The Time-Series Behavior of House Prices: A Transatlantic Divide?

Journal of Housing Economics 11, 1–23 (2002) doi:10.1006/jhec.2001.0307, available online at http://www.idealibrary.com on

The Time-Series Behavior of House Prices: A Transatlantic Divide?1 Geoffrey Meen Centre for Spatial and Real Estate Economics, Department of Economics, School of Business, The University of Reading, PO Box 219, Whiteknights, Reading RG6 6AW, England E-mail: [email protected] Received April 25, 2001 At first sight, data on real house prices in the U.S.A. and the U.K. appear to suggest that behavior has differed over time in the two countries at both the national and subnational levels. Furthermore, empirical estimates of the main house price elasticities in the literature appear to differ. In this paper, we ask whether the differences are really as great as previous work suggests. We argue that, by adopting a common methodological framework, the same theory can explain behavior in both countries. Also, there are important similarities in subnational house price trends that are not immediately evident from inspection of the data. 䉷 2002 Elsevier Science (USA)

1. INTRODUCTION Even a cursory examination of the international literature reveals significant differences in the concerns of American and British housing researchers. Largely, these variations reflect differences in the policy concerns and institutional frameworks between the two countries. For example, tenure structures and mortgage markets differ. Nevertheless, there are significant areas of overlap in the literature and this paper is concerned with one of these common areas. The basic question we ask is whether (as appears to be the case from the literature) there are true differences in behavior in real house prices between the two countries or whether the differences are illusory, arising from different methodological approaches. Section 2 introduces some of the key data, showing how price trends differ between the two countries. Section 3 looks, first, at the theoretical foundations of house price models, which are not in principle different between the two countries. Models are generally consistent with a life-cycle framework. Nevertheless, between theoretical specification and empirical implementation, models diverge significantly. We compare the structures of different models. The empirical findings look wildly different. We then conduct nesting tests to return the countries to a common framework including previously omitted variables. We find, on a 1

Thanks go to an anonymous referee for many useful suggestions on an earlier draft. 1 1051-1377/02 $35.00 䉷 2002 Elsevier Science (USA) All rights reserved.

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single equation basis, that the results are surprisingly similar. Furthermore, in both, cointegration exists in a manner that suggests arbitrage conditions hold in the long run. Why then do price trends differ between the countries? The answer lies in the system solutions. If we look at a wider stock-flow framework, the differences arise from variations in price elasticities of supply. The weaker longrun real price trends in the U.S. are consistent with stronger supply elasticities. Section 4 is concerned with the subnational level. There are three questions. First, do regional prices converge or diverge in each country? Second, what is the nature of any spatial interactions? Third, what role do credit markets play in explaining price patterns? We suggest, speculatively, that variations in debt gearing across locations make some cities or regions more likely to experience booms and busts than others. Section 5 draws conclusions. We find that, although there are differences in behavior between the two countries, they are nowhere near as large as the literature indicates. 2. TRENDS IN THE U.S. AND THE U.K. One of the basic building blocs of theoretical housing economics suggests that any positive demand shock will lead to a temporary increase in real house prices, due to short-run inelastic housing supply, but prices will overshoot and, in the long run, prices will change in line with construction costs. If construction costs rise with general prices in the economy, then long-run real house prices would be expected to be constant or, in a stochastic environment, stationary. If, therefore, real prices are found to be nonstationary (and measurement errors can be excluded), then this simple empirical finding would at least indicate that a modification or extension to a major element of housing economic theory is required.2 A prime candidate concerns the land market. Since a significant component of house prices comprises the cost of land, clearly land markets play a central role in any explanation of housing market behavior. Differences in land market conditions—in terms of both price and availability—contribute to house price variations at both international and regional levels. Malpezzi (1999), for example, demonstrates for the U.S. how the strength of planning controls affects the longrun ratio of house prices to incomes. Figures 1a and 1b plot real house price trends for both the U.K. and the U.S. In the case of the U.S., data are derived from repeat sales, taken from the Freddie Mac database. Data are presented quarterly from 1975. For the U.K., Department of the Environment, Transport and the Regions (DETR) mix-adjusted prices3 are used quarterly from 1968. For each country, residential prices are deflated by a 2 Among the other candidates is the possibility of nonstationary real construction costs (arising, perhaps, from differences in productivity between industries), Ball and Wood (1999). 3 We do not discuss the large literature on measurement errors associated with the different methods of constructing house price indices (see Meen 2001 for a survey). We take the data as given.

HOUSE PRICES IN THE U.S. AND U.K.

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FIG. 1a. Real house prices—U.S. (1995 ⫽ 100). Source: Freddie Mac Conventional Mortgage House Price Index.

general measure of consumer prices. Since the emphasis of our later empirical work is on long-run trends, it is on this aspect of the data that we concentrate. Even casual observation (confirmed by unit root tests below) suggests that real prices in each country are trended. But the scales of the two charts are not the same and, when the two are superimposed in Fig. 1c, it is clear that trends are more severe in the U.K. Furthermore, although not shown here, house prices relative to household incomes have fallen over time in the U.S., but this has not been the case in the U.K. An important question, therefore, is whether the same theory is capable of explaining both sets of results. Table I conducts both Augmented Dickey–Fuller (ADF) and Phillips–Perron tests for stationarity of real house prices. Tests are carried out both with and without trends; the figures in brackets are the MacKinnon critical values at the 5% level for the rejection of the hypothesis of a unit root. In both countries, unit roots in real prices cannot generally be rejected and real prices appear to be difference stationary. Moving below the national level, Table II compares subnational nominal house price changes. Although they are not strictly comparable in size, the table compares the nine U.S. census divisions against the U.K. standard regions. In the U.S., the divisions show considerable diversity in nominal house price growth

FIG. 1b. Real house prices—U.K. (1995 ⫽ 100). Source: DETR.

