Dominant Units and Spatial Dependence in Housing Markets

Dominant Units and Spatial Dependence in

Housing Markets

Tom van Nes (S2401614) January 16, 2018

MSc. Thesis

Abstract

This paper uses a recently developed method to analyse the temporal and spatial char-acteristics of a dynamic system of house prices in the Dutch province Drenthe. The analysis assumes a dominant municipality. A shock in the dominant unit aects the other municipalities in Drenthe through time and space. Identication of the dominant municipality is executed using established methods and a novel approach introduced in this paper. This novel approach attempts to single out the most central municipal-ities by viewing the province as a network. The ndings indicate that Meppel, and to a lesser extent Assen, are likely to be the dominant municipalities. Estimation of the dynamic system reveals that house prices in neighbouring municipalities have a sizeable inuence. Additionally, a shock to house prices in Meppel decays quickly and has the highest impact on sparsely populated municipalities.

Keywords: House prices, spatial dependence, dominant unit JEL Classication: C21, C23, R23

1 Introduction

In this paper the spatial and temporal characteristics of house prices in the Dutch province of Drenthe are studied. The incredible rise in house prices in Western countries have led to increased interest in the mechanisms that determine this surge of house prices. In the business centre of the Netherlands, known as the Randstad, prices have risen by an av-erage of 15% in one year (Marktinformatie Koopwoningen, 2017). Residential real estate occupies a large share of the total wealth of most citizens. As such, the price determinants of residential real estate are of great interest. The price paid for a house is not only due to its intrinsic value but consists of many more factors. Among these numerous factors are geographical traits, supply and demand dynamics and funding availability.

A part of the literature on the real estate market focuses on the inuence of spatial traits of house prices. The market in the United Kingdom in particular has been studied exten-sively, and a spatial pattern has been discovered. Price changes in one region or city often ripple out towards other regions. This pattern is referred to as the ripple eect. In the UK the ripple eect moves from the South East region, which includes London, to the rest of the country. The leading research on the temporal and spatial eects of changes in house prices comes from Holly et al. (2011). Their conclusion is similar to the general opinion stated above. Their research decomposed the entire UK Island into several regions. To add to the general knowledge of spatial traits of housing economics, this paper will focus on a single province in the Netherlands instead of the Netherlands as whole. Seeing as how residential markets can be very local in nature, it is important to focus on these local characteristics too.

An interesting human trait is the herd behaviour we tend to practice1_{. In the act of} ap-praising house prices, a large weight is attached to aspects of surrounding real estate. This means that house prices in two close regions will follow a similar trend. Further extending the herd analogue, some of the previous literature points to there being leaders in the price following process. In the Netherlands that would be Amsterdam for the rest of country (van Dijk et al.,2007), in the UK London appears to be the dominant region (Holly et al.,

2011) and Glasgow leads the herd in the Scottish Strathclyde region (Jones & Leishman,

2006). The dominant position of a region or city is often credited to migratory ows of workers that prefer to live in or close to the city where their work is located. Given the importance and volatility of house prices, eective housing policy will require knowledge of the existence of these dominant units. The examples mentioned in this paragraph so far are fairly obvious outcomes. For the Dutch province Drenthe, this is not as obvious. This makes Drenthe an interesting region to investigate. Dominant unit analysis will be performed using several methods. A novel method incorporates network theory. To com-pare the results of this novel method, I also perform the tests Holly et al. use in terms of selecting a dominant unit.

Using a dataset containing housing transactions in Drenthe during 1993Q1 and 2014Q4, the interregional dynamics of housing prices are studied. The rst half of the methodology is focused on determining the dominant unit(s) in the province of Drenthe. Three methods are included in this paper. The rst method borrows from network theory and denes the dominant municipality as the one that is most central in the network of municipalities. The second and third methods are common in spatio-temporal analysis of house prices. By estimating the long run error coecients between the price series and testing for weak exogeneity of each series a conclusion on the dominant entity in the system is reached. The second half of the methodology uses the evidence on the dominant unit to quantify

the inter-municipal relationships between house prices in all 12 municipalities in Drenthe. The coecient estimates are then used to construct impulse-response functions that put the relationships in perspective. The research question this paper will answer is:

Is there a dominant municipality in Drenthe and if so, which one(s)? How do house price changes in the assumed dominant municipality aect house prices in other municipalities in Drenthe?

The main results of this paper can be divided into two parts. Firstly, the analysis on the dominant municipality in the province Drenthe is executed. This paper nds that looking at the centrality of a municipality in the Drenthe network, Assen en Meppel come up as leading in house price changes. The other two measures deliver slightly dierent results. While Meppel is long run causal for most other municipalities regarding house price changes, Assen is only long run causal for about half of the municipalities. The dierence between the centrality measures and the other tests on dominance is small, and intuitively the outcome of the network analysis is solid. Secondly, the estimation results of the price equations that are the foundations of the dynamic system used to project inuences of a shock to the system are twofold. The outcome rendered by assuming Meppel as the dominant municipality is convincing and is compatible with the common literature. The coecients of the estimation procedure with Assen as the dominant municipality are unstable, giving rise to a diverging impulse response graph.

The paper contributes to the existing stock of literature in a couple of ways. First, similar work mostly focuses on house prices on a regional level. This ignores the local nature of housing prices. Spatial dynamics of house price movements are expected to play a larger role at the municipality level. By keeping the analysis limited to just Drenthe, this thesis lls the gap of spatio-temporal knowledge on this geographic level. Secondly, the combina-tion of network theory and dominant units in housing markets is an unexplored eld. The combination is well motivated in theory and delivers relatively sound results. Lastly, the research on house prices in Drenthe is very limited as the region does not receive as much attention as the housing market in the Randstad. Nevertheless, insights in rural markets are of equal importance.

The remainder of this paper is set up as follows: rstly, a short overview of relevant ex-isting literature is discussed. Then, the used dataset is elaborated on briey. The section thereafter presents the methodology applied in this paper. The subsequent section shows and examines the results. Finally, there is a conclusion that summarizes the main ndings and presents policy implications and further extensions to the used methodology.

2 Literature Review

There is a vast amount of literature available on the dynamics of house prices and their characteristics. This section highlights the theoretical grounds that support the methodol-ogy and results. The literature review is divided in several paragraphs to provide insights regarding the dominant unit selection and the estimation of the temporal and spatial dif-fusion of house prices.

Long run relationships in regional house prices

share of the literature focuses on long run relationships among regional house prices. The common theory is that house prices in dierent regions are cointegrated. Cointegration provides evidence of a long run relationship between two variables. Examples of work on this subject is the work of Alexander et al. (1994) and Macdonald and Taylor (1993), who nd that such relationships exist for British regions. More recent studies approach the long run convergence by using a pairwise approach developed by Pesaran (2007). This method shows that co-movement of two series requires the dierence between them to be stationary and have a constant mean. Abbott and de Vita (2013) employ this method but do not nd evidence of convergence in the long run for UK regional house prices. Cross-sectional de-pendence in housing transactions is also covered by Durán and Elhorst (2017). Extending the work of Pesaran (2004; 2015), Durán and Elhorst use the cross-sectional dependence test (CD) and nd evidence in favour of strong and weak cross-sectional dependence in the housing market of the northern provinces in the Netherlands.

