Heterogeneity in Dutch house price dynamics:
an empirical study on house price segments
Niels P. B. van der Windt (10525777)
MSc Thesis MSc Business Economics Specialization Real Estate Finance
University of Amsterdam
Thesis supervisor: prof. dr. Marc K. Francke Second reader: dr. Marcel A.J. Theebe
Abstract
This paper investigates the presence of heterogeneity in house price dynamics across price segments in the Dutch housing market. A novel aspect of this study is that it will explore heterogeneity across price segments, which has not been discussed in the existing literature. By means of error-correction models, house price changes in several price segments are explained. This study makes use of disaggregated price segment-specific data that cover the period between 1985 and 2013. Heterogeneity across price segments is confirmed by marked differences in the impact of house price determinants and the extent of mean-reversion. No significant differences are found in the degree of serial correlation across price segments. Although the significance of the findings is limited, the differences across price segments confirm the expectation of heterogeneity. From a policy perspective, regard should be given to the current findings when contemplating the desired effect of modern policies.
Table of contents
Abstract ... 2
1. Introduction ... 5
2. Literature review ... 8
2.1. House price determinants ... 8
2.2. House price models ... 10
2.3. Heterogeneity in house price dynamics ... 12
2.4. Hypotheses ... 14
3. Data ... 18
3.1. House price indices ... 18
3.2. Demand-side variables ... 19
3.3. Supply-side variables ... 21
3.4. Data description ... 22
3.4. Validity checks ... 25
4. The model ... 26
4.1. The error-correction model ... 26
4.2. Asymmetric error-correction ... 27
5. Empirical results ... 28
5.1. Long-term relationships ... 28
5.1.1. Determination of the long-term model ... 28
5.1.2. Final long-term models ... 30
5.1.3. Validity of the long-term models ... 33
5.2. Short-term relationships ... 34
5.2.1. Determination of the short-term model ... 34
5.2.2. Asymmetric error-correction ... 35
5.2.4. Validity of the short-term models ... 38
5.3. Heterogeneity across price segments ... 39
5.3.1. Demand-side variables ... 39
5.3.2. Supply-side variables ... 40
5.3.3. Extent of mean-reversion ... 41
5.3.4. Degree of serial correlation ... 41
5.3.5. Significance of findings ... 41
6. Conclusion ... 44
References ... 48
Appendices ... 51
Appendix A: Data sources ... 51
Appendix B: Figures ... 52
5 1. Introduction
The Financial Crisis has had an enormous impact on the Dutch housing market. After a period of rapidly increasing prices, they fell in excess of 19 percent between 2008 and 2013 (Statistics Netherlands, 2014). Several studies have tried to explain these large price fluctuations and possible overvaluations prior to the crisis (Francke
et al., 2009; Hofman, 2005; International Monetary Fund, 2009; Kranendonk and Verbruggen, 2008). In these
studies, macroeconomic variables (e.g. income and interest rates) were used to explain national house price movements. In other words, these studies considered the housing market as homogeneous.
However, Capozza et al. (2002) recognized heterogeneity in the U.S. housing market. They found that house price dynamics vary across regional U.S. markets. Turning to the Dutch housing market, The Dutch Central Bank (DNB) conducted a study (Galati et al., 2013) on heterogeneity in house price dynamics using subjective house prices on the basis of a self-assessment of households. They found that the speed of convergence and the efficiency of housing markets differ across market segments. Moreover, a study by Brounen and Huij (2004) explored the impact of fundamentals on house price developments. As a result, differences in the impact across geographical location, degrees of urbanization and house types are recognized. Furthermore, De Vries and Boelhouwer (2005) analyzed the link between house prices and housing supply in different regions of the Netherlands. They recognized that housing supply has a different impact on house prices in the main Dutch cities than in other regions.
The aforementioned studies by Brounen and Huij (2004), De Vries and Boelhouwer (2005) and Galati et
al. (2013) provide a first step in exploring heterogeneity in Dutch house price dynamics. Recently, Francke and
Van der Minne (2013) investigated the price development of houses bought by first-time home buyers. When comparing their study with the existing house price literature, one can conclude that the determinants of price changes in this segment are different from the ones affecting the overall housing market. This implies a degree of heterogeneity in house price dynamics across price segments. On the other hand, aside from literature studies it is expected that house prices across price segments respond differently. This is due to the characteristics of
6 participants in the three price segments, which ultimately lead to differences in the impact of house price determinants. Furthermore, the supply of housing varies across the price segments which might lead to heterogeneity in Dutch house price dynamics. Therefore, this thesis will investigate possible heterogeneity across price segments in the Dutch housing market. Building on previous findings, this study aims to answer the following research question: “Is there a degree of heterogeneity in house price dynamics across price segments in the Dutch
housing market?”.
In order to answer this question, detailed disaggregated data on real estate transactions and income statistics are provided by respectively the Dutch Association of Realtors and Property Consultants (NVM) and Statistics Netherlands (CBS). These datasets are used to create price segment-specific variables to improve the validity of this study. They cover the period between 1985 and 2013 and thus also include the impact of the Financial Crisis on the housing market. This research makes a distinction between three house price segments, namely the lower, middle and upper price segment.
The analysis is comprised of three parts. Firstly, the existing house price literature is reviewed to uncover the wide variety of house price determinants. Secondly, house price determinants are used to explain prices in the three segments. Both demand- and supply-side variables are taken into account. The analysis is conducted by using error-correction house price models which are common in the house price literature. An error-correction house price model is able to explain long- and short-run relationships between fundamentals and house prices, controlling for housing market characteristic. The second part of the analysis provides three models explaining the price changes in different segments. The last step in the analysis comprises of a comparison of the models to indicate whether heterogeneity across price segments exists. Studies by Capozza et al. (2002) and Galati et al. (2013) explain heterogeneity by differences in serial correlation and mean-reversion coefficients. At the same time, Brounen and Huij (2004) and De Vries and Boelhouwer (2005) explain heterogeneity by differences in house price determinants. In this paper both approaches are used, as a result house price determinants and their impacts, the degree of serial correlation and mean-reversion coefficients across price segments are analyzed.
7 A novel aspect of this study is that it will explore the presence of heterogeneity across price segments, which has not been discussed in the existing literature. Where most studies focus on heterogeneity in terms of serial correlation and mean-reversion only, heterogeneity will be explained by differences in the determinants at the same time. The study covers a long sample period including the Financial Crisis, possibly leading to novel insights. A new research area regarding heterogeneity makes this a valuable study in understanding house price dynamics in the Netherlands.
As heterogeneity implies, house prices may respond differently to house price determinants, and thus react differently to policies that have an influence on these determinants. Thus, this study is important for policy makers. Furthermore, real estate managers can take advantage of this research because they can use the results to predict house prices by segment. Lastly, because this study focuses on a new area of heterogeneity, not having been discussed in the existing literature, the findings are also relevant to the academic field.