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FIG. 1c. Real house prices. U.S. and U.K. (1995 ⫽ 100).

over the period 1975–1998 with the coastal districts showing the strongest increases over sustained periods. There is no obvious similarity in long-run spatial price movements. The second part of the table, for the U.K. over the period 1969–1998, shows considerably more uniformity. We conduct more formal tests in Section 4 and consider possible reasons for the differences.

3. REAL HOUSE PRICES—ARE THERE REALLY ANY DIFFERENCES? Figure 1c suggested that (i) both countries experience upward trends in real prices, but (ii) the trends differ between the two countries. Can the same theory explain behavior in both countries? We argue that it can and that the very different empirical results for the two in the literature are explainable in terms of (i) the translation from theory to empirical specification—often the two are only loosely linked—and (ii) different price elasticities of supply.

TABLE I Stationarity Tests for Real House Prices ADF Intercept Levels First difference Levels First difference

Phillips–Perron Intercept & trend

U.S.: 1976Q2–1999Q3 ⫺2.27 (⫺2.89) ⫺3.17 (⫺3.46) ⫺2.86 (⫺2.89) ⫺2.89 (⫺3.45) U.K.: 1969Q3–1999Q3 ⫺2.05 (⫺2.89) ⫺4.20 (⫺3.45) ⫺3.52 (⫺2.89) ⫺3.50 (⫺3.44)

NB: ADF tests are fourth order

Intercept ⫺0.95 (⫺2.89) ⫺7.18 (⫺2.89) ⫺1.10 (⫺2.88) ⫺6.80 (⫺2.88)

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HOUSE PRICES IN THE U.S. AND U.K. TABLE II Nominal House Price Growth—U.S. and U.K. (Annual Average Percentage Changes) U.S. Census Division

Growth Rate (%)

U.K. Region

Growth Rate %

New England Middle Atlantic South Atlantic East South Central West South Central West North Central East North Central Mountain Pacific

6.7 6.2 5.2 5.0 4.2 4.8 5.5 5.8 7.8

U.S.

5.7

South East (excl. London) E. Anglia South West East Mids. West Mids. Wales Yorks. North North West Scotland U.K.

10.8 10.1 10.5 10.6 10.1 10.2 10.4 9.8 10.3 9.8 10.6

3.1. The Theory of House Prices The life-cycle model is the starting point for most modern house price models, the first example in a U.K. context being Buckley and Ermisch (1982). Since then the approach has been used by Meen (1990), Giussani and Hadjimatheou (1990, 1991), Ashworth and Parker (1997), Brown et al. (1997), Holly and Jones (1997), Muellbauer and Murphy (1997), Pain and Westaway (1997), and Meen and Andrew (1998). The model derives the marginal rate of substitution between housing and a composite consumption good, ␮h/␮c , given by

␮h /␮c ⫽ G(t)[(1 ⫺ ␪ )i(t) ⫺ ␲ ⫹ ␦ ⫺ g˙ e /g(t)],

(1)

where G(t) ⫽ real purchase price of dwellings ␪ ⫽ household marginal tax rate i(t) ⫽ market interest rate ␦ ⫽ depreciation rate on housing ␲ ⫽ general inflation rate (.) ⫽ time derivative ␦, ␲, ␪ are assumed to be time invariant. This is the widely used standard definition of the real housing user cost of capital and represents the real price of housing services, where (g˙e/g(t)) is the expected real capital gain. The definition may be extended to include such elements as property taxes, maintenance expenditures, and transactions costs but, at least in time-series models, movements in (1) are dominated by changes in the interest

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rate and in capital gains on housing.4 Market efficiency also requires the following arbitrage relationship to hold, where R(t) represents the real imputed rental price of housing services: G(t) ⫽ R(t)/[(1 ⫺ ␪ )i(t) ⫺ ␲ ⫹ ␦ ⫺ g˙ e /g(t)].

(2)