Short-run: the ripple eect

Other research focuses on short term causality between house prices. Meen (1999) notes that, while short term movements can be very large, in the long run prices will adhere to an equilibrium-like price pattern. A change in house prices in one region tends to ow to other regions. This spatial diusion of regional house prices is referred to as the ripple eect hy-pothesis. Early work on this hypothesis is done by Giussiani and Hadjimatheou (1991) by including changes in London house prices in their regression for other regions. Meen does a similar study on the UK house market and comes up with four explanations for the ripple eect. Households take advantage of dierences in house prices between regions. Related to this, he argues that buyers moving from regions with a high price average cause the price level in the destination region to move upwards as well. Muellbauer and Murphy (1994) nd that this consideration also holds for investors who see increased returns in lower-value regions. Price appreciation may exist because of investment intentions, not purely consumption intentions. Furthermore, search costs and information asymmetry allow for spatial arbitrage to exist, reinforcing the ripple eect. Lastly, regional price patterns can exist even though no links between regions are apparent.

The Dutch housing market is investigated by van Dijk et al.(2007). In order to investigate clustering of regions they develop a latent class panel time series model. The designation of a region to a cluster is based on the relationship between house prices and macroeconomic variables, as well responses to shocks in house prices. Van Dijk et al. nd that the regions can be divided in two classes. A shock in the dominant unit is propagated to class one rst and ows to to the regions in class 2. Amsterdam is used as a starting point, and serves a purpose as dominant unit. Drenthe amongst others belongs to the class that is experiencing the eects of a house price shock in Amsterdam at a later stage.

The ripple eect on a local level

Ripple eect analysis is not limited to studies on a regional level. From a theoretical per-spective ripple eects are not perfectly compatible with the supply and demand mechanism in housing markets. Demographics and economic conditions dier signicantly across re-gions (Canarella et al.,2012;Ashworth & Parker,1997). Jones and Leishman (2006) argue that local housing markets are likely to be stronger on a local level than on a regional level. The underlying theory is that housing migration is of a greater scale on a local level. This leads to more signicant ripple eects. By testing for Granger causality among Glasgow and other local housing markets, Jones and Leishman nd that Glasgow acts as a leading market in the local government region Strathclyde, but not for every local housing market. The VAR approach in Jones and Leishman's paper conrms the Granger causality out-come. Additionally, consumer demand for housing is aected by neighbourhood eects as these eects impact the choice of housing location (Ioannides & Zabel,2003). Moreover, the local nature of spatial relationships between housing markets is attributable to the way residential real estate commonly is valued. House price appraisers base their valuation on characteristics of comparable real estate. Examples of these characteristics are: time since the sale of the comparable, location or size of the rooms (Brueggeman & Fisher,2006). The spatial aspect of house prices

An important aspect of spatial analysis is procedure chosen to construct the spatial weights matrix W. A spatial weight matrix quanties distances between selected units. Spatial weights matrices are a crucial part of spatial econometric analysis and come in many forms. Common specications are (Getis & Aldstadt,2010):

1. Spatial contiguous neighbors 2. Inverse distance

3. Lenghts of shared borders

4. Bandwidth as the nth nearest neighbor distance 5. Ranked distances

The driving force behind the choice of the spatial weights matrix should always be un-derlying theory. In hedonic models of housing price estimation the most common spatial weight matrix is the distance-decay matrix: the importance of each spatial unit decays as distance increases (Baranzini et al.,2008).

Dominant units

One of the aims of this paper is to determine a leading unit in terms of house price changes. The theoretical base for assuming a dominant unit is the migratory ow of workers (Zabel,

2012; Cameron & Muellbauer, 1998). Historically, workers will move to residential areas that are within their budget while being close to their workplace. In a consumer demand framework, Kohlhase (1986) shows that labour and housing demand are complementary variables. The choice of dominant units in a data set is not unique to spatial and tem-poral diusion analysis in house markets. In a paper by Konstantakis et al. (2015), a macroeconomic GVAR model is constructed. The construction of the model allows for several economies to have a dominant role in international trade. In order to determine these dominant economies, the authors start with the creation of a trade weight matrix. Using the results of Brody (1997), Konstantakis et al. claim that a system of economic interconnections depends on the ratio of the modulus of the sub dominant eigenvalues to the dominant one. The power of an economy can be determined by comparing the ratio of its eigenvalue to a given threshold.2 _{The dominant economies are then selected using} network theory measures. Network theory allows for the identication of the most central unit in a system.

Network theory is not an alien concept in economics. Goyal (2012) poses that network the-ory is relevant to economics for two reasons. Social interaction between individual agents is integrated in economic theory. Secondly, these social interactions allow for the transmission of imperfect or asymmetric information. Therefore network theory seems very applicable to real estate markets as they are governed by distorted information (Levitt & Syverson,

2008). In a recent study on spatial and temporal house price diusion, Teye and Aheleg-bey (2017) introduce the network approach to house price markets. Using the Bayesian Graphical Vector Autoregression technique they identify the most dominant provinces in the Netherlands. Drenthe is shown to be the most dominant province in the subperiod 2005Q3  2016Q1. The outcome is theorized to be a result of rural migration by seniors who migrate to less urbanized areas, see de Jong et al. (2016).

All in all, the theoretical grounds on house price dynamics are broad. As always there is room for extensions to prior research. This paper aims to add to current knowledge on dominant units in housing markets, and the dynamics that determine house prices in a rural region.

Given the existing literature I postulate the following hypotheses:

Hypothesis 1: The dominant subregion within a clearly dened region can correctly be de-termined by applying network theory to pairwise correlation coecients of municipal house price data.

An analysis of signicant pairwise correlations between house prices should uncover con-nected municipalities based on house prices. The most central municipality is assumed to act as a price leader in a region.

Hypothesis 2: The dominant municipality in the province of Drenthe is either Assen, Mep-pel or Hoogeveen. A combination of these is possible too.

As the network approach allows for multiple possible dominant units, this study will not limit its scope to one potential dominant unit. Judging by their individual importance regarding distance to a households' workplace, Assen, Meppel and Hoogeveen seem proper options for dominance in Drenthe.

Hypothesis 3: The ripple eect hypothesis holds on a municipal level.

Literature on housing economics emphasizes the local nature of housing markets. As such, spatial eects are expected to be very strong. The temporal aspect of the ripple eect hypothesis should be less relevant but still apparent. Geographical distance among all considered units is considerably smaller compared to the studies by Holly et al. (2011) and Helgers and Buyst (2016). That being said, the information individual buyers have should still be asymmetric. Therefore, the temporal ripple eect of a house price change should still be visible.

3 Data

The data used are house transactions that took place in the period between 1993Q1 and 2014Q4. To correct for ination, the dataset is deated by the CPI with 2010 as baseline. The region selected is Drenthe, a province in the north of the Netherlands. The values for the CPI are from the OECD. In this paper average square meter prices will be used. The choice for m2_{prices eliminates variability due to dierence in house size (Visser et al.,2008).}

The employed dataset belongs to a larger set of house properties constructed by the NVM3_. There are a total of 12 municipalities in Drenthe. The geographical layout of Drenthe is shown in Figure1. The methodology is divided into two sections: establishing the dominant unit(s) and estimating the dynamic system of house prices using the identied dominant units. The estimation procedure incorporates a spatial term. This spatial term is based on a spatial weights matrix. The spatial weights matrix quanties shared geographical borders between cross-sectional units in the dataset.