This paper will proceed as follows. At first, it discusses the literature on house price models, house price determinants and heterogeneity. This review section will ultimately end in several hypotheses indicating a degree of heterogeneity. Secondly, the data used in this research are described. In that section, the data sources and the preparation of price segment-specific variables are discussed. The third section contains a detailed description of the model applied in this research. The next section comprises of an empirical analysis, in which the models for each price segment are defined. Subsequently, the models are compared using the hypotheses formulated earlier. Finally, the results are summarized in the concluding section. In addition, several implications and directions for further research are discussed.
8 2. Literature review
Before starting the empirical analysis, this section will discuss the relevant literature with regard to heterogeneity in housing markets. First this literature section will shed some light on house price determinants for both international and national housing markets. Furthermore, the house price models commonly used in the literature are discussed. Following the analysis on house price models, studies taking into account the heterogeneity in house price dynamics are discussed. This will be done by first reviewing international studies, whereas studies where heterogeneity in the Dutch housing market are considered subsequently. Finally, the research question will be translated into hypotheses, and introduced in the last paragraph of this chapter.
2.1. House price determinants
Based on empirical studies, house price determinants can be distinguished into three main types: macroeconomic drivers, institutional/geographic factors, and funding arrangements (Galati et al., 2011).
Macroeconomic drivers of international house price movements are documented in a number of papers, including Adams and Füss (2010), Englund and Ioannides (1997), Hort (1998), Malpezzi (1999), and Meen (2002). Adams and Füss (2010), for example, make use of aggregate data to explain house price movements for 15 countries. In their study, economic activity (as a function of real money supply, real consumption, real industrial production, real GDP, and employment), the long-term interest rate, and construction costs are used to explain house price movements. Furthermore, Englund and Ioannides (1997) also compared house price dynamics across several OECD countries. They showed that the lagged GDP growth rate and the real rate of interest have strong significant power in explaining real house prices. In addition, Hort (1998) explained real house price fluctuations in Sweden by real income, real user costs, and real construction costs. A study by Malpezzi (1999) used real income per capita, population and the mortgage interest rate to approximate real house price changes. Lastly, Meen (2002) compares real house price changes of the U.S.A. and the U.K. by using real disposable income, real interest rate, population, and real wealth as explanatory variables. To conclude, a wide range of variables is used to explain international house price movements. Despite the variety of variables, it is noted that the relevance of
9 income and the interest rate is confirmed in the majority of the international house price literature (e.g. Adams and Füss, 2010; Hort, 1998; Malpezzi, 1999; Meen, 2002).
With regard to the Netherlands, literature on house price determinants is often provided by public institutions such as the Netherlands Bureau for Economic Policy Analysis (CPB) and The Dutch Central Bank (DNB). Most of these house price studies choose relevant macroeconomic variables based on a comparison of existing studies on Dutch house prices. For instance, the CPB (Verbruggen et al., 2005) compared five Dutch studies on house prices. Subsequently, the CPB used a set of macroeconomic variables derived from this comparison for determining the effects of house price drivers. Furthermore, Francke et al. (2009) explain Dutch house prices by using the mortgage interest rate and modal labor income after an analysis of the current house price literature. Even when a single country is considered, it turns out that a wide variety of variables is present. The importance of the interest rate and income is also noted for the Netherlands.
The second group of drivers: the institutional/geographic factors, is generally discussed in studies comparing cities or regions, and uses disaggregated data. For instance, Green et al. (2005) found that highly regulated metropolitan areas show lower price elasticity of supply. Furthermore, Himmelberg et al. (2005) compared 46 metropolitan areas and stated that housing markets are a local phenomenon. They found that prices in supply-inelastic cities are higher in relation to rents, and the sensitivity of house prices to interest rates increases. Moreover, a study focusing on the Netherlands by De Vries and Boelhouwer (2005) showed that the housing supply can have a different impact across regions. Turning to demographics, Takáts (2012) compared 22 countries and found that demographics significantly affect house prices. Engelhardt and Poterba (1991) and Hort (1998) found the opposite. A study by Francke (2010a) focusing on price developments in regions with a shrinking population in the Netherlands, shows that the household size significantly affects price developments. However, no evidence was found of a significant impact on house prices by changes in the number of households or population. Considering studies on Dutch house prices, it is noticed that these rarely include demographic variables.
10 Lastly, house price fluctuations are explained by funding arrangements. Considering the role of mortgage finance, Tsatsaronis and Zhu (2004) analyzed house prices of three groups of countries formed by mortgage finance characteristics. Factors explaining house prices differ significantly across these groups. In addition, Calza
et al. (2013) found that shocks to monetary policy have a significantly stronger impact on residential investment
and house prices in countries with more flexible and developed mortgage markets. With regard to literature on funding arrangements in the Netherlands, Swank et al. (2002) contributed with a study regarding the tax treatment of owner-occupied housing and the impact on the housing market. It turns out that the favorable tax conditions in the Netherlands tend to create house price explosions. Additionally, a recent study by Timmermans (2012) showed that the impact of changes in the loan-to-value mortgage cap has an impact on house prices.
The drivers of Dutch house price fluctuations used in existing literature are summarized in Table 11. It can be concluded that a wide range of variables are used to explain house price changes. Dutch house price models commonly use macroeconomic variables, which can be seen in Table 1. The final selection of variables depends on several conditions (e.g. those governing the use in an error-correction model) and will be discussed in the data and methodology section of this paper.
2.2. House price models
Housing markets have some extraordinary characteristics. For instance, supply cannot immediately react to demand for housing. This is especially so in the highly regulated Dutch housing market (Swank et al., 2002). As a consequence, housing markets are characterized by low-elasticity of supply. This results in a housing market wherein supply and demand are rarely in equilibrium. Besides this feature, several studies recognize housing markets as inefficient markets (Case and Shiller, 1989; Malpezzi, 1999). For instance, Case and Shiller (1989) recognized that house prices are predictable; a change in house prices last year can be used to predict the change of house prices in this year.
1 Note that Francke et al. (2009) show that some variables do not meet the conditions of the model used in these studies (De Vries and Boelhouwer, 2004; Verbruggen et al., 2004). Therefore, findings of these studies have to be interpreted with caution. More about this subject will be discussed in the methodology section of this report.
