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Spatial and temporal diffusion in the Dutch housing
market
Paul Mak | S2329891 | Pauljmak@gmail.com
June 12, 2019
Abstract
This paper examines the spatial and temporal diffusion of housing prices in the north of the Netherlands. Particular attention is paid to the ripple effect hypothesis, which states that shocks to housing markets are propagated from a dominant municipality to surrounding municipalities. Exploratory analysis on dominancy proposes Groningen to be treated as a dominant municipality. However, there is lack of evidence that supports long-run convergence of housing prices towards an equilibrium between Groningen and the non-dominant municipalities. In contrast, for almost all the municipalities evidence is found that housing prices are converging towards a price equilibrium between neighbouring municipalities. This result implies that local housing markets are affecting each other, which should be considered by policy makers.
JEL classification: C23, C33, R31
Keywords: Housing prices, Spatial dependence, the Netherlands
Master’s Thesis Economics Course code: EBM877A20 Supervisor: Prof. dr. J.P. Elhorst University of Groningen
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1. Introduction
A shock in prices in a dominant housing market tends to propagate to other housing markets, i.e. an increase in housing prices in region A may also increase the housing prices in region B, while shocks to prices in region B don’t have a lasting effect on prices in region A. This pattern is the so-called ‘ripple effect’. The ripple effect is not exactly the same as spatial diffusion, although both concepts are strongly related to each other. The ripple effect presumes a dominant region, whereas spatial diffusion is the effect on a region originating from surrounding regions. This paper sheds new light on the ripple effect in the Netherlands by focusing on the diffusion of house prices, conditioned on the origin (the dominant municipality) of the shock.
The analysis of spatial spillovers in the (Dutch) housing market is important, because housing prices affect numerous other markets. For example, a change in housing prices affects consumption and savings, as well as migration and labour mobility. Previous literature indicate that regional housing markets are not independent. Evidence has been found for both long- and short-run integration. Long-run integration refers to the situation in which regional housing markets tend to converge to an equilibrium relation in the long-run. For example, Holly et al. (2011) found that UK housing prices are long-run converging. They showed that, after an exogenous shock to housing prices, the expected price differential between two regions moves to zero as time increases. The opposite is found by Abbott and De Vita (2013), who studied the same market. A better understanding of the housing market dynamics is important in shaping economic policy. If there exists a ripple effect, a regional shock in housing prices will transmit to other regions. Not only the regional housing markets will be affected, but it will have implications for the nationwide housing market. Highly integrated markets suggest that policies should be targeted nationwide. Also, it is important to identify the origin of the ripple effect. This way, policy makers are able to efficiently target their policies. If it turns out that housing markets are segregated, policies targeted at local markets are sufficient.
3 Two main questions will be answered in this paper. First, this paper investigates whether one of the municipalities can be classified as dominant1. The following question will be answered: If any, which
municipality can be classified as dominant?
It is expected that Groningen acts as a dominant municipality in the sample, for the following reasons. Groningen is the largest municipality in the sample. It has more than 200.000 inhabitants, which is almost twice as much as the second largest municipality, Leeuwarden. Furthermore, Groningen has the most adjacent municipalities and is centrally located in the sample area. Also, Groningen is the most important economic centre in the sample. Unfortunately, there is no data on GDP per municipality available, but when examining GDP per capita one level higher, the region where Groningen belongs to has the highest GDP per capita. It is likely that Groningen has a large share in this. Other large municipalities, like Leeuwarden, Emmen, or Assen, may also be suitable candidates for being dominant. After the analysis on the dominant municipality in the sample, this paper examines the housing prices in a spatial and temporal dimension. The question to be answered is as follows: Is there evidence for a ripple effect between municipalities in the north of the Netherlands?
This question automatically implies that there is a dominant municipality. To build forth on the first question, it is expected that the results show a housing price diffusion pattern, whereby shocks to prices in Groningen gradually propagate to prices in other municipalities.
The analysis on the dominant municipality shows that Groningen is indeed a suitable candidate. However, when the housing price model is estimated the results don’t favour the inclusion of Groningen as a dominant municipality. The Wu-Hausman exogeneity test provides mixed evidence on Groningen being treated as dominant. Moreover, housing prices in only a few municipalities are affected by Groningen prices in the long-run. In contrast, for almost all the municipalities holds that housing prices are converging towards a price equilibrium between neighbouring municipalities. This is a relevant result for policy makers, because they should take into account the spatial interaction between housing markets.
The rest of this paper is organized as follows: The next section provides an overview of the most relevant literature regarding this study. Section 3 explains the methodology and the model used for the empirical analysis. Section 4 describes the data. Section 5 presents the estimation results and discusses them. Finally, section 6 gives a short summary, a conclusion and its implications.
2. Literature review
Numerous papers have studied the spatial and temporal diffusion patterns among regional housing prices. Meen (1999) states that three components are determining regional housing prices: (i) factors that influence housing prices in all regions, (ii) differences caused by variations in economic growth, and (iii) differences captured by spatial dependence and coefficient heterogeneity. The third component
1 That is, the housing market of that municipality can be classified as dominant. It is important to note that when this paper
4 is related to the ripple effect, and Meen (1999) explains this effect from an economic point of view. He provides four explanations: (i) migration, (ii) equity transfer, (iii) spatial arbitrage, and (iv) spatial patterns. First, migration refers to people moving from high housing price regions, to low price regions. This will drive up the housing prices in the latter regions. Alexander and Barrow (1994) provide this argument as an explanation for their finding that housing prices in the south of the UK cause price movements in the north and midlands. The second explanation refers to the phenomenon that buyers from high price regions have greater buying power in low price regions. This concept of equity transfer is related to the concept of migration, although households don’t have to physically move to the other regions. The same effect could be reached by investments. Moving to or investing in other regions may drive up the prices in those regions. Thirdly, housing markets are not fully efficient due to search costs. The presence of these costs may give rise to a ripple effect. When new information becomes available in a region, this information will be transmitted over time to the other regions. If housing markets were fully efficient, differences in return would be eliminated by arbitrage. Differences in housing prices would be random. Finally, a common mechanism may lead to a ripple effect, even if housing markets are not spatially connected. For example, economic growth starting in one region, with other regions catching up later, can drive up the prices in this region. When the economic growth spurt reaches the other regions, housing prices in these regions will also start to increase, i.e. the housing markets follow the pattern of a ripple effect.
5 in the north of the Netherlands, over the time period 1993 to 2014. The north of the Netherlands exhibits the largest gas field in Europe. Gas extraction has led, and still does, to many small earthquakes. Consequently, the market value of houses started to depreciate. The Dutch gas-extracting company (NAM2) compensates homeowners for this depreciation. However, it is hard to estimate the magnitude
of the housing price depreciation. Durán and Elhorst (2018) try to estimate it by using a hedonic housing price model. Their approach accounts for both weak and strong cross-sectional dependence. Again, using the adjusted CD-test and exponent α-estimator for unbalanced micro datasets, Durán and Elhorst (2018) find highly significant evidence for strong cross-sectional dependence. Since the same region, only with an extension of the time period, is analysed in the current paper, it is expected that strong cross-sectional dependence is present in the data used. Consequently, it is important to include common factors in the model. Furthermore, Elhorst and Durán (2018) find it difficult to lower the value of α close to ½. Therefore, they argue that it is also important to include spatial lags. Ignoring spatial lags may lead to biased estimates.
