University of Amsterdam
Faculty of Economics and Business
MSc Business Economics: Real Estate Finance
June 15
Testing for the
convergence of housing
affordability in Europe
MASTER THESIS
MARTIN MURRUSTE (10599487) SUPERVISOR: PROF. DR. JOHAN CONIJN
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Abstract
This thesis applies convergence theory to the residential real estate market and tests for stochastic convergence of the housing affordability ratios among European capital cities. A pairwise approach in combination with unit root tests is used to measure and test for long-run convergence. Studying quarterly data for the period 2003:Q4 to 2013:Q4 for 13 urban regions in Europe, the results demonstrate limited evidence of long-term convergence towards an average affordability ratio.
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Table of contents
Abstract ... 2
1 Introduction ... 4
1.1 Central research question ... 4
1.2 Research sub-questions... 5 2 Literature review ... 7 2.1 Affordability ... 8 2.2 Convergence ... 12 2.3 Institutional background ... 16 3 Methodology ... 18
4 Data and descriptive statistics ... 21
5 Results ... 26
6 Robustness checks ... 30
7 Conclusion ... 33
8 References ... 36
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1 Introduction
The European Union currently consists of 28 countries with different financial and cultural backgrounds. From a financial perspective, the EU has the goal to reduce economic and social inequalities between member-states. Convergence of GDP per capita has often been considered a good indicator of measuring this dispersion between countries.
1.1 Central research question
This research applies convergence theory to the residential real estate market, from an affordability perspective. The topic of the paper is to measure the average house price in capital cities and compare it to the average monthly wage in the country. Thus, a question of interest is whether the simple house price-to-income ratio (defined as the affordability ratio in this study) has experienced convergence during the last ten years in European capital cities. The purpose of this thesis is to assess stochastic convergence in the affordability of housing using a pairwise approach. Common determinants of house prices and affordability ratios in different sub-markets are not considered.
A possible explanation for the convergence of the ratio is that evidence for the catch-up effect of house prices and wages (Ramskogler, 2010) has been found in Europe. At the same time, the overall price convergence has been present and will continue to occur as a result of European integration (European Comission, 2007). This provides ammunition for the hypothesis that the price per unit of a housing (€/ m²) and its relation to the average wage (affordability ratio) are also moving along and towards a long-run average.
The question of the existence of a long-term average ratio and the convergence of the value is interesting as housing prices play an important role in an economic system. Residential real
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estate makes up a significant fraction of GDP, and a home is often the largest single asset of a private household. The ECB (2003) distinguishes between four types of channels through which fluctuations in house prices have an impact on the economy as a whole. Firstly, house prices are channeled through a relatively inelastic residential construction market. Secondly, the higher cost of consuming housing services has an effect on non-housing consumption through the wealth effect. Thirdly, the collateral value of real estate assets influences the ability and cost to borrow via the credit channel. And finally, a households´ disposable income is directly affected by the interest rate prevailing in the mortgage market. As a result, large movements in house prices influence consumption and capital allocation. From a macroeconomic perspective, these changes in prices impact inflation, demand and monetary policy decisions.
1.2 Research sub-questions
As already discussed, affordability is a function of the ratio between two terms; one is the nominal dwelling price per square meter in the capital city region, and the other the average national salary. Therefore, the purpose of the first sub-question is to define and measure affordability in terms of the multiple of average income required to buy a square meter of residential property in 13 different capital cities across Europe. Several methods can be used to determine affordability in the housing market. This research presents four techniques to calculate affordability and chooses one of them in order to check the convergence.
Measuring convergence leads to the second sub-question of this study: what methods are used to evaluate the convergence hypothesis in the general growth literature. Different ways of determining convergence are discussed in the methodology section of the thesis.
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The general concept of convergence drives the third sub-question: how is it assessed at the housing market level and how can it be approximated. This work provides a brief introduction of the roots of the convergence hypothesis and presents an overview of six articles on the catch-up effect of house prices. After considering different approaches, a pairwise comparison of affordability ratio differentials using unit root testing is chosen. This method, introduced by Pesaran (2004), has recently been used by Abbott and De Vita to study the convergence of house prices in London (2012), as well as in the UK more generally (2013).
Previous studies in this area (Hiebert & Roma, 2010) have focused on a few European markets, showing mixed results regarding the convergence of city-level house prices. This paper posits that one of the ways to measure housing market conditions is to compare house prices to the average income. Analyzing this ratio adds a new perspective to the field of research. If this ratio deviates significantly from the long-run average, house prices could be over- or undervalued. The Economist (2014) publishes data on global house prices and has created an interactive tool that enables comparison of house prices with average incomes across countries; these ratios have had relatively different trends in different markets during the last decade. This brings us back to the question of convergence towards a long-run average.
Firstly, the above-mentioned long-run average ratio can be found by analyzing house prices and looking at average incomes across countries. This study includes quarterly data for the period 2003:Q4 to 2013:Q4 (41 quarters) for 13 urban regions in Europe (Tallinn, Riga, Vilnius, Warsaw, Helsinki, Stockholm, Oslo, London, Amsterdam, Brussels, Berlin, Paris and Copenhagen).
Secondly, the time series data of the affordability ratio can be tested for different types of convergence. Empirical methodologies for testing convergence hypotheses include beta and
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sigma convergence analysis. Additionally, panel unit root tests can be applied to test for convergence among the affordability ratio of different regional housing markets in Europe. The main aim of this thesis is to measure convergence in the affordability of housing across European capital city regions using a pairwise approach. It shall not attempt to identify common determinants of house prices in different sub-markets.
In the remainder of this paper, the next section gives an overview of the existing literature regarding the affordability of real estate. The third section presents the methodology used in this research and illuminates the hypothesis to be tested. The fourth section outlines the data used, providing a discussion of summary statistics. A presentation of the main results and findings are contained in section five. Next, section six presents robustness checks and additional results. The final section contains concluding remarks.
2 Literature review
The existing literature on the subject of the affordability ratio convergence can be divided into two sub-fields: research on the convergence of house prices in Europe and the more general definition of affordability in housing. The majority of research regarding convergence in the housing market has been based mainly on nominal prices. On the other hand, the concept of affordability is addressed in many different ways. The simplest method of measuring affordability, namely dividing nominal house prices by per capita disposable income, can be further extended by evaluating the ability to service mortgage debt or by identifying disequilibrium between the rental and owner-occupied markets.
First, this literature review commences with four different ways to analyze affordability in the housing market. Secondly, an introduction of convergence theory follows and includes an
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explanation of how the general concept is not only relevant for GDP per capita growth, but also applicable to other price levels, including residential real estate. Finally, a brief overview of the institutional and economic background in Europe is provided.
2.1 Affordability
Households face a trade-off in the allocation of income between housing and non-housing consumption. The proportion of income spent on housing costs is one of the most widely used affordability measures. For example, Stone (2006) states that the standard rule of thumb ratio of housing cost to income has been 25% until the 1980s and around 30% thereafter in the United States. The corresponding ratio amounts to 23% of total household consumption expenditure in the EU (Pittini, 2012). Alternatively, the National Association of REALTORS (NAR) calculates a housing affordability index based on the assumption that the median income has to be sufficient to qualify for a mortgage loan on a typical median priced home (National Association of REALTORS, 2014).
