Is Urban Land Price Adjustment More Sluggish than Housing Price Adjustment? Empirical Evidence

Abstract

This article hypothesises that, due to factors such as thin trading and lack of publicly available data on transactions in the land market, urban land prices react more sluggishly to shocks in market fundamentals than housing prices do. Based on a vector error-correction model utilising quarterly data for the Helsinki Metropolitan Area in Finland over 1988Q1–2008Q2, the empirical analysis provides support for this hypothesis. In particular, the results suggest that new information regarding the market fundamentals is more rapidly reflected in housing prices than in land prices. Nevertheless, it is the housing price level, instead of land prices, that adjusts towards a cointegrating long-run equilibrium between housing prices, land prices and construction costs.

Keywords

housing price land price dynamics cointegration impulse responses

Introduction

It is well known that housing prices and urban land prices are tightly linked. On the one hand, the price of a house consists of the replacement cost of the physical structure together with the value of land upon which the house is built. On the other hand, the price of vacant land zoned for housing is dependent on the housing price level. Therefore, the prices of housing and land zoned for housing are simultaneously determined.

In a frictionless and efficient market, price changes in the market for vacant land zoned for housing should not lag those in the housing market; at least there is no theoretical model suggesting such dynamics. Yet, because of informational reasons due to factors such as thin trading and lack of publicly available sales data in the land market, it is possible that housing appreciation leads the price changes perceived in the market for vacant land. The empirical results by Rosenthal (1999), for example, imply that any inefficiency in the housing market must lie in the market for land.¹

Lead–lag relations between the housing and land markets would have implications for the informational efficiency of the land market and for the predictability of land prices. Nevertheless, while a number of studies such as Titman (1985), Capozza and Helsley (1990) and Cunningham (2006), just to name a few, have analysed the price determination of vacant land, empirical research on the linkages between housing and land prices is still scarce. There appear to be only a couple of previous empirical studies examining in detail these dynamics. Ooi and Lee (2006) find that changes in housing prices exhibit predictive power with respect to land price movements, but not vice versa, in Singapore. Du et al. (2011), in turn, observe a bidirectional predictive relationship between housing and land prices in China.

Because of the scarcity of empirical examination on the dynamics between residential land and housing prices, further analysis on the dynamics is desirable. This article aims to contribute to filling the gap. We examine the predictive power between housing and land prices, and compute impulse response functions and variance decompositions to compare the dynamics of the prices. Although impulse responses and variance decompositions give important information regarding the dynamics of and main driving factors behind housing and land price growth and volatility, this appears to be the first study on the subject that examines rigorously the responses and decompositions.

The empirical analysis is based on quarterly data over 1988Q1–2008Q2 on single-family housing prices and on prices of vacant land zoned for single-family housing in the Helsinki Metropolitan Area (HMA) in Finland. It is shown based on a vector error-correction model (VECM) that housing prices react more rapidly than land prices to unexpected changes in the market fundamentals. That is, even though housing prices react to shocks sluggishly, the land market absorbs new relevant information even more slowly. Moreover, housing price movements exhibit significant predictive power with respect to land price changes even when market fundamentals are included in the VECM. It is the housing price level, instead of land prices, that adjusts towards a cointegrating long-run equilibrium between housing prices, land prices and construction costs, however. Therefore, land prices Granger cause housing prices indirectly through the cointegrating relation indicating that land prices exhibit predictive power with respect to housing price growth through the long-term dynamics. In line with the theory, the results show that housing and land prices are major ‘driving forces’ behind each other.

The empirical findings are of relevance to anyone who is interested in housing and land market dynamics—for instance, to construction companies, real estate brokers, landowners and investors as well as to policy-makers and housing economists. In particular, the estimated models entail predictability implications which affect the optimal behaviour of, for example, construction companies and landowners, and the analysis yields information on the main driving factors behind the urban housing and land market dynamics.

The paper proceeds as follows. The next section discusses the determination of urban housing and land prices theoretically. The literature review is provided in the third section, while the data used in the empirical analysis are introduced in section four. The fifth section presents the econometric methodology of the empirical analysis, after which the findings from the analysis are presented. In the end, the paper is summarised and concluded.

Theoretical Considerations

Due to the tight linkages between the markets for housing and urban land, housing prices and prices for land on which to build housing are simultaneously determined. Potepan (1996) derives a simple theoretical model of the metropolitan housing market that addresses the simultaneous determination of housing prices and undeveloped land prices.² Equilibrium in the housing and urban land markets results in the following reduced-form equations for the unit price of housing (H) and the unit price of vacant land zoned for housing (L) in period t

H_{t} = H_{t} (L_{t}, C_{t}, λ_{t})

(1)

L_{t} = L_{t} (H_{t}, C_{t}, γ_{t})

(2)