Chudik and Pesaran (2013) show that a dominant unit can be seen as a common factor to the other units. This means that accounting for cross-sectional dependence can be achieved by including a dominant unit in the regression. Shocks to the dominant unit propagate to the other units, while shocks to the other units don’t have an immediate impact on the dominant unit. Holly et al. (2011) apply this finding to UK housing prices. The authors incorporate a dominant region into their analysis, thereby examining the contemporaneously and spatially propagation of shocks from the dominant region to the other regions. Their a priori hypothesis of London being viewed as the dominant region is confirmed by the estimates of the error correction coefficients, and later also by a Wu-type of exogeneity test. Their analysis takes both the short- and long-run properties of the UK housing market into account. Moreover, by using impulse response analysis the authors show that the effects of a shock in housing prices decays much faster along the time dimension than along the spatial dimension. This means that a shock to London decays within a few years, while the shock is still felt in regions further away. Helgers and Buyst (2016) apply a similar econometric model as Holly et al. (2011) to the Belgium housing market. They examine the ripple effect, with a particular interest in housing price diffusion in the presence of a linguistic border. Thereby, they also allow for a dominant region. Using the same methodology as Holly et al. (2011), they find evidence for Antwerp to be a dominant city. Gong et al. (2016) study spatial properties of ten housing markets in China, among which spatial causality, convergence, and diffusion patterns. They also apply a model similar to the model of Holly et al. (2011). They use Granger causality tests to examine whether there is a spatial leading-lag relationship between housing prices in different regions. Granger causality shows whether historical price changes in one region help predicting current price changes in the other region. Although the Granger causality test is useful in revealing interrelationships between regions, it doesn’t say anything about whether these regions hold a long-run
2 Nederlandse Aardolie Maatschappij (NAM) is held responsible for both material and non-material damage caused by the
6 equilibrium relationship. Therefore, the long-run convergence properties should be examined. Gong et al. (2016) investigate both concepts and based on the Granger causality tests conclude that there exists a leading-lag relationship between the Chinese housing markets. However, there is a lack of evidence for long-run cointegration and convergence. Therefore, they don’t include a dominant city in their model.
Pesaran and Yang (2019) examine dominant units in U.S. production networks. The authors develop a dominance estimator and apply their approach to identify the top five most dominant sectors in the U.S. economy. They show that the presence of dominant sectors results in aggregate effects when those sectors are hit by shocks. According to Pesaran and Yang (2019), sectors can be classified as dominant when their outdegrees (the share of a sector’s output used as intermediate inputs by all the other sectors in an economy) are not bounded in the number of production units in an economy. The estimator of the degree of dominance, δ, turns out to be same as the exponent of cross-sectional dependence of Bailey et al. (2016). The current paper will use this approach as an exploratory analysis on selecting the dominant municipality. Section 3.3 elaborates more on this concept.
Other relevant studies on long- and short-run properties of housing prices include Brady (2014), who studies the spatial diffusion of housing prices in U.S. states. He does so by estimating impulse response functions using a single equation SAR panel model. His findings confirm the existence of spatial diffusion of housing prices. Otto and Schmid (2018) examine the spatiotemporal properties for German building land using both a spatial dynamic panel data model and a spatial autoregressive model. They find evidence of a ripple effect, which decreases very fast with the distance from the shock. Zhang et al. (2019) find a comparable result. They study spatial dependence in the Canadian housing market, by also using a spatial dynamic panel data model and different forms of the spatial weight matrix. Finally, van Dijk et al. (2011) describe regional housing prices in the Netherlands. They cluster the analysed regions in two classes and examine how the different classes react to shocks in GDP and the interest rate. They find evidence for differences in the housing price dynamics between the two clusters. By building on to the previous literature, this paper provides a comprehensive insight into the Dutch housing market. An extensive dataset is examined, covering 55 municipalities in the north of the Netherlands from the period 1993 to 2017. A particular interest is paid to the ripple effect, and new methods are applied to determine the dominancy of the municipalities.
3. Model and methodology
7 3.1 Cross-sectional dependence
As pointed out in section 2, it is important to account for cross-sectional dependence when it is present in the data. It is highly expected that strong cross-sectional dependence is present in the data, but to formally test for it, this paper uses the CD-test developed by Pesaran (2004, 2015). The CD-test points out whether there exists, weak sectional dependence (the null hypothesis), or strong cross-sectional dependence (the alternative hypothesis). The CD-test is defined as:
𝐶𝐷 = √2 𝑇 𝑁⁄ (𝑁 − 1) ∑𝑁−1𝑖=1 ∑𝑁𝑗=𝑖+1𝜌̂𝑖𝑗, (1)
where T denotes the number of observations on each municipality, N denotes the number of municipalities, and 𝜌̂𝑖𝑗 denotes the correlation coefficient between the time series for each pair of municipalities i and j.
Next to the CD-test, the exponent α-estimator developed by Bailey et al. (2016)3 will be applied.
The exponent α-estimator measures the degree of cross-sectional dependence, whereby 𝛼 ≤1 2 corresponds to weak cross-sectional dependence, 1
2< 𝛼 ≤ 3
4 indicates moderate cross-sectional dependence, and 3
4< 𝛼 ≤ 1 indicates strong sectional dependence. The strongest form of cross-sectional dependence is reflected by 𝛼 = 1. Bailey et al. (2016) points out that α cannot be estimated consistently if it takes a value on the interval (0,1
2). Therefore, they suggest a two-step approach. Since the values on the interval (0,1
2) of the α-estimator correspond to weak cross-sectional dependence, the CD-test can point out whether this problem occurs. The α-estimator is only inconsistent if the null hypothesis of weak cross-sectional dependence of the CD-test cannot be rejected. If the CD-test points out that the form of cross-sectional dependence is strong, the α-estimator is greater than ½ and it can indicate how strong the form of cross-sectional dependence is.
3.2 Long-run properties
It is expected that the housing price series are non-stationary. To test for stationarity, the augmented Dickey-Fuller (ADF) test will be applied. When the housing price series turn out to be first-order stationary (I(1)), they may still be used without differencing if the series are cointegrated. Cointegration can be described as the relationship between two I(1) variables, whereby the residuals of the cointegrating relationship are I(0). In this case there exists a long-run relationship between the two variables. The existence of two cointegrated variables not only has implications for the long-run behaviour of the variables, but also for their short-run behaviour. The variables have to be driven to their long-run equilibrium relationship by some sort of mechanism. This mechanism is called an error-correction mechanism, which also influences the short-run dynamics. To provide evidence of the ripple
8 effect, it is important to study the long-run properties of the housing prices. The ripple effect hypothesis implies that differences between housing markets can be large in the short-run, but in the long-run the relative housing price pattern tends to be restored.