In principle, Eq. (2) provides a direct test of housing market efficiency. But surveys by Gatzlaff and Tirtiroglu (1995) and Cho (1996) both confirm that, over a wide range of American studies, covering different spatial areas, house price inflation and excess returns on housing are highly autocorrelated and investors can make persistent excess returns. One view is that autocorrelation arises from the existence of transactions costs, both financial (which are higher in the U.S. than in the U.K.) and in terms of search costs, which limit the spatial range of the search. Therefore, although excess returns exist, exploitable trading rules are not necessarily available. Much less information is available on the efficiency of the British housing market, although it would be surprising if the British market were found to be efficient while the American market was not. In one of the few comparable British studies, Barkham and Geltner (1996) find that the market is semistrongly inefficient and housing returns are predictable on the basis of past stock market returns. Although market efficiency tests may be conducted through an analysis of autocorrelation structures, our interest concerns the long-run trends. Therefore, we turn to more structural models of house prices, still based on Eq. (2). One approach would be to estimate Eq. (2) allowing for possible lags. Prices are simply the discounted present value of rental payments. Meese and Wallace (1994), in fact, find that these variables cointegrate for northern California. Although the arbitrage condition does not hold at every point in time, in the long run, it does hold. This might be expected, perhaps, in the presence of transactions costs or credit market constraints. However, if we are to compare the U.S. and U.K., testing in this form is not possible, because of the absence of suitable rental data. Therefore, we have to substitute for the expected determinants of R(t). But, as soon as we do so, possible specification errors are introduced since the determinants are not known with certainty. Although (R) represents the market clearing price of housing services and, hence, provides clues, the precise choices of determinants vary between researchers, both within countries and internationally. We are no longer testing the arbitrage condition directly and, indeed, many studies pay only lip service to the theory in practice. This leads to the possibility of omitted variable biases. To see this, it is useful to set out the model in a little more detail. From Poterba (1984), for example, Eq. (2) also constitutes a housing stock demand function. If, as in Meen (1990) 4 The introduction of credit market constraints can also be handled (see Dougherty and Van Order 1982, Meen 1990).

HOUSE PRICES IN THE U.S. AND U.K.

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and Meen and Andrew (1998), we assume that (R) is related to real per household personal disposable income (RY ), the stock of dwellings (H ), the number of households (HH ), and real household wealth (W ), then a log-linear approximation gives gt ⫽ ␣1 ⫹ ␣2(hh)t ⫹ ␣3(ry)t ⫺ ␣4(h)t ⫹ ␣5(w)t ⫺ ␣6(rr)t ⫹ ␧1t.

(3)

Notice that the housing stock appears in the equation, since it affects (negatively) the market clearing rent. The second half of the Poterba model determines the current housing stock, which is related to the profitability of new construction (influenced positively by real house prices and negatively by construction costs) and the size of the pre-existing stock. If the stock were to be omitted from (3), there would be no feedback from new supply to prices. ht ⫽ ␤1 ⫹ ␤2(g)t ⫺ ␤3(cc)t ⫹ ␤4(h)t⫺1 ⫹ ␧2t,

(4)

where CC ⫽ real construction costs G ⫽ real house prices H ⫽ housing stock supply HH ⫽ population RR ⫽ real interest rate (the denominator in (2)) RY ⫽ real per household incomes W ⫽ real wealth lower case denotes logarithms. Equations (3) and (4) could be simulated jointly (and we do so below) or (4) could be substituted into (3), in which case (cc) would appear in the price equation. Two important points arise; first, what happens to the income coefficient if (H ) is omitted from (3)? Clearly this depends on the covariance between the two terms, but a priori (since the relationship is likely to be positive) we might expect the income coefficient to be biased downwards. Second, construction costs appear in a reduced form equation. If, as theory suggests, prices rise in line with construction costs in the long run, then we might expect the two to cointegrate. However, the relationship between prices and costs is a systems property. By conditioning on the housing stock, the relationship no longer necessarily holds. If the housing stock (through new construction) is related to construction costs as in (4), a long-run relationship can still hold in a two-equation model of prices and housing construction. This is the basis of the Poterba (1984) model. However, the relationship depends on full stock equilibrium occurring, which could take decades. Therefore, we may never observe any relationship between prices and construction costs in the data and the effect of construction costs in

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an appropriately conditioned price equation is unlikely to be significant. With these points in mind we consider, first, some estimation results for the U.K., which we then compare with the U.S. employing a common framework. 3.1.1. The U.K. Long-run efficiency (in the Meese and Wallace sense) requires cointegration between (g) and (RY, H, HH, W, RR). Since Engle–Granger estimates of the cointegration vectors are more likely to suffer from small sample biases, we derive estimates of the parameters from the long-run solution to an autoregressive distributed lag (ADL) equation using these variables.5 Imposing data-validated restrictions, and respecifying the ADL in error correction form yields the results in the first four columns of Table III. The long-run parameters are given in the same columns of Table IV. In each case, the ADF cointegration statistics (with four lags) are close to their critical values. Compared with (3), there is one small specification change. Now (RY ) is total rather than per household income. This simplification means that (HH ) can be dropped from the equation and is permissible because the absolute values of the coefficients on the two variables are insignificantly different from each other. For the U.K., two sets of estimates are presented, varying by time period. Columns (1) and (2) end in 1990, whereas columns (3) and (4) continue to 1996. U.K. house price models have experienced particular problems in the nineties and changes in the income distribution between young and older households are thought to have been particularly important. Therefore the latter columns employ a proxy to capture the change (see Meen and Andrew 1998 for details). If the results of columns (1) and (3) are compared, it can be seen that the coefficients are very similar, after making allowance for the distribution change. Therefore our results are not dependent on the chosen time period. From the first and third columns of Table IV, two points stand out. First, the long-run elasticity with respect to the housing stock appears high in both equations, at approximately ⫺2. But, in practice, since new construction per annum is only approximately 1% of the stock, the effect of new construction on prices is not dramatic. Second, and critically, the income elasticity of house prices is very high indeed and is one of the key differences between U.K. house price studies and those in the U.S. This result appears in almost all British work (see Meen 2001 for a comparison). Note, however, that current income is the regressor here rather than permanent income. In fact, in this instance, the distinction is not of great importance. To see this, suppose that permanent income can be written as a weighted average of past actual levels of income. Smoothing of income in this way has no effect on its order of integration. Alternatively, transitory income may be considered as a stationary process. In either case, it makes 5 Johansen estimates for the U.K. gave similar parameter values and one cointegrating vector was found.

