939. We consider real disposable income, which is real personal income net of tax and is thus the part of consumers' total income that is available to spend on servicing debts from house purchases. The higher real disposable income, the higher demand (though the magnitude of the increase will depend on the income-elasticity of demand for houses). Figure 4 plots real disposable income per capita. There appears to be a slight trend in the growth of the series over time, which could reflect population dynamics, though in the past decade or so it has levelled off to a plateau. Thus, though disposable income is (at least theoretically) a driver of house demand and prices, it is not visibly accountable for the surge in house price growth since the late 1990s.

[FIGURE 4 OMITTED]

Our two contenders for policy instruments are the ratios of the total value of new buyers' mortgage loans to the incomes of those households and to the total value of the property purchased by those buyers, respectively, and these represent loans issued at the margin. These variables directly affect the purchasing power of consumers. Availability of credit in general usually affects liquidity constrained consumers the most. But as house prices tend to be multiplicative functions of buyers' total incomes, loan availability affects the majority of new buyers. Throughout the period over which house prices have experienced more persistent growth, the loan-to-income ratio has also experienced a dramatic upward swing, as depicted in figure 5. This illustrates that the past two decades or so have seen not only falling costs of borrowing for consumers but also rising availability of loans, both of which have boosted consumer demand. The loan-to-value ratio however does not seem to corroborate this story. Nevertheless, it is important to note that the relationships between house prices and the loan-to-income and loan-to-value ratios are not necessarily unidirectional. Loans secured on the value of houses would rise as do house prices, indicating that there could be some endogeneity between the series.

[FIGURE 5 OMITTED]

We also consider the number of households and the housing stock, and the ratio of the two (plotted in figure 6). If the stock of housing were to rise, we would expect house prices to weaken as supply would have risen relative to demand. According to a recent OECD report (2011), since the mid-1990s land use planning policy has been excessively restrictive, hampering the responsiveness of supply to demand, 'contributing to creating housing shortages and reducing affordability'. However; figure 6 illustrates that, although the ratio of households to housing stock grew from a shortfall in demand of around 15 per cent in the first part of our sample, since the 1980s the ratio has remained at around 0.98, indicating that the rising number of households over this period has been met by growth in the housing stock almost one-to-one. Nevertheless, we should test for the impact of these supply-side factors in our regression.

We also test various dummy variables, to account for housing market responses to various legislation changes over our sample period. These include the surge in housing demand that preceded the ending of the double mortgage interest tax relief in 1988, the impact of the change in monetary policy at the end of 1989 when the UK joined the Exchange Rate Mechanism, the introduction of Right-to-Buy schemes in 1979 and Buy-to-Let mortgages in the 1990s, as well as the stamp duty 'holiday' in 2009. Some were excluded because they were not significant in the long-run equation.

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Estimation of real house price equation

To estimate our equation for real house prices, we build on the model developed in Barrell et al. (2004). Their model took a reduced form demand equation of the form derived by Meen (2002) and estimated it as an error correction equation. Our set of variables comprises real house prices (rpb), the real borrowing rate (brr), the 3-month nominal interest rate (r3m), the loan-to-income ratio (lty), the loan-to-value ratio, per capita real disposable income (pcdi), the ratio of the number of households to the housing stock (blobs), the number of households (hh) and our set of legislation dummies. Augmented Dickey-Fuller tests for the stationarity of the variables indicated that most are integrated of order one (in both levels and logs), as illustrated in table 1. When tested separately, the number of households was integrated of order zero, and the housing stock was I(1) at the 5 per cent level, which means that only the latter should be included in an equation that cointegrates in the long run. However the ratio of the two is I(1).

We include all our variables except the short-run nominal interest rate and the dummies in an Engle-Granger cointegrating relationship (1987), estimating a linear equation using ordinary least squares with log real house prices as the dependent variable. Our resulting long-run equation contains log per capita real disposable income, the ratio of households to housing stock, the loan-to-income ratio, and the borrowing rate, and we also estimated a regression that included the log of the housing stock as an alternative to the ratio of households to housing stock. An ADF test on the estimated residuals from the first long-run equation leads to the rejection of the null hypothesis that a unit root is present at the 5 per cent level, indicating that the long-run equation cointegrates. 'The equation including the log of the housing stock did not cointegrate, and the housing stock had a positive sign, which would not be expected. The ratio of the number of households to the housing stock was also wrongly signed. However, we also found that a more parsimonious specification of the long-run equation which omits the households--housing stock ratio also cointegrates, as we can see from table 2 below. According to Davidson (1998), this suggests that the households-housing stock ratio contains no significant relevant information in the long-run equation. He notes that, given the choice between two cointegrating sets, the more parsimonious model is the better one. We therefore consider this adequate justification for their exclusion from the final model. It is possible that a regional model of house prices would be able to capture supply-side factors such as the housing stock-to-household ratio.