According to equations (1) and (2), H and L are dependent on each other and on construction costs (C). γ stands for the factors that determine urban land supply. These factors include topographical restrictions, legal land use restrictions and non-urban land prices, which are generally hard to cater for in an econometric time-series analysis such as the one conducted in this study. λ, in turn, denotes the variables that determine the demand schedule for housing. Based on the life-cycle model of the housing market, housing demand is determined by the user cost of housing capital and the rental price level

λ_{t} = λ_{t} (U_{t}, R_{t})

(3)

U_{t} = (1 - T_{t}) i_{t} + ϕ - δ - E (P_{t + 1} - P_{t} + π_{t})

(4)

R_{t} = R_{t} (Y_{t}, D_{t}, S_{t})

(5)

where, R stands for the real imputed rental income and U is the user cost of housing capital as a fraction of housing prices. U is determined by the after-tax market interest rate [(1–T_t)i_t], risk premium (ϕ) to compensate homeowners for the higher risk of owning than renting, property taxes and depreciation of housing (δ), and the expected nominal housing appreciation [E(P_t+1–P_t+π_t), where P is the natural log of real housing price level and π is the inflation rate]. Depreciation refers to the maintenance and repair costs that are necessary to maintain constant quality of the structure. Since the imputed rental income is not directly observable, it is assumed that R is determined by the real per capita income (Y), population (D) and housing stock (S). We assume that S also caters for the influence of land use restrictions (γ) on land and housing supply.

The supply-side institutional constraints of the planning system considerably vary between countries and regions and notably affect housing market dynamics (Glaeser and Ward, 2009; Gyourko et al., 2008; Huang and Tang, 2012). The planning system influences directly the supply of land zoned for housing and thereby the land price level. Moreover, the planning system affects housing prices indirectly through the supply of housing in (5) and through L in (1). Since the housing price level is determined by the value of the physical structure together with the value of land, any factor that affects the price of land should affect the housing price level in a similar manner.

The land use restrictions may also be time varying. For instance, in the UK the planning system has been made more responsive to the housing market (for example, the post-Barker planning system). There have not been notable institutional alterations in the planning system in Helsinki during the sample period, though. Nevertheless, we test for the stability of the estimated parameters in the empirical analysis.

Since L and C are both producer costs for developers and negatively related to the supply of housing, an increase in these variables should raise the housing price level. As volatility in C appears to be largely due to changes in the profit margins in the HMA case (see the Appendix, Figure A1), a rise in C is expected to increase L: greater profit margins increase developers’ incentives to acquire and build vacant land. Also, housing price growth increases the demand for land. Furthermore, growth in population and income raises rental prices augmenting demand for housing and land, whereas greater housing supply and greater user cost of housing cause lower housing and land prices. Therefore, the partial derivatives can be presented as follows

\begin{array}{l} \partial H / \partial L \geq 0; \partial H / \partial C \geq 0; \partial H / \partial Y \geq 0; \\ \partial H / \partial D \geq 0; \partial H / \partial S \leq 0; \partial H / \partial U \leq 0 \end{array}

(6)

\begin{array}{l} \partial L / \partial H \geq 0; \partial L / \partial C \geq 0; \partial L / \partial Y \geq 0; \\ \partial L / \partial D \geq 0; \partial L / \partial S \leq 0; \partial L / \partial U \leq 0 \end{array}

If the markets were frictionless and efficient, price changes in the market for vacant land zoned for housing should not lag those in the housing market. At least, the theoretical literature does not present any analytical model exhibiting structural relations that would suggest such dynamics. However, this paper hypothesises that, due to the generally better liquidity, a greater number of market participants and greater information flows in the housing market than in the land market, housing prices react to shocks in the market fundamentals more rapidly than vacant land prices do. It is therefore suggested that the market for vacant land is less informationally efficient than the housing market. In this article, ‘efficiency’ relates to the speed at which new information regarding the market fundamentals is reflected in the prices.

Previous Empirical Literature

There are some previous studies—for example, Manning (1988), Ozanne and Thibodeau (1983) and Potepan (1996), in which the relationship between housing prices and land prices is studied. Moreover, some papers (Glaeser and Ward, 2009; Tse, 1998) examine the interaction between housing prices and land supply. Davis and Heathcote (2007) find the contemporaneous correlation between detrended real land and housing prices to be as high as 0.92 in the US. None of these studies investigates the dynamics and potential lead–lag relations between housing and land prices, however.

Previous empirical research examining in detail the dynamics between residential land and housing prices is scarce. Using quarterly data for the period 1990–2005 for Singapore, Ooi and Lee (2006) find land and housing prices to be cointegrated and housing price movements to exhibit predictive power (in terms of Granger causality) with respect to land price movements, but not vice versa. Du et al. (2011), in turn, use quarterly panel data for four Chinese cities for the period 2001–09 to demonstrate that there is bidirectional Granger causality between housing and land prices in the long run, while the Granger causality is unidirectional from land to housing prices in the short run. While these studies are in line with each other in terms of cointegration between land and housing prices, they are in contradiction regarding the direction of short-run Granger causality.