TABLE III Error Correction Models of House Prices: U.K. and U.S. U.K.

Constant ln (g)⫺1 MRAT⫺3 ln (W )⫺1 ln (H)⫺1 ln (RY) ⌬ ln (RY)⫺1 RR RR⫺1 R2 Standard error of estimation DW

1969(3)–1990(4)

1969(3)–1990(4)

1969(3)–1996(1)

1969(3)–1996(1)

1981(3)–1998(2)

1981(3)–1998(2)

(1)

(2)

(3)

(4)

(5)

(6)

⫺2.371 (5.2) ⫺0.170 (8.7) ⫺0.011 (3.1) 0.056 (6.5) ⫺0.318 (3.6) 0.433 (5.5) 0.217 (2.6) ⫺0.006 (9.8) — 0.831 0.015 1.70

⫺2.487 (5.1) ⫺0.154 (7.5) ⫺0.002 (0.7) 0.045 (5.2) — 0.186 (4.2) 0.204 (2.3) ⫺0.007 (11.5) — 0.803 0.016 1.55

⫺2.135 (4.8) ⫺0.160 (8.5) ⫺0.012 (3.2) 0.056 (6.5) ⫺0.306 (3.7) 0.402 (5.4) 0.263 (3.2) ⫺0.006 (10.0) — 0.814 0.015 1.90

⫺2.347 (5.0) ⫺0.148 (7.5) ⫺0.002 (0.8) 0.044 (5.2) — 0.174 (4.1) 0.247 (2.9) ⫺0.007 (11.8) — 0.789 0.016 1.77

1.043 (4.7) ⫺0.080 (2.6) — 0.056 (4.5) ⫺0.611 (4.9) 0.217 (3.8) ⫺0.249 (2.6) — ⫺0.001 (2.4) 0.410 0.006 1.48

0.120 (0.9) ⫺0.070 (1.9) — 0.033 (2.4) — ⫺0.037 (1.3) ⫺0.039 (0.4) — ⫺0.001 (2.1) 0.182 0.007 1.10

HOUSE PRICES IN THE U.S. AND U.K.

Estimation period

U.S.

Note. Dependent variable: ⌬ ln (g). t-values are given in brackets. Each equation includes seasonal dummies. The UK model includes dummies for the abolition of double mortgage interest tax relief in 1988. Columns (3) and (4) include a variable to capture changes in the distribution of income, (see Meen and Andrew 1998 for further details). MRAT is a measure of financial liberalisation in mortgage markets that took place in the eighties in the UK but is not relevant to the US over the estimation period.

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TABLE IV Long-Run House Price Relationships: U.K. and U.S.

Estimation period ln (RY) ln (W) ln (H) RR ADF(4)

U.S.

1969(3)–1990(4)

1969(3)–1990(4)

1969(3)–1996(1)

1969(3)–1996(1)

1981(3)–1998(2)

1981(3)–1998(2)

(1) 2.54 0.33 ⫺1.87 ⫺0.035 ⫺2.64

(2) 1.21 0.29 — ⫺0.045 ⫺3.16

(3) 2.51 0.35 ⫺1.91 ⫺0.035 ⫺2.77

(4) 1.18 0.30 — ⫺0.044 ⫺3.36

(5) 2.71 0.70 ⫺7.64 ⫺0.013 ⫺2.63

(6) ⫺0.53 0.47 — ⫺0.016 ⫺2.74

Note. Dependent variable: ln (g).

GEOFFREY MEEN

U.K.

HOUSE PRICES IN THE U.S. AND U.K.

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little difference to the coefficients of the cointegrating vector whether current or an estimate of permanent income is used. Four further points may be noted. First, in line with Table III, the majority of British price relationships are estimated as error correction equations. This form of model is much more common in the U.K. (and Europe as a whole) than in American work on housing markets, although two of the American models considered below can be interpreted in this way. Second, for the reasons discussed above, British studies rarely include construction costs as a regressor, although this is more common in American studies. Third, it is worth stressing again that the conditioning variables are central to the equation’s properties. If the housing stock is not in the equation, then there is no feedback from new construction to prices. Either other variables have to be included to capture supply effects or the equation is misspecified. In the second and fourth columns of Tables III and IV, the housing stock variable is removed. In line with expectations, the income elasticities are heavily biased downwards. Indeed, the income elasticity is now much closer to unity— implying an approximately constant price–income ratio. In fact, the effects on the income coefficients are more noticeable than on the other variables. The results are also closer to those found internationally. By removing the feedback term, the single equation attempts to proxy the properties of the two-equation system. Table III also shows that the equation fit is noticeably poorer. The moral is that systems properties matter, whereas single equation results can be highly misleading. Fourth, to show this further, we augment the price equation with a housing construction equation, assuming different price elasticities of supply ranging from 0.3 to 10, i.e., from the inelastic to the approximately perfectly elastic. Therefore the model consists of a version of Table III, column (3) (see Meen 1998 for details), plus an equation for new construction, linked by the pseudo-identity that the change in the housing stock is equal to new construction (i.e., an equation similar to (4)). Figure 2 looks at the effect on prices of a permanent 1% increase in income under the different supply elasticity values.