11 Table 1. Variables explaining house price changes in the Netherlands
Article Variable (1) (2) (3) (4)c (5) (6)d (7)e Long-term model Construction costs X Housing stock X X X Real GDP X
Real household wealth X X
Real income a X X X X
Real (mortgage) interest rate X X X X X
User costs X
Short-term model
Deviation from long-run equilibrium X X X X X X
Housing stock X X X
Lagged house price X X X
Real (mortgage) interest rate X X X X X X X
Real GDP X
Real household wealth X
Real income a X X X X X X
Return on stock markets X
Scarcity of housing X
Seasonal or annual effects X X X
Unemployment rate X Statistics Sample period 1975 2002 1970 2002 1974 2004 1981 2003 1985 2003 1965 2009 1970 2011 Data frequency b HY Y Q Y Q Y Y R² Long term: Short term: 0.75 0.76 0.76 - - - 0.98 0.89 0.73 - 0.99 - 0.94 0.85 Articles: (1) Boelhouwer et al. (2004) (2) OESO (2004) (3) Hofman (2005) (4) Verbruggen et al. (2005) (5) Brounen and Huij (2004) (6) Francke et al. (2009) (7) Timmermans (2012)
Comments:
a. Diversity in type of income (e.g. gross income) b. M = Monthly, Q = Quarterly, HY = Halfyearly, Y =
Yearly
c. Brounen and Huij (2004) explain nominal house price changes
d. Francke et al. (2009) use a linear trend in their long-term model
e. Timmermans (2012) uses the LTV ratio as explanatory variable also
12 To allow for these peculiar housing market characteristics, an error-correction model (ECM) functions well as a house price model. Another advantage of an ECM is that it combines both levels and differences in house price determinants. An ECM consists of two models, namely a long- and short-term one. The long-term model estimates an equilibrium or long-run house price. The short-term model attempts to explain the short-run relationships and captures the impact from the deviation of actual house prices from the equilibrium price in the previous period. As a result, an ECM is able to explain long- and short-run relationships between fundamentals and house prices. Examples of error-correction models in the house price literature are Francke (2010b), Gallin (2006), Hort (1998), Malpezzi (1999) and Meen (2002). To use an ECM correctly, the variables in the model should satisfy several conditions. Remarkably, as is noted by Francke et al. (2009), numerous studies on Dutch house prices do not satisfy these conditions.
With regard to house price models, a distinction can be made in demand-side and demand-and-supply-side models. Demand-demand-and-supply-side models determine house prices by using variables that explain the demand for housing only, whereas demand-and-supply models add supply-side variables. In these latter models, there is a feedback from supply to house prices. Studies using demand-side models are Boelhouwer et al. (2004), Francke et al. (2009), and Hofman (2005). Francke et al. (2009) proposed to expand their model by using a supply factor, but Boelhouwer et al. (2004) did not find extra explanatory power of adding housing supply to their current model. In addition, Hofman (2005) stated that the supply of housing in the Netherlands is very inelastic and therefore does not take a supply-side into account. Studies that do not omit supply-side variables are OESO (2004), Verbruggen
et al. (2005), and Timmermans (2012). However, these studies did not find strong significant estimates for the
supply-side variables. In order to give a complete view on the determinants of house prices, the relevancy of supply-side factors will be analyzed in this paper as well.
2.3. Heterogeneity in house price dynamics
The majority of house price studies consider housing markets as homogeneous. In these studies macroeconomic variables are used to explain national house price fluctuation. However, a study by Capozza et
13
al. (2002) shows a degree of heterogeneity with respect to geographic locations by comparing US metropolitan
areas. They confirm heterogeneity in terms of differences in serial correlation and mean-reverting coefficients. The amount of serial correlation, also called autocorrelation, denotes how well a current change of house prices can be predicted based on past changes of house prices. Besides, heterogeneity can be explained by changes in mean-reverting coefficients, these show the extent of reversion of actual house prices to their long-run equilibrium; when mean-reverting coefficients are high, house prices return back to their fundamental value rather quickly. Turning back to the findings of Capozza et al. (2002), they found that serial correlation and mean-reverting coefficients vary between metropolitan areas due to differences in city size, population growth, real income growth, and real construction costs. More specifically, they document that higher population growth leads to more serial correlation in house prices in the different metropolitan areas. Moreover, serial correlation is higher in metropolitan areas with higher real income. Lastly, they show evidence that higher real construction costs result in a higher degree of serial correlation and a lower mean-reversion.
Another study, by Gao et al. (2009), clusters U.S. housing markets into two groups, namely cyclical (or volatile) and non-cyclical (or tame) housing markets. Their results show that cyclical markets have a higher degree of serial correlation. As a consequence, house prices in cyclical markets tend to have larger price cycles. Next to that, they concluded that serial correlation is higher in upward periods than in downward periods.
Turning again to a study regarding the Dutch housing market, DNB (Galati et al., 2013) studied heterogeneity in house price dynamics by using a large panel of Dutch households. In addition to findings of Capozza et al. (2002), they also found that the degree of urbanization, type of house, the year of construction, the type of mortgage financing and households’ sentiment about the medium-term outlook for income has an impact on the serial correlation and mean-reversion coefficient.
To summarize, studies by Capozza et al. (2002), Gao et al. (2009), and DNB (Galati et al., 2013) focused on heterogeneity in terms of serial correlation and mean-reversion. Besides that, heterogeneity can be explained in terms of the different impact of house price determinants. For instance, De Vries and Boelhouwer (2005) analyzed the link between house prices and housing supply in different regions of the Netherlands. They found
14 that housing supply has a different impact on house prices in the main Dutch cities (Amsterdam, Rotterdam, The Hague and Utrecht) compared to other regions. Moreover, Brounen and Huij (2004) arrived partly at the same conclusion and found that scarcity, which can be seen as a proxy for the housing stock, has a larger impact on the price development of the Noord Holland province in comparison to other provinces. In addition, Brounen and Huij (2004) show that the impact of fundamentals vary across different house types and degrees of urbanization. However, the study by Brounen and Huij (2004) has some caveats. At first, variables used in their study are not the commonly used in current literature on house prices (e.g. it does not take an income variable into account) and turn out insignificant in most cases. Besides that, they used aggregated macroeconomic variables to explain price developments across market segments and regions. For example, national unemployment rates and national scarcity indicators are used to explain price developments of regions and house types. However, scarcity might differ across regions and house types, thus scarcity rates have to be market segment- or house type-specific. More recently, Francke and Van der Minne (2013) focused on the lower price segment of the Dutch housing market. Their study gives insights into the determinants of price fluctuations of houses bought by first-time buyers. They showed that the price development of the lower price segment is largely derived from the mortgage restrictions set by the NIBUD (National Institute for Family Finance Information). The determinants found in their study are different than the ones concerning the overall housing market which indicates a diversity of determinants across price segments.
To conclude, according to the aforementioned literature on the segmentation in the Dutch housing market (Brounen and Huij, 2004; Francke et al., 2009; Galati et al., 2013), it is expected that there is heterogeneity across different price segments.
2.4. Hypotheses
To answer the research question several hypotheses are formulated. As mentioned earlier, the existing literature explains heterogeneity in several ways, namely by differences in the impact of determinants on price changes (Brounen and Huij, 2004) and by differences in mean-reversion and serial correlation coefficients
15 (Capozza et al., 2002; Galati et al., 2013; Gao et al., 2009). The expectations are translated into five hypotheses. The expected differences in house price determinants income and interest rates (which as discussed in the literature review section are important in the majority of studies), are defined in hypotheses 1 and 2. Expectations regarding the effects of supply factors are translated into hypothesis 3. Hypotheses 4 and 5 comprise expectations with regard to the extent of mean-reversion and the degree of serial correlation across price segments.