3_{Nederlandse Vereniging van Makelaars en Taxateurs, a Dutch branch of real estate agents and}

Figure 1: Map of Drenthe

Source: Provincie Drenthe

Table8in the Appendix describes the shared borders between municipalities. For compar-ison, a complete map of the Netherlands has been included in the Appendix. This paper limits itself to municipalities in Drenthe, meaning that interactions between regions in and outside of the sample are ignored. For example, one can expect that changes in house prices in the city of Groningen can have signicant inuence on bordering municipalities. Nevertheless, the study is limited to data from Drenthe as policy-making by institutions representing Drenthe can only inuence house prices in Drenthe. This assumes price inu-ence from Groningen or Zwolle is more or less exogenous as far as provincial policy-making is concerned. Moreover, the results of Teye and Ahelegbey (2017) provide evidence for the dominance of Drenthe as a province.

Figure 2: House prices per m2 _{in Drenthe from 1993Q1 to 2014Q4}

Municipality Mean Std. Dev. Min Max Obs Aa en Hunze 1298,57 482,49 463,18 1915,39 88 Assen 1106,56 422,36 414,63 1626,84 88 Borger Odoorn 1193,45 438,92 412,57 1759,55 88 Coevorden 1112,82 395,29 391,85 1578,38 88 Emmen 1035,45 366,06 402,48 1513,69 88 Hoogeveen 1143,01 415,05 410,71 1623,29 88 Meppel 1331,35 492,32 450,67 1852,43 88 Midden-Drenthe 1227,08 450,85 414,71 1786,97 88 Noordenveld 1251,90 447,12 443,99 1880,71 88 Tynaarlo 1330,51 495,77 497,55 1962,15 88 Westerveld 1387,79 510,83 449,38 2058,02 88 De Wolden 1401,31 500,87 500,15 1990,49 88

Municipality Mean Std. Dev. Min Max Obs Aa en Hunze 1316,92 577,91 162,52 3170,24 3393 Assen 1149,13 464,25 211,38 3272,55 11931 Borger Odoorn 1273,54 540,40 211,56 3217,44 3091 Coevorden 1135,43 482,77 205,01 3091,96 5198 Emmen 1062,57 444,12 214,36 3247,70 14790 Hoogeveen 1138,61 476,68 204,07 3021,64 7229 Meppel 1369,36 523,27 264,80 3031,68 5209 Midden-Drenthe 1295,59 507,72 227,15 3063,49 4338 Noordenveld 1308,61 531,46 215,43 3296,07 4759 Tynaarlo 1384,67 572,66 243,18 3242,75 4556 Westerveld 1408,87 592,99 253,05 3053,99 2562 De Wolden 1417,49 582,71 208,48 3285,36 2466

Table 2: Summary statistics: micro data

Two tables with summary statistics are presented. Table 1 shows the summary statistics of aggregated dataset which is used in estimating spatial and temporal dynamics. Aggre-gation of the data is done by taking the average of house price transactions from the micro dataset of each quarter. The summary statistics of the aggregated data reveal that house prices in the sparsely populated municipalities (De Wolden, Westerveld and Tynaarlo) tend to be higher per square meter. The standard deviations of these municipalities are higher as expected. Table2presents the summary statistics of the complete micro dataset that is used to perform the network theory measures when selecting a dominant unit. The means are higher compared to the aggregated data. Moreover, the minimum and maxi-mum values are further apart. This is due to the fact that the outliers are not averaged out. Tests regarding stationarity of the data are redundant. As will be highlighted in the section on methodology, the price equations will incorporate error correction mechanisms that allow for cointegration between the series. Cointegration between two time series exists if both series are not stationary in levels, but the dierence between both series is stationary (Granger,2004). There will be a test for the presence of cointegration.

4 Methodology

The methodology used in this paper is explained in two sections. Section 1 discusses the methods that are used to determine the dominant unit(s). Section 2 breaks down the econometric model that estimates the dynamic system used to work out the eects of a shock in the dominant municipalities house prices.

4.1 Dominant unit

would be the network of municipalities in Drenthe. The relations of interest are those between house transactions in dierent municipalities. Square meter prices do not lend themselves well for this analysis. Instead, pairwise correlations between house prices are used to nd signicant relations between municipalities without having to resort to multiple regressions. There are a few steps necessary to arrive at a conclusion. First, the correlation matrix R of pairwise correlations between house transaction prices is constructed. For each possible pair of municipalities a corresponding correlation coecient is calculated. The dataset suers from an unbalanced number of observations as the number of transaction taking place in one municipality most likely diers from the amount of transactions in another municipality. Thus, the method by Elhorst and Duran (2017) is used as it is designed to deal with an unbalanced number of observations when calculating a correlation matrix. By design the matrix R will be symmetric. The resulting correlation matrix R is a NxN matrix, with 1

2(N × (N − 1))unique elements. As there are 12 unique municipalities

included, N is equal to 12 and as such we have 66 unique elements in R. Correlation matrix R has elements rij (i, j = 1, ..., N ). Table 9 contains the calculated correlation matrix R

and can be found in the Appendix.

The correlation matrix R allows for the determination of the number of dominant munici-palities. The method applied is similar to the approach in Konstantakis et al. (2015). In their paper, the elements of the matrix to which the network theory methods are applied represent trade ows between countries. As explained by Konstantakis et al., it is possible to determine the number of dominant entities in an economic system by analysing the eigenvalue distribution of such a system. The distribution does not reveal which unit is the dominant unit. The identication of the dominant units is explained afterwards. Brody (1997) showed that the behaviour of a system describing economic interconnections is dependent on the ratio of the modulus of the sub dominant eigenvalues to the dominant one. The closer to zero a ratio is, the smaller the power of the entity is. Formally this amounts to:

Let λ(D) = λ(1) denote the dominant eigenvalue of the correlation matrix R and the non-dominant normalized eigenvalues as: ρ(i) ≡ |λ(i) \ λ(D)|, for i = 2, 3, ..., N, where N is equal to the number of municipalities in the dataset.

In line with Konstantakis et al. the threshold that determines dominance is assumed to be 0.40. Therefore the number of dominant municipalities in Drenthe is i∗_{, such that}

ρ(i∗) > 0.40.

As the number of dominant entities is established, it is possible to proceed to the identi-cation of the dominant municipalities. Again, the methodology is (partly) based upon the work by Konstantakis et al. In their study the identity of the dominant unit(s) is revealed by means of network theory.