FIG. 2. Effect on house prices of different supply elasticities. Source: Meen (1998).

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The figure shows that, if housing supply is perfectly inelastic, the increase in demand will be choked off by higher prices. At the other extreme, if supply is fully elastic, output will increase to the point at which prices are unchanged. Unsurprisingly, therefore, higher supply elasticities induce lower long-run income elasticities of house prices; in the diagram a value of 2.0 induces an income elasticity of house prices of approximately unity. To stress the point, the ratio of house prices to income in the long run not only is determined by the direct estimate of the coefficient on income in the house price equation, but is a systems property depending also on the effect of the housing stock on prices and the price elasticity of new housing supply. A supply elasticity of 10 is sufficient to reduce the income elasticity of prices to approximately zero, the condition we expect to hold if supply is perfectly elastic. In this case, prices will rise in line with construction costs. But a value of 10 is well outside the range of British findings, although it is not outside the range found for some other countries. The differences are often attributed to the strength of planning controls (see Malpezzi 1999, for example). These simulations suggest, therefore, that differing real house price movements across countries can be consistent with the same underlying theoretical model. Real house price trends are determined by the system and stronger real trends in the U.K. than in the U.S. are consistent with weaker supply responses. By itself, the fact that we find a high income elasticity of house prices in the U.K. is not an indication of stronger long-run real house price trends. Instead the critical factor is the international variation in supply elasticities. Most British studies suggest that the elasticity is less than one. American estimates are notably higher, although findings vary considerably according to the chosen methodology. Topel and Rosen (1988), for example, find a value of approximately three. These points are explored further in the next section.

3.1.2. The U.S.A. We choose three models as typical of the American literature; DiPasquale and Wheaton (1994), Abraham and Hendershott (1996) and Malpezzi (1999). The last two can broadly be interpreted within the error correction framework (although not following the standard approach) whereas the first cannot, although it still stresses the importance of adjustment lags. Perhaps surprisingly, none appeals directly to life-cycle theory to derive the underlying model, although given the difference between theoretical specification and empirical implementation to which we referred above, the estimated models are not necessarily inconsistent. Nevertheless the specifications set out below as Eqs. (5)–(7) show considerable diversity:

HOUSE PRICES IN THE U.S. AND U.K.

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DiPasquale and Wheaton (1994). gt ⫽ ␥1(H/HH )t ⫹ ␥2(WAGE )t ⫹ ␥3(OWN )t ⫹ ␥4(U )t ⫹ ␥5(R)t ⫹ ␥6(g)t⫺1.

(5)

Abraham and Hendershott (1996). ⌬ln(g)t ⫽ ␣1 ⫹ ␣2⌬ln(C )t ⫹ ␣3⌬ln(RY )t ⫹ ␣4⌬(r)t ⫹ ␣5⌬ln(g)t⫺1 ⫹ ␣6(ln(g*) ⫺ ln(g))t⫺1.

(6)

Malpezzi (1999). ln(PH/Y )t ⫽ ␤1ln(RY )t ⫹ ␤2⌬ln(RY )t ⫹ ␤3ln(POP)t ⫹ ␤4⌬ln(POP)t

(7) ⫹ ␤5(RM )t ⫹ ␤6(REG)t (also includes geographical measures),

where g ⫽ real house price, (*) denotes equilibrium value H ⫽ housing stock HH ⫽ number of households WAGE ⫽ per capita permanent income OWN ⫽ home-ownership rate U ⫽ user cost of capital R ⫽ rent index C ⫽ construction cost index RY ⫽ real income r ⫽ Treasury bill rate PH ⫽ nominal house price Y ⫽ nominal income POP ⫽ population RM ⫽ mortgage interest rate REG ⫽ measure of planning regulation stringency. Equation (5) is estimated in linear form and, hence, the coefficients are difficult to compare with the other models. Nevertheless the variables used in the specification are similar to those in British models. Perhaps the major difference is the inclusion of a rental index, which almost never appears in British time-series studies. This reflects the fact that the private rental sector is much smaller in the