Hypothesis 1: Income variables have a greater impact on the price developments of lower price segments as compared to higher price segments. Houses in the lower price segment are primarily bought by first-time
buyers, due to their affordability. First-time buyers are the group of participants that have the lowest amount of equity. Therefore, the amount of money that they can spend on their first house depends largely on the mortgage amount they are able to obtain. This group of buyers usually chooses the maximum mortgage loan (De Vries, 2014). As a result, mortgage lending standards are relevant in explaining price movements for houses bought by first-time buyers i.e. houses in the lower price segment. The maximum loan amount is set by the NIBUD and largely depends on the income of a household. Thus, income is expected to be relevant in explaining house price developments for the lower price segment in comparison to the other price segments.
Hypothesis 2: Interest rates have a greater impact on the price developments of higher price segments as compared to lower price segments. Interest rates can be seen as an indicator of the state of the economy. In
other words, when interest rates are high, the economy is probably in a good state. So when economic conditions are favorable, people are willing to purchase houses in the higher price segments. Therefore, it is expected that interest rates have a greater impact on prices in the higher price segments. To conclude, higher price segments might be more sensitive to changes in interest rates.
Hypothesis 3: Supply factors are more relevant in explaining the price development of the lower price segment as compared to higher house price segments. Supply factors used in the existing literature on Dutch
house prices are the housing stock, the scarcity of the housing market, and construction cost indices (see Table 1). It is hypothesized that supply factors are more relevant in explaining price developments of the lower price segment. As mentioned, the willingness of participants in this price segment (especially young adults i.e. first-time
16 buyers) to form a household and to purchase a house is different from participants in other price segments. It is expected that first-time buyers are less likely, compared to other participants in the housing market, to wait for favorable economic circumstances to purchase a house. As a consequence, first-time buyers might be willing to pay more for a house when houses are scarce. It should be noted that differences in the construction cost index as a supply-factor do not only measure differences in the supply. Another reason for differences in the effects of construction costs between the price segments is possible. That is because house prices are constituted by two elements, namely land value and the value of the improvements (building value). The ratio between these two elements differs per price segment. More specifically, the higher the total value, the higher the land value relative to the building value (Bostic et al. 2007). It is hypothesized that houses with a lesser fraction of value derived from land experience a higher impact of construction costs. To sum up, supply factors are more relevant in explaining price developments for the lower price segment.
Hypothesis 4: House prices in lower price segments adjust more quickly to their long-run equilibrium (i.e. display greater mean-reversion) than house prices in higher price segments. Reservation prices set by participants
in the market are usually based on existing sales. When there are not enough comparable sales available, participants have to use sales distant in time or location. As a consequence, markets with a lower level of transactions have higher information costs. It is easier to obtain the most recent market information in a market with a higher level of transactions, as a result prices in these markets should adjust more quickly to their long-run equilibrium. Houses in the lower price segment are transacted the most due to their affordability and the large amount of participants in this segment. This is confirmed by higher average turnover ratios2 in comparison to other price segments. Therefore it is expected that prices of the lower price segments have a higher degree of mean-reversion.
Hypothesis 5: House prices in lower price segments experience a higher degree of serial correlation than house prices in higher price segments. As mentioned in the literature review section, in an inefficient market actual
17 prices will deviate from their long-run equilibrium prices. Besides that, inefficient markets are characterized by a degree of serial correlation. Participants, like developers or investors, can contribute from this inefficient pricing by adding supply. These participants can arbitrage inefficient pricing when house prices exceed their equilibrium. After new construction is added, prices will go down, which will eventually result in less serial correlation. Therefore, it is expected that serial correlation is lower in markets where supply can respond quickly to demand. Based on the scarcity indicators, it can be concluded that houses in the lower price segments are scarcer than houses in the higher price segments3. Thus supply is not quickly responding to demand in the lower price segments. To summarize, it is expected that the degree of serial correlation is the highest for lower price segments.
The aforementioned hypotheses will be tested in the results section, chapter 5, of this paper.
18
3. Data
As mentioned earlier, fundamentals used in the literature on Dutch housing markets are diverse. House price determinants used in existing literature are summarized in Table 1 in the literature review section. The aim is to test as many potential explanatory factors as possible to give a complete overview of the determinants of Dutch house prices. Data for this research are divided into house price indices and variables reflecting the demand- and supply-side of the Dutch housing market. All time-series consist of yearly data for the period 1985 to 2013. In this section, data sources and the preparation of the variables will be discussed.
3.1. House price indices
Data regarding house prices are provided by the Dutch Association of Realtors and Property Consultants (NVM). It contains transaction prices with house characteristics, which are available from 1985 to 2014. In order to determine the price developments of specific house price segments, quantile regression methods are implemented in hedonic price models.
Hedonic price indices have an advantage over price indices based on averages or medians. In a hedonic price model, underlying property characteristics (amount of floor space, property type, etc.) and transaction prices are used to determine the price development over time, whereas price indices based on averages and medians solely take the transaction prices into account. By taking averages of transaction prices, it assumes that the underlying mix of properties and their characteristics are constant over time. However, this assumption is questionable because sample selection bias might occur. A hedonic price model corrects for this bias and can be used in this study thanks to the availability of data on house prices and house characteristics.
In order to determine the price developments of the specific price segments, quantile regression methods are incorporated into the hedonic price models. In comparison with ordinary least squares (OLS) regression which estimates coefficients explaining the conditional mean, quantile regressions give estimates that approximate a conditional median or percentile. With regard to this study, quantile regression methods are used to estimate house prices on a specific percentile. The percentiles are based on transaction prices in each year of the sample
19 period. It should be noted that several institutions use price developments of different house types as a proxy for price segments. For example, detached houses as a proxy for the upper price segment. However, within a house type, houses fall into different house price segments (e.g. cheap and expensive apartments). The quantile regression method uses all transactions regardless of house type to create a price index. This results in a more reliable and valid price index reflecting a price segment. More information on, and examples of, quantile regressions can be found in Koenker and Hallock (2001).
As mentioned, the percentiles used in the quantile regressions reflect a price segment. To make a clear distinction between the price developments of price segments, wide ranges are chosen. Where the 10th percentile reflects the price development of the lower price segment, the median (the 50th percentile) is used to determine the price development of the middle price segment. Lastly, the price development of the upper price segment is calculated using the 90th percentile.
As a result, three house price indices reflecting the development of each house price segments are created. The output of the three quantile regressions is shown in Appendix C, Table 1 to 3. To construct real house price indices the consumer price index will be used. The consumer price index is provided by Statistics Netherlands (CBS).