In sum, as the dynamics between residential land and housing prices are still an underresearched topic, more research on the dynamics is desirable. This article aims to contribute to filling the gap. In addition to examining cointegration and Granger causalities between housing and land prices, we compute the impulse response functions and variance decompositions to study the dynamics. This appears to be the first study on the subject that examines rigorously the impulse responses and variance decompositions.

Data

The econometric analysis is conducted based on quarterly data for the period 1988Q1–2008Q2 for the Helsinki Metropolitan Area (HMA).³ All the data series are provided by Statistics Finland unless mentioned otherwise. The housing price index (H) describes the price development of single-family houses and the land price index (L) depicts the evolution of the price level of vacant land zoned for single-family houses. Both price indices are quality adjusted. L is based on the hedonic model by Peltola and Väänänen/the National Land Survey of Finland (2007). The ownership structure of land is highly dispersed in the area. Most of the stock of vacant land zoned for single-family housing is owned by individual households and other small investors.

The construction cost variable (C) incorporates the developers’ profit margin. The construction cost index, reported by Rapal Ltd, is based on tender prices of new housing construction in the HMA. To proxy for the other supply-side variable in the analysis—i.e. for housing stock (S)—the analysis includes the overall housing stock (total number of dwellings) in HMA divided by the total number of households in the area. The dwellings-to-households ratio is used to avoid multicollinearity complications. Also, some other supply-side variables, housing opportunities in terms of vacancy rate or new housing construction in particular, might contain information regarding the dynamics of the system. The estimated model does not include these variables, though, since the Akaike information criteria (AIC) prefer the model including S but not the other potential variables. Unfortunately, there are no reliable vacancy rate data for the HMA. Therefore, the inclusion of vacancy rate could not be tested. Note also that the development sector in the area has characteristics of both oligopolistic and monopolistic competition. On the one hand, the number of large developers is less than ten. On the other hand, there are multiple smaller developers especially in the single-family housing market.

The aggregate disposable income variable (Y) caters for both population and income growth in the HMA. Since the disposable income data are annual, we estimate the quarterly variation based on the quarterly nation-wide income level index. This is likely to produce a fairly good approximation for the quarterly aggregate income figures.

The most complicated variable to measure is the user cost of housing capital (U). In particular, the derivation of expected housing price growth is problematic. This study uses an econometric prediction model to estimate the expected nominal housing appreciation in a given period. The prediction model incorporates both an error-correction term—i.e. the adjustment of nominal housing price level towards its long-run relationship with the nominal aggregate income—and lagged housing price and income changes. The variables in the model are selected based on the AIC.⁴ The prediction model fits the data well. The model is summarised in Table A1 in the Appendix. Note that the long-run relationship is based on a longer sample period and slightly different dataset from the one reported earlier.

Similarly to the previous literature, ϕ is assumed to be time-invariant. Following Himmelberg et al. (2005), ϕ is set to 2 per cent. The assumed level of ϕ does not affect the empirical result, though. The real after-tax mortgage rate is used as the interest rate variable. Because the mortgage rate data, provided by the Bank of Finland, are available only since 1989Q3, the average lending interest rate concerning the whole outstanding loan stock is used to estimate the evolution of the mortgage rate during the early sample period. Due to a tax reform that changed the deductibility rules of mortgage interest payments, T is the average marginal income tax rate in Finland from 1988 to 1992 and the capital income tax rate from 1993 onwards.

The proxy for δ is calculated as the average per square metre maintenance costs (including taxes and repairs needed to maintain constant quality) of privately financed housing divided by the average per square metre sales price of privately financed housing. The cost data are at an annual level. Quarterly variation in δ is estimated based on the housing section of the property maintenance cost indices.

Only real values are employed in the study, except for the model for expected housing appreciation. Nominal values of H, L, C and Y are deflated by the cost of living index to get the real variables. Finally, natural logarithms are taken from all the series except for U.

Although hedonic price indices are employed, there appears to be substantial short-run measurement error in the house and land price series. That is, the hedonic indices are probably not able to track perfectly the time variation in the quality of transacted houses and land parcels. In particular, due to thin trading in the markets the price series are likely to include ‘noise’ in the short run—i.e. the short-run variation of the price series is probably overlarge. Since the apparently substantial noise in the price series might disturb the results of the econometric analysis, Hodrick–Prescott (HP) filtered price indices are used. To avoid extracting actual short-term dynamics, as small a tuning parameter for HP filter as 1.5 is employed. Even such a small tuning parameter yields notably smoother indices than the original ones (see Figure A1 in the Appendix).⁵Figure 1 exhibits the series included in the empirical analysis.

Figure 1.

Plot of the variables included in the empirical analysis.

The dramatic rise since 1988 in housing and land prices was largely a consequence of the financial market liberalisation in the late 1980s that was followed by a boom in bank lending (for example, Oikarinen, 2009a, 2009b). The housing and land markets finally collapsed at the beginning of the 1990s. The drop in housing and land prices was deepened by a severe recession in the early and mid 1990s. Also, C decreased drastically during 1990–93. This was largely due to a drop in the profit margins: the construction cost index that includes profit margins decreased substantially more than an alternative construction cost index that excludes profit margins (see the low part of Figure A1). After the mid 1990s, housing and land prices have grown substantially faster than Y. In 2008Q2, the population of HMA reached 1.02 million.