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U.K. and renting has not been seen as a close substitute for owner-occupancy.6 This is the only model of the three to include the housing stock as a regressor. The Abraham and Hendershott model, (6), is concerned with the identification of “bubbles” and is estimated over 30 MSAs over the period 1977–1992. The coefficient ␣5 is interpreted as a “bubble builder” and ␣6 as a “bubble burster,” reacting to the difference between the equilibrium and actual house prices. This is the only model to include a measure of construction costs. The estimated value of the elasticity is 0.35 for the country as a whole and 0.57 for inland areas alone; by contrast, nationally, the dynamic income coefficient (␣3) is 0.73. Abraham and Hendershott find that only the coastal areas provide evidence of speculative bubbles and suggest that this may be related to the fact that coastal regions are more supply-constrained in terms of land. Equation (7) sets out only the longrun equation in the Malpezzi model, which is embedded in an error correction framework. The equation estimates the price to income ratio directly. One of the most interesting features is the model’s finding that regulatory stringency has a strong effect on the price-income ratio. Although there is a considerable variation in specifications, the equations are not fundamentally different in terms of variable choice. Neither are the choices noticeably different from those used in the U.K. Each could readily be nested. The approach we adopt, therefore, is to ask whether American data yield results similar to those found for the U.K., despite the fact that real prices and price to income ratios differ. The results are shown in columns (5) and (6) of Tables III and IV. With the exception of a lag on the real interest rate variable (which the data suggest is empirically preferable), the specification is as close as possible to that used for the U.K. and also covers a high proportion of the variables used in Eqs. (5)–(7). But the model could certainly be improved by, for example, recognizing the greater importance of the private rental market in the U.S. Nevertheless the equation demonstrates the main issues and, in fact, ARCH tests revealed no evidence of heteroscedasticity, although Breusch–Godfrey tests indicated some evidence of autocorrelation. Compared with the British results, the R2 is lower, but so is the standard error of estimation. These probably reflect the fact that American real prices are less volatile and less trended than those in the U.K. Although there are clearly differences from the British results, the key finding is that, from column (5) of Table IV, the income elasticity of house prices is well in excess of 2 and is not dissimilar to the British findings. But the elasticity is considerably greater than usually found in American studies. The moral is that, by appropriate conditioning, in this case on the housing stock, we find results that are much more comparable internationally. Column (6) provides further 6

Although there is evidence, since the early nineties, that young households are now spending longer as renters before moving onto owner-occupation, which is why “traditional” price models broke down at that time and we needed to include a distribution variable in Table III.

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support; if the housing stock is omitted from the equation, as in the U.K., the income coefficient falls dramatically and becomes insignificantly different from zero. In fact, the results in column (6) are far from satisfactory on any econometric criteria. But notice also that, in column (5), the coefficient on the housing stock is much larger than for the U.K. Not only does it appear to be the case that the price elasticity of housing supply is larger in the U.S., but the effect of the stock on prices is greater. Because of these two results, falling price to income ratios in the U.S. are consistent with constant or rising ratios in the U.K., but the same theoretical approach is relevant to both countries. 4. SUBNATIONAL DIFFERENCES The most appropriate spatial scale for housing analysis is a thorny issue7 but, in this section, we concentrate on regional movements, where the spatial delineations are determined by administrative boundaries. Almost inevitably, these regions will not correspond to any recognisable housing market area, which ought to be defined on the basis of substitutability between properties. The spatial definitions vary by country. In the U.S., for the moment, we consider census divisions and in the U.K. the Standard Statistical Regions. Our concern is whether the two countries exhibit any common spatial patterns, and the explanations that can be put forward for any patterns. In Section 2, house price growth rates for the American census divisions showed very different longrun trends from the British regions with no obvious patterns. Nevertheless, we can dig a little deeper. Pollakowski and Ray (1997), in fact, conduct an exercise for the U.S., using the Freddie Mac data over the period 1975 to 1994 and suggest that interactions may occur from the gradual dissemination of information across space following any shock, both through individual contact and through the news media. Although, in an efficient market, we might expect all areas to react at the same time to a common shock, there are many reasons why lags may arise. However, we would expect that price relationships between contiguous areas would be stronger since information can be transmitted more quickly. In fact, at the census division level, Pollakowski and Ray find a relationship between spatial prices, but the relationship is no stronger between contiguous than noncontiguous regions. In further work on the Greater New York area, contiguity appears to be a more important factor. But there are methodological extensions that can be added to Pollakowski and Ray’s work. Apart from the trivial extension of the sample period to 1999, we attempt to look for cointegrating relationships between the divisions. Pollakowski and Ray’s work examines, in a VAR framework, the relationship between house price inflation rates. Equally important is the relationship between the levels of prices. 7 Indeed it might be argued that, in the U.S., a national housing market has no real meaning and a great deal of U.S. research has concentrated on the subnational level.

16

GEOFFREY MEEN TABLE V Number of Cointegrating Equations—U.S. Group

NENG, MATL, ENC MATL, NENG, SATL, ENC, ESC SATL, MATL, ESC ESC, MATL, SATL, WSC, ENC WSC, ESC, WNC, MTN, PAC ENC, NENG, MATL, ESC, WNC WNC, WSC, ENC, MTN, PAC MTN, WSC, WNC, PAC

No. of cointegrating vectors 1 2–3 1 3–4 1 2 1 0–1

Note. NENG ⫽ New England. MATL ⫽ Mid Atlantic. SATL ⫽ South Atlantic. ESC ⫽ East South Central. WSC ⫽ West South Central. WNC ⫽ West North Central. ENC ⫽ East North Central. MTN ⫽ Mountain. PAC ⫽ Pacific.