The subjective nature of housing affordability is further complicated by several approaches to affordability itself. Stone (2006) contrasts housing affordability to affordable housing. According to him, the latter is a relationship between housing and people´s preferences and constraints. Some people can afford every house no matter what the price is. For others, no house is affordable. In this sense, the author suggests answering three crucial questions for the proper definition of affordability: to whom, on what standard, and for how long should housing be affordable. In this regard, the current research examines the affordability of living space for a person with an average income.
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More objectively, different mathematical measures can be applied to assess affordability conditions in the housing market. One of the most basic ways to analyze the current situation is to compare average nominal house prices to per capita disposable income and relate it to the long-term average. As stated by the OECD (2005), this is not a sufficient measure to determine purchasing power of housing consumers, as it does not directly take into account the financing costs of a mortgage. For example, in the year 2005, the price-to-income ratios in many OECD countries had exceeded their long-term averages by more than 40%. At the same time, significantly decreased interest payments had kept housing affordable (OECD, 2005).
Hence, interest rate expenses are incorporated in several other equations and models for evaluating affordability. Bourassa (1996) splits up the calculation of measuring affordability of homeownership into two parts. In the first part, a household´s liquid wealth has to be higher than the down payment for an underlying loan. The second constraint, that the debt service (including both interest as well as amortization) should be lower than the income available for regular mortgage payments, should also be fulfilled. His study calculates an affordability measure that is based on both above-mentioned borrowing constraints.
Brounen, Neuteboom and Dijkhuizen (2006) use net financing costs of a mortgage as a nominator and net household income as a denominator to calculate an affordability measure from a debt-service ratio viewpoint. The net mortgage payments take into account tax reliefs, additional costs required by banks or governments and other subsidies. The net household income is described as a households’ after-tax disposable income. After considering all the national mortgage market specifics, the authors compute the national affordability index for each country for the period 1970 to 2003. They find that the housing markets in the
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Netherlands and the United Kingdom have seen the highest decrease in affordability since the middle of 1980s. In this research, when comparing the per square meter price to the average income, the same tendency is only observed for the Netherlands. During the last ten years, the average price-to-income ratio in the capital of the Netherlands has shown a relatively small decrease of 0.04% quarterly, on average. At the same time, the average quarterly increase has been 0.45% in London since the end of 2003.
Affordability could also be addressed by equilibrium in the housing market regarding renting or purchasing a home. The cost of owning a house or an apartment should equal expenditures made to rent a property. The cost of owner-occupied housing includes the foregone interest on capital invested in house, taxes on private property, maintenance and depreciation costs, as well as the owner´s nominal capital gain (Poterba, 1992). Hence the market should be in equilibrium when these costs are equal to cost of renting. Similarly to price-to-income ratios, the OECD (2005) reports that in the countries with high house price increases (the United Kingdom, Ireland, the Netherlands and Spain), actual price-to-rent ratios were significantly above their long-term averages in 2004. This can be a sign of unaffordable housing (from the homeowners’ perspective) and overvaluation in the market.
Tables 1 and 2 summarize four methods to determine the affordability of housing. This research is closest in formulation to the simplest approach used in the report by the OECD (2005). Nominal house prices are replaced by the price of a square meter in the capital region and the national average gross monthly income is used instead of per capita disposable income. The simplest method is mainly used because of data limitations, particularly due to the non-transparent nature of the real estate markets and relatively short period of available data.
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Furthermore, this study measures convergence using an average price-to-income ratio, rather than defining a long-term equilibrium, because the observed data is only available for the past 10 years. OECD (2005) Bourassa (1996) 𝐴𝐴𝐴𝐴𝑡𝑡= 𝑃𝑃𝑌𝑌𝑡𝑡 𝑡𝑡 𝑊𝑊 ≥ 𝐷𝐷 𝐷𝐷 ≥ 𝑟𝑟𝑟𝑟 𝑝𝑝𝑌𝑌 ≥ (𝑟𝑟 − 𝐷𝐷)𝑖𝑖𝑚𝑚 𝐴𝐴𝐴𝐴𝑡𝑡 – affordability ratio 𝑃𝑃𝑡𝑡 – nominal house price 𝑌𝑌𝑡𝑡 – per capita disposable income
𝑊𝑊 – household liquid wealth 𝐷𝐷 – deposit on a house 𝑟𝑟 – value of a house 𝑟𝑟 – minimum deposit ratio
𝑌𝑌 – income from sources other than liquid investments
𝑝𝑝 – maximum proportion of income that can be spent on mortgage payments
𝑖𝑖𝑚𝑚 – mortgage interest rate In equilibrium the price-to-income ratio is around its
long-term average. A value exceeding the average could be an indicator of overvaluation in the housing market
In equilibrium the household wealth (W) must be sufficient for a down payment on a house (D) and the income (𝑝𝑝𝑌𝑌) has to cover mortgage payments ((𝑟𝑟 − 𝐷𝐷)𝑖𝑖𝑚𝑚)
Table 1: Different methods to assess affordability
Brounen, Neuteboom & Dijkhuizen (2006) Poterba (1992) 𝐷𝐷𝐷𝐷𝐴𝐴𝑡𝑡=[𝑎𝑎𝑎𝑎𝑡𝑡+ 𝐼𝐼𝑡𝑡(1 − 𝜏𝜏1𝑌𝑌− 𝜏𝜏2)]𝐷𝐷𝑡𝑡+ 𝐴𝐴𝑡𝑡
𝑡𝑡 𝐴𝐴 = �𝑖𝑖 + 𝜏𝜏𝑝𝑝+ 𝑚𝑚 + 𝛿𝛿 − 𝜋𝜋 �𝑃𝑃𝐻𝐻 𝐷𝐷𝐷𝐷𝐴𝐴𝑡𝑡 – debt service ratio
𝑎𝑎𝑎𝑎𝑡𝑡 – additional costs 𝐼𝐼𝑡𝑡 – gross mortgage rate 𝜏𝜏1 – average mortgage relief 𝜏𝜏2 – other non-fiscal subsidies 𝐷𝐷𝑡𝑡 – outstanding mortgage debt 𝑌𝑌𝑡𝑡 – net household income
𝐴𝐴 – rental value 𝑖𝑖 – interest rate 𝜏𝜏𝑝𝑝 – property taxes 𝑚𝑚 – maintenance costs 𝛿𝛿 – depreciation costs 𝜋𝜋 – inflation rate 𝑃𝑃𝐻𝐻 – house price To maintain the affordability (debt service ratio)
equilibrium, Increasing housing prices can be compensated by the favorable tax treatment of mortgage interest or by other subsidies.