It is assumed that the housing price series are cointegrated. The price series are plotted in section 4, figure 2. This figure also suggest that the price series are cointegrated. To formally test for cointegration, this paper applies the Engle-Granger (EG) cointegration test for each pair of municipalities. The EG-test for cointegration is a two-step residual-based test, developed by Engle and Granger (1987). In the first step, prices of municipality i are regressed on prices of municipality j and a constant. Then, the residuals of this regression are calculated. Secondly, if the two variables are cointegrated, the error term is I(0). The Dickey-Fuller test will be applied to test for stationarity of the error term. The critical values are more negative than those of the standard (A)DF-test, because the OLS estimator in step one will make the residuals look as stationary as possible. When the null hypothesis of non-stationary residuals can be rejected, the two variables are cointegrated.
3.3 Dominant municipalities
This paper applies three methods for the identification of dominant municipalities. The first method is based on the recently developed dominance estimator by Pesaran and Yang (2019). The second method is based on the amount of pairwise price correlations, applied before by Bailey et al. (2015). These two methods are used for exploratory purposes. As mentioned before, it is expected that Groningen will come forth as the dominant municipality. The third method, applied before by Holly et al. (2011), will serve as a confirmation of the outcome of the first two methods.
3.3.1 Exploratory dominancy analysis
Pesaran and Yang (2019) provide an alternative way to determine the dominance of a unit. As mentioned before, they propose an estimator of the degree of dominance, δj, and apply it to U.S. production networks to identify the most dominant sectors in the U.S. economy. The value of this estimator depends on the outdegree of a network dj:
𝑑𝑗 = ∑𝑁𝑖=1𝑤𝑖𝑗, (2)
where wi,j denotes the spatial weight between municipality i and j.
Formula (2) basically is the column sum of the row-normalized 𝑁 × 𝑁 spatial weight matrix, W. Row-normalization of the spatial matrices is a standard practice in spatial econometrics. This means that the rows are scaled such that the weights sum to one:
𝑊𝑖,𝑗𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑= 𝑊𝑖,𝑗
9 The dominance estimator itself is denoted by:
𝛿̂𝑗,𝑇 =
𝑇−1∑𝑇𝑡=1ln 𝑑𝑗,𝑡−(𝑇𝑁)−1∑𝑇𝑡=1∑𝑁𝑖=1ln 𝑑𝑖,𝑡
ln 𝑁 , (4)
for j = 1, 2, …, N, and t = 1, 2, …, T.
In the pure cross-section case (𝑇 = 1), formula (4) reduces to:
𝛿̂𝑗=
ln 𝑑𝑗−𝑁−1∑𝑁𝑖=1ln 𝑑𝑖
ln 𝑁 (5)
Dominant units are decomposed into weakly and strongly dominant units. A unit is strongly dominant if 𝛿𝑗= 1, weakly dominant if 0 ≤ 𝛿𝑗≤ 1, and non-dominant if 𝛿𝑗= 0. There are three possible combinations of dominant units. The first one consists of a fixed number of strongly dominant units. The remaining units are non-dominant. The second combination consists of a number of weakly dominant units. The other units are non-dominant. The third possibility is that there are a fixed number of strongly dominant units, and other units will be weakly dominant. It is impossible for all units to be dominant. Like the exponent α-estimator of Bailey et al. (2016), the dominance estimator δ cannot be consistently estimated if its value falls below ½. Therefore, only estimates of 𝛿̂𝑗> 1/2 should be considered. The dominance estimator will be calculated two times. First, the estimator will be based on the first-order binary contiguity matrix. Second, the estimator will be based on the inverse distance matrix. Section 3.5 elaborates on the form of these spatial weight matrices.
Another exploratory method that will be used to examine which municipality is dominant is based on the pattern of price correlations across municipalities. Bailey et al. (2015) apply this method to measure the spatial connections between housing prices in the USA. The correlation matrix is denoted by:
𝑅̂ = (𝜌̂𝑖𝑗), (6)
for i = 1, 2, …, N - 1, and j = i + 1, i + 2, …, N, where 𝜌̂𝑖𝑗 is the correlation of the price changes between municipality i and j.
In total 𝑁(𝑁−1)
2 pairwise price correlations will be determined. After that, the pairwise correlations will be tested for significance by applying the Holm (1979) multiple testing procedure. Municipalities that are possibly dominant are expected to have a high number of significant pairwise price correlations.
3.3.2 Confirmation of the exploratory analysis
10 and Lin (1995). The following bivariate vector error correction model (VECM) with k lags will be estimated:
∆𝑝0,𝑡= 𝜙0,𝑖(𝑝0,𝑡−1− 𝑝𝑖,𝑡−1) + ∑𝑙=1𝑘 𝛼0,𝑖,𝑙 ∆𝑝0,𝑡−𝑙+ ∑𝑘𝑙=1𝑏0,𝑖,𝑙 ∆𝑝𝑖,𝑡−𝑙 + 𝜀0,𝑖,𝑡 (7) ∆𝑝𝑖,𝑡 = 𝜙𝑖,0(𝑝0,𝑡−1− 𝑝𝑖,𝑡−1) + ∑𝑙=1𝑘 𝛼𝑖,0,𝑙 ∆𝑝𝑖,𝑡−𝑙+ ∑𝑘𝑙=1𝑏𝑖,0,𝑙 ∆𝑝0,𝑡−𝑙+ 𝜀𝑖,0,𝑡 (8)
This model will be estimated for the municipality that comes forth as dominant from the exploratory analysis in combination with each non-dominant municipality. The dominant municipality is denoted by 0. Therefore, formula (7) is the equation that will be estimated for the proposed dominant municipality. Formula (8) is the equation that will be estimated for each non-dominant municipality. ∆𝑝𝑖,𝑡 represents the growth rate of the housing prices in municipality i at time t. 𝑝𝑖,𝑡−𝑙 represents the l-year lagged housing prices in municipality i. The number of lags is based on the likelihood-ratio (LR) test statistic, whereby the maximum lag-order is set to four. 𝜀0,𝑖,𝑡 and 𝜀𝑖,0,𝑡 are the error terms. The terms 𝜙0,𝑖 and 𝜙𝑖,0 are the error correction coefficients. When the error correction coefficient is significant, it is assumed that prices are long-run caused by the other municipality. This means that to show the dominancy of the proposed dominant municipality, the error correction coefficient in formula (7) should be insignificant, while it should be significant in equation (8). If this is the case, housing prices in the dominant municipality are long-run causing prices in the other municipalities, while prices in the dominant municipality are not long-run caused by prices of the other municipalities. In other words, a shock to housing prices in the dominant municipality will have a permanent effect on prices of the other regions. A shock to housing prices in a non-dominant municipality will at most have a short-run effect on prices in the dominant municipality. After some time, the shock effect in the dominant municipality will fade away.