Nine census divisions are a lot to include in a single Johansen cointegrating system. Therefore we look at the relationship between house prices in contiguous divisions alone. This means that there is a maximum of five variables in any regression. Table V sets out the estimated number of cointegrating equations for each grouping. In some cases the number of relationships is not entirely clear, depending on the chosen test, and so a range is presented. In general, there is some evidence of cointegration amongst groups of divisions. Nevertheless the pattern is complex. Furthermore, there are few, if any, areas which appear to be weakly exogenous and act as “drivers” for the rest of the country. Also, as Pollakowski and Ray found, the coefficients of the models do not show readily interpretable patterns between regions.8 By contrast, in the U.K., a considerable amount of empirical work has already been conducted on the relationship between regional house prices set in a cointegration framework. A major concern of the British literature has been the so-called “ripple effect.” Over successive cycles, house prices have risen first in the southeast and gradually spread out over the rest of the country. As a result, regional price differentials exhibit considerable short-term volatility, but longer-term relativities tend to be restored. These distinctive properties of the regional data and the idea of a ripple effect have made this a fertile area for tests of unit root processes and cointegration between prices in the regions. The best known studies are those by MacDonald and Taylor (1993) and Alexander and Barrow (1994). Since both of these conduct similar estimation exercises to those in Table V, we simply summarize their findings. MacDonald and Taylor consider three questions: (i) is there a stable long-run relationship between regional house prices? (ii) is there a segmentation in house prices between North and South? (iii) is there a ripple effect? 8

The coefficients are not presented here but are available from the author.

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They, first, conduct bivariate Engle–Granger cointegration tests for all pairs of regions, followed by Johansen tests on all 11 British regions together, finding that there are up to nine cointegrating relationships. The paper tests for the presence of the ripple effect by constructing a moving average representation of the VAR and calculating the effects of shocks beginning in London on the other regions. There is strong support for the view that there is a stable set of long-run relationships among the prices. Also, there is some weak evidence of segmentation between the North and South and the ripple effect, indeed, appears to exist. Alexander and Barrow’s work is closely related but, in contrast to MacDonald and Taylor, a narrower range of pair wise cointegrating regions is found using Johansen tests. A vector error correction model is, then, used to test for causality through weak exogeneity restrictions and evidence is found of causality running from southeast England (the London area). Multivariate tests suggest that there are three cointegrating vectors amongst the regions, although the conclusion is dependent on the lag length in the VECM. In conclusion, all empirical work in the U.K. has suggested that a strong set of long-run regional price relativities exist, although the details differ between studies. The spatial price linkages in the U.S., at least at this highly aggregated level, are much less clear. 4.1. Can Theory Provide Any Common Ground? It appears, therefore, that there are very different patterns between the U.S. and the U.K. at this spatial scale. These could arise simply because of the differences in spatial dimensions, but if we look further, we can still find some common features, using a different strand of the literature on debt gearing. Consider the following model, based on an extension of the export base model used in Fujita et al. (1999). This can be used to demonstrate that house prices become more sensitive to income changes in the presence of downpayment requirements. Stein (1995) and Lamont and Stein (1999) develop more complex models. Since some parts of the country have higher downpayments than others, it follows that some areas will be more volatile:

where PH ⫽ house price Y ⫽ income DC ⫽ downpayment ratio.

PH ⫽ ␥Y/(1 ⫺ DC )

(8)

DC ⫽ ␣PH,

(9)

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To show this, in line with the house price models of Section 3, we assume that the supply of housing is fixed or at least inelastic due to land constraints, so that house prices are determined by demand; but demand is constrained by the available downpayment (DC ). If all households face constraints, as they become wealthier, they can afford larger loans. In this case, Eq. (8) says that the loan value, (1-DC )PH is a fixed percentage (␥ ) of income.9 If the downpayment ratio is equal to zero (DC ⫽ 0), there is a simple proportionality between prices and incomes so that the income elasticity of house prices is equal to one. But, as shown above, all empirical evidence for the U.K. suggests that the elasticity is greater than one and, appropriately conditioned, we cannot reject the result for the U.S. Therefore, we require that the representative agent is neither too rich (the rich may not require a downpayment) nor too poor (i.e., is not constrained out of the market altogether). If (DC ⫽ 0), however, and if households meet any downpayment constraint, then, as incomes rise (or, at the national level, the economy expands), house prices rise more than proportionately. However, this result is also dependent on Eq. (9) where the downpayment ratio increases with the level of house prices. Meen (2001) presents empirical evidence to support this. One reason is that for existing owner-occupiers who decide to move, at higher prices, their own property will have increased in value, reducing the size of the required percentage advance. Typically existing owner-occupiers have considerably higher downpayment percentages than first-time buyers. Substituting (9) into (8), yields a quadratic equation with two roots determined by PH ⫽ 1 ⫾ 冪1 ⫺ 4␣␥Y/2␣.

(10)

In fact, one of the roots has no economic meaning since it implies that prices are decreasing in income. The equation is also only defined for real roots up to the point ␥Y ⫽ 1/4␣. As an example, for ␥ ⫽ 2.0, DC ⫽ 0.2 (at Y ⫽ 1), and ␣ ⫽ 0.08, the relationship between house prices and incomes is plotted in Fig. 3. In this simple model, the ratio of mortgage repayments to incomes always remains constant. Higher incomes generate a proportionately higher demand for mortgage loans, but since prices rise more than proportionately to income, the downpayment ratio has to rise. Under this arbitrary set of parameter values, the implied income elasticity of house prices over the range for which the function is defined turns out to be approximately 2.7, which is not dissimilar to the findings above. Therefore, at (DC ⫽ 0), the income elasticity of house prices is one, but at (DC ⫽ 20%), the elasticity rises to 2.7. Variations in the downpayment ratio— whether imposed by lenders or resulting from the individual decisions of households—increase the volatility of house prices in response to income changes. Now assume that ␣ ⫽ 0.04; i.e. the downpayment ratio is less dependent on 9

I thank a referee for this interpretation.