3.2. Demand-side variables
Demand-side variables used in this research are the total disposable household income, average disposable household income, the mortgage interest rate and the number of households. The average disposable household income and the total disposable household income are price segment-specific.
Data on disposable household income are made available by the CBS on special request4 and through her latest publications. Income data on request are subdivided into income classes, based on deciles, and cover the period from 1978 to 2011. For 1986 to 1988, a subdivision of income into deciles was missing. For missing years, the development of the total household disposable income and the deciles’ percentage difference between
20 1985 and 1989 is used to interpolate the data. To expand the sample period, income data for 2012 and 2013 are obtained from publications regarding income statistics of the Netherlands. For 2012, income data has recently publicly been published by the CBS for each of the different income classes. With regard to 2013, detailed income data are not available but are extrapolated by using the increase in total disposable household income for 2013, as provided by the CBS. This assumes that income inequalities did not increase in 2013, which was certainly not the case in 2012 (Statistics Netherlands, 2013).
In order to calculate the effect of total disposable household income on house prices, the total disposable household income is divided into groups of participants for each price segment. Income classes reflecting the participants for each house price segment are determined by using mortgage loan requirements and total equity as an indication5. The lowest income class used in this study (and thus the participant for the lower house price segment) contains the lowest 10 to 30 percent of incomes, i.e. the 2nd and 3rd decile. The lowest decile of incomes is excluded because this group is considered irrelevant. According to the method used to match income classes with house price segments, the majority of this income class cannot afford an owner-occupied house. On average over the sample period, 10.1 percent of the households in this lowest decile own a house indicating that this lowest income class mainly contains participants in the rental sector, and are thus irrelevant for this paper. With regard to the other price segments, participants for the upper price segment have an income which represents the highest 20 percent (the 9th and 10th decile). Finally, incomes of participants for the middle price segment fall between the lower and upper class, i.e. the 4th to 8th decile. To construct real variables, the income variables are deflated by the consumer price index provided by the CBS.
The number of households is also part of the data provided by the CBS. These data show the total number of households and the number of households by deciles. It should be noted that the number of households is the same for each decile. Because the income classes are determined by deciles, the number of households is
5 The income classes relevant for each house price segment are determined by using a rule of thumb estimating the price of an house a household can afford: ݄ݑݏ݁ݎ݅ܿ݁ ൌ ͶǤͷ݄ݑݏ݄݈݁݀݃ݎݏݏ݅݊ܿ݉݁ ݐݐ݈ܽ݁ݍݑ݅ݐݕ. According to Schilder and Conijn (2012), in 2012, the maximum mortgage loan is estimated by 4.5 times the household gross income. The total equity data are provided by the CBS also. Note that the income classes are matched with house price segments for 2012.
21 proportionately distributed by the number of deciles used for each income class. As a result, the total number of households and the number of households per price segment show similar annual percentage changes.
Variables denoting the average disposable income per household for each price segment are created by dividing the total disposable household income per price segment by the number of households in each price segment. These variables are also deflated by the consumer price index to create real incomes.
The mortgage interest rate is the last demand-side variable, and it is provided by the Mortgage Shop (De Hypotheekshop) for the period 1973-2013. The mortgage interest is a nominal average 5-year fixed annuity rate. Two variables are used in this study, namely the nominal and real mortgage interest rate. The nominal mortgage interest rate is corrected by using the consumer price index to create a variable in real terms.
3.3. Supply-side variables
The housing stock can be seen as a supply-side variable. Housing stock data for 1921 to 2011 are provided by the CBS. These aggregated data provide information concerning the total housing stock only and do not have a division into price segments. Using these data under the assumption that the housing stock shows the same development for every price segment is an option.
To make a distinction between price segments, an option is to create a proxy for supply by using the scarcity of housing in a specific price segment. An example of a scarcity indicator is used in a study by Brounen and Huij (2004). Scarcity is calculated as the number of transactions (in a year) divided by the houses for sale (on the 1st of January). The ratio calculated is also called the turnover ratio. Scarcity is lower when the number of houses for sale increases holding the number of transactions constant. The scarcity is calculated for each price segment, where percentiles (0-20, 20-80, 80-100) based on transaction prices are used to calculate the price limits of the transactions and houses for sale in a price segment.
Another supply-side variable is the construction cost index. It is provided by the CBS. Data are available from 1915 to 2013. To construct a real index, the consumer price index is used as well.
22 3.4. Data description
All variables except both mortgage interest rate variables are expressed in natural logarithms. The variables used in this paper are summarized in Table 2. Table 3 includes the descriptive statistics of the aforementioned variables.
Table 2. Variables
Variable Description
hlps Log house price lower price segment - Log cpi
hmps Log house price middle price segment - Log cpi
hups Log house price upper price segment - Log cpi
ylps Log total disposable household income lower class - Log cpi
ymps Log total disposable household income middle class - Log cpi
yups Log total disposable household income upper class - Log cpi
y.avlps Log average disposable income per household lower class - Log cpi
y.avmps Log average disposable income per household middle class - Log cpi
y.avups Log average disposable income per household upper class - Log cpi
inom Mortgage interest rate
ireal Mortgage interest rate - Inflation1
gdp Log gdp - Log cpi
c Log construction costs - Log cpi
hs Log housing stock
hh Log number of households
slps Log scarcity lower price segment
smps Log scarcity middle price segment
sups Log scarcity upper price segment
1 ܫ݂݈݊ܽݐ݅݊ ௧ൌ
షభെ ͳ
23 Figures 1 and 2, see next page, represent the real house price and the first difference of the real house price over time, both expressed in natural logarithms. The price developments of house price segments follow a similar pattern with small differences in the price fluctuations implying that house price movements between the price segments do not differ much. For all price segments, real house prices peaked in 2007, after which the Financial Crisis started and house prices started falling. On average, real house prices in the lower price segment increased by 2.6%, which is 2.5% in case of both the middle and upper price segment.