The panel of included municipalities can be represented by a nite graph G(V,E), where V is the vertex set and E the edge set. The vertex set V is the set of nodes in the graph. In this paper each node represents a municipality. The edge set contains the row ele-ments of the correlation matrix R, essentially capturing all relationships between a given municipality and the other municipalities. The edge set E is assumed to be of the form E = {p1,1, . . . , p1N; . . . ; pN,N}. As a result, the edge elements pij (i, j = 1, ..., N ) represent

Prior to assessing the centrality of each node, it is important to note that the methodology of Konstantakis et al. is performed on a matrix containing elements that are either 0 or positive. This does not hold for the correlation matrix R that is used in this paper. There are pairwise correlations that have a negative sign, see Table 9. In order to be able to correctly form a conclusion on the centrality of the municipalities, the correlation matrix R is transformed into an adjacency matrix, A. For this transformation, this paper builds upon Bailey et al. (2016) and Zuo et al. (2011). Zuo et al. use an adjacency matrix to gain insights into connectivity within the brain-network. The adjacency matrix is constructed by replacing correlation coecients from the matrix by either a 0 or 1 depending on their statistical signicance: aij = ( 1, if pij is signicant 0, if pij is not signicant (1) Following Bailey et al. signicance for each pairwise correlation is determined by simply calculating the corresponding t-value and using Holm's procedure (Holm,1979) to establish signicance α:

t = p s

N − 2

1 − p2 (2)

where n is the amount of observations used to calculate the correlation coecient. Again, N is equal to the number of municipalities. Since this methodology involves evaluating numerous hypotheses, the problem of multiple testing arises: the more hypotheses that are evaluated, the higher the probability of a Type 1 error becomes. To control for the family wise error rate (FWER), the probability of a Type 1 error occurring, Holm's procedure is introduced. First, the p-values of all n individual tests for signicance of the correlation coecients determined using (2) are ordered according to:

p1 ≤ p2≤ ... ≤ pn (3)

Let H01, H02, . . . , H0nbe the associated family of hypotheses. For the correlation matrix R

constructed earlier, this means that n = 66 tests will be evaluated. For a given signicance level α, let k be the place of the p-value in the above order. Holm's procedure rejects a null hypothesis H0k if:

pk≤

α

n + 1 − k (4)

This ensures that α > F W ER. Using the constructed adjacency matrix A it is possible to examine which nodes in the graph are dominant. The following node theory measures will be used to quantify centrality of each node: degree centrality, altered based power and beta based power.

Degree centrality

For a graph G(V,E), degree centrality shows the number of ties a node is connected to. Degree centrality (DC) can be calculated using the formula below, keeping in mind that we use an adjacency matrix:

Following Konstantakis et al., the largest DC value belongs to the dominant municipality and the second largest DC value to the second dominant municipality.

Altered Based Power

The altered based power of a node takes into account the degree of centrality of surrounding nodes. Altered based power is given by the following formula:

AC_(i)= N X j=1  aij ∗ DC_(j)−1  (6) The motivation for this formula is that if the neighbours of a node are non-central, the node itself is considered to be central. A higher value of a node's altered based power corresponds with higher dominance.

Beta centrality

Beta centrality was developed by Bonacich (1987) as an extension to eigenvector centrality and can identify centrality power of a node not only with respect to adjacent neighbours but also for neighbours the node is not directly linked to. The formula for beta centrality is given by:

BC = (I − βA)−1A ∗ 1 (7)

where I is the identity matrix, β is a discount parameter, 1 is a column vector of ones and A is the adjacency matrix. Formula 7 returns a column vector of BC values. The BC value of a single node i is equal to the ith _{value in the resulting column vector. The}

discount parameter β reects the relation of the status of one node to all other nodes. A positive β signies a complementary relationship among the nodes while a negative sign assumes that one relationship precludes other possible relations. The magnitude of β is larger if further ties are taken into account. Since a correlation between house prices in two municipalities does not rule out other correlations a positive β seems t. The maximum value that Bonacich uses for β in his paper is 0.5. This paper takes a middle ground, choosing a value of 0.25 for β. Again, the larger the value of BCi, the greater the power

of that particular node.

To stay close to the methodology of Holly et al. (2011), two extra measures on dominance are considered. The network analysis can be compared to these two measures to validate the result of the network analysis. Holly et al. look at the outcome of the Wu-statistic testing procedure where every region is considered to be dominant in turn. This procedure is demonstrated in the next section since its interpretation hinges on the econometric model that is used to estimate the house price diusion over space and time. Furthermore, Holly et al. base their decision regarding the dominant unit on the error correction coecients in a cointegrating vector autoregression (VAR). There is substantial evidence that in the long run house prices in two related regions tend to return to a normal price pattern. Estimating cointegrating bivariate VAR models for every possible pair of municipalities provides information on the long run equilibrium between these pairs. The relevant form for this paper is shown in formula8.

Because this paper uses quarterly data, the parameter l is set to 4. The term φ(i,0) is

called the error correction coecient. If the error correction coecient in the equation for municipality i is signicant, we assume that the house prices in the other included munic-ipality are long run forcing with respect to the house prices in municmunic-ipality i. The house prices in a municipality with the most long run forcing relationships will be considered a dominant unit.

The choice of dominant unit in this paper will depend on a combination of the outcomes of the network centrality measures, cointegrating bivariate VAR and the Wu-Hausman exogeneity test. A last requirement is that the dominant unit has to make sense intuitively, i.e. make sense from an economic point of view.

4.2 Econometric model

The econometric model follows the framework of Holly et al. (2011), and is also applied in Helgers and Buyst (2016). The point of interest lies in the diusion of house prices in space and time, pi,t, where time is indexed by t = 1, 2, ..., T and space is indexed by i = 0, 1, ..., N.

Note that since there are 12 municipalities, the value of N from here on is 11. Furthermore, based on the methodology elaborated on in the previous section, the possibility of the existence of a single or more dominant municipality is assumed. If the selection of the dominant unit provides multiple dominant municipalities, estimation of the model is done separately such that each estimated model will assume only one dominant municipality. Shocks in the dominant municipality have an immediate impact on all other municipalities, while the immediate eects of a shock in other municipalities are non-existent. Lagged eects of shocks from non-dominant municipalities to the dominant municipality are not ruled out. The model allows for error-correcting mechanisms that incorporate equilibria among neighbouring municipalities, as well as the dominant municipality. For the dominant municipality, municipality 0, the price equation is written as follows:

∆p0,t = φ0,s p0,t−1− ¯ps0,t−1
+ a0+ k X l=1 b0,l∆p0,t−l+ k X l=1 c0,l∆¯ps0,t−l+ ε0,t (9)

For the other municipalities i = 1, 2, . . . , N, the following equation is estimated: ∆pi,t = φi,s pi,t−1− ¯psi,t−1
+ φi,0(pi,t−1− p0,t−1)

+ ai+ k X l=1 bi,l∆pi,t−l+ k X l=1 ci,l∆¯psi,t−l+ k X l=1 di,l∆p0,t−l+ ε0,t (10)

where ¯ps_i,t is the spatial variable for municipality i dened by ¯ ps_it= N X j=0 sijpjt, with N X j=0 sij = 1, for i = 0, 1, ..., N. (11)

The term φ(i,s)in formula10represents the error correction term that measures the speed

of adjustment of house prices in a municipality relative to house prices in neighbouring municipalities. Similarly, φ(i,0) depends on the price in the dominant municipality. The

term φ(i,0) is excluded in the price equation for the dominant unit. ai is a constant. The

lag length k. Testing for the signicance of multiple lags when the order of lags exceeds 1 is done jointly using a Wald test. The spatial variable is implemented as a simple average of prices in neighbouring municipalities. The weights sij are equal to 1/ni if i and j share

a border and zero otherwise, with ni being the number of neighbouring municipalities for i.

The resulting matrix is row-standardized as is common practice in spatial analysis (LeSage,

2008).