In equilibrium the net income from homeownership must be zero and the ratio of the rental value to house price (𝑃𝑃𝐻𝐻𝑅𝑅) has to equal the user cost of owner-occupied housing �𝑖𝑖 + 𝜏𝜏𝑝𝑝+ 𝑚𝑚 + 𝛿𝛿 − 𝜋𝜋 �
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2.2 Convergence
Convergence theory has its roots in growth economics (Barro & Sala-i-Martin, 2004). Growth is thereby defined as an increase in the GDP per capita measure. It is usually expected that countries that significantly lag behind in the economic development process should catch up with the richer countries at a faster pace than more developed ones. At some point in time, GDP per capita should converge to the long-term equilibrium value across different economies. The idea of convergence is also applicable to prices in an economic system. The European Union has experienced continued price convergence over the past decade, which has largely been driven by the catch-up of prices in EU12 countries towards EU15 levels (OECD, 2012b). According to the OECD, price differences are still high for the EU as a whole. Nominal housing price differences across countries are even higher and should be compared with living standards. In this regard, the affordability ratio is a simple measure of relative housing prices. The literature on house price convergence across countries in Europe is limited, even though the catch-up effect of housing market fundamentals (per capita income, interest rates) has gained considerable attention. Long-run convergence in city-level house prices in Europe has been surveyed by Hiebert and Roma (2010). One of their theories predicts that house prices may converge because of the previously mentioned convergence in fundamentals. On the other hand housing is a non-tradable good across geographic areas, which leaves no opportunity for arbitrage. Their research does not end the debate- they only find limited empirical evidence of the convergence of house prices when examining the dynamics of price levels within the four biggest euro area countries (Germany, Italy, France and Spain). The authors use unit root tests
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with the null hypothesis of non-stationarity. This means that rejection of the null hypothesis implies stationarity and prices tend to converge to their long-run average.
Similarly, European residential property markets have experienced some convergence in housing prices, as uncovered by Smullen and MacDonald (2007). Their prediction of non-convergence is based on one of the characteristics of the real estate market; the underlying traded assets are unique. On the contrary, the argument for convergence is supported by the single market and currency. Discussing the topic, they distinguish two groups of countries: one with countries that have shown convergence (Germany, Italy, France, Spain, Greece, Finland, Portugal, and Belgium) and another, where prices have diverged (Ireland, the United Kingdom, and the Netherlands). Trends are expected to remain different in the near future, as the diversity of regulatory systems and cultural aspects remains large across Europe.
The literature on the euro area also includes a paper from Vansteenkiste and Hiebert (2009), who find that the standard deviation of house prices across 10 euro area countries have decreased (σ-convergence) when comparing periods of 1989-1997 to 1998-2007. It is supposed to be a result of co-movements in housing market fundamentals, increasing financial market integration and/ or convergence of the risk premium prevailing in the housing market. The authors mention several factors that have an influence on the empirical results: measurement issues, non-market forces, institutional factors and structural economic change. Their main finding, that house price spillovers as a result of domestic shocks are relatively small for other countries in the euro area, is based on country-specific factors (economic structure, structural features and policies) as well as cross-country linkages.
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More research on convergence at the city level has been done on the United Kingdom residential property market. For example, Cook (2012) tests β-convergence across regional house prices in the United Kingdom using a method based on conditional probabilities of high and low growth rates. He predicts that so-called ripple effect lead to convergence over the long-run, as short-term shocks in house prices in one region are transmitted to other regions. Using an alternative measure to examine price movements, Cook argues for convergence during cyclical periods. According to him, the importance of convergence and divergence lies in its influence on economic policy and private sector wealth. By categorizing regional house price series into high/low growth groups, and classifying these further by initial value, simple and conditional probabilities can be compared and convergence identified. As in several other studies, mixed results are found and convergence over the whole sample period is not proven to be the case. But dividing the sample period into cyclical sub-periods helps to uncover convergence across the whole of the cycle (especially during cyclical downturns).
Abbott and De Vita (2013) clarify that two further issues complicate convergence theory in the housing market. Convergence can possibly be found only in subgroups of regions, and in the existence of an already mentioned ripple effect. The authors debate on using an alternative test to check for regional house price convergence. This method, the pairwise approach, relies on unit root testing between distinct pairs of regions. Similarly to previous research, they find no evidence of long-run stochastic convergence among UK regional residential property markets. Neither is there convergence of subgroups or an equilibrium level of house prices, towards which values tend to move. Their outcomes are based on the analysis of the unit root, and
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trending properties of the logarithm of house price changes across 12 regions in the UK over the period 1983 to 2008.
In contrast to the previous studies that have failed to find clear convergence in the UK, Holmes and Grimes (2005) approach regional house price convergence by testing for stationarity, while using a principal components methodology. They believe that if regional house price shocks do not spill over (again, the ripple effect!) to other areas, inequality in wealth distribution may arise (people owning houses in regions with increasing prices will be better off). On the other hand, if the effect of house price shocks has an impact across the regions, the divergence in wealth distribution can only be temporary. Considering a low adjustment process towards equilibrium in house price ratios, the research results suggest that there is convergence in regional property prices in the long-run.
Tables 3 and 4 provide an overview of the literature given above. Evident is that only limited or weak evidence of house price convergence in both UK and European market is found. Diverging trends are also reported, and their underlying causes studied by Hilbers, Hoffmaister, Banerij and Shi (2008). Their empirical evidence supports the significance of the effect of the most commonly used factors explaining house prices. User costs, demographic factors and output per capita all play a significant role in driving house price developments.
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(2010) Smullen & MacDonald (2007) Vansteenkiste & Hiebert (2009) Type of convergence City-level dispersion from
the national index Convergence to the mean Co-movement of international house prices Test of convergence Levin–Lin–Chu
Augmented Dickey Fuller Phillips-Perron
N/A Global vector autoregression (GVAR) methodology Basis for test Nation-wide house price
index Country-level average house price Euro area aggregate house price inflation Results Limited evidence of
long-term convergence Mixed results (distinguish between a converging and a non-converging group
Low spillovers from the local house price shocks
Table 3: Literature review on convergence
Cook
(2012) Abott & De Vita (2013) Holme & Grimes (2005) Type of convergence β-convergence of house
prices in the UK Pairwise tests of UK regional house prices Regional deviation from the average UK house price Test of convergence Conditional probabilities Augmented Dickey Fuller
DF-GLS KPSS
DF-GLS Phillips-Perron Basis for test Average growth rate and
average initial value No need for a benchmark UK house price Results Convergence found only
in cyclical sub-samples No long-run convergence Week evidence of long-run convergence
Table 4: Literature review on convergence
2.3 Institutional background
House prices and affordability levels are not only determined by per capita income and available interest rates in the mortgage market. The structure of the housing market, with its institutional background, is influenced by cultural and socio-economic developments. Firstly, there are huge differences in ownership structures across countries in Europe. Rental market plays an important role in western European countries like Germany, Denmark, Austria, France and the Netherlands (Deloitte, 2013). On the other hand, according to Deloitte, Eastern European countries have a high rate of homeowners with a low number of mortgages; a situation which has often been caused by privatization of the properties for non-market prices. Additionally, the
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homeownership rates are found to be positively correlated with house price appreciation (Hilbers, Hoffmaister, Banerij, & Shi, 2008). Hilbers et al. 2008 analyze the relationship between the average house price growth rates of 1990-2004 and home ownership ratios in 14 European countries. They speculate that the increasing homeownership rates after the beginning of the 2000s could be a combination of weak stock markets and convergence of nominal interest rates. Thus, household preferences between owning and renting a home still differ across Europe. Secondly, the availability and pricing of mortgages vary between countries. Using a mortgage loan requires a down payment in the form of personal equity. Lower loan-to-value (LTV) ratios make it difficult for people with insufficient liquid equity to access mortgage financing. For a first time house buyer this ratio can differ from 60% to 90% within Europe (ECB, 2009). Different countries also have their preferences when it comes to choosing between an adjustable-rate-mortgage (ARM) or a fixed-rate-adjustable-rate-mortgage (FRM). For example, the average share of ARMs has been around 80% in Spain, Ireland and Portugal during the last 6 years compared to the EU´s average of 35.8% (EMF, 2013). On the contrary, the average share is 20% or lower in the Netherlands, Germany and Belgium.