Table 1 reports descriptive statistics of the differenced series. Land prices have been more volatile than housing prices and construction costs. This is as expected and in line with the previous empirical findings (Bostic et al., 2007; Davis and Heathcote, 2007). The difference between the volatilities is relatively small, though. The divergence between the standard deviations is somewhat greater if longer-horizon price changes are used. All the variables are highly autocorrelated. Unsurprisingly, the contemporaneous quarterly correlations between the differenced H, L and C series are statistically highly significant (Table 1). Furthermore, the DF-GLS unit root test indicates that while U is stationary, H, L, C, Y and S are non-stationary in levels but stationary in differences.

Table 1.

Descriptive statistics and correlations of the differenced variables and DF-GLS unit root test results over 1988Q1–2008Q2

Variable	Mean (percentage, annualised)		Standard deviation (annualised)	Jarque–Bera test for normality (p-value)	Ljung–Box test for auto-correlation (p-value, 4 lags)
Housing price	2.2		7.9	0.05	0.00
Land price	6.4		9.4	0.10	0.00
Construction costs	−1.1		6.7	0.03	0.00
Aggregate income	3.2		4.0	0.00	0.02
Stock/households	0.1		0.4	0.00	0.00
User cost	3.4		12.7	0.08	0.00
	Correlation coefficients
	H	L	C	Y	S
Housing price (H)	1
Land price (L)	0.80**	1
Construction costs (C)	0.61**	0.46**	1
Aggregate income (Y)	0.34**	0.31**	0.35**	1
Stock/households (S)	−0.28*	−0.12	−0.29**	−0.22*	1
User cost (U)	−0.92**	−0.81**	−0.55**	−0.21*	0.12
Variable	DF-GLS statistics level (lags)			DF-GLS statistics difference (lags)
House price	−1.1 (2)^c			−4.0** (1)
Land price	−1.1 (3)^c			−2.7** (1)
Construction costs	−1.2 (1)^c			−5.0** (0)
Aggregate income	0.6 (4)^c			−2.5* (3)
Stock/households	−1.2 (5)^c			−2.4* (4)
User cost	−3.2** (1)

Notes: The descriptive statistics and correlation coefficients are those of differenced variables—i.e. of growth rates. * and ** denote for statistical significance at the 5 per cent and 1 per cent levels respectively, regarding the correlation coefficients and DF-GLS unit root test. Critical values at the 5 per cent and 1 per cent significance levels in the DF-GLS test are -1.95 and -2.60 respectively. The number of lags included in the DF-GLS tests is decided based on the general-to-specific method. It can be seen from Figure 1 that housing and land prices trend upwards over time. Moreover, the deterministic constants in the unit root tests for H, L, C, Y and S are significant. Therefore, a deterministic constant (^c) is included in these tests. In the case of U and all the differenced variables, the intercept is not significant as expected. Therefore, these tests do not include deterministic variables. As the log transformation removes the possible quadratic trends in the data, the inclusion of deterministic time trend is not relevant here.

Econometric Methodology

As the housing price level is determined by the values of land and physical structure, H and L could be pairwise cointegrated, or a long-term relation in terms of cointegration could take place between H, L and C. There also could be cointegrating relations between the prices and market fundamentals. Therefore, we use the Johansen (1996) Trace test to test for cointegration between the variables. The vector error-correction model (VECM) used in the Trace test is the following⁶

Δ X_{t} = μ + Γ_{1} Δ X_{t - 1} + \dots + Γ_{k} Δ X_{t - k} + αβ ‘ X_{t - 1} + ε_{t}

(7)

where, ΔX_t is X_t-X_t₋₁; X_t is a five-dimensional vector of the non-stationary variables in period t; µ is a five-dimensional vector of drift terms; Γ_i is a 5 x 5 matrix of coefficients for the lagged differences of the variables at lag i; k is the number of lags included in the model; α is a vector of the speed of adjustment parameters; β‘ forms the cointegrating vector(s); and ϵ is a vector of white noise error terms. β‘ includes the five stochastic variables but no deterministic variables.

The selection of the number of cointegrating vectors (r) is made by comparing the estimated Trace statistics with the quantiles approximated by the Γ-distribution (Doornik, 1998). After selecting r, we apply the general-to-specific methodology to impose restrictions on β and α (see for example, Juselius, 2006). We first examine which variables can be excluded from the cointegrating vector(s). The restrictions on β are tested by the Bartlett small-sample corrected likelihood ratio (LR) test reported in Johansen (2000). Then, we test for weak exogeneity of the variables, given the restrictions on β. That is, using the small-sample corrected LR test, we investigate whether the alpha can be restricted to equal zero for some variables. The restrictions on β and α are imposed one at the time. After each additional restriction, we test whether more restrictions can be imposed. The 10 per cent level of significance is used as a threshold value in the tests. We also examine the stability of the potential long-term relations by the recursive and backwards recursive Test of Beta vs Known Beta and Max Test statistics (Juselius, 2006).