In the price equations, error correction dynamics are allowed, even though the dynamics theoretically depend on cointegration between the series. The current setup assumes the dominant municipality is cointegrated with its neighbours, and that other municipalities are allowed to be cointegrating with both the dominant and neighbouring municipalities. Furthermore, Holly et al. (2011) note that the price change in the dominant municipality, ∆p0,t, is included as a contemporaneous eect in the price equations for the non-dominant

municipality. This implicitly means that, conditional on the dominant municipalities' price variable and lagged eects, the shocks ε0,t are approximately independent across

munici-palities i. Consequently, it is assumed that ∆¯p0,tis weakly exogenous in the price equations

for i = 1, 2, ..., N. The assumption of weak exogeneity can be tested using Wu's proce-dure (1973). Wu's procedure is similar and asymptotically equal to Hausman's procedure (Hausman, 1978). Hausmans procedure tests for exogeneity by testing the signicance of the dierence between an OLS and IV model. The instruments used in the IV model would be ∆p0,t and ∆ps0,t. First the residuals of the price equation of the dominant municipality

are estimated by: ˆ ε0,t = ∆p0,t− ˆφ0,s p0,t−1− ¯ps0,t−1
− ˆa0− k X l=1 ˆ b0,l∆p0,t−l− k X l=1 ˆ c0,l∆¯ps0,t−l (12)

Then an auxiliary regression is run by including the estimated residuals in the price equa-tion ∆pi,t for i = 1, 2, ..., N :

∆pi,t = φi,s pi,t−1− ¯psi,t−1
+ φi,0(pi,t−1− p0,t−1)

+ ai+ k X l=1 bi,l∆pi,t−l+ k X l=1 ci,l∆¯psi,t−l+ k X l=1 di,l∆p0,t−l+ λiεˆ0,t+ ε0,t (13)

The coecient λi is tested using a Wald test in order to calculate the t-value for the

hypothesis λi = 0. If the hypothesis is rejected Wu's procedure tells us that the residuals

carry additional information that is not yet included in the other variables in formula

13. Rejection of the Wald test points to the endogeneity of the contemporaneous eect ∆p0,t. Dominance of a municipality implies that the contemporaneous eect of region 0 is

exogenous. The Wu test for weak exogeneity is performed for all municipalities, allowing each municipality to be dominant in turn.

Lastly, after having estimated every price equation separately using OLS, the entire system of equations is solved. Similar to Holly et al., a Generalized Impulse Response Function (GIRF) is simulated, showing the eects over time and space of a shock in the price of the dominant municipality. The GIRF method allows for contemporaneous correlations across regions and i and j for i, j = 1, 2, . . . , N. For elaborate discussion on GIRFs, see Pesaran and Shin (1998).

5 Results

5.1 Dominant unit

munic-ipality. The outcomes of the eigenvalue ratios are available in Table 11 in the Appendix. There is one ratio (0.38) fairly close to the threshold. This is for the given threshold of ρ(i∗) > 0.40. For reference, the calculated adjacency matrix A is included in Table 10 in the Appendix. In the construction of the adjacency matrix in formulas2 4a signicance level α of 5% is maintained.

Municipality Degree Centrality ABP BC

Aa en Hunze 0.09 1.00 -2.34 Assen 1.00 55.10 13.34 Borger-Odoorn 0.27 6.24 -1.50 Coevorden 0.27 6.87 -0.44 Emmen 0.09 1.00 -2.34 Hoogeveen 0.18 2.57 -2.88 Meppel 0.64 25.20 6.16 Midden-Drenthe 0.27 6.87 -0.44 Noordenveld 0.45 13.57 0.87 Tynaarlo 0.27 4.77 -2.09 Westerveld 0.18 2.57 -2.88 De Wolden 0.27 6.24 -1.50

Table 3: Centrality Measures

Error Correction Equation Error Correction Equation for Meppel (p0t) for Assen (p0t)

Regions EC Coef t-ratio R2 EC Coef t-ratio R2 Aa en Hunze ***0.185 2.61 0.309 -0.125 -0.94 0.229 Assen ***0.200 4.40 0.391 - - -Borger Odoorn 0.169 0.92 0.270 ***-0.253 -3.07 0.398 Coevorden 0.117 1.33 0.306 0.066 0.57 0.231 Emmen **0.232 2.17 0.374 ***-0.191 -2.67 0.408 Hoogeveen **0.095 2.23 0.297 ***-0.227 -2.60 0.412 Meppel - - - ***-0.251 -4.40 0.391 Midden-Drenthe ***0.144 3.09 0.331 0.077 0.59 0.357 Noordenveld ***0.158 3.42 0.370 0.038 0.26 0.375 Tynaarlo ***0.216 4.47 0.381 0.077 0.43 0.232 Westerveld 0.087 0.84 0.306 *-0.159 -1.89 0.247 De Wolden ***-0.512 -3.98 0.405 ***-0.214 -2.77 0.337

The error correction coecient of Meppel and Assen is calculated by estimat-ing the coecient of the error term φ(0,i) in ∆p0,t = φ0,i(p0,t−1− pi,t−1) + a0+

P3

l=1b0,l∆p0,t−l+P 3

l=1c0,l∆pi,t−l+ ε0,t. The reported R2 is the adjusted R2. ***

means the error correction coecient is signicant at the 1% level, ** at the 5% level and * at the 10% level.

Table 4: Error Correction Coecients in Cointegrating Bivariate VAR(4) of Log of Real House Prices of Meppel/Assen and other municipalities

outcomes in Table4, the impulse response of a shock to house prices in Assen can prove to be unstable. Looking at the signs of the error correction coecients, there is a clear dierence between the estimates of Meppel and Assen. A positive sign in this context means that if the prices in Meppel are high, house prices in the other municipality will adjust towards prices in Meppel.

Lastly, the choice of candidate for dominant unit is based on the Wu-Hausman statistic. In table5the Wu statistics are reported. A municipality is considered to be a good t for a dominant unit if its residuals are insignicant when incorporated in the price equations of other municipalities. The municipality is then considered weakly exogenous. There is little evidence of endogeneity of residuals. Exceptions are the residuals of Westerveld and Coevorden. According to the Wu-Hausman statistic, in the situation where these two municipalities are considered dominant there is a chance of simultaneity bias exist-ing. Simultaneity bias occurs when an independent variable is jointly determined by the dependent variable.

signi-AAH ASS BOO COO EMM HOO MEP MDR NOO TYN WES WOL AAH x 0.67 0.32 -0.10 -1.47 ***-2.84 -1.54 -1.26 **2.59 0.14 -1.29 0.37 ASS 1.59 x -0.05 *1.88 1.92* 0.28 0.98 0.27 1.53 -1.59 -0.25 0.95 BOO ***2.81 *1.99 x **2.07 0.03 -1.65 **-2.38 1.10 0.97 1.48 -0.07 0.06 COO -0.29 -0.18 1.40 x 0.33 -1.21 -1.45 0.36 -1.16 0.42 *-1.78 -0.74 EMM 0.11 -0.47 0.23 -0.11 x -0.42 *-1.77 -1.52 -1.10 *-1.67 -0.74 0.49 HOO -0.44 -0.75 -0.16 -0.52 0.82 x 0.85 -0.74 -1.59 *-1.67 -0.60 0.50 MEP 0.69 -1.07 -0.03 -0.36 -1.22 -1.52 x 0.81 -0.32 -0.29 0.12 0.80 MDR -1.25 0.85 -0.32 ***-2.95 -1.50 -1.48 -0.76 x -1.56 1.30 **-2.08 -0.20 NOO -1.59* -0.69 ***-3.39 0.94 0.01 -1.33 -0.10 **-2.10 x -1.34 *-1.93 0.32 TYN ***-3.84 ***-2.72 -0.61 *-1.86 -0.95 *-1.72 -0.03 **-2.20 **-2.27 x **-2.23 **-2.47 WES 1.45 -1.24 0.13 *-1.96 -0.28 0.08 0.35 -0.15 0.48 -1.06 x -0.53 WOL 1.08 -1.23 -0.37 0.15 0.37 0.87 0.27 -0.83 0.43 *-1.83 0.71 x

The rst row denes the assumed dominant municipality for each column. The rst column denes which municipality's price equation Wu's exogeneity test is performed upon. *** means the error correction coecient is signicant at the 1% level, ** at the 5% level and * at the 10% level.