Table 3. Descriptive Statistics
Variable Description Obs Mean Std. Dev. Min Max
' hlps 28 0.0257 0.0539 -0.0987 0.1234 ' hmps 28 0.0249 0.0513 -0.0947 0.1314 ' hups 28 0.0247 0.0506 -0.0940 0.1452 Ylps x € 1,000,000 29 18,055 5,834 9,980 26,793 Ymps x € 1,000,000 29 81,774 26,105 42,118 121,217 Yups x € 1,000,000 29 65,554 23,807 31,088 102,137 Y.AVlps x € 1 29 8,771 2,112 6,303 11,720 Y.AVmps x € 1 29 13,218 3,293 8,890 17,699 Y.AVups x € 1 29 23,943 5,882 15,007 32,030 inom % 29 5.95 1.77 3.65 9.78 ireal % 29 3.96 1.92 1.19 7.60 ' gdp 29 0.0200 0.0229 -0.0482 0.0561 ' c 29 0.0033 0.0337 -0.0779 0.0720 HS 27 6,437,630 564,016 5,384,000 7,266,000 HH 29 6,700,241 566,028 5,613,000 7,569,000 Slps 29 4.00 2.00 0.86 7.94 Smps 29 3.20 1.82 0.38 6.30 Sups 29 1.58 1.03 0.14 4.52
24 As mentioned earlier, house price movements across price segment do not vary considerably. However, the underlying demand and supply factors do, as large differences are noticed between price segment-specific variables for incomes (y and y.av) and scarcities (s). These differences are shown in Figures 3 and 4, which represent the first difference of the log of real total disposable income and the log of scarcity over time. By looking at the scarcities, it can be noted that houses in the lower price segment are the scarcest during almost the entire
-0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1985 1990 1995 2000 2005 2010 Figure 1. Log real house price (h)
Lower price segment Middle price segment Upper price segment
-0,15 -0,10 -0,05 0,00 0,05 0,10 0,15 0,20 1986 1991 1996 2001 2006 2011 Figure 2.
' Log real house price ('h)
Lower price segment Middle price segment Upper price segment
-0,04 -0,02 0,00 0,02 0,04 0,06 0,08 0,10 0,12 1986 1991 1996 2001 2006 2011 Figure 3.
' Log real total disposable income ('y)
Lower price segment Middle price segment Upper price segment
-3,00 -2,00 -1,00 0,00 1,00 2,00 3,00 1985 1990 1995 2000 2005 2010 Figure 4. Log scarcity (s)
Lower price segment Middle price segment Upper price segment
25 sample period. In 1999, the scarcity was highest for the middle and upper price segments. This is in line with findings of the CPB (Verbruggen et al., 2005) who recognize that the scarcity of housing was highest in the late 90s. Graphs of other variables containing the development over time are provided in Appendix B, Figures 1 to 8.
3.4. Validity checks
In order to satisfy the conditions of an error-correction model (ECM) the variables have to be valid. The validity checks concern the order of integration of the variables and correlation between the variables, to avoid multicollinearity in the regressions. An ECM requires co-integration between the dependent variable, the house price, and the independent variables; the house price determinants. To be added in a co-integration relation, series have to be integrated of order one or in short: I(1). All the series are tested for a unit root against both mean stationarity and trend stationarity. This is done by augmented Dickey-Fuller (ADF) tests. Results including the interpretation of the unit root tests, both for the levels and first differences of the variables, are reported in Appendix C, Table 4. Concluding, house price indices (hlps, hmps, hups), the log real gdp (gdp), the log housing stock (hs), the
log real total disposable household income of the middle class (ymps), and the log real average disposable income
of the upper class (y.avups) are not I(1). Although using the aforementioned variables will formally violate the
conditions for using an error-correction model, it is expected that the results will still be interpretable.
To avoid multicollinearity in the regressions, correlations between the variables are analyzed. Multicollinearity occurs when two or more independent variables are highly correlated, i.e. a linear combination between two or more independent variables exists, which will lead to less interpretable results. Correlation matrices containing the possible variables for each model are presented in Appendix C, Table 5. As can be concluded, gdp (gdp) is highly and significantly correlated with income variables (y and y.av). Using these combinations of variables in the same regression might give some multicollinearity implications. In order to take these issues into account, multicollinearity tests will be conducted during the empirical analysis.
26
4. The model
To find out whether heterogeneity in house price dynamics across price segments exists, the model adopted in this research has to contain several features. First, it has to function well as a house price model and thus allow for housing market characteristics. Secondly, the model should be able to give the required input to test for heterogeneity. An error-correction model (ECM) fits these requirements. In this section, the ECM will be explained first. Secondly, adjustments will be made to the model to allow for other (possible) characteristics of the housing market which will also be tested in this study.
4.1. The error-correction model
An error-correction model is estimated using an Engle and Granger two-step procedure (Engle and Granger, 1987). In this model, two equations are used to determine both the long- and short-term relationships. The stages of the Engle and Granger two-step procedure are specified in equation (1) and (2). Where the first stage (1) can be seen as the long-term model, the second stage (2) is the short-term model. In both steps, coefficients are estimated by ordinary least squares (OLS) with heteroskedasticity-robust standard errors.
݄௧כൌ ߚଵݔଵǡ௧ ǥ ߚݔǡ௧ ߟ௧ (1)
ο݄௧ ൌ ߙο݄௧ିଵ ߜ൫݄௧ିଵെ ݄௧ିଵכ ൯ ߛοݔ௧ ߝ௧ (2)
The first stage in this procedure estimates the fundamental or long-run equilibrium house price. This is done by regressing the fundamentals (ݔǡ௧ሻon house prices according to equation (1). In this long-term model house prices are explained by the levels of fundamentals. In order to formally satisfy the conditions of a long-term co-integrating relationship, the residuals obtained from this co-integrating regression have to be stationary. To confirm stationarity in the residuals obtained from the co-integration regression, ADF tests on the residuals should meet the critical values for co-integration tests provided in MacKinnon (2010). The residuals of the long-run equation form the error-correction term (ect). Accordingly the error-correction term is calculated as in equation (3).
27 In the second stage, the short-run relationships are explored by including the residuals from the long-run equilibrium, as is shown in the short-term model (2). In this model, the first differences of fundamentals are used to explain the short-run changes in house prices. The addition of the first lag of the error-correction term to the short-term model will capture the impact of deviations from the long-run equilibrium. This second stage attempts to explain the deviation from the equilibrium, and tries to put the actual house prices back to their equilibrium whenever these move away. Theߙ andߜ capture the degree of serial correlation and the extent of mean-reversion respectively. ο݄௧ିଵ can be seen as a bubble builder which captures market’s inefficiency, where the deviation from the long-run equilibrium, or ݁ܿݐ௧ିଵ, functions as a bubble burster (Francke et al., 2009).
In both stages, a general-to-specific modeling approach is used to create the best approximation of house prices derived from fundamentals. For each price segment, a different error-correction model is estimated based on fundamentals that are relevant for explaining the price developments of that specific price segment.
4.2. Asymmetric error-correction
Most studies on house prices use a symmetric error-correction term, symmetric as in similar speeds of adjustment to the fundamental price when actual house prices are under- or overvalued (i.e. ሺ݄௧െ ݄௧כሻ ൏ Ͳ or ሺ݄௧െ ݄௧כሻ Ͳ respectively). However, several studies (Abelson et al., 2005; Gao et al., 2009; Verbruggen et al., 2005) show that an undervaluation of house prices adjusts more quickly than in case of an overvaluation, this feature is also known as downward price rigidity. This can be explained by sellers in weak markets that are often unwilling to sell their house at current market prices. In order to make a model that gives the best approximation of house price changes, an asymmetric error-correction model is also tested in this study. An ECM with an asymmetric error-correction is specified in equation (4). In model (4), ߜ measures the degree of mean-reversion in case of undervaluation, where ߮ denotes the difference in mean-reversions in case of under- and overvaluation. The degree of mean-reversion in the case of an overvaluation can be estimated by ሺߜ ߮ሻ.