If we detect one or more long-run relations that include either H or L or both, we base the follow-up analysis on the VECM given in equation (7). If such cointegration is not found, the further analysis relies on a model that excludes αβ‘X_t−1—i.e. on a conventional VAR model.

A VECM or VAR model is a suitable and convenient way to study the co-movement and dynamics of various economic variables (Juselius, 2006; Sims, 1980). This also applies to the dynamics between housing prices, land prices and the market fundamentals, since H and L are simultaneously determined, the dynamics of housing and land price movements typically include autocorrelation and sluggish adjustment to changes in the fundamentals, and since at least some of the fundamentals are expected to be endogenous with respect to H and L.

We estimate two separate models to study the dynamics: a pairwise model that includes housing and land price changes as the only stochastic variables in the short-term dynamics and a multiple variable model that includes the fundamentals as well. The estimated models are used to test for Granger causalities between the variables. A finding that z Granger causes y does not necessarily imply that z causes y. It merely means that current and historical observations of z are statistically significant in predicting future value of y. Granger causalities are tested by a standard F-test.

The multiple variable model is also used to derive the impulse responses of housing and land price movements to unanticipated changes in the fundamentals and in the prices themselves. This paper employs the ‘generalised’ impulse response function (GIRF) developed by Pesaran and Shin (1998). The GIRF does not require orthogonalisation of shocks and is invariant to the ordering of the variables in the model. This is desirable, since the theory does not give clear guidance as to which of many possible parameterisations one should use in the impulse response analysis. Furthermore, we use the Choleski decomposition to derive the forecast variance error decompositions for the price movements (see for example, Enders, 2004), since the ‘generalisation’ cannot be applied to variance decomposition.

Empirical Results

The small-sample corrected Johansen Trace test suggests the existence of one cointegrating relationship between the variables (see Table 2). Based on the LR test, housing stock and income can be excluded from this long-run relation. Hence, there is a cointegrating relation between H, L and C.⁷ The test statistics also suggest that only H and S react to deviation from the cointegrating long-run relation. The p-value for the five restrictions imposed on the model is 0.24.

Table 2.

Cointegration test results

H₀ (rank)	Trace test p-value		Trace test small-sample corrected p-value
r = 0	0.00		0.00
r = 1	0.01		0.18
r = 2	0.04		0.18
r = 3	0.18		0.27
	H	L	C	S	Y
Test for exclusion (p-value), 1	0.00	0.00	0.01	0.16	0.08
Test for exclusion (p-value), 2	0.00	0.00	0.02		0.14
Test for exclusion (p-value), 3	0.00	0.00	0.04
Test for weak exogeneity (p-value), 1	0.08	0.25	0.17	0.00	0.10
Test for weak exogeneity (p-value), 2	0.05		0.29	0.00	0.19
Test for weak exogeneity (p-value), 3	0.08			0.00	0.24
Test for weak exogeneity (p-value), 4	0.07			0.00
Estimated long-run relation (standard errors in parenthesis)
H = 0.459L+ 0.446C
(0.013) (0.053)
Speed of adjustment parameters	DH	DL	DC	DS	DY
	−0.055	–	–	0.033	–
	(0.032)			(0.004)
Diagnostics of the model in Trace test
Equation for	DH	DL	DC	DS	DY	system
JB (p-value)	0.82	0.81	0.91	0.19	0.01	0.14
LM(2)	0.82	0.11	0.83	0.23	0.82	0.46
ARCH(2)	0.63	0.75	0.24	0.02	0.62	0.99

Notes: The sample period is 1988Q1–2008Q2. The tested model includes two lags in differences and only the non-stationary variables. The SIC suggest the inclusion of only one lag in differences, but more lags are needed in order to extract significant autocorrelation in the residuals. The small-sample corrected test statistics are those suggested in Johansen (2002). Exclusion from the cointegrating relation and weak exogeneity restrictions are tested by the Bartlett small-sample corrected LR test by Johansen (2000). The restrictions imposed on the cointegrating relation and on the speed of adjustment parameters are decided based on the general-to-specific methodology. The imposed restrictions are signified by bolded values. JB denotes the Jarque–Bera test on the normality of residuals; LM(2) is the second-order Lagrange multiplier test on residual autocorrelation; and ARCH(2) is the second-order Lagrange multiplier test on the homoscedasticity of the residuals. System refers to tests imposed on the full system. Seasonal dummies are not included in the model relying on the SIC. The inclusions of the stationary U would not significantly alter the results.

In the long-term relation that is normalised with respect to H, the coefficients on L and C sum up close to one. This is as expected, since H is determined by its two components, the values of land and physical structure. The recursive test statistics, shown in Figure 2, indicate that the long-run relation is quite constant over time. Only one of the four statistics (backward recursive ‘Known Beta’) suggests that there has been significant instability in β for a short period of time during the sample period. Figure 2 also presents the deviation of housing price level from the cointegrating relation.