In the final housing price diffusion model, the housing price growth in the dominant region, ∆𝑝0,𝑡, appears as a spatial effect in the price equation of the other regions, see equation (13). It is possible to test for weak exogeneity of ∆𝑝0,𝑡 by performing a Wu type of exogeneity test (Wu (1973)). This way, the dominance of a municipality can be confirmed. Once the model of the dominant municipality is estimated, the residuals are denoted by:
𝜀̂0,𝑡 = ∆𝑝0,𝑡− 𝜙̂0,𝑠(𝑝0,𝑡−1− 𝑝̅0,𝑡−1𝑤 ) − 𝛼̂0− 𝛼̂0,1Δ𝑝0,𝑡−1− 𝑏̂0,1Δ𝑝̅0,𝑡−1𝑤 (9)
After that, the following auxiliary regression will be estimated for each municipality separately: ∆𝑝𝑖,𝑡 = 𝜙𝑖,𝑠(𝑝𝑖,𝑡−1− 𝑝̅𝑖,𝑡−1𝑤 ) + 𝜙𝑖,0(𝑝𝑖,𝑡−1− 𝑝0,𝑡−1) + 𝛼𝑖+ 𝛼𝑖,1∆𝑝𝑖,𝑡−1+ 𝑏𝑖,1∆𝑝̅𝑖,𝑡−1𝑤 + 𝑐𝑖,0∆𝑝0,𝑡+
𝜆𝑖𝜀̂0,𝑡+ 𝜂𝑖,𝑡 (10)
11 exogenous to the evolution of housing prices in the other municipalities. Not rejecting the null would suggest that the results are not subject to the simultaneity bias, i.e. housing prices in the dominant municipality causes prices in non-dominant municipalities, but prices in non-dominant municipalities do not cause prices in the dominant municipality. In this case the proposed dominant municipality may indeed be dominant.
3.4 The spatial-temporal housing price diffusion model
As mentioned before. this paper follows the spatial-temporal housing price diffusion model developed by Holly et al. (2011). With a few modifications, this model has also been applied by Helgers and Buyst (2016) and Gong et al. (2016). Helgers and Buyst (2016) apply an extended version of the model to the Belgian housing market, thereby examining the effects of the language border on the spatial-temporal diffusion of housing prices. Gong et al. (2016) apply the model to the Chinese housing market, with the modification that they abandoned the dominant city from the model specification. This paper does allow for the possibility of a dominant municipality. Every municipality will be analysed for dominancy, see section 3.3. The proposed dominant municipality will be included into the model. The changes in housing prices of a municipality are influenced by both the short- and long-run housing price changes in the dominant municipality and in neighbouring municipalities. The model is represented by equations (11) and (13). All prices are denoted in the natural logarithm of real housing prices. The model will be applied to half yearly aggregated data at the municipal level. For the dominant municipality, denoted by 0, the following linear price equation will be estimated by OLS:
∆𝑝0,𝑡= 𝜙0,𝑤(𝑝0,𝑡−1− 𝑝̅0,𝑡−1𝑤 ) + 𝑎0+ ∑ 𝑎0,𝑙∆𝑝0,𝑡−𝑙 𝑘0,𝑎 𝑙=1 + ∑ 𝑏0,𝑙∆𝑝̅0,𝑡−𝑙𝑤 𝑘0,𝑏 𝑙=1 + 𝜀0,𝑡, (11) for t = 1, 2, …, T.
Price equation (11) is allowed to be error correcting, meaning that prices in the dominant municipality may converge to prices in the neighbouring municipalities. Furthermore, price growth in the dominant municipality may depend on its own lagged price growth. Finally, shocks to the non-dominant
municipalities have no immediate impact on the dominant municipality, although lagged effects of shocks from non-dominant neighbouring municipalities are allowed. ∆𝑝0,𝑡 represents the growth rate of the housing prices in the dominant municipality at time t. 𝑝0,𝑡−𝑙 represents the l-year lagged housing prices in the dominant municipality. 𝑝̅0,𝑡−𝑙𝑤 is the spatial variable. It represents the l-year lagged
housing prices in the neighbouring municipalities:
𝑝̅𝑖,𝑡𝑤 = ∑𝑁𝑗=0𝑤𝑖,𝑗𝑝𝑗,𝑡, (12)
12 𝑎0 represents the constant term. 𝑎0,𝑙 is the coefficient that shows how the housing price growth in the dominant municipality is influenced by its l-year lagged housing price growth. The number of lags, 𝑘0,𝑎, is determined by using the Bayesian information criterion (BIC). The maximum number of lags is set to four. 𝑏0,𝑙 is the coefficient that shows how the housing price growth in the dominant municipality is influenced by the l-year lagged housing price growth in the neighbouring municipalities. Again, the number of lags, 𝑘0,𝑏, is determined by using the BIC and the maximum number of lags is set to four. Finally, 𝜀0,𝑡 represents the error term.
Shocks in housing prices to the dominant municipality are propagated to the other municipalities simultaneously and over time. In contrast, shocks to the non-dominant municipalities may have only little impact on the dominant municipality. For the remaining, non-dominant municipalities the following linear price equation will be estimated by OLS:
∆𝑝𝑖,𝑡 = 𝜙𝑖,𝑤(𝑝𝑖,𝑡−1− 𝑝̅𝑖,𝑡−1𝑤 ) + 𝜙𝑖,0(𝑝𝑖,𝑡−1− 𝑝0,𝑡−1) + 𝑎𝑖+ ∑ 𝑎𝑖,𝑙∆𝑝𝑖,𝑡−𝑙 𝑘𝑖,𝑎 𝑙=1 + ∑ 𝑏𝑖,𝑙∆𝑝̅𝑖,𝑡−𝑙𝑤 𝑘𝑖,𝑏 𝑙=1 + ∑ 𝑐𝑖,𝑙∆𝑝0,𝑡−𝑙 𝑘𝑖,𝑐 𝑙=1 + 𝑐𝑖,0∆𝑝0,𝑡+ 𝜀𝑖,𝑡, (13) for i = 1, 2, …, N, and t = 1, 2, …, T.
13 3.5 Spatial weight matrix
The spatial structure is defined by a (𝑁 × 𝑁) spatial weight matrix, W. The spatial weight matrix is a priori defined by the researcher and it defines whether and to what extent the different regions influence each other. The value and significance level of the interaction parameters depend on the specification of the spatial weight matrix. Therefore, it is important to carefully choose the appropriate spatial weight matrix. In the existing literature, there are multiple popular ways of constructing W. The spatial weight matrices which are most applicable to this research are the p-order binary contiguity matrix and the inverse distance matrix. In this paper, the model will be estimated using both a first-order binary contiguity matrix and an inverse distance matrix. Using both matrices and comparing the results ensures the robustness of the model. The first-order binary contiguity matrix defines whether municipalities i and j share common borders:
𝑊𝑖,𝑗𝑏𝑐 = {1 𝑖𝑓 𝑚𝑢𝑛𝑖𝑐𝑖𝑝𝑎𝑙𝑖𝑡𝑖𝑒𝑠 𝑖 𝑎𝑛𝑑 𝑗 𝑠ℎ𝑎𝑟𝑒 𝑐𝑜𝑚𝑚𝑜𝑛 𝑏𝑜𝑟𝑑𝑒𝑟𝑠
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (14)
Unlike Holly et al. (2011), in this paper the model will also be estimated using the inverse distance matrix. This matrix defines the inverse distance between the centres of municipalities i and j:
𝑊𝑖,𝑗𝑖𝑑= 1
𝑑𝑖,𝑗, (15)
where di,j represents the distance between municipality i and j. Both matrices will be row-normalized.