Table 5: Wu Test Statistics

cant. The Wu statistic shows that Meppel as a municipality is weakly exogenous in 9 out of 11 price equations. A probable explanation for the outcome is that, looking at the map of the Netherlands, Meppel is located close to Zwolle. The ripple eect theory tells us that changes in house prices tend to ow from one region to another in a quicker fashion if the mutual distance is smaller. Zwolle is a relative large city and close to the Rand-stad. As conrmed by van Dijk et al. (2007), Amsterdam is the dominant region in the Netherlands. As a consequence, price changes in Meppel might react rst to price changes in Amsterdam in Drenthe. Other decent choices are De Wolden or Assen. De Wolden has the same characteristics as Meppel but is a far sparser municipality. Since all other literature uses densely populated regions as dominant unit, Meppel is better suited. Assen has high centrality values and is located at a geographical important point in Drenthe, close to Groningen. The number of signicant error correction coecients is the lowest of all regions however. Nevertheless, the price equations will also be estimated with Assen as the assumed dominant due to Assen being the most central municipality in terms of corre-lations. The Wu-test statistics do not indicate endogeneity issues with the residuals from test equations with Assen as the dominant municipality. As a nal check, the Johansen test for cointegration is performed. The resulting trace statistics are available in Table

5.2 Estimation results

There will be two tables with estimation results. First, a matrix of coecients is estimated for using Assen and Meppel as the assumed dominant unit. Tables 6 and 7 summarize the estimates yielded by equations 9 and 10. For the respective dominant unit, there is no error correction term with respect to the dominant unit (EC2 in the table). Also, the dominant unit lag eects are left out in the row of the dominant unit. The optimal lag orders for each region are shown in the three most right columns. They are selected based on the estimate with the lowest value for the Akaike Information Criterion. Estimates for the error correction coecients are found in column 2 and 3. The rst of the two columns, EC1, shows the error correction term relative to a municipalities' neighbours. A surprising result is the signicance of each of the error correction coecients relative to the neighbouring municipalities.

Regions EC1 EC2 Own lag Neighbour Meppel Meppel Wu-stat kia kib kic

eects Lag eects Lag eects Cont. eects

MEP ***-0.528 - -0.111 *-0.197 - - - 1 1 -(-4.59) - (-1.03) (-1.76) - -AAH ***-0.468 ***-0.351 -0.034 0.126 -0.011 ***0.530 -1.54 1 1 1 (-3.24) (-2.95) (-0.29) (0.56) (-0.07) (4.17) ASS **-0.314 -0.016 *-0.193 -0.228 **0.209 ***0.319 0.98 1 2 1 (-2.35) (-0.23) (-1.87) (2.70) (2.11) (3.66) BOO ***-0.445 ***-0.848 *0.188 -0.235 - ***0.779 **-2.38 1 1 0 (-3.63) (-5.77) (1.85) (-1.61) - (5.96) COO **-0.609 0.01 -0.066 -0.146 ***0.724 *0.227 -1.45 2 1 2 (-2.60) (0.10) (-0.04) (-0.57) (12.25) (1.75) EMM *-0.249 0.01 ***-0.399 -0.117 ***0.492 ***0.272 *-1.77 1 1 2 (-1.81) (0.09) (-3.62) (-1.10) (10.00) (2.79) HOO **-0.434 0.124 -0.347 -0.102 **0.278 *0.199 0.85 1 1 1 (-2.30) (0.98) (-3.30) (-0.68) (2.53) (1.80) MDR **-0.435 -0.19 -0.306 0.234 0.245 ***0.459 -0.76 2 1 1 (-2.51) (-1.47) (-2.03) (0.93) (1.48) (3.09) NOO **-0.216 -0.042 ***-0.366 0.202 *0.275 ***0.382 -0.10 1 1 1 (-2.04) (-0.54) (-3.16) (1.09) (1.69) (2.87) TYN **-0.374 -0.131 -0.07 ***-0.382 0.421 ***0.468 -0.03 1 1 1 (-2.41) (-1.47) (-0.85) (-2.98) (3.17) (3.43) WES **-0.464 *-0.370 0.109 0.317 - ***0.458 0.35 1 2 0 (-2.35) (-1.90) (1.00) (2.72) - (3.04) WOL *-0.422 -0.283 -0.017 0.189 **0.403 ***0.668 0.27 1 1 1 (-1.26) (-1.26) (-0.13) (-0.80) (2.08) (4.39)

T-ratios are reported in brackets below their corresponding coecients. *** means the error correction coecient is signicant at the 1% level, ** at the 5% level and * at the 10% level. Optimal lag lengths are reported in the far right columns. If the optimal lag length exceeds one, the reported statistic is an F-statistic that tests the joint signicance of the sum of lags. Each equation includes an intercept.

Compared to the results of Holly et al. and Helgers and Buyst, neighbouring municipalities appear to inuence each other signicantly more than prices of a entire region do. This is the expected outcome. Structural dierences in house prices between two municipalities lead to unrealistic arbitrage opportunities.

The coecients of the error correction terms can be interpreted as the speed of adjustment or convergence towards the equilibrium between the neighbouring municipalities. For ex-ample, the coecient φ0,s that represents speed of adjustment of house prices in Meppel

relative to neighbouring municipalities is −0.528. This says that in one quarter, the price in Meppel corrects for 52.8% towards the equilibrium between Meppel and its neighbours. The error correction coecients relative to Meppel are signicant for Aa en Hunze, Borger Odoorn and Westerveld. At rst, this appears to be contradictory to the bivariate VAR estimates in section5.1. Error correction coecients in aforementioned section are signi-cant for 9 out of 11 municipalities with respect to Meppel.