Thirdly, the structure of the regulatory environment and its degree of stringency have an effect on the level of housing affordability. Besides examining the nature of equilibrium housing prices and testing whether prices tend to revert to an equilibrium ratio between price and income, Malpezzi (1999) investigates the impact of the regulatory environment on the ratio for major metropolitan areas (MSA) in the US. He concludes that more stringent regulations lead to higher equilibria. Typically the objectives of government interventions (housing allowances,
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public housing, development restrictions) are to address market inefficiencies or redistribution of income and wealth.
Lastly, socio-economic factors like age and educational qualifications can have an effect on the measured affordability ratio. Montagnoli and Nagayasu (2013) report a significant effect of age and academic qualifications on the house price to earnings ratio (HPER) in the United Kingdom. From the twelve UK regions investigated, the ones with younger population tend to have higher HPERs, as younger people starting their careers have no other choice than to buy a more expensive house relative to their earnings. The academic qualification variable implies that low-qualified people are in a similar position to the young: they tend to purchase a higher valued property in relation to their income. Besides the age and qualification, the authors also confirm that the mortgage rate is an important explanatory variable for the affordability ratio.
3 Methodology
This section begins with a discussion of several methods of determining convergence in general. It continues with choosing a technique (pairwise approach) and suggesting a methodology (ADF and DF-GLS tests) to measure and test the long-run convergence in the affordability of housing. The central feature of the measurement of convergence has been assessed in a number of different ways in the growth literature. The so-called beta-convergence implies a negative relationship between the change of a variable and its initial starting value. This denotes that entities with a lower initial ratio are expected to reach an equilibrium level faster than those with a higher one. On the other hand, the series with higher values are supposed to grow at a slower pace than their counterparts. Sigma-convergence describes a situation where the distribution of the observed data is becoming more equal every period. This means that the
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standard deviation (represented by the Greek letter sigma, σ) of a sample is decreasing over time. In the current context, the cross-country distribution of the price to income ratio should narrow for convergence.
Furthermore, two varieties of convergence are distinguished in the classical literature- conditional and absolute convergence (Sala-i-Martin, 1996). If all markets converge to the same steady state level, the convergence is called absolute (unconditional). As already mentioned in the previous paragraph, the less developed markets are expected to grow at a higher rate in this case. On the contrary, conditional convergence assumes that the markets of different regions converge to their own steady state. Conditional convergence is probably more likely to be found in the real estate markets when the models are tested for international housing markets.
Recently, the ´pairwise approach´ has gained popularity as a method for measuring long-run convergence (Hiebert & Roma, 2010) (Abbott & De Vita, 2013) (Pesaran, 2004). One of the advantages is that convergence across all of the combinations can be tested without use of a benchmark. Besides that, the pairwise method does not require the measured time series of the affordability ratio to have identical underlying economic conditions, like mortgage rates, regulatory environments and population growths (Pesaran, 2004). Additionally, the convergence can be measured for a large number of countries or cities simultaneously. As a first step, this approach compares all possible pairs of affordability ratio differentials among cities. After that, unit root tests are employed to determine which pairs of cities appear to have trend-reverting behavior.
Stochastic convergence can be tested by performing Augmented Dickey-Fuller (ADF) test. The null hypothesis of the test assumes that a variable has a unit root (i.e. is non-stationary).
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Therefore, a rejection of the null is needed to argue for a stationary process, implying no unit root. The affordability ratio differential variable for each pair is defined as the difference between ratios of the two observed cities at time point t; 𝒅𝒅𝒊𝒊𝒊𝒊𝒊𝒊 = 𝑟𝑟𝑖𝑖𝑡𝑡− 𝑟𝑟𝑗𝑗𝑡𝑡.
The ADF test uses an ordinary least squares (OLS model) regression of the first difference (∆𝑑𝑑𝑖𝑖𝑗𝑗𝑡𝑡) against its own lagged values (𝛽𝛽𝑖𝑖𝑗𝑗𝑑𝑑𝑖𝑖𝑗𝑗,𝑡𝑡−1) and the lagged differences (𝛿𝛿𝑖𝑖𝑗𝑗𝑖𝑖∆𝑑𝑑𝑖𝑖𝑗𝑗,𝑡𝑡−𝑖𝑖) in the form of the following equation:
∆𝑑𝑑𝑖𝑖𝑗𝑗𝑡𝑡 = 𝛼𝛼𝑗𝑗𝑖𝑖 + λt + 𝛽𝛽𝑖𝑖𝑗𝑗𝑑𝑑𝑖𝑖𝑗𝑗,𝑡𝑡−1+ � 𝛿𝛿𝑖𝑖𝑗𝑗𝑖𝑖∆𝑑𝑑𝑖𝑖𝑗𝑗,𝑡𝑡−𝑖𝑖+ 𝜗𝜗𝑖𝑖𝑗𝑗𝑡𝑡 𝑟𝑟𝑖𝑖𝑖𝑖
𝑖𝑖=1
Alfa (𝛼𝛼𝑗𝑗𝑖𝑖) and lambda (λt) are optional constant and trend terms respectively which can be selected when testing for a unit root using STATA 12. The same notation is applied to house price differentials in Abbott & De Vita (2013).
According to Pesaran (2004), test of pair-wise output convergence consist of two stages. In the second stage, the hypothesis that the gap 𝑟𝑟𝑖𝑖𝑡𝑡− 𝑟𝑟𝑗𝑗𝑡𝑡 is not trended has to be tested. This assumes that the first stage unit root hypothesis has already been rejected. In this research, a total of N*(N-1)/2= 13*12/2 = 78 unique city pairs have to be analyzed, if these tests are applied to 13 cities.
The research design is further improved by using the DF- Generalized Least Square (DF-GLS) test. This modified version of the Dickey-Fuller test was first proposed by Elliott, Rothenberg & Stock (1996). They argue that the modified test has higher power in case of an unknown mean or linear trend and it works well in small samples. The DF-GLS test is using the same above-mentioned model as standard ADF.
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The data needed to test for unit roots in the time series is quite straightforward as the model relies only on its own lagged values and differences. Before applying both types of stationarity tests, a variable describing the affordability ratio difference between all of the city pairs has to be created. Comparing all possible pairs of observed capital cities gives us 78 time series variables which are to be modelled in an ADF and DF-GLS framework.
The hypothesis that the affordability ratio difference is stationary and moves towards a long run average can be tested by OLS t-statistic, testing for 𝛽𝛽𝑖𝑖𝑗𝑗 = 0 (null hypothesis) in the equation given above. Rejecting the null, the alternative hypothesis, 𝛽𝛽𝑖𝑖𝑗𝑗 ˂ 0 is that 𝑑𝑑𝑖𝑖𝑗𝑗𝑡𝑡 is stationary, has no unit root, and the two time series of the ratios are convergent. Care has to be taken when choosing critical values for the ADF statistics. Under the null hypothesis of a unit root, the ADF does not have a normal distribution and the usual critical values from the normal distribution cannot be used (Stock & Watson, 2012). The one-sided ADF test has significantly larger critical values than the standard normal distribution. The large-sample critical values of the ADF statistics are given in Stock & Watson -2.86 (intercept only) and -3.41 (intercept and time trend) at the 5% level. The critical values of the tests depend further on the number of lags used, as well as the sample size.
