analysis of real estate bubbles in eight residential ......single household’s account for a major...
TRANSCRIPT
ANALYSIS OF REAL ESTATE BUBBLES IN EIGHT RESIDENTIAL MARKETS
TESTING FOR ECONOMETRIC REGIME SHIFTS AND CONCORDANCE OF BUBBLE INDICATORS USING
FUNDAMENTAL BASED METHODS
By Robert Kuert
Examiner: Prof. Didier Sornette Supervisors: Dr. Dorsa Sanadgol, Diego Ardila Alvarez
Master Thesis