4. Data
The main source of data is the Dutch Association of Real Estate Brokers and Real Estate Valuers (NVM4), covering housing transactions in the three northern provinces of the Netherlands: Drenthe,
Friesland, and Groningen. The dataset consists of data on 329.927 housing transactions in the period 1993 to 2017. Garage boxes and land are excluded from the analysis. The dataset only includes properties sold by the NVM. The market share of the NVM is high, but not 100%. Therefore, the dataset doesn’t capture all the housing transactions. Theoretically this could lead to biased results. In practice the results will be reliable enough, because the NVMs market share is sufficiently high, approximately 80%.
The micro data are transformed into half yearly aggregated data at the municipal level (T = 50). Where most other papers regarding this subject choose for quarterly aggregated data, this paper chooses for half yearly aggregated data. This choice is made to ensure that each period covers sufficient housing transactions. At the same time, the number of time periods is large enough to include a maximum of four time lags.
14 At the time of the last housing transaction covered in the dataset, the three provinces Drenthe, Friesland, and Groningen consisted of 12, 24, and 23 municipalities respectively. Four municipalities are excluded (Vlieland, Terschelling, Ameland, and Schiermonnikoog)5, because the amount of housing
transactions is too limited to produce reliable results. Moreover, it is likely that housing prices in these municipalities are influenced by other forces. One of these forces could be the high number of recreational houses in these municipalities. It could be that recreational houses follow a different pricing pattern, which influences the results. Therefore, the total number of municipalities in the sample is 55 (𝑁 = 55). Figure 1 displays a map of these municipalities.
The housing transactions are denoted in nominal prices (euro’s). Using the Consumer Price Index (CPI) for the years 1993 to 2017, the nominal prices are transformed into real prices. Therefore, changes in the housing prices are not affected by inflation. Data on the CPI is collected from the Organisation for Economic Co-operation and Development (OECD). Quarterly CPI statistics are converted into half yearly statistics, whereby 2015 serves as the base year. Finally, the housing prices are transformed into natural logarithms. Table A.1 shows the descriptive statistics of the micro data for each municipality. Table A.2 shows the descriptive statistics of the aggregated date for each municipality.
Figure 2 displays the development of the natural logarithm of real housing prices, using 1993 as a base year. Examination of this figure suggests that the prices are cointegrated. They follow a similar pattern over the period 1993 to 2017. During the first years of the period studied, housing prices increased tremendously. Among others, this was due to a lack of dwellings, decreasing mortgage interest, and high credit accessibility. Moreover, income increased during this period. Housing prices started to decrease from 2008 onwards. This was mainly caused by the 2007-2008 financial crisis. This lasted until 2013. Since then the Dutch housing market is recovering.
5. Results
5.1 Cross-sectional dependence
The cross-sectional dependence test of Pesaran (2004, 2015) is used to examine cross-sectional dependence in the housing prices. The statistic obtained equals 242.775 and the null hypothesis of weak cross-sectional dependence can be rejected at the 1% significance level. This statistically highly significant outcome indicates that cross-sectional dependence is present in the data. The exponent α-test of Bailey et al. (2016) gives an estimate of α equal to 0.9859, which is very close to unity. This suggests that the degree of cross-sectional dependence is strong. As mentioned before, this paper controls for the strong form of cross-sectional dependence by using a dominant municipality as a common factor to the other municipalities.
5 Vlieland, Terschelling, Ameland, and Schiermonnikoog are the islands above Friesland (see figure 1). They are all located
15
Figure 1. Map of the provinces and municipalities in the sample.
= Drenthe = Friesland = Groningen
1 Aa en Hunze 12 Westerveld 23 Leeuwarden 34 Bedum 45 Marum 2 Assen 13 Achtkarspelen 24 Leeuwarderadeel 35 Bellingwedde 46 Menterwolde 3 Borger-Odoorn 14 Dantumadiel 25 Littenseradiel 36 De Marne 47 Oldambt 4 Coevorden 15 De Friese Meren 26 Menameradiel 37 Delfzijl 48 Pekela 5 De wolden 16 Dongeradeel 27 Ooststellingwerf 38 Eemsmond 49 Slochteren 6 Emmen 17 Ferwerderadiel 28 Opsterland 39 Groningen 50 Stadskanaal 7 Hoogeveen 18 Franekeradeel 29 Smallingerland 40 Grootegast 51 Ten Boer 8 Meppel 19 Harlingen 30 Súdwest-Fryslân 41 Haren 52 Veendam 9 Midden-Drenthe 20 Heerenveen 31 Tytsjerksteradiel 42 Hoogezand-Sappemeer 53 Vlagtwedde 10 Noordenveld 21 het Bildt 32 Weststellingwerf 43 Leek 54 Winsum 11 Tynaarlo 22 Kol. en Nieuwkruisland 33 Appingedam 44 Loppersum 55 Zuidhorn
Source: Statistics Netherlands (CBS). Adjustments are made by the author.
16 5.2 Long-run properties
The augmented Dickey-Fuller (ADF) test for stationarity reveals that all the municipalities are I(1) at the 1% level. The only exception in this is the municipality Harlingen, which is I(0) at the 5% level. Therefore, it should be taken into account that the coming results for Harlingen are very likely to be spurious.
It is assumed that the housing price series are cointegrated. To formally test for cointegration, the Engle-Granger (EG) cointegration test is applied to all 𝑁(𝑁−1)
2 = 1485 pairs of housing price series. Table 1 shows the fraction of municipalities that are cointegrated in total and for each province separately. The results indicate a high amount of cointegrating relations between the different municipalities. It has to be noted that a relatively large part of the relations that are not cointegrated involve the large municipalities (Assen, Leeuwarden, Groningen). Particularly the relations of these large municipalities with the municipalities in the province of Drenthe show a lack of cointegration. This could influence the results for these municipalities. There are no large differences in the amount of cointegrating relations between the provinces. In total, 94.2% of the pairs of housing price series are cointegrated.
Table 1. Fraction of municipalities that are cointegrated.
Within each province
Drenthe Friesland Groningen All
0.848 (66) 0.958 (190) 0.957 (253) 0.942 (1485)
Notes: Cointegration is determined using the Engle-Granger cointegration test. Cointegration is determined at the 10% significance level, using the critical values calculated by MacKinnon (2010). The number of relations tested for cointegration is shown between the brackets.
5.3 Dominant municipality
5.3.1 Exploratory dominancy analysis
Table 2 displays the results of the exploratory analysis on which municipality could be treated as dominant. The second and third columns show the dominance estimator of Pesaran and Yang (2019) using the binary contiguity and the inverse distance matrix respectively. The fourth column shows the amount of pairwise correlations that are significant at the 1% level.
17
Table 2. Exploratory dominancy analysis, by using the Pesaran and Yang (2019) dominance estimator
and the number of pairwise price correlations.