ο݄௧ ൌ ߙο݄௧ିଵ ߜ൫݄௧ିଵെ ݄௧ିଵכ ൯ ߮൫݄௧ିଵെ ݄௧ିଵכ ൯ ା
28 5. Empirical results
In this section, the house price determinants from section 2 are tested in different long- and short-term models in order to explain the price development of houses in each price segment. To start, the long-term relationships are determined. Subsequently, house price determinants explaining the short-term relationships are analyzed. Finally, the models explaining the price developments of the specific house price segments are compared and the hypotheses from section 2 are tested. For the sake of simplicity, price segments will be mentioned as followed: LPS (lower price segment), MPS (middle price segment), and the UPS (upper price segment).
5.1. Long-term relationships
In order to determine the long-term relationships for each price segment, a general-to-specific modelling approach is used. In this process, all variables are added in the model first. Subsequently insignificant variables are omitted from the regression using a stepwise process. As a result, only significant explanatory factors remain in the model. The variables used in the long-term relationships are specified in contemporaneous and level form. The estimation results of the co-integration relationships for all price segments are presented in Appendix C, in Table 6, 7 and 8 for the LPS, the MPS, and the UPS respectively.
5.1.1. Determination of the long-term model
At first, all possible explanatory variables are included in model (1) for all price segments. In general the GDP variable is not favorable in the long-term relationship; including the GDP results in insignificant variables and wrong signs for the income variables. This might be a result of multicollinearity due to the high correlations between GDP and the income variable (y.av) and between GDP and the number of households. According to the validity checks, gdp is not I(1). To create a valid and more significant model, gdp is excluded in the next model. Model (2) includes the average disposable income per household, the real mortgage interest rate, the number of households, the construction costs, and the scarcity indicator. Using this combination of variables results in insignificant coefficients for the scarcity and income variables.
29 As discussed previously in the literature review, studies on Dutch house prices using a combination of demand-and-supply-side have some caveats. It should be noted that all these studies include the real mortgage interest rate. In contrast, Adams and Füss (2010) and Francke and Van der Minne (2013) use interest rates in nominal terms as a demand-side factor. In model (3) real mortgage interest rates are replaced by nominal ones. It results in a better fit for all price segments, with significant effects of the supply-side factors like construction costs and scarcity. Economically speaking, a better fit with nominal instead of real mortgage interest rates might mean that households do not consider inflation to a large extent. It should be mentioned that to construct a proper real interest rate variable, the interest rate has to be deflated with the expected instead of actual inflation. This is however not the case in most of the house price literature. The question regarding the impact of nominal versus real interest rates on house prices may need some further research.
Returning to model (3), it includes the average disposable income per household, the nominal mortgage interest rate, the number of households, and the construction cost, and scarcity indicator. These factors explain house price movements with adjusted R-squares of 0.99, 0.98, and 0.98, for the LPS, MPS, and UPS respectively, with low root mean square errors (RMSEs). A transformation of variables can possibly increase the fit. It is recognized by Hofman (2005) that there is a highly significant long-run relationship between house prices and total disposable household income. Therefore, a transformation is performed which results in model (4). Here the average disposable income per household and number of households are replaced by total disposable household income. This results in a better fit, especially for the MPS and UPS in terms of stronger significant variables and higher ADF-test statistics. In order to test the relevance of supply factors, model (5) excludes the supply variables. It turns out that including supply-side variables significantly improves the long-term model.
In addition to the aforementioned steps, several other options to enhance the model are explored. For instance, construction time is taken into account. This is done by including lags of the supply-side variables which results in model (6). The inclusion of the lags6 gives a better explanation of real house prices in terms of more
30 explanatory power and lower errors, but ADF-test statistics on residuals are lower in all cases. Furthermore, adding a trend to the model turns out insignificant and results in other insignificant variables as well. However, the inclusion of a trend without supply-side factors results in a significant explanatory model. In this model, the trend is significantly negative for all price segments, indicating that house prices are decreasing over time as a result of some unobserved factors. This is in contrast with Francke et al. (2009) who find a significant positive trend by using the real average modal labor income and the real mortgage interest rate as explanatory variables. The difference might be a result of different income variables. Using the real total disposable household income derived from the number of households, results in a negative trend regardless of the mortgage interest rates being in real or nominal terms. The average income variable used by Francke et al. (2009) does not correct for the increasing number of households over time, which will ultimately be reflected in the trend component. With regard to improving the model, omitting supply-side factors but including a trend is still not better than a demand-and-supply side model without a trend.
5.1.2. Final long-term models
For all price segments, model (4) gives the best estimation of house prices in the long-run considering goodness of fit and stationarity in the residuals. Model (4) uses the real total disposable household income (yt),
the nominal mortgage interest rate (inom,t), the real construction costs (ct), and scarcity (st) to explain house price
movements. The estimation results of the final long-term model for all price segments are shown in Table 4. Taking the coefficients for the lower price segment as an example, results have to be interpreted as follows: (i) a 1% increase in the real total disposable household income increases real house prices by 1.30%; (ii) a 1% point increase in the nominal mortgage interest rate reduces real house price by 5.24%; (iii) a 1% increase in real construction costs raises real house prices by 0.97%; (iv) a 1% increase in scarcity, will raise real house prices by 0.11%.
31 Other studies using the real total disposable household income variable find coefficients of 0.841 (OESO, 2004) and 1.333 (Verbruggen et al., 2005) at the aggregate level. Findings differ slightly from the former study, which might be due to the set of variables used. OESO (2004) uses the real mortgage interest rate and does not include a construction cost index. Turning to the effects of the nominal mortgage interest rate, these do not vary much from effects of (real) interest rates found in other studies, namely -8.59 (Francke et al., 2009), -3.1 (OESO, 2004), and -5.91 (Verbruggen et al., 2005). The differences can be explained by the interest rate variable (in
Table 4. Final long-term models
Variables 1
Price segment
Lower Middle Upper
hlps,t hmps,t hups,t yt 1.295 *** 0.828 *** 0.716 *** (0.120) (0.116) (0.119) inom,t -5.243 *** -5.677 *** -5.568 *** (0.442) (0.431) (0.369) ct 0.973 *** 1.307 *** 1.134 *** (0.116) (0.125) (0.136) st 0.108 *** 0.0364 ** 0.0415 ** (0.0169) (0.0157) (0.0193) Constant -6.138 *** -4.853 *** -3.906 *** (0.657) (0.796) (0.778) No. of observations 29 29 29 Adjusted R-square 0.989 0.982 0.983 R-square 0.991 0.985 0.985 RMSE 0.0385 0.0466 0.0450 F 827.6 778.9 904.3 ADF-test statistic -4.201 -3.656 -3.843
Robust standard errors in parentheses. Significance levels: *** p<0.01, ** p<0.05, * p<0.1 1 Note that for the yt and st variables, the price segment-specific variables are used (e.g. ylps,t)
32 -0,10 0,00 0,10 0,20 0,30 0,40 0,50 -0,60 -0,40 -0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1985 1990 1995 2000 2005 2010
Lower price segment
-0,10 0,00 0,10 0,20 0,30 0,40 0,50 -0,60 -0,40 -0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1985 1990 1995 2000 2005 2010
Middle price segment
Figure 5. Actual house prices versus estimated long-run house prices
-0,10 0,00 0,10 0,20 0,30 0,40 0,50 -0,60 -0,40 -0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1985 1990 1995 2000 2005 2010
Upper price segment
33 nominal instead of real terms) and by differences in the set of variables used. The largest difference noticed is with the study by Francke et al. (2009). This might be due to the exclusion of the supply-side. In general, it can be concluded that the coefficients between this study and the existing literature differ because of variations in the set of variables used and the sample period studied.