4 Data and descriptive statistics
Finding data on nominal house prices (the numerator of the affordability ratio) in different European countries is a complex task. The process gets even more complicated as the interest of this research focuses on the unit price (€ per square meter) of housing in capital regions. In spite of inconsistent databases and multiple sources, data were collected for 13 capital cities. Square meter prices for Central and Eastern European capital cities (Warsaw, Vilnius, Riga and
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Tallinn) can be obtained from the market researches of Ober Haus Real Estate Advisors, the largest real estate service group in the region. Prices for Scandinavian capitals (Helsinki, Stockholm, Oslo and Copenhagen) are found from the databases of Bank of International Settlements (BIS), Statistics Sweden, Norwegian Association of Real Estate Agents and Association of Danish Mortgage Banks. Greater London house prices are published by the national Land Registry. Dwelling prices for Amsterdam as well as Brussels are reported by the respective national bureaus of statistics (Statistics Netherlands and Statistics Belgium respectively). Paris per square meter prices are also reported by the BIS, and data on prices in Berlin is available from empirica, an independent economic and social science consultancy in Germany.
Statistics about Sweden, the United Kingdom, the Netherlands and Belgium include only prices for the whole property. In these cases, the price of a dwelling is divided by the average useful floor area per dwelling in that country. The average size of a dwelling is 92.8 m² in Sweden, 86.9 m² in the UK, 98 m² in the Netherlands and 81.3 m² in Belgium (Dol & Haffner, 2010).
The denominator of the affordability ratio, the average monthly gross wage, is usually reported by the national statistics office.
The sample period begins in 2003:Q4 and ends at 2013:Q4. A period of 41 quarters is an optimal choice to be able to include as many countries as possible. During these ten years, Europe´s real estate market has gone through a full business cycle- from a boom to bust. For the convenience of usage, capital cities are named after their airports: TLL (Tallinn), RIX (Riga), VNO (Vilnius), WAW (Warsaw), HEL (Helsinki), ARN (Stockholm), CPH (Copenhagen), OSL (Oslo), LCY (London), AMS (Amsterdam), BRU (Brussels), BER (Berlin) and CDG (Paris).
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Capital cities could be divided into three subgroups based on geographical locations- CEE cities (TLL, RIX, VNO, WAW), Scandinavian cities (HEL, ARN, CPH, OSL) and western European ones (LCY, AMS, BRU, BER, CDG). The mean of the affordability ratio differs between subgroups, being highest (2.2) in the CEE region and lowest in Scandinavia (1.0). The same applies to the standard deviations: the highest 0.692 in the CEE and the lowest 0.084 in Scandinavian cities. Figure 1 shows the evolution of the affordability ratios for all the cities.
Affordability ratio differentials 𝑑𝑑𝑖𝑖𝑗𝑗𝑡𝑡 = 𝑟𝑟𝑖𝑖𝑡𝑡− 𝑟𝑟𝑗𝑗𝑡𝑡 are calculated by subtracting the ratio for city j from the ratio for region i. There are a total of 78 unique city combinations after pairing all possible capital cities. The average absolute difference is 0.84 between two cities with a standard deviation of 0.580. As can be seen from Figure 2, which presents the maximum difference in ratio between each pair, the highest variations have actually decreased during the last decade. Figure 3 displays the average difference between all pairs, and is also showing a decreasing trend. Both declining absolute maximum differences as well as a reduction in
City Mean Std. Dev Min Max
TLL 1,57 0,430 1,04 2,47 RIX 2,60 1,342 1,30 5,04 VNO 2,45 0,613 1,80 3,72 WAW 2,37 0,384 1,84 3,24 HEL 1,05 0,060 0,93 1,13 ARN 1,18 0,073 1,04 1,31 CPH 0,66 0,121 0,54 0,93 OSL 1,03 0,083 0,86 1,16 LCY 1,88 0,098 1,70 2,13 AMS 0,90 0,073 0,79 1,07 BRU 0,76 0,071 0,58 0,85 BER 0,74 0,048 0,69 0,85 CDG 2,14 0,155 1,75 2,41 0 1 2 3 4 5 Ra tio 2003q3 2006q1 2008q3 2011q1 2013q3 Date
Figure 1: Evolution of the affordability ratios Table 5: Summary statistics
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average value of a differential, are factors to consider convergence in the housing affordability ratio.
Coming back to the underlying factors behind the affordability ratio, square meter price and average wage have both experienced growth in every surveyed capital city during the past decade. There is a low positive correlation (0.32) between the growth of wages and the increase in housing unit prices as can be seen from Figure 4. If Riga, a clear outlier, is dropped from the sample, the correlation rises to 0.75. Again, groups can be distinguished when the plotted data
1 2 3 4 5 M ax D if fer enc e 2003q3 2006q1 2008q3 2011q1 2013q3 Date .6 .8 1 1 .2 1 .4 A v er age D if fer enc e 2003q3 2006q1 2008q3 2011q1 2013q3 Date TLL RIX VNO WAW HEL ARN CPH OSL LCY AMS BRU BER CDG 20 40 60 80 100 120 P ric e G ro wt h 0 50 100 150 Wage Growth 1000 2000 3000 4000 5000 P ri c e per s qm 2003q3 2006q1 2008q3 2011q1 2013q3 Date
Figure 4: Correlation between the growth of wages and
the housing price inflation Figure 5: Nominal per square meter prices of subgroups Figure 2: Maximum difference in affordability ratio Figure 3: Average ratio difference between all pairs
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points are visually analyzed. Capital cities (TLL, WAW, and VNO) of less developed CEE countries have seen the highest increase in wages and prices. This is consistent with the convergence hypothesis that poorer economies are catching up with wealthier countries. Similarly, neighboring cities like Helsinki-Stockholm and Paris-London have also shown comparable growth figures. Relatively high growth rates of per square meter price for western European cities is measured in Brussels. This could be explained by Brussels being the political capital of the EU.
Nominal per square meter prices have tended to exhibit an upward trend throughout the last decade, although periods of falling values have been experienced in all countries. As expected, the nominal values are highest in Scandinavian subgroup (over 3000 €/ m²), followed by western European cities (over 2000 €/ m², with an exception of London) and CEE (over 1000 €/ m²). Averages of subgroups are graphed in Figure 5.
Unit prices have been growing at the highest rate in CEE countries, namely 1.5% annually. In comparison, the growth rate in Scandinavia has been 30 basis points lower. Western Europe has shown a growth of only 1%. The highest volatility of the growth rate of per square meter prices, 5.3% is observed in the Central and Eastern European subgroup. In contrast, the corresponding values are around 2.2% in Scandinavia and 1.5% in a group consisting of countries in Western Europe.
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5 Results
In this section, the results of empirical analysis using two different unit root tests are provided. Thereafter, economic meaning is given to the controversial outcomes and the results are related to other recent studies on the same topic.
Results are first presented for unit root tests on all possible pairs of affordability ratio differentials. The standard ADF test is conducted on 13x 12/ 2= 78 unique pairs of cities and includes T= 41 quarterly observations from 2003:Q4 to 2013:Q4. These 78 tests are all performed at the 5% level of significance, with and without including trend terms in the regression. To argue for the overall convergence between cities, the number of rejections of the null hypothesis should be close to the nominal size of the test (Pesaran, Smith, Yamagata, & Hvozdyk, 2009). The rejection probabilities range from 6.4% (5 out of 78) in the case of ADF (choosing the lag length using the Schwarz information criterion) to 39.7% (31 out of 78) in the case of DF-GLS tests (lag length selected by the SIC).