Figure 2.

Deviation of housing price level from the long-run relation, and the Max and Known Beta test statistics.

The multiple-variable VECM includes DH, DL, DC, DY, DS and DU (where D denotes differenced series), whereas the pairwise model includes only DH and DL. U is included in the model in differences, since this is clearly preferred by the AIC and Schwarz Bayesian Information Criteria (SIC). The lag length is decided by the SIC. However, more lags are included if the LR test at lag length two indicates that the residual series for DH or DL exhibit autocorrelation. The pairwise VAR includes three lags and the other reported models have two lags. The Hansen (1992) stability test accepts the stability of the estimated parameters.

As Table 3 shows, both housing and land price movements are highly predictable and Granger caused by themselves, suggesting that past and current price growth can be used to predict future price development. The models also show evidence of DH Granger causing DL. The predictive power of DH with respect to DL remains highly significant even when the fundamentals are included in the model. L, instead, Granger causes DH indirectly through the long-run relation. In other words, housing prices react to deviations from the long-term relation between H, L and C, and housing price growth can be predicted by the deviations: if housing price level is over (below) its long-run equilibrium level with L and C, housing price growth is expected to be smaller (greater) in the future. The adjustment speed of housing prices towards the long-term relation is 7.6 per cent, while the alpha is 0.031 in the equation for supply. Although S does not belong to the cointegrating relation, it is not unexpected that it reacts to deviation of housing prices from the relation: high housing prices relative to land prices and construction costs make new construction attractive thereby inducing greater supply.

Table 3.

P-values in the Granger causality tests

	Explanatory variable
	DH	DL	DC	DY	U	DS	eqe	Adj. R²
Dependent variable
Pairwise model
	VAR
Housing price growth	0.00	0.57						0.83
Land price growth	0.00	0.00						0.89
	VAR augmented with an error-correction term for DH
	0.00	0.22					0.07	0.87
	0.00	0.00						0.87
Multiple variable VECM model
Housing price growth	0.00	0.43	0.81	0.68	0.72	0.93	0.07	0.86
Land price growth	0.00	0.00	0.16	0.90	0.29	0.06		0.89

Notes: The reported p-values are based on a standard F-test. Statistically significant values at the 10 per cent level are bolded. The pairwise VAR includes three lags, while the ‘augmented’ VAR and the multiple variable VECM have two lags. The models include a dummy variable that takes the value one in 1991Q1 and is zero otherwise to cater for an outlier observation of DH and to fulfill the assumption of normally distributed residuals. Relying on the SIC, seasonal dummy variables are not included in the models. eqe is the equilibrium error—i.e. deviation of H from the long-run relation.

The GIRFs from the multiple variable model are shown in Figure 3 for housing and land prices and their changes. The impulse responses have the expected signs. To make it easier to compare the reaction patterns, the graphs include the reactions of both prices to a given shock simultaneously. While the reactions of price changes, shown up to three years from the shock, show the differences between the short-term reaction speeds, the price level reactions are pictured up to a 10-year horizon and provide information regarding the long-term impacts of various shocks on housing and land prices. The impulse responses correspond to reactions to shocks that are one standard error in magnitude. The responses can be regarded as showing the economic significance of the shocks and the impulse responses essentially summarise the dynamics of the model.

Figure 3.

Impulse responses of housing and land prices and their changes to a standard error shock in each of the variables included in the VECM.

The GIRFs indicate that new information is reflected more sluggishly in vacant land prices than in housing prices, even though the housing price adjustment is also slow. First, the immediate reaction of land prices to unexpected changes in the market fundamentals is notably weaker than that of housing prices. Secondly, while the reaction of DH peaks one to two quarters after the shocks in fundamentals, the response of DL generally peaks 2-4 quarters after the shocks. Thirdly, it takes longer for the response of DL than that of DH to converge close to zero. Fourthly, the reaction speeds of housing and land prices to unexpected changes in each other notably differ: the housing price reaction is more rapid. For instance, H absorbs 31 per cent of the eventual long-run impact of a DL shock within one-quarter of the shock, while L absorbs only 18 per cent of the long-run impact of a DH shock. The shocks in DH and DL originate from factors other than the fundamentals included in the model, such as changes in preferences or in the risk associated with housing and land markets.

H overshoots more than L after the shocks, however. This is mostly because it is H that adjusts towards the long-term relation between H, L and C over the long run. Nevertheless, in line with the reported faster reaction of the housing market than the land market, H responses peak earlier than those of L. The difference is 2–5 quarters depending on the origin of the shock.

The GIRFs also indicate that the impact of changes in the market fundamentals is greater on L than on H. Therefore, the response of C is also necessarily smaller than that of L. Hence, in areas where the land component of the housing price level is greater relative to the physical structure component, housing prices are generally expected to react more strongly to changes in interest rates and income: the greater the value of land relative to the construction costs of a house, the more volatile the housing price level is likely to be.