Municipality BC matrix (𝜹̂𝒋) ID matrix (𝜹̂𝒋) Price correlations (𝝆̂𝒊𝒋)
Aa en Hunze 0.108 0.054 27 Assen -0.137 -0.094 38 Borger-Odoorn 0.018 0.038 36 Coevorden 0.012 0.015 34 De wolden -0.022 0.046 37 Emmen -0.107 0.049 39 Hoogeveen -0.043 0.021 30 Meppel -0.173 0.044 36 Midden-Drenthe 0.066 0.014 31 Noordenveld 0.037 0.045 34 Tynaarlo 0.022 0.023 17 Westerveld 0.124 0.027 43 Achtkarspelen 0.013 -0.014 20 Dantumadiel -0.004 -0.099 25 De Friese Meren -0.075 0.035 32 Dongeradeel -0.056 0.009 1 Ferwerderadiel 0.016 -0.016 4 Franekeradeel 0.084 -0.067 27 Harlingen -0.229 -0.012 1 Heerenveen 0.024 -0.039 32 het Bildt -0.056 0.050 26 Kollumerland en Nieuwkruisland -0.010 -0.002 8 Leeuwarden 0.114 0.022 39 Leeuwarderadeel -0.015 -0.018 18 Littenseradiel -0.080 0.033 1 Menameradiel 0.006 -0.038 3 Ooststellingwerf 0.009 0.052 23 Opsterland 0.009 -0.022 30 Smallingerland 0.054 -0.052 8 Súdwest-Fryslân 0.070 0.028 3 Tytsjerksteradiel 0.008 0.031 28 Weststellingwerf -0.072 0.019 34 Appingedam -0.177 0.012 4 Bedum -0.022 -0.038 0 Bellingwedde -0.051 -0.061 20 De Marne -0.002 0.013 1 Delfzijl 0.006 -0.005 11 Eemsmond -0.008 -0.086 3 Groningen 0.156 0.053 49 Grootegast -0.035 0.045 25 Haren -0.223 0.009 0 Hoogezand-Sappemeer 0.056 -0.064 13 Leek 0.001 0.039 14 Loppersum 0.067 -0.029 4 Marum -0.098 0.010 20 Menterwolde -0.035 0.017 20 Oldambt -0.006 0.018 21 Pekela 0.004 -0.023 7 Slochteren 0.116 -0.044 2 Stadskanaal 0.051 -0.030 34 Ten Boer -0.131 -0.020 7 Veendam -0.045 -0.050 7 Vlagtwedde -0.013 0.028 19 Winsum -0.043 -0.133 1 Zuidhorn 0.052 -0.035 15
18 The number of significant pairwise correlations is showed in the last column. Groningen exhibits the most pairwise price correlations (49), followed by Westerveld (43), Emmen (39) and Leeuwarden (39). As expected, Groningen exhibits the most price correlations. This result suggests that Groningen may indeed be treated as dominant. It is surprising that Westerveld has the second most price correlations, because it is a very small municipality and from a theoretically point of view not an eligible candidate to be dominant.
5.3.2 Confirmation of the exploratory analysis
Given our a priori expectation of Groningen being dominant and the results in the previous section, now the method to determine the dominant municipality used by Holly et al. (2011) will be applied to Groningen. The bivariate VECM(k) model of (7) and (8) is estimated to determine the long-run causality properties of Groningen to the other municipalities and vice versa. The optimal lag-order selection is based on the LR test statistic. The final prediction error (FPE), Akaike’s information criterion (AIC), Bayesian information criterion (BIC), and Hannan-Quinn information criteria (HQIC) are used as complements to the LR test. The maximum lag-order is set to four. Table 3 displays the results. In 46 of the 54 equations, the error correction coefficient is significant for the other municipality. This means that Groningen is long-run causing housing prices in those 46 other municipalities. It is unclear why the error correction coefficient is not significant for the eight municipalities that are left, and it is hard to think of any economic theory that could explain this result. 15 of the 54 error correction coefficients are significant for Groningen. Therefore, it is assumed that only 15 other municipalities are long-run causing prices in Groningen. Most of these municipalities have a large number of housing transactions (e.g. Assen, Hoogeveen, Meppel, Leeuwarden), or are located near Groningen (e.g. Tynaarlo, Bedum, Ten Boer). This may be an explanation why these municipalities are long-run causing housing prices in Groningen. For a few other municipalities it remains unclear (e.g. Midden-Drenthe, het Bildt).
The results presented in table 3 indicate that Groningen could indeed be treated as dominant. As a final test for the eligibility of Groningen as a dominant municipality, the Wu-Hausman test for exogeneity is applied. The test statistics are reported in tables 4 and 5. These results are discussed in sections 5.4.1 and 5.4.2.
5.4 Spatial-temporal housing price diffusion model estimation
19
Table 3. Error correction coefficients in a bivariate VECM(k).
EC equation for Groningen (7) EC equation for other municipalities (8) Municipality i Error-correction coefficient (𝝓𝟎,𝒊) Error-correction coefficient (𝝓𝒊,𝟎)
Aa en Hunze -0.123*** 0.007 Assen -0.314*** 0.381*** Borger-Odoorn -0.001 -0.010*** Coevorden -0.009 0.050** De wolden -0.016 -0.087*** Emmen -0.003 0.022** Hoogeveen -0.057* -0.112*** Meppel -0.155*** -0.093* Midden-Drenthe -0.062* 0.089 Noordenveld 0.000 -0.006*** Tynaarlo -0.118** 0.066 Westerveld -0.005 -0.077*** Achtkarspelen -0.031 0.147* Dantumadiel -0.001 0.031*** De Friese Meren -0.026 -0.082*** Dongeradeel 0.016 0.088** Ferwerderadiel -0.051 0.358** Franekeradeel -0.045 0.279*** Harlingen -0.152*** 0.662*** Heerenveen -0.005 0.022** het Bildt -0.067** 0.294* Kol. en Nieuwkruisland -0.031 0.186 Leeuwarden -0.346*** 0.279** Leeuwarderadeel -0.005 -0.042** Littenseradiel -0.015 -0.099*** Menameradiel -0.035 0.191*** Ooststellingwerf -0.007 0.047*** Opsterland 0.000 -0.015*** Smallingerland -0.050 0.174* Súdwest-Fryslân -0.009 -0.109*** Tytsjerksteradiel -0.001 -0.008** Weststellingwerf -0.014 -0.110*** Appingedam -0.142** 0.370*** Bedum -0.096* 0.282** Bellingwedde -0.025 0.134** De Marne 0.015 0.052 Delfzijl 0.010 0.047* Eemsmond -0.031 0.280*** Grootegast -0.056* 0.104 Haren 0.004 0.055*** Hoogezand-Sappemeer 0.023 0.158* Leek -0.032 -0.092** Loppersum -0.045 0.287** Marum -0.007 0.175*** Menterwolde -0.030 0.201** Oldambt -0.026 -0.073*** Pekela 0.008 0.072** Slochteren -0.008 0.312*** Stadskanaal -0.009 0.043** Ten Boer -0.083* 0.156 Veendam -0.182** 0.164 Vlagtwedde -0.050* 0.248*** Winsum 0.006 0.246** Zuidhorn 0.003 0.138*** Notes: *, **, and *** represent significance at the 10%, 5%, and 1% level respectively.