The rejection rate is only 7.7% (6 out of 78 tests) when using ADF without a trend term in the regression for all the pairs. As several graphs show a trend that occurs over time, the trend term is added and the tests are run again. Not surprisingly, 22 (28.2% of the total sample) additional converging pairs are found. The underlying graphs for these pairs exhibit clear up- or downward trends. Pairs rejecting the statistical null hypothesis from both regressions don´t overlap, so the standard ADF test detects 28 (35.9% of total) stationary pairs in total. Table 6 shows the number of pairs rejecting the unit root hypothesis using both ADF and DF-GLS tests, with lag lengths chosen according to the SIC and Ng–Perron sequential t-methods.
27 Order selection criterion Unit root tests
Deterministic ADF DF-GLS
Model with an Intercept only Ng–Perron sequential t 6/78 30/78
Model with an Intercept only Min SIC 5/78 31/78
Model with an intercept and trend term Ng–Perron sequential t 22/78 27/78
Model with an intercept and trend term Min SIC 6/78 20/78
Table 6: Number of pairs rejecting the null hypothesis of ADF and DF-GLS tests for unit root at 5% significance level
Using a modified Dickey-Fuller test for a unit root, DF-GLS rejects a higher fraction of tests performed on the stationarity of the affordability ratio differentials. The null hypothesis of a unit root could be rejected 45 out of 78 times at the 5% significance level (using different lag lengths). This result is in line with the higher statistical power of the DF-GLS test in small samples. The maximum lag order is set to be 9 according to the Schwarz criterion.
STATA 12 also reports three different methods for choosing the optimal amount of lags. Average optimal lag length was 4.05 from the the Ng–Perron sequential t, 2.10 from the minimum Schwarz criterion (SC), and 2.12 from the Ng–Perron modified Akaike information criterion (MAIC).
After the pairs rejecting the null hypothesis of unit root have been identified, the documentation of convergence continues with determining all pairs that are stationary around a constant mean. The affordability ratio differential, 𝑟𝑟𝑖𝑖𝑡𝑡− 𝑟𝑟𝑗𝑗𝑡𝑡, must not be trended under the convergence theory. As a result, standard ADF identifies only 5 converging pairs that are both stationary and have no time trend. The number of converging pairs also decreases when co-trending is considered for DF-GLS testing: 31 out of 45 pairs satisfy both of the conditions. The detailed results, for both the ADF and the DF-GLS unit root tests, are shown in the appendix. The selection of lag order is made by using the minimum Schwarz information criterion (SIC) and tests are performed assuming that the series are stationary around a mean instead of around a linear time trend. The absolute value of test statistics greater than the 5%
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critical value (also in absolute terms) marks a converging pair with a stationary affordability ratio differential and without a time trend.
The outcomes in the appendix (Table 10) present proof for the convergence for cities belonging to Central and Eastern European countries. The convergence pattern of the affordability ratio is similar for Tallinn, Riga and Vilnius: the price-to-income ratio tends to converge between the Baltic and other European countries. In western European region, convergence is only found for Copenhagen-Amsterdam, Copenhagen-Berlin, Oslo-Amsterdam and Oslo-Berlin pairs. Interestingly, in this setting, Warsaw is closer to the group of western countries (converging only with Riga and neighboring Vilnius).
The test results could be further examined by dividing cities again into tree above-mentioned subgroups: CEE, Scandinavia and western European countries. First group, CEE consists of N (N- 1)/ 2= 6 city pairs. Two of these pairs (RIX-WAW and VNO-WAW) show convergence. The same amount of pairs is presented in Scandinavian group. But none of the tests for unit roots report evidence of convergence. Similarly, the last and largest group includes ten non-converging pairs.
Stationary affordability ratio time series in the Baltics (TLL, RIX and VNO) could be explained by significant house price fluctuations during the past 10 years. Loosened mortgage lending standards, low real interest rates, partial deductibility of mortgage interest payments and weak rental markets led to increased demand for housing in the area before 2008. Nominal housing prices per square meter had increased by more than 150% from the beginning of 2000s in all Baltic capitals.
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This situation changed dramatically during the crisis period. In Estonia, Latvia and Lithuania, household disposable income fell by 4-14% from the year 2008 to 2009 (Eurostat, 2014). This had a negative impact on the prices and on the quality of banks´ loan portfolios. According to the European Commission, the imbalances in the adjusted affordability index (house price-to-GDP per capita ratio) increased noticeably in the years up to 2007 (Kosicki & Bukeviciute, 2012). Based on the analysis of the affordability index and price-to-rent ratio, the Baltic States had experienced high deviations from the equilibrium level of house prices up to 2007, with a correction thereafter. The positive results on the convergence found in this research could be justified by the fact that the indicator had returned to the initial reference point levels by 2011. The economic meaning behind these results is that large deviations from the long-run trend in affordability ratio could be a sign of another housing bubble. Low interest rates and increasing amounts of mortgage lending are leading to increasing prices in the housing market by further decreasing affordability. In addition, mortgage interest rate deductibility in Estonia has encouraged borrowing by households, driving up residential real estate prices.
These results are, in the context of the more general research, in line with findings in previous studies based on EU residential real estate price convergence. Even though Hiebert & Roma (2010) test convergence of house prices only at the national level in Germany, Spain, France and Italy, their results for weak long-run convergence could be generalized to the wider region. According to their OLS findings, income differentials and population differences play a role in explaining city-level house price dispersions.
In this research, the affordability ratio already captures the effect of income differentials between countries. Measuring the price-to-income is done by using the average salary as a
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denominator. Thus, differences in demographics and socio-economic conditions of different countries and regions in Europe could explain the existence of distinct affordability ratio levels moving more or less together in time.
Smullen and Macdonald (2007) argue for the continuing low degree of convergence, using the same rationale that social attitudes towards owning a home, gaps in living standards and regulatory frameworks of property markets, are and will remain diversified in Europe. Considering the actual price of housing in different countries to corresponding GDP per capita over time, they state that there is no reason for this value to be the same across regions. Even though the GDP per capita levels could be converging in European countries.
In addition to economic and social differences, residential real estate markets are still local in their nature, despite the European convergence process in general. Real estate is a non-tradable good. Non-tradable goods are not traded internationally and the price determination is not taking place in the world market (Jenkins, Kuo, & Harberger, 2011). Furthermore, even if commercial real estate can be bought and sold internationally, housing demand is highly dependent on the local population.
6 Robustness checks
To check the robustness of the results, another test for stationary time series, the Kwiatkowski– Phillips–Schmidt–Shin (KPSS) test is applied to the same dataset. The KPSS method for analyzing time series data in order to address stationarity was developed by Kwiatkowski, Phillips, Schmidt and Shin (1992). The authors express concerns about the fact that standard unit root tests, which are also used in this research, fail to reject the null hypothesis of a unit root too
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often. They argue that economic time series lack of information about a unit root and should be tested with a null hypothesis of stationarity against the alternative of a unit root.
Thus, affordability ratio differentials for converging city pairs should not be able to reject the null hypothesis of level stationarity. The level stationarity means again that the differential is stationary around a mean instead of around a trend (same restriction was used before for the ADF as well as the DF-GLS).