Figure 4 graphs the forecast error variance decompositions for housing and land price levels up to 10-year horizon. The variance decompositions show the proportion of the movements in a series that are due to its ‘own’ shocks versus due to shocks in the other variables in the model. The ordering of the variables in the baseline Choleski decomposition is as follows: S-Y-C-U-H-L. This ordering reflects the fact that S cannot react immediately to any of the shocks. It is further assumed that Y does not contemporaneously respond to innovations in any of the variables except for S, but may affect these variables within the quarter. The ordering also reflects the common assumption that interest rate changes are transmitted to the economy with lag (through U in the estimated model). H and L are placed the last to allow an immediate impact of all the fundamentals on the prices. Since housing appreciation has direct predictive power with respect to land price growth, L is the last variable in the ordering. However, as the ordering between H and L can affect the decompositions, Figure 4 also depicts decompositions computed based on an ordering where L is placed before H.

Figure 4.

Variance decompositions for housing and land prices.

The variance decomposition suggests that ‘direct’ shocks in the housing and land markets, some of which may be changes in supply restrictions or in expectations that are not catered for by the other variables in the model, have a major impact on housing and land prices. In the long horizon, over 60 per cent of the forecast error variance of H and over 70 per cent of L is due to innovations in either housing or land price movements. The share of supply-side fundamentals (S and C) is greater than that of demand-side fundamentals (Y and U). This is insensitive to the ordering between the fundamentals. The ordering between H and L does not influence the share of fundamentals, but it notably affects the share of the variances explained by DH and DL shocks. Therefore, while the prices are evidently major drivers of each other, the variance decomposition does not give a clear-cut indication as to which of the prices is a more important driver of the housing and land price determination over the long horizon. However, it appears that housing prices are a more important driver at least in the two to seven-year horizon. Moreover, the averages taken of the two alternative orderings indicate that housing price shocks account for a somewhat greater share of land price determination (29 per cent) than the other way round (21 per cent) at the 10-year horizon.

Summary and Conclusions

It is common knowledge that housing prices and the price of vacant land zoned for housing are tightly linked. Indeed, the prices of housing and of urban land on which to build housing are simultaneously determined. In a frictionless and efficient market, vacant land price movements should not lag changes in housing prices; at least, there is no theoretical model suggesting such dynamics. Nevertheless, this paper hypothesises that, due informational factors such as thin trading and lack of publicly available sales data in the land market, land prices react more slowly than housing prices to changes in the fundamentals.

The empirical analysis supports the hypothesis. Based on quarterly data over 1988Q1–2008Q2 for the Helsinki metropolitan area (HMA) in Finland, the estimated vector error-correction model shows that new information regarding the market fundamentals is more rapidly reflected in housing prices than in land prices, although the housing price response is also far from rapid. The econometric analysis also indicates that housing price movements Granger cause land price changes. However, housing prices instead of land prices adjust towards the long-run equilibrium between housing prices, land prices and construction costs.

The most important message of the empirical analysis is that, in line with the theory, housing and land prices seem to be major ‘driving forces’ behind each other, and that urban land price and housing price movements can be used to predict themselves and each other. Whether this predictability can be employed to gain abnormal returns depends crucially on the transaction costs and liquidity of the market. Anyhow, the predictability should affect the optimal behaviour of, for example, construction companies and landowners.

The impulse response analysis also indicates that land price shocks significantly affect the housing price level. Therefore, any policy decisions that are expected to decrease the value of vacant residential land are likely to yield more affordable housing prices.

This article contributes to filling the gap regarding empirical evidence on the dynamics between urban housing and land prices. Several questions that are out of the scope of this study remain unanswered, though. For instance, it would be interesting to examine the influence of the institutional environment on the dynamics between housing and vacant land prices. Furthermore, since the ownership structure of land may notably influence the operation of the market (Dowall and Ellis, 2009), it is also desirable to study the dynamics in markets where the ownership structure is not as highly dispersed as in Helsinki.

Footnotes

Appendix 1. Prediction Model for Nominal Housing Price Growth

The expected nominal housing appreciation used in the computation of U is based on an error-correction model (ECM). The error-correction mechanism in the model is based on a stationary long-run relation between nominal housing prices and nominal aggregate income. In order to have a sufficiently long sample period for the estimation of the stationary long-run relationship, the overall HMA housing price data that also include flats and row-houses are used to estimate the long-run relationship. The long-run relationship is estimated by the Johansen (1996) methodology employing data over 1975Q1–2008Q2. The Johansen Trace test statistics together with the estimated long-run relation and ECM are summarised in Table A1.

Acknowledgements

The author wishes to thank three anynomous referees, Luis H. Alvarez, Martin Hoesli, Risto Peltola and the participants at the 25th American Real Estate Society Annual Meeting and at the XXXI Annual Meeting of the Finnish Society for Economic Research for helpful comments that improved the paper.