Regions EC1 EC2 Own lag Neighbour Assen Assen Wu-stat kia kib kic

eects Lag eects Lag eects Cont. eects

ASS 0.091 - **-0.235 **0.226 - - - 1 1 -1.06 - 2.12 2.14 - -AAH ***-0.716 ***0.079 -0.164 0.214 - ***0.491 0.67 1 1 0 -3.78 0.60 -1.42 1.11 - 3.12 BOO ***0.487 0.112 ***-0.867 *0.428 *0.468 ***0.549 *1.99 2 2 2 3.91 1.26 35.39 3.47 3.58 3.86 COO ***-0.657 ***0.313 ***1.154 0.209 0.171 ***0.339 -0.18 3 1 1 5.68 4.27 67.51 1.44 1.46 3.17 EMM **0.165 ***0.309 ***-0.502 -0.023 ***0.288 ***0.359 -0.47 1 1 1 2.51 6.26 -6.33 -0.35 3.36 4.5 HOO ***-0.320 ***0.329 ***-0.474 0.085 0.303 ***0.405 -0.75 1 1 1 4.79 0.09 -6.48 0.99 3.45 4.89 MEP 0.092 ***0.179 ***-0.437 0.024 **0.225 ***0.483 -1.07 1 1 1 1.06 3.75 -4.46 0.28 2.06 4.66 MDR ***0.367 ***0.358 ***-0.924 **0.492 - 0.209 0.85 2 1 0 2.66 3.43 69.05 2.65 - 1.62 NOO *0.205 ***0.378 ***-1.018 0.169 **0.461 ***0.387 -0.69 2 1 2 1.76 3.39 68.83 1.18 5.9 2.87 TYN *0.201 ***0.687 ***-1.438 *0.382 ***0.278 ***0.536 ***-2.72 3 3 1 1.92 -1.47 72.03 7.55 2.7 6.04 WES ***0.753 -0.022 -0.886 ***0.970 - **0.265 -1.24 2 2 0 5.84 -0.27 51.49 15.33 - 2.04 WOL ***0.792 *0.104 ***-1.294 0.157 **0.226 ***0.363 -1.23 3 1 1 8.9 1.99 73.22 1.36 2.15 3.67

T-ratios are reported in brackets below their corresponding coecients. *** means the error correction coecient is signicant at the 1% level, ** at the 5% level and * at the 10% level. Optimal lag lengths are reported in the far right columns. If the optimal lag length exceeds one, the reported statistic is an F-statistic that tests the joint signicance of the sum of lags. Each equation includes an intercept.

A possible explanation for this result is that prices do not necessarily converge to a equi-librium reached by Meppel, but in the long run prices adapt to prices in neighbouring municipalities. Since distances between each municipality are small, price movements in each municipality are likely to be quite intertwined. This is of course related to the arbi-trage scenario explained earlier. Turning to the short-term dynamics of the system, the dierent types of lagged eects are reported in columns 4 up to 7. Lag lengths are shown to be short, two lags being the maximum. Own lagged eects are not as relevant in move-ments of house prices. There are only 4 signicant lag eects reported. This is remarkable as economic intuition would predict the change in prices to be highly dependent on its own prices from previous years. Case and Shiller indicate the presence of positive serial correla-tion in single family house prices (1989). The same observation holds for the neighbour lag eects where only two of the twelve coecients are signicant. Coecients of lag eects of Meppel are quite relevant in the short term. Out of 11 coecients, 6 are signicant. For the contemporaneous eects, every single one of them is signicant. All contemporaneous eect coecients have positive signs, indicating that an increase in house prices in Meppel means that at the same time house prices in the non-dominant municipalities increase. E.g., for a 1% rise positive change in house prices in Meppel, house prices in Tynaarlo (TYN) experience an increase of 0.47%. The interpretation is expressed in percentages as house prices are transformed to logarithms. Unlike the ndings of Holly et al., there does not seem to be a relation between the distance to Meppel and the size of the coecient of the contemporaneous eect. On the other hand, the magnitude of the eect does appear to be related to the population density of the municipality. Emmen (EMM), Assen (ASS) and Hoogeveen (HOO) are all densely populated, while De Wolden (WOL) and Borger Odoorn (BOO) are sparsely populated. A general result of the house price equation seems to be short-run importance of the dominant municipality and the long run convergence of house prices to the neighbouring average.

Having looked at the dynamics of the system with Meppel as dominant unit, this paper now elaborates on the resulting estimates with Assen as the assumed dominant municipal-ity. The estimation results are presented in Table7. The outcomes for the error correction coecients measured relative to the neighbouring municipalities (EC1) are mostly signi-cant, except for Assen. Contrary to the results with Meppel as the dominant municipality, the error correction coecients measured relative to Assen (EC2) are mostly signicant. This is peculiar as the cointegrating VAR analysis did not give the same result when taking Assen as the dominant unit. The chosen framework and/or dataset might be structured in such a way that when correcting for error correction inuence from neighbouring mu-nicipalities, Assen does take on a strong dominant role. Furthermore, some of the signs of the error correction coecients are positive. In traditional cointegrating VAR models, this can indicate an unstable system. When a move from the equilibrium occurs, i.e. a positive shock in house prices in Assen, house prices in a positively signed municipality will move away from the equilibrium instead of correcting the dierence. Given that the setup employed by this paper diers from the traditional form, this does not necessarily indicate a problem. The consequences will be visible in the impulse response analysis that is demonstrated in the second half of this section.

have positive signs and can thus be interpreted in an opposite fashion compared to the own lag eects. Similar to the results with Meppel as the assumed unit, contemporaneous eects are largely signicant, indicating steady inuence of movements in house prices in Assen on house prices in the rest of Drenthe. Distance from Assen does seem to be related to the magnitude of the contemporaneous coecient. Aa en Hunze (AAH), Borger Odoorn (BOO) and Tynaarlo (TYN) are all direct neighbours. The estimation results presented in table6 and 7 give a feel for the structure of the house price dynamics between the 12 municipalities, but do not give a clear view on the complete inuence of changes in house prices in Meppel on house prices in the non-dominant municipalities. To visualize the spa-tial and temporal diusion of a shock on prices in Meppel, impulse response are plotted in a graph. The impulse response are generalized, meaning that unlike orthogonalized impulse responses, there is no ordering involved in deriving the impulse responses. Orthogonalized impulse response analysis is most common in VAR systems and place the eect of shocks in a particular sequence. In a generalized impulse response, there is no such predetermined sequencing.

Figure 3: Generalized Impulse Response Function (GIRF) of one unit s.e. shock to Meppel house prices

Figure 4: GIRF of a one s.e. shock to Meppel house prices on house prices in all munici-palities over time and space

Figure 5: Generalized Impulse Response Function (GIRF) of one s.e. shock to Assen house prices

In Figure4the results of the GIRF are plotted, taking distance from Meppel into account. The expected outcome would be that the further away from Meppel a municipality is from a spatial perspective, the slower a shock will be fully die out. Also, initial eects of the shock should theoretically be of a smaller magnitude the farther away a municipality is. The observed outcome does not comply with this expectation. As we can see, the shocks appear to be fairly heterogeneous with respect to time and distance. Logically, this is not unrealistic. Given that the distance between municipalities is quite small compared to the distance between larger regions e.g. provinces, the asymmetry in individuals' information is solved faster. The duration of the diversion from the equilibrium price is not a surprise. Dolde et al. (1997) nd that neighbouring regions generally catch up with price dierences in 4 quarters. As for the third hypothesis, the plotted impulse responses show little con-rmation for the existence of a ripple eect on a local level.

In Figure5 the response to a shock in house prices in Assen is plotted. As mentioned in the discussion on the estimated coecients of the system with Assen as the dominant unit, the house prices in all municipalities diverge and will eventually reach innity. Together with the low amount of signicant cases where Assen is long run forcing prices in other municipalities, there is enough evidence to reject the status of Assen as dominant unit. This conclusion reinforces the projection on the amount of dominant units in the network as shown in the section on possible dominant units. In Table11, there is no subdominant value above the set threshold of 0.40, meaning there is only one dominant unit possible.