Interestingly, this time the null hypothesis of stationarity is rejected for the Eastern European cities, with an exemption of Warsaw. According to the test results, ratio differentials between the capitals of the Baltic countries and all other cities exhibit unit root behavior in all possible pairs. Instead, convergence is observed within subgroups of Scandinavian and western European cities. In Scandinavia, three pairs out of six (HEL-ARN, HEL-OSL, ARN-OSL) fail to reject the null hypothesis of the KPSS when the tests are performed with two lags (Table 12 in the appendix). The same proportion of pairs (5 out of 10) indicate level stationarity when the test is conducted for western European cities. London-Brussels, London-Berlin, London-Paris, Amsterdam-Berlin and Brussels-Paris all have level reverting time series of affordability ratio differentials.
This can be a result of differences in the construction of ADF and KPSS tests. Pesarana (2004) presents an example of a contradictory outcome of pairwise test, where 𝑦𝑦1𝑡𝑡− 𝑦𝑦2𝑡𝑡 and 𝑦𝑦1𝑡𝑡− 𝑦𝑦3𝑡𝑡 are both stationary with constant means by application of the KPSS test. Therefore, 𝑦𝑦2𝑡𝑡− 𝑦𝑦3𝑡𝑡 should also be stationary. But according to him, this doesn´t have to be the case in small samples because of the low power of testing for stationarity or unit roots. Mixed results may also be obtained due to imperfections in both tests. Besides that, the KPSS test is relatively
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sensitive to the lag length used: testing with the first lag only, the null hypothesis of stationarity will be rejected for 15 additional pairs out of 25. As the typical test for stationarity is the ADF and the KPSS is a complementary test used to see whether a time series is between stationarity and non-stationarity, the DF-GLS is chosen as a better fit for this research. The main advantage for DF-GLS is the higher power of the test in small samples.
According to the KPSS test, affordability ratio differentials between the capital of Poland, Warsaw (WAW) and other western (LCY, AMS, BRU, BER, CDG) as well as northern European capitals (HEL, ARN, CPH, OSL) are converging. These converging patterns of the time series are similar to the results of the Baltic countries described earlier. The average per square meter price in Warsaw had more than doubled in the 2003-2007 period. Since its 2007:Q3 peak, the average price has experienced a decline of almost 20% and the average price-to-income ratio has returned to the level of 2003. In contrast to Estonia, Latvia and Lithuania, Poland did not see a significant fall in income during the crisis. Instead, booming prices and household borrowing were decreased by the Polish Financial Supervision Authority (KNF) tightening lending regulations for mortgage loans (OECD, 2012a). New lending policies set limits for the debt service as a share of monthly income, and imposed maximum loan-to-value ratios.
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7 Conclusion
The purpose of this research was to define, measure, and test for stochastic convergence of the housing affordability ratios among European capital cities. The affordability ratio was calculated for 13 cities and the pairwise approach implemented to measure long-run convergence between city pairs. The advantage of the method is that analysis of all 78 pairs can be performed without a benchmark to compare them against. Furthermore, the test results can be divided into regional groups, thereby studying convergence within specific geographic areas. It is found that the empirical analysis of the unit root gives controversial results. According to the DF-GLS tests, the strongest convergence appears to be taking place between the Eastern European and Western European countries. The shape of the graphs of the converging pairs are all similar in that the affordability ratio differential has experienced a large deviation from the long-term average in the first half of the 10-year period. On the other hand, ADF and KPSS tests tend to detect converging city pairs which are exhibiting more fluctuations around a given average (see Figure 6 to Figure 12 in the appendix). As such, the use of different methods is yielding different results.
The mixed outcomes are in line with the limited evidence of long-term convergence in the related literature, especially at the EU level (Smullen & MacDonald, 2007) (Vansteenkiste & Hiebert, 2009). Convergence found between the capitals of the Baltic States and the rest of Europe can be explained by significant house price fluctuations during the past 10 years. Worsening affordability issues in the Baltics over the 2005 to 2009 period have been raised by Kolbre and Kallakmaa-Kapsta (2013) and are clearly seen in the quarterly research reports of the housing affordability index calculated by Sweden’s largest bank, Swedbank (2014).
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Several limitations are worthy of note in interpreting the results of this research. First, the data only cover a short time span; from 2003 to 2013. The power of unit root tests is relatively low in short time periods and could be only partially compensated by using DF-GLS in combination with standard ADF tests. Besides that, the data collection in general was more challenging than expected. Different countries across Europe are using a variety of methods (e.g. price per square meter, price per dwelling unit) to report housing prices, if at all. The latter is especially true for eastern European real estate markets, of which the most transparent are the Baltics and Poland. Second, methodological issues arise when testing for stochastic convergence in the affordability of housing. Other than unit root tests being problematic at short time intervals, they cannot differentiate stationary from non-stationary processes well enough, and tests including a constant and trend in the regression have less power than the ones including only a constant (Zivot & Wang, 2006). As a robustness check for the results obtained by the ADF and DF-GLS, the KPSS test with the null hypothesis of stationarity was used in this research.
Lastly, the main aim of this thesis was to examine stochastic convergence in the affordability of housing. Therefore, no attempt was made to identify common determinants of the affordability ratio itself.
The central finding; no overall convergence in affordability ratios across European capital city regions, can be justified by the fundamentals of the local housing markets. These differences, in turn, result from local economic conditions. Thus, the continued existence of a housing affordability gap has implications for the evaluation of house prices, the assessment of social inequality across countries, and can be used to guide national housing policies.
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Firstly, the affordability indicator can be applied to identify over- or undervaluation in the housing market. This was perfectly illustrated by the Baltic countries experiencing a rapid growth both in house prices as well as affordability ratios (decreasing affordability!) during the first half of the study period. Secondly, inequalities in affordable housing are causing disparities in health and environmental conditions of living and working (Oxley, 2004). Affordable and good quality housing is an important determinant for people´s wellbeing. Lastly, local governments can apply and evaluate national housing policies regarding prevailing affordability ratio levels. The future research could investigate and identify common determinants of housing affordability ratio in different sub-markets and extend the examined time period to the long-run equilibrium rate of affordability.
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9 Appendix
ADF4 TLL RIX VNO WAW HEL ARN CPH OSL LCY AMS BRU BER CDG
TLL - -1,134 -1,400 -1,874 -1,951 -1,686 -1,853 -1,671 -1,117 -1,988 -1,773 -1,929 -1,753 RIX - -1,207 -1,661 -1,751 -1,712 -1,750 -1,658 -1,543 -1,806 -1,720 -1,785 -1,637 VNO - 1,757 1,574 1,724 1,423 1,360 1,280 1,575 1,566 1,607 1,130 WAW - -1,951 -2,111 -2,205 -2,152 -1,360 -2,137 -2,447 -2,234 -1,693 HEL - -1,404 -1,503 -2,692 -1,815 -0,619 -3,232 -2,341 -3,495 ARN - -1,637 -2,177 -1,378 -0,044 -3,053 -2,036 -3,163 CPH - -1,510 -0,004 -2,424 -1,319 -1,484 -1,515 OSL - 0,004 -2,424 -1,319 -1,484 -2,826 LCY - -0,308 -2,246 -1,975 -2,946 AMS - 0,083 -1,392 -1,929 BRU - -1,708 -3,270 BER - -2,996 CDG -
Table 7: Values of the test statistics from the standard ADF unit root tests. The number of lags is set to four and the trend term is excluded. Grey shaded values in the table indicate converging pairs. This means, that the null hypothesis of a unit root can be rejected and the affordability ratio differential is stationary. The 5% critical value is -2.969.