20 5.4.1 Model estimation using the first-order binary contiguity matrix
The spatial weight matrix used is the row-normalized first-order binary contiguity matrix. The results are presented in table 4. The second column represents the long-run convergence towards neighbouring municipalities. The error correction term that captures price deviations from neighbouring municipalities is statistically significant in 44 out of 55 municipalities. Moreover, all the estimates have the right sign. They are all negative, meaning that housing prices in municipality i are converging to the housing price equilibrium between adjacent municipalities. A more negative error correction coefficient means that the price adjusts faster to the equilibrium. 6 of the 11 municipalities that don’t show convergence to neighbouring municipalities are located next to or near the border of other (Dutch and/or German) municipalities that are not part of the sample. It could be that these six municipalities interact with municipalities outside the sample and that this is the reason for not showing convergence towards municipalities inside the sample. There is no evidence for province borders playing any role in long-run housing price properties.
The third column represents the long-run convergence towards an equilibrium between the dominant municipality, Groningen, and the other municipalities. The results present mixed evidence on long-run convergence towards Groningen. The error correction term that captures deviations of municipality i housing prices from Groningen prices is statistically significant in only 12 of the 54 municipalities. This is in contrast with the previous outcomes presented in table 3, which showed that prices in Groningen are long-run causing prices in 46 other municipalities. A factor that could be responsible for this result is that the short-run prices are affected by a long-run equilibrium, but this an equilibrium between prices in neighbouring municipalities and not an equilibrium between a municipality and Groningen. This explanation is more likely for municipalities located closer to Groningen. For some municipalities an explanation for the lack of convergence towards Groningen could be the presence of earthquakes. Especially those municipalities located in the earthquake area are likely to follow a different housing price pattern than Groningen. Furthermore, for all 12 significant estimates, the sign is opposite of what is expected. The positive sign implies divergence from prices in Groningen. A more positive error correction coefficient means that prices diverge faster from the equilibrium. These 12 municipalities are spread over the map, such that there is not any pattern that can be discovered. Migration towards the dominant municipality could be an explanation. Housing prices in the municipality that is left behind may decrease, while prices in the growing municipality, Groningen, may increase6. Moreover, the Wu-Hausman statistic is significant in 20 out of 54 equations, meaning
that for those municipalities the null hypothesis of exogeneity can be rejected. These results raise questions on the dominancy of Groningen.
6 Meen (1999) suggests that people move from high price regions to low price regions, resulting in a ripple effect. The
21 Besides the long-run effects, the model also allows for short-run and spatial effects. Those effects are reported in the columns four to seven. The number of lags used are reported in columns 9 to 11. For lag-orders higher than one, the estimates reported are the sum of the lagged coefficients. The associated standard errors are reported between the brackets. Because both the dependent and the regressors are logarithms, a one percent change in the regressor leads to a x percent change in the dependent variable. For example, a 1% increase in housing prices in Groningen one time period before results in an increase of 0.33% in current Groningen prices. Surprisingly, the estimates of the own lag effects are statistically significant for only 15 price municipalities. It was expected that it would be significant for all municipalities, because it is likely that prices are time dependent. The neighbour lag effects (the spatial effect) are also mainly insignificant. Moreover, they are mostly negative. This is in contrast with the findings of Holly et al. (2011), Helgers and Buyst (2016), and Gong et al. (2016). They all found strong evidence for spatial spillover effects from the neighbouring regions. In most equations, the neighbour lag effect is included with only one time lag, which corresponds to half a year. It could be that the spatial effect needs more time before it reaches neighbouring municipalities.
Following the BIC, the Groningen lag effect is included in only 13 price equations. In all these equations, the lag effect is positive and significant. However, it is unclear why it is these equations that the Groningen lag effects should be included. There is not some sort of pattern that can be discovered. The contemporaneous effect of Groningen on the other municipalities is positive and statistically significant in 31 of the 54 equations. It seems to be the case that this effect is rather insignificant for municipalities that are located further away from Groningen.
5.4.2 Model estimation using the inverse distance matrix
22
Table 4. Estimation of the spatial-temporal housing price diffusion model, using the first-order binary contiguity matrix. Municipality i EC1 (𝝓𝒊,𝒘) EC2 (𝝓𝒊,𝟎) Own lag
24 Hoogezand-Sappem. -0.742*** 0.193* -0.140 -0.632** - 0.276 1.11 1 1 0 0.387 (0.175) (0.108) (0.136) (0.257) (0.250) Leek -1.121*** -0.038 0.215 -0.230 - 0.595** -1.28 1 1 0 0.524 (0.232) (0.099) (0.149) (0.242 (0.263) Loppersum -1.082*** 0.195 -0.231 -0.554 - 0.262 -1.81* 1 2 0 0.554 (0.294) (0.190) (0.158) (0.522) (0.375) Marum -0.903** 0.096 -0.038 0.167 - 0.796* -1.29 1 1 0 0.310 (0.350) (0.175) (0.183) (0.390) (0.452) Menterwolde -0.908*** 0.221 0.015 -0.248 1.163*** 0.645* -2.01* 1 1 1 0.379 (0.264) (0.169) (0.145) (0.383) (0.423) (0.371) Oldambt -0.333 0.012 -0.936*** 0.127 0.736*** 0.691*** -1.91* 2 1 1 0.545 (0.218) (0.085) (0.296) (0.188) (0.234) (0.213) Pekela -1.114*** -0.057 0.143 -0.299 - 0.310 -0.37 1 1 0 0.489 (0.224) (0.106) (0.146) (0.288) (0.336) Slochteren -0.600*** -0.091 -0.079 -0.012 - 0.778** -0.84 1 1 0 0.358 (0.216) (0.176) (0.146) (0.304) (0.70) Stadskanaal -0.124 -0.020 -0.458*** 0.981** - 0.462 0.03 1 4 0 0.480 (0.237) (0.105) (0.160) (0.469) (0.280) Ten Boer -0.645* 0.132 -0.119 -0.219 - 1.055*** -2.09** 1 1 0 0.273 (0.365) (0.252) (0.164) (0.326) (0.371) Veendam -0.335** -0.020 -0.273* -0.206 - 0.672** 0.62 1 1 0 0.341 (0.128) (0.103) (0.148) (0.233) (0.257) Vlagtwedde -0.732*** -0.050 0.095 0.145 - 0.670 -0.51 1 1 0 0.405 (0.217) (0.135) (0.155) (0.428) (0.537) Winsum -0.822*** 0.075 -0.066 0.006 - 0.560** 0.27 1 1 0 0.510 (0.231) (0.159) (0.125) (0.245) (0.263) Zuidhorn -0.843*** 0.161 -0.062 0.064 - 0.367 -2.42** 1 1 1 0.334 (0.267) (0.133) (0.162) (0.251) (0.269)
Notes: *, **, and *** represent significance at the 10%, 5%, and 1% level respectively.
The model for Groningen (the dominant municipality) is represented by equation (11). The model for the other (non-dominant) municipalities is represented by equation (13). “EC1”, “EC2”, “Own lag effect”, “Neighbour lag effect”, “Groningen lag effect”, “Groningen contemporaneous effect” relate to the estimates of 𝜙𝑖𝑤, 𝜙𝑖0, ∑ 𝑎𝑖,𝑙
𝑘𝑖,𝑎 𝑙=1 , ∑ 𝑏𝑖,1 𝑘𝑖,𝑏 𝑙=1 , ∑ 𝑐𝑖,𝑙 𝑘𝑖,𝑐 𝑙=1 , and 𝑐𝑖,0 respectively.