6 Conclusion

This paper makes use of the methodology developed by Holly et al. (2011) to explore the spatial and temporal characteristics of house prices in the Dutch province Drenthe. Moreover, it presents a novel way of determining a dominant unit in a housing market. The dataset focuses on quarterly house prices per square meter over the period between 1993Q1 and 2014Q4 in each of the twelve municipalities in Drenthe.

The rst half of the analysis provides evidence of Assen and Meppel both display character-istics of dominant municipalities. Three tests are performed to assess which municipality in Drenthe is leading in house price changes. First, an correlation framework is constructed where only signicant pairwise correlations are retained. The leftover adjacency matrix A is exposed to methods that calculate the centrality of each municipality. The most central municipality is assumed to be dominant. The second method estimates cointegrating bi-variate vector autoregressive (VAR) models for each possible pair of municipalities. The resulting error correction coecients give rise to possible candidates for dominance. The third method assesses the validity of a municipality as a dominant one by investigating their exogeneity in price equations of the other municipalities. In section2two hypotheses on dominant were posited. The rst hypothesis expects network theory to have its place in predicting a dominant unit with regard to house prices. The network theory measures have signicant overlap with the outcomes of the cointegrating bivariate VAR model and exogeneity test in predicting the dominant unit. The second hypothesis expects either Assen, Meppel or Hoogeveen to be dominant looking at their status in Drenthe. Given the evidence presented in the rst half of the results, the hypotheses regarding Meppel are correct. Assen turns out to be a weak candidate for dominant municipality after estimating price equations and plotting impulse reponse functions. The three methods on dominant units do not support Hoogeveen as a dominant unit.

the equations, lagged dierences of prices in the dominant municipality, neighbouring mu-nicipalities and the municipality itself are added. These estimates are used to construct generalized impulse response functions (GIRF) to a shock in house prices in the dominant municipality. The course of the GIRFs are plotted allowing for a in depth analysis of the spatial and temporal diusion of a change in house prices. There is some heterogeneity in the estimation results with either Meppel or Assen as the dominant unit. The estimates with Meppel being dominant show house prices converging to the average of neighbour-ing house prices. Short run changes are mostly caused by movements in house prices in Meppel. Turning to Assen, there is a increased importance in the long run inuence of the house prices in the dominant unit. The estimated coecients with Assen as the assumed dominant unit exhibit explosive behaviour in the wake of a shock to house prices in Assen because of the positive signs of the error correction terms. The impulse response analysis for the Meppel estimates shows little evidence for the third hypothesis: a shock to house prices in Meppel appears to spread to all twelve municipalities equally quickly. These re-sults suggest that the ripple eect does not quite occur when conning the study to a single province. Furthermore, the plotted GIRF of a shock to Meppel house prices reveals that price changes tend to ow from densely populated areas like Meppel, to sparsely populated areas such as De Wolden.

There are some limitations to the paper. By just focusing on Drenthe, it is possible that some interactions are ignored. Given earlier literature, information ows from large sur-rounding cities like Groningen or Zwolle could prove to be of high inuence on house prices in Drenthe. The network centrality analysis used in determining the dominant unit analy-ses the matrix of pairwise correlations between house prices. It does so by examining the matrix of signicant correlations, the adjacency matrix A. The adjacency matrix does not distinguish between signs of the correlations. In the paper by Bailey et al., this information is preserved by setting up separate matrices for positive and negative signicant correlation coecients. It is not unthinkable that the sign of a correlation coecient of house prices in two municipalities matters for the interpretation of their relationship.

The ndings of this paper show that even on a local level, there is enough evidence that spatial dependence is still important on this scale. For policymakers responsible for one province this means that policy focused on just a single municipality has consequences for the entire region. Seeing as how important Meppel and Assen are for the province of Drenthe, they are likely to be given considerable attention. Policy-making should therefore include thorough analysis of spatial eects when addressing the house market.

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Appendix 1. Municipalities and neighbours

Municipality (abbreviation) Neighbours Municipality (abbreviation) Neighbours

Aa en Hunze (AAH) ASS, BOO, COE, MDR, TYN Meppel (MEP) WES, WOL

Assen (ASS) AAH, MDR, NOO, TYN Midden-Drenthe (MDR) AAH, ASS, COE,

HOO, NOO, WES

Borger Odoorn (BOO) AAH, COE, EMM Noordenveld (NOO) ASS, MDR, TYN

Coevorden (COE) AAH, BOO, EMM, Tynaarlo (TYN) AAH, ASS, NOO

HOO, MDR

Emmen (EMM) BOO, COE Westerveld (WES) HOO, MEP, MDR, WOL

Hoogeveen (HOO) COE, MDR, WES, WOL De Wolden (WOL) HOO, MEP, WES

Table 8

Appendix 2. Map of the Netherlands

Figure 6

Appendix 3. Correlation matrix R

AAH ASS BOO COO EMM HOO MEP MDR NOO TYN WES WOL

Appendix 4. Adjacency matrix A

AAH ASS BOO COO EMM HOO MEP MDR NOO TYN WES WOL

AAH 0 1 0 0 0 0 0 0 0 0 0 0 ASS 1 0 1 1 1 1 1 1 1 1 1 1 BOO 0 1 0 0 0 0 1 0 0 0 0 1 COO 0 1 0 0 0 0 0 1 1 0 0 0 EMM 0 1 0 0 0 0 0 0 0 0 0 0 HOO 0 1 0 0 0 0 1 0 0 0 0 0 MEP 0 1 1 0 0 1 0 0 1 1 1 1 MDR 0 1 0 1 0 0 0 0 1 0 0 0 NOO 0 1 0 1 0 0 1 1 0 1 0 0 TYN 0 1 0 0 0 0 1 0 1 0 0 0 WES 0 1 0 0 0 0 1 0 0 0 0 0 WOL 0 1 1 0 0 0 1 0 0 0 0 0

In the adjacency matrix a "1" indicates that the municipalities have a border in common, "0" indicates the opposite.

Appendix 5. Eigenvalue ratios

The values presented are the ratios of all non-dominant eigenvalues to the dominant eigenvalue. The numbers in the left column do not necessarily represent the order of municipalities maintained in this paper.

Appendix 6. Johansen test for cointegration

Regions Trace statistic for Assen Trace statistic for Meppel

Aa en Hunze **5.66 ***10.49 Assen - **4.23 Borger Odoorn **6.04 ***12.90 Coevorden ***9.61 ***12.19 Emmen **5.89 ***6.58 Hoogeveen ***8.31 ***6.50 Meppel **4.28 -Midden-Drenthe ***8.26 ***11.44 Noordenveld ***10.47 ***5.59 Tynaarlo **6.33 ***7.27 Westerveld ***7.16 ***13.04 De Wolden **4.39 ***10.42

The trace statistics reported are based on a the Johansen test with 2 lags. Rejection of the null hypothesis indicates existence of one or more cointegrating equations. ** indicates signicance at a 5% level, *** indicates signicance at a 1% level. Critical values of the test are 3.76 for the 5% level and 6.65 for the 1% level.