Funding

Financial support from the OP Bank Group Research Foundation and the City of Helsinki is gratefully acknowledged.

Notes

References

Bostic

R. W.

Longhofer

S. D.

Redfearn

C. L.

(2007) Land leverage: decomposing home price dynamics, Real Estate Economics, 35, pp. 183–208.

Capozza

D. R.

Helsley

R. W.

(1990) The stochastic city, Journal of Urban Economics, 28, pp. 187–203.

Case

K. E.

Shiller

R. J.

(1989) The efficiency of the market for single-family homes, American Economic Review, 79, pp. 125–137.

Cunningham

C. R.

(2006) House price uncertainty, timing of development, and vacant land prices: evidence for real options in Seattle, Journal of Urban Economics, 59, pp. 1–31.

Davis

M. A.

Heathcote

(2007) The price and quantity of residential land in the United States, Journal of Monetary Economics, 54, pp. 2595–2620.

Doornik

J. A.

(1998) Approximations to the asymptotic distributions of cointegration tests, Journal of Economics Surveys, 12, pp. 573–593.

Dowall

D. E.

Ellis

P. D.

(2009) Urban land and housing markets in the Punjab, Pakistan, Urban Studies, 46, pp. 2277–2300.

(2011) The impact of land policy on the relation between housing and land prices: evidence from China, The Quarterly Review of Economics and Finance, 51, pp. 19–27.

Enders

(2004) Applied Econometric Time Series. New York: Wiley.

10.

Glaeser

E. L.

Gyourko

(2007) Housing dynamics. Discussion Paper No. 2137, Harvard Institute of Economic Research,.

11.

Glaeser

E. L.

Ward

B. A.

(2009) The causes and consequences of land use regulation: evidence from Greater Boston, Journal of Urban Economics, 65, pp. 265–278.

12.

Gyourko

Saiz

Summers

(2008) A new measure of the local regulatory environment for housing markets: the Wharton residential land use regulatory index, Urban Studies, 45, pp. 693–729.

13.

Hansen

B. E.

(1992) Parameter instability in linear models, Journal of Policy Modeling, 14, pp. 517–533.

14.

Himmelberg

Mayer

Sinai

(2005) Assessing high house prices: bubbles, fundamentals and misperceptions, Journal of Economic Perspectives, 19, pp. 67–92.

15.

Huang

Tang

(2012) Residential land use regulation and the US housing price cycle between 2000 and 2009, Journal of Urban Economics, 71, pp. 93–99.

16.

Johansen

(1996) Likelihood-based Inference in Cointegrated Vector Auto-regressive Models. Oxford: Oxford University Press.

17.

Johansen

(2000) A Bartlett correction factor for tests on the cointegrating relations, Econometric Theory, 16, pp. 740–778.

18.

Johansen

(2002) A small sample correction of the test for cointegrating rank in the vector autoregressive model, Econometrica, 70, pp. 1929–1961.

19.

Juselius

(2006) The Cointegrated VAR Model: Methodology and Applications. Oxford: Oxford University Press.

20.

Manning

C. A.

(1988) The determinants of intercity home building site price differences, Land Economics, 64, pp. 1–14.

21.

Oikarinen

(2009a) Household borrowing and metropolitan housing price dynamics: empirical evidence from Helsinki, Journal of Housing Economics, 18, pp. 126–139.

22.

Oikarinen

(2009b) Interaction between housing prices and household borrowing: the Finnish case, Journal of Banking & Finance, 33, pp. 747–756.

23.

Ooi

J. T. L.

Lee

S.-T.

(2006) Price discovery between residential land & housing markets, Journal of Housing Research, 15, pp. 95–112.

24.

Ozanne

Thibodeau

(1983) Explaining metropolitan housing price differences, Journal of Urban Economics, 13, pp. 51–66.

25.

Peltola

Väänänen

(2007) Asuntotontin Hinta. Publications of the National Land Survey of Finland 105.

26.

Pesaran

H. H.

Shin

(1998) Generalized impulse response analysis in linear multivariate models, Economics Letters, 58, pp. 17–29.

27.

Potepan

M. J.

(1996) Explaining intermetropolitan variation in housing prices, rents and land prices, Real Estate Economics, 24, pp. 219–245.

28.

Rahbek

Hansen

Dennis

J. G.

(2002) ARCH innovations and their impact on cointegration rank testing. Working Paper No. 22, Centre for Analytical Finance, University of Copenhagen.

29.

Rosenthal

S. S.

(1999) Residential buildings and the cost of construction: new evidence on the efficiency of the housing market, Review of Economics & Statistics, 81, pp. 288–302.

30.

Sims

C. A.

(1980) Macroeconomics and reality, Econometrica, 48, pp. 1–48.

31.

Titman

(1985) Urban land prices under uncertainty, American Economic Review, 75, pp. 505–514.

32.

Tse

R. Y. C.

(1998) Housing price, land supply and revenue from land sales, Urban Studies, 35, pp. 1377–1392.