ADF2 TLL RIX VNO WAW HEL ARN CPH OSL LCY AMS BRU BER CDG
TLL - -1,252 -2,058 -1,527 -2,075 -2,312 -2,257 -1,918 -1,909 -2,206 -2,441 -2,369 -1,721 RIX - -1,319 -1,759 -1,863 -1,758 -1,784 -1,716 -1,742 -2,073 -1,767 -1,922 -1,708 VNO - -1,689 -1,157 -1,128 -1,137 -1,066 -0,934 -1,197 -1,012 -1,241 -0,964 WAW - -1,463 -1,333 -1,853 -1,291 -0,942 -1,872 -1,385 -1,548 -1,424 HEL - -1,516 -1,546 -2,911 -1,919 -0,403 -3,759 -2,138 -3,082 ARN - -1,182 -1,754 -1,036 -0,561 -3,047 -1,682 -2,709 CPH - -1,530 -1,576 -2,184 -1,069 -1,662 -1,540 OSL - -1,576 -2,184 -1,069 -1,662 -2,609 LCY - -0,701 -2,851 -2,973 -2,431 AMS - -0,560 -0,731 -2,107 BRU - -4,068 -2,204 BER - -2,704 CDG -
Table 8: Values of the test statistics from the standard ADF unit root tests. The number of lags is set to two and the trend term is excluded. Grey shaded values in the table indicate converging pairs. This means, that the null hypothesis of a unit root can be rejected and the affordability ratio differential is stationary. The 5% critical value is -2.964.
DFGLS TLL RIX VNO WAW HEL ARN CPH OSL LCY AMS BRU BER CDG
TLL - -1,613 -1,348 -1,940 -2,877 -3,097 -2,741 -2,538 -2,889 -3,303 -2,111 -3,377 -2,364 RIX - -1,195 -2,449 -1,592 -2,822 -2,872 -2,831 -2,624 -2,976 -1,554 -2,942 -2,552 VNO - -3,257 -3,939 -3,865 -3,048 -3,159 -3,071 -4,876 -3,478 -3,807 -2,839 WAW - -0,859 -1,188 -0,873 -1,123 -1,211 -0,913 -0,885 -1,009 -0,943 HEL - -0,873 -2,194 -1,164 -1,735 -0,547 -1,107 -1,308 -1,216 ARN - -1,406 -2,320 -1,140 0,468 -2,117 -0,819 -1,406 CPH - -1,695 -0,805 -3,232 -1,744 -2,753 -1,551 OSL - -0,805 -3,232 -1,744 -2,753 -1,273 LCY - -0,414 -1,034 -1,041 -1,660 AMS - 0,563 -0,822 -0,612 BRU - -1,772 -1,460 BER - -1,005 CDG -
Table 9: Values of the test statistics from the DF-GLS unit root tests. The number of lags is chosen by the Ng-Perron sequential t and the trend term is excluded. Grey shaded values in the table indicate converging pairs. This means, that the null hypothesis of a unit root can be rejected and the affordability ratio differential is stationary. The 5% critical value depends on the number of lags used.
40
DFGLS TLL RIX VNO WAW HEL ARN CPH OSL LCY AMS BRU BER CDG
TLL - -1,613 -2,244 -1,422 -2,889 -3,097 -2,741 -2,548 -2,889 -3,276 -3,573 -3,377 -2,364 RIX - -1,195 -2,402 -3,020 -2,544 -2,872 -2,633 -2,799 -3,263 -2,987 -2,942 -2,280 VNO - -3,290 -2,978 -2,954 -2,657 -2,768 -3,071 -3,404 -2,758 -3,055 -1,795 WAW - -0,859 -1,188 -0,873 -1,123 -1,211 -0,913 -0,885 -1,009 -1,420 HEL - -0,873 -2,194 -1,566 -1,203 -0,352 -1,167 -1,308 -1,216 ARN - -1,524 -1,708 -0,778 -0,551 -1,736 -0,935 -1,406 CPH - -1,542 -1,731 -3,232 -1,267 -2,709 -0,425 OSL - -1,731 -3,232 -1,267 -2,709 -1,273 LCY - -0,730 -1,582 -1,662 -1,660 AMS - 0,510 -0,461 -0,612 BRU - -0,493 -1,523 BER - -1,005 CDG -
Table 10: Values of the test statistics from the DF-GLS unit root tests. The number of lags is chosen by the minimum Schwarz information criterion (SIC) and the trend term is excluded. Again, grey shaded values in the table indicate converging pairs. This means, that the null hypothesis of a unit root can be rejected and the affordability ratio differential is stationary. The 5% critical value depends on the number of lags used.
KPSS1 TLL RIX VNO WAW HEL ARN CPH OSL LCY AMS BRU BER CDG
TLL - 1,580 0,798 1,050 1,250 1,260 1,020 1,380 1,290 1,050 1,310 1,090 1,510 RIX - 1,530 1,520 1,520 1,520 1,510 1,570 1,530 1,470 1,550 1,480 1,630 VNO - 1,340 1,270 1,300 1,150 1,350 1,280 1,190 1,340 1,160 1,500 WAW - 0,521 0,525 0,478 0,542 0,530 0,416 0,533 0,476 0,627 HEL - 0,468 1,510 0,183 0,205 1,060 0,408 0,629 0,631 ARN - 1,480 0,284 0,381 1,480 0,272 0,609 0,527 CPH - 1,780 1,240 0,760 1,720 1,070 1,810 OSL - 1,240 0,760 1,720 1,070 0,719 LCY - 0,646 0,332 0,213 0,523 AMS - 1,390 0,628 1,210 BRU - 0,858 0,438 BER - 0,727 CDG -
Table 11: Values of the test statistics from the KPSS stationarity tests. The tests are performed with one lag. Grey shaded values in the table indicate converging pairs. This means, that the null hypothesis of stationarity cannot be rejected. The 5% critical value is 0.463.
KPSS2 TLL RIX VNO WAW HEL ARN CPH OSL LCY AMS BRU BER CDG
TLL - 1,070 0,579 0,722 0,847 0,857 0,698 0,934 0,879 0,717 0,889 0,742 1,020 RIX - 1,040 1,030 1,030 1,030 1,030 1,060 1,040 0,996 1,050 1,000 1,100 VNO - 0,923 0,868 0,890 0,794 0,920 0,880 0,813 0,914 0,795 1,020 WAW - 0,361 0,365 0,332 0,374 0,370 0,291 0,371 0,331 0,435 HEL - 0,340 1,020 0,134 0,151 0,744 0,311 0,453 0,462 ARN - 1,010 0,204 0,275 1,080 0,208 0,432 0,388 CPH - 1,210 0,870 0,522 1,170 0,733 1,240 OSL - 0,870 0,522 1,170 0,733 0,525 LCY - 0,469 0,246 0,156 0,379 AMS - 0,990 0,438 0,863 BRU - 0,611 0,325 BER - 0,523 CDG -
Table 12: Values of the test statistics from the KPSS stationarity tests. The tests are performed with two lags. Grey shaded values in the table indicate converging pairs. This means, that the null hypothesis of stationarity cannot be rejected. The 5% critical value is 0.463