25
Table 5. Estimation of the spatial-temporal housing price diffusion model, using the inverse distance matrix. Municipality i EC1 (𝝓𝒊,𝒘) EC2 (𝝓𝒊,𝟎) Own lag
27 Hoogezand-Sappem. -0.539*** 0.071 -0.189 -0.301 - 0.343 0.41 1 1 0 0.318 (0.158) (0.105) (0.142) (0.335) (0.268) Leek -1.308*** -0.074 0.281* -0.052 - 0.443* -1.51 1 1 0 0.589 (0.236) (0.092) (0.149) (0.325) (0.257) Loppersum -0.905*** 0.009 -0.187 0.152 - 0.141 0.90 1 1 0 0.498 (0.265) (0.172) (0.159) (0.550) (0.419) Marum -1.119*** -0.083 0.200 2.596*** - 0.236 0.47 1 3 0 0.540 (0.299) (0.163) (0.160) (0.665) (0.410) Menterwolde -0.992*** 0.211 0.077 -0.509 1.192*** 0.539 1.21 1 1 1 0.405 (0.257) (0.155) (0.148) (0.633) (0.428) (0.387) Oldambt -0.811*** 0.020 -0.615** 0.335 0.442** 0.432** 1.05 2 1 1 0.652 (0.248) (0.074) (0.291) (0.356) (0.215) (0.204) Pekela -1.319*** 0.105 0.177 -0.068 - 0.101 -0.55 1 1 0 0.515 (0.267) (0.123) (0.148) (0.501) (0.348) Slochteren -0.687*** -0.246 0.102 0.058 - 0.686* 0.01 2 1 0 0.440 (0.199) (0.161) (0.304) (0.498) (0.368) Stadskanaal -0.266 0.087 -0.487*** 0.573 - 0.566* -1.54 1 1 0 0.236 (0.284) (0.140) (0.169) (0.383) (0.329) Ten Boer -0.704*** 0.057 -0.073 -0.360 - 0.961** -1.02 1 1 0 0.356 (0.239) (0.159) (0.159) (0.536) (0.383) Veendam -0.340** 0.007 -0.289* 0.072 - 0.568** 0.39 1 1 0 0.324 (0.155) (0.108) (0.151) (0.326) (0.263) Vlagtwedde -0.989*** 0.157 0.115 0.641 - 0.470 -0.22 1 1 0 0.367 (0.286) (0.181) (0.153) (0.681) (0.543) Winsum -0.579*** -0.171 -0.083 -0.015 - 0.409 1.75* 1 1 0 0.448 (0.188) (0.136) (0.147) (0.468) (0.320) Zuidhorn -1.232*** -0.009 0.668** -0.195 - -0.088 -0.04 2 1 0 0.547 (0.231) (0.089) (0.264) (0.334) (0.229)
Notes: *, **, and *** represent significance at the 10%, 5%, and 1% level respectively.
The model for Groningen (the dominant municipality) is represented by equation (11). The model for the other (non-dominant) municipalities is represented by equation (13). “EC1”, “EC2”, “Own lag effect”, “Neighbour lag effect”, “Groningen lag effect”, “Groningen contemporaneous effect” relate to the estimates of 𝜙𝑖𝑤, 𝜙𝑖0, ∑ 𝑎𝑖,𝑙
𝑘𝑖,𝑎 𝑙=1 , ∑ 𝑏𝑖,1 𝑘𝑖,𝑏 𝑙=1 , ∑ 𝑐𝑖,𝑙 𝑘𝑖,𝑐 𝑙=1 , and 𝑐𝑖,0 respectively.
28
6. Conclusion
This paper carefully examines the spatial and temporal diffusion of housing prices in 55 municipalities in the north of the Netherlands, based on half yearly prices covering the period 1993 to 2017.
The paper starts with an analysis of the stationarity of the housing price series. The augmented Dickey-Fuller test shows that all the series are stationary after first differencing, except for the municipality Harlingen, which is I(0). After that, the Engle-Granger cointegration test reveals that the housing markets are highly interdependent, since 94.2% of the 1485 pairs of housing markets are cointegrated. An important aspect of this paper is the inclusion of a dominant municipality in the model. Multiple approaches are used to determine which municipality could be classified as dominant. As an exploratory analysis, the Pesaran and Yang (2019) dominance estimator and the Bailey et al. (2015) price correlation approach are applied. As expected, Groningen comes forth as an eligible candidate. Next, the approach of Holly et al. (2011) is applied to verify the dominance of Groningen. A bivariate VECM(k) is estimated to determine the long-run causality between housing prices in Groningen and the other municipalities. The results show that Groningen prices are long-run causing prices in many other municipalities, while prices in a relatively few other municipalities are long-run causing prices in Groningen. As a final test for the dominance of Groningen, the Wu-Hausman test is applied. When the binary contiguity matrix is used to estimate the model, the Wu-Hausman test statistics shows mixed evidence on the dominance of Groningen. In contrast, when the inverse distance matrix is used, Groningen prices are exogeneous in almost all the prices equations of the other municipalities. Except for the Wu-Hausman test statistic, the results of the model estimation using the inverse distance matrix are generally the same as when the binary contiguity matrix is used. The evidence of long-run housing price convergence towards an equilibrium between prices in neighbouring municipalities is high. In contrast, there is little evidence of long-run price convergence towards an equilibrium between the non-dominant municipalities and the non-dominant municipality. This result questions the existence of a ripple effect. Therefore, it also questionable whether there exists a dominant municipality, or whether Groningen is the right municipality to be treated as dominant. Besides the long-run effects, this paper also examined the short-run dynamics. Overall, the own and neighbour lag effects don’t seem to affect the housing prices. Also, the lagged Groningen prices are affecting only a few other municipalities.
Overall, little evidence is found for the existence of a ripple effect, but the results provide strong evidence on long-run housing price convergence towards an equilibrium between prices in neighbouring municipalities. This is a relevant result for policy makers, because it stresses the importance of considering spatial diffusion when shaping policy for the housing market. Local housing markets are affected by each other. Therefore, housing policies should not be targeted at local markets, but at a higher regional level.
29 are not included in the model could affect the housing market. For example, Helgers and Buys (2016) also include the GDP level. Moreover, some municipalities in the sample comprise of highly different characteristics that can affect the market. For example, the population density in Groningen is 31 times as high as in Westerveld. Finally, the model includes only one dominant municipality, while it is also possible that there are multiple dominant municipalities. It is possible that municipalities in the west of Friesland are more affected by Leeuwarden than by Groningen. Also, municipalities in the sample could be influenced by municipalities outside the sample. Further research could consider these problems. Another point of interest could be the influence of markets across the national border. It is possible that housing prices in border municipalities are affected by, for example, prices of German municipalities. Similar, Holly et al. (2011) study price shocks to London coming from housing price developments in New York. Further research could elaborate on this subject.
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Appendix
Table A.1. Descriptive statistics of the micro data.
# Municipality Obs. Mean Std. Dev. Min. Max.
32
Table A.2. Descriptive statistics of the aggregated data.
# Municipality Obs. Mean Std. Dev. Min. Max.