We then embed the preferred specification of the long-run equation into an error correction equation, adding in dynamic terms including two lags of changes in the dependent variable as well as the change in the three-month nominal interest rate and the legislation dummies. The final specification, excluding dummies, is reported in table 3 below. (1)

Our final model contains only demand-side variables, and as such represents an inverse demand function, as in Barrell et al. (2004). The model suggests that house prices are chiefly driven by per capita real disposable income, the loan-to-income ratio, and negatively by the real borrowing rate. Recent research by the OECD indicates that the key drivers of the recent surge in house price growth are 'higher income and an increase in the number of households', and though lower mortgage rates have also contributed to increased house price growth, they find their contribution relatively modest (2011, p. 63). The importance of household income is well-established in literature on house prices, and on this aspect our model is in accordance with tradition. However, the absence of demographic variables (other than income) and the importance of the loan-to-income ratio in our model contrasts with the OECD research. They estimate a similar error correction model which places a much higher emphasis on the shortfall of housing supply in meeting demand, whereas our model emphasises those variables that affect households' liquidity constraints and purchasing power.

The error correction term suggests real house prices adjust slowly and, therefore, given their oscillatory nature, on average real house prices would deviate away from equilibrium for a period of five years before gradually self-correcting over a further five-year period. Notably, real disposable income per capita has almost a unit coefficient. Though the loan-to-income ratio (which has stabilised at around 3.1 since 2004) would theoretically seem more important as loans fund the lion's share of house purchases, it only has a semi-elasticity of around 0.4. It is notable that we found no clear evidence of Granger causality between real house prices and the loan-to-income ratio in either direction. Nevertheless, we consider this to be unimportant, primarily on the grounds that Granger causality, tests determine statistical but not economic causality, and secondly the ratio was significant in our regressions. That either series is not statistically useful for forecasting the other does not mean that an underlying economic relationship is not present.

Endogenous dynamics are also important in the model as is to be expected, though the effect dies out over time as the second lag has a smaller coefficient. In addition, the change in the 3-month nominal interest rate has a statistically significant effect on real house prices in the short run. The ERM-related dummies are not significant in the final equation as it includes the change in the nominal interest rate and this picks up the effect of the rise in interest rates at this time, increasing mortgage front loading noticeably.

Equilibrium real house prices

Using our estimated equilibrium house price equation to address the first of our policy questions outlined above, we take the estimated equation and use this to measure potential mis-valuation of house prices as compared to the dynamic steady state equilibrium following Nickell (1985). Our final equation comprises a long-run trend equation plus some short-run dynamics, which are not just white noise, but evolve over time with a non-zero mean. We capture the trends in the short-run dynamics with 10-year moving averages of the actual data for these variables. We then calculate the long-run dynamic steady state path of real house prices, and estimate by how much actual real house prices departed from this over the period. Figure 7 illustrates the deviations of real house prices from their equilibrium, which we may call the percentage overvaluation, and vice versa for deviations below zero.

This shows that in 2007 real house prices were around 20 per cent higher than their sustainable equilibrium level given the driving factors. There has been a correction in the housing market since, and as of 2010 quarter 3 they were only marginally above trend. This is, however, a slightly misleading figure, due to the abnormally low interest rates that the Bank has set following the crisis, which has fed into borrowing rates. As borrowing rates have a negative impact on equilibrium house prices, lower rates will have inflated our estimate of the trend, disguising the real extent of the recent overvaluation. If we consider the trajectory of real prices in a world where real borrowing rates were at the same levels as they were at the end of 2007 and with no changes in current real house prices, then the estimated overvaluation would be higher. This is illustrated by the dotted line in figure 8. In this case we find that real house prices would in fact be 11 per cent higher than their sustainable equilibrium. Given that real interest rates will rise over the next few years, we would expect to see downward pressure of 1 to 2 per cent a year on real house prices over the next five years or so.

[FIGURE 7 OMITTED]

Policy simulations

Our final model includes the loan-to-income ratio as one of the long-run components of the error correction equation, and we suggest that this could be used as a policy instrument to regulate the growth of house prices. In order to investigate its efficacy, we analyse the effect of using the loan-to-income ratio as a policy instrument with our in-house global econometric model, NiGEM. We simulate a 20 per cent permanent reduction in the loan-to-income ratio starting from the first quarter of 2011, taking the level from 2.95 times income to 2.45 times income, as was last seen in 2000, as we can see from figure 5 above. This allows us to gauge what we might have seen in the housing market if the loan-to-income ratio had not risen so drastically over the past ten years. The impact of this shock on real house prices is plotted in figure 8. The results of this simulation suggest that a 20 per cent shock to the loan-to-income ratio induces house prices to fall by 25 per cent of their base forecast values by 2015 (responding with almost unit elasticity to the loan-to-income ratio), narrowing to around 20 per cent in the longer run. The stock of the mortgage debt of households would be almost 8 per cent lower than our baseline by 2016 in this scenario.