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FIG. 3. House prices and incomes (␣ ⫽ 0.08).

house price changes. This becomes important when we discuss regional differences. Figure 4 now shows that the function becomes approximately linear and the elasticity of house prices with respect to income falls. Therefore the lower the value of ␣, the weaker is house price volatility. One further issue arises. As noted above, in this simple version of the model, the repayment to income ratio is constant (for given interest rates) but at the cost of an expanding downpayment ratio. In fact, in Fig. 3, the down payment ratio reaches a maximum of approximately 50% under the assumed set of parameters. This is probably unreasonable for most first-time purchasers, although not for many existing owner-occupiers. If the constraint becomes binding, then, the purchaser could (i) increase repayments through a larger mortgage (but repayment constraints will eventually bind) (ii) reduce housing demand by purchasing a smaller home (iii) remain as a renter for a longer period of time. But in terms of the figures, the imposition of a fixed downpayment percentage implies a linear relationship between prices and incomes. This is the same as assuming that

FIG. 4. House prices and incomes (␣ ⫽ 0.04).

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␣ ⫽ 0.0, i.e., similar to Fig. 4. Therefore, superimposing the two graphs gives Fig. 5 so that the house price function kinks at the point where the constraint binds. The locus of the lower points represents the highly nonlinear price function. Turning to regional patterns, in the U.K. loan to value ratios (equal to one minus the downpayment ratio) are lower in the southeast of England than in the north. Excluding London, in 1999, the average loan to value ratio (for all buyers) was approximately 67% in the southeast but 75% in the north. Although the differential varies over the cycle, the ratio is always higher in the north and, in both regions, the ratio falls at times of increasing house prices in line with Eq. (9). From the model above, we expect the region with the lowest loan to value ratio (highest downpayment ratio) to experience the strongest fluctuations in house prices. This is precisely what we observe. In Britain, over the period from 1969 to 1999, the standard deviation of annual house price inflation in the southeast was 12.7% compared with 9.9% in the north. Therefore, prices are noticeably more volatile in the south. Now if we look at American cities rather than census divisions, some similarities exist. Engelhardt (1994), compares median house prices, average downpayment percentages for first-time buyers, and an estimate of the average time taken to save to meet the down payment across a range of American cities. Two points stood out in his results. First, in the very expensive coastal cities of California and the northeast, the average saving period is much longer than in lower priced cities. Second, in line with the British regional findings, the average down payment is positively correlated with the level of house prices. We might expect, therefore, that the census divisions within which the most expensive cities lie will experience the highest degree of price volatility, and this turns out to be the case. Over the period 1976–1999, the standard deviation of house price inflation was 7.6% in the Pacific division and 7.7% in New England. These compare with the American average of 3.3%. Notice that this provides an alternative to the explanation based on bubbles advocated by Abraham and Hendershott (1996). Although our

FIG. 5. Constrained and unconstrained prices and incomes.

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conclusions must remain speculative and require confirmation at a finer spatial level, there do appear to be related spatial patterns in price volatility between the two countries, even if the long-run trends are not the same.

5. CONCLUSIONS A reading of the literature on time-series housing market models in the U.S. and U.K. would suggest that the two countries operate in very different ways. Indeed there are important differences in terms of tenure structure and mortgage markets, for example. The results from empirical models would also suggest that there are major differences. But, because of differences in methodological approach, it has always been difficult to tell whether true behavioral differences exist between the two countries. In this paper, we have tried to see whether, in fact, the observed differences in results are an artefact of the methodologies. In the cases we have examined, the similarities are more striking than the differences.

APPENDIX: DATA The following data were used in estimation. (i) U.K. g ⫽ PH/PC GW ⫽ Personal sector gross financial wealth (£m); (Financial Statistics) H ⫽ Owner-occupied housing stock (000s); (Housing & Construction Statistics) MRAT ⫽ Measure of mortgage rationing (derived from Meen 1990) PC ⫽ Consumers’ expenditure deflator (1995 ⫽ 100); (Economic Trends) PH ⫽ Index of mix-adjusted second-hand house prices (1990 ⫽ 100); (DETR) RR ⫽ Real interest rate: post tax mortgage interest rate (%); (Financial Statistics) minus the one period lagged rate of annual nominal house price inflation RY ⫽ Real personal disposable income (£m 1995 prices); (Economic Trends) W ⫽ GW/PC. (ii) U.S. g ⫽ PH/PC NW ⫽ Personal sector net financial wealth ($ bn); (Flow of Funds A/Cs, Federal Reserve)

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H ⫽ Owner-occupied housing stock (quarterly interpolation of annual estimates, millions); (US Census Bureau web site) PC ⫽ Consumers’ expenditure chain price index (1996 ⫽ 100); (National Income & Product Accounts) PH ⫽ Freddie Mac Conventional Mortgage House Price Index (1995 ⫽ 100); (www.freddiemac.com/finance/cmhpi/) RR ⫽ Real interest rate: 3 month Treasury Bill rate (%); (Federal Reserve Bulletin) minus the one period lagged rate of annual nominal house price inflation RY ⫽ Real personal disposable income ($ bn, 1996 prices); (National Income & Product Accounts) W ⫽ NW/PC.

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