The fundamental house prices estimated by the long-term models and the actual house prices are shown in Figure 5. Furthermore, the residuals are included in the graphs. As mentioned earlier, the residuals denote the deviation of the actual house price from the fundamental house price, i.e. ሺ݄௧െ ݄௧כሻ,. For all price segments, the residuals were highest in 2000. In this year, overvaluation of house prices was highest over the sample period. It is noted that all residuals follow the same path: where the LPS and MPS show the most similar route (U = 0.944;
p < 0.001), the residuals of the long-term model for the LPS and UPS differ the most (U = 0.915; p < 0.001).
5.1.3. Validity of the long-term models
Regarding the validity for using an error-correction model, it can be concluded that most variables satisfy the conditions. However, the real total disposable household income variable of the middle class (ymiddle) and all
house prices variables are not I(1). As discussed in the previous section, the inclusion of these variables might not have a negative impact on the results. To test whether co-integration relations exist, augmented Dickey-Fuller tests are applied to confirm stationarity in the residuals of the long-term models. To test for co-integration, critical values are calculated from the response surfaces provided in MacKinnon (2010). As a result, critical values for each long-term model are -5.807, -4.93, and -4.52 for 1%, 5%, and 10% significance levels respectively. The t-values from ADF-tests on the models residuals are all around -4, as shown in Table 4. As a consequence, for all price segments the null hypothesis of no co-integration cannot be rejected. Nevertheless, as mentioned earlier, it is expected that a longer sample period will confirm a co-integration relation.
7 The critical t-value for a co-integration test can be calculated according to the following formula: ߚ
ஶ ߚଵȀܶ ߚଶȀܶଶ by using the response surfaces provided in MacKinnon (2010). Where the values of the ߚஶǡ ߚଵǡ ߚଶ are given based on the number of N and the significance level. In this formula, T is the number of observations in the unit root test. With a 1% significance level the critical value for the ADF-test on the long-term model’s residuals is: -4.9587 – 22.140/28 – 37.29/282 = 5.80.
34 Another validity-check concerns multicollinearity. Tests are conducted to analyze whether multicollinearity occurs within the models. Test results can be found in Appendix C, Table 9, wherein variance inflation factors (VIF) are shown. For each variable, VIF values show the increase of variance over the case of no correlation among the dependent variables. As a rule of thumb, VIF values should not exceed 10. In all models VIF values do not exceed 10, indicating that there is no multicollinearity.
5.2. Short-term relationships
After the long-term relationships are determined, the short-term relationships in the ECMs are analyzed. As in the procedure to determine the house price determinants in the long-run model, the stepwise general-to-specific approach is used for estimating short-run relationships. In the short-run, changes in house price determinants ('xt) are used to predict the changes in house prices ('ht). Results of all estimated models can be
found in Appendix C, Table 10 to 12. These models are estimated by OLS with heteroskedastic-robust standard errors.
5.2.1. Determination of the short-term model
First, possible determinants of short-run changes in house prices are included in model (1). In detail, changes in the average disposable household income ('y.avt), the mortgage interest rate ('inom,t), the number of
households ('hht) and the supply factors, construction costs ('ct) and scarcity ('st), are included. Furthermore,
the lagged error-correction term (ectt-1) and the lagged change in real house price ('ht-1) are added to model (1).
As mentioned in the model section, 'ht-1 is included to capture the speculative influences on the market or the
market’s inefficiency (i.e. the degree of serial correlation). Differences across price segments are noticed between the significance of factors impacting the short-run change in house prices. Factors significant for all price segments are the average disposable household income, the lagged change in house prices, the mortgage interest rate, and the error-correction term. For all price segments, the number of households is not strongly significant in the short-term. Therefore, the number of households is excluded in model (2). This results in a slightly better fit. However both supply factors (construction costs and scarcity) are not found to be strongly significant at the same time.
35 Consequently, in model (3) and (4) the construction costs and scarcity indicators are separately included. It turns out that construction costs perform better in explaining short-term movements. Including the scarcity indicator together with the mortgage interest rate and income only, results in a less significant error-correction term. In model (5), the average household disposable income is replaced by the real total disposable household income. This does not improve the model, and might be a result of the total disposable household income being derived from the number of households which turned out insignificant in model (1).
In studies by Hofman (2005), Timmermans (2012), and Verbruggen et al. (2005), lagged series are added to the short-term model. Ultimately, after several combinations were tested to improve the model, a new variable containing last year’s change and this year’s change in the mortgage interest rate, '0.5(inom,t + inom,t-1), replaces
the interest variable ('inom,t ) in model (6). For the LPS, a lagged component of interest rates has a negligible
impact. But for both the MPS and UPS the goodness of fit slightly increased. However, models with the addition of a lagged interest rate enter a critical region for the Durbin-Watson statistic. As a consequence, model (3) is the best model so far.
In addition, supply-side factors are excluded in model (7). It turns out that a model omitting supply-side factors has a lower explanatory power with higher errors. In other words, supply-side factors are also relevant in the short-run relationship. This is in line with findings of Verbruggen et al. (2005) and Timmermans (2012), who recognize that supply factors are relevant in the short-run.
5.2.2. Asymmetric error-correction
As mentioned in the model section, this study will test for an asymmetric error-correction. Therefore, all aforementioned models are tested with an asymmetric error-correction. Only the best performing model (3) featured with an asymmetric error-correction is shown in the tables as model (8). The additional ݁ܿݐ௧ିଵା in model (8) denotes the difference in mean-reversion when house prices are overvalued. In line with findings of Francke
et al. (2005), the ݁ܿݐ௧ିଵା turns out insignificant in all cases indicating that house prices do not react significantly different in case of an under- or overvaluation. In addition, a study by the CPB (Verbruggen et al., 2005) uses an