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Conclusion

The loan-to-income ratio for new mortgages may be difficult to reduce, and it certainly cannot be reduced at the speed suggested here, but policies to reduce it will almost certainly put downward pressure on house prices. Our results should be seen as illustrative. It is not clear from our results that changes in loan-to-value ratios would have the same impact, and indeed they appear to be caused by house prices, and are not a cause of them. Clearly major increases in the supply of housing would be liable to put downward pressure on prices, but changes in supply over the past thirty years have just about kept pace with household formation, and hence it is statistically difficult to find a role for supply-side factors, although common sense as well as economic theory tell us it should be there.

House price dynamics have been a major factor affecting booms and recessions in the UK for more than forty years, and policy is now being set to help stabilise house prices and reduce loan growth. House prices have been overvalued for much of the past decade, but with current low borrowing costs they look about right. However borrowing costs are likely to rise over the next five years as policy rates set by the Bank of England move from 'crisis' levels near zero to 'normal' levels of around 5 per cent. These increases are likely to induce real house prices to fall by around 2 per cent a year for the next five years. This note suggests that the increase in the loan-to-income ratio for new buyers that took place from 2000 onwards was a major factor behind the increase in house prices. The note also illustrates that the loan-to-income ratio would be an effective policy instrument for regulating the housing market. The loan-to-income ratio is expected to fall in the near furore, which provides further evidence that real house price growth will be negative over the next five years. The OECD proposes housing supply should be made more responsive to demand. We find that regulation should focus rather on limiting loan availability such that loans are issued more in line with income.

DOI: 10.1177/0027950111411374

REFERENCES

Barrell, R., Davis, E.P., Karim, D., Liadze, I. (2010), 'Bank regulation, property prices and early warning systems for banking crises in OECD countries', Journal of Banking and Finance, 34, pp. 2455-64.

Barrell, R., Kirby, S. and Riley, R. (2004), 'The current position of UK house prices', National Institute Economic Review (189), pp. 57-60.

Davidson, J. (1998), 'Structural relations, cointegration and identification: some simple results and their application', Journal of Econometrics, 87(1), pp. 87-113.

Engle, R. and Granger, C. (1987), 'Co-integration and error correction: Representation. estimation and testing', Econometrica, 55(2), pp. 251-76.

Holly, S. and Jones, N. (1997), 'House prices since the 1940s: cointegration, demography and asymmetries', Economic Modelling, 14(4), pp. 549-65.

Meen, G. (2002), 'The time-series behaviour of house prices: a transatlantic divide?', Journal of Housing Economics, 11(I), pp. 1-13.

Nickell, S. (1985), 'Error correction, partial adjustment and all that--an expository note', Oxford Bulletin of Economics and Statistics, 47, 119.

OECD (March 2011), Economic Surveys: United Kingdom 2011, OECD Publishing. http://dx.doi.org/10.1787/eco_surveys-gbr-2011-en.

NOTE

(1) We also estimated the error correction model using the first specification of the long-run equation (including the household-housing stock ratio), and found that the ratio was not significant at this stage.

Table 1. Orders of integration

            ADF-statistic      p-value

l(rph)          *-3.42          0.05       I(1)
dl(rph)       ***-4.97          0.00
R3m              -2.16          0.22       I(1)
d(r3m)       ***-10.66          0.00
Brr              -2.29          0.18       I(1)
d(brr)       ***-12.53          0.00
Lty              -0.98          0.76       I(1)
d(lty)        ***-7.01          0.00
Ltv              -1.72          0.42       I(1)
d(ltv)        ***-6.80          0.00
l(pcdi)          -1.56          0.80       I(1)
dl(pcdi}     ***-18.21          0.00
hhhs             -3.17          0.11       I(1)
d(hhhs)       ***-6.35          0.00
l(hh)         ***-4.34          0.01       I(0)
l(hs)            -1.70          0.74       I(1)
dl(hs)        ***-6.36          0.00

Notes: sample period: 1963Q4 to 201OQ3. *** significant at the 1%
level; ** significant at the 5% level; * significant at the 10% level.

Table 2. Cointegration of the long-run (ADF tests)

                          Spec. 1          Spec. 2          Spec. 3
                          (ratio)      (housing stock)      Neither

ADF-statistic              -4.45            -3.75            -4.14
5% significance level      -4.42            -4.42             4.10

Table 3. Error correction equation for house prices

                 Error            Real          Loan-to-
               correction    borrowing rate      income
                                  (-1)            (-1)

coefficient      -0.052          -0.023          0.393
p-value           0.000           0.015          0.006

               Log (per cap.    dlog (real price    dlog (real price
                disposable           houses              houses
               income (-1))           (-1))               (-2))

coefficient        0.773              0.559               0.291
p-value            0.003              0.000               0.000

                Change in 3-
              month interest
                 rate (-1))

coefficient       -0.004
p-value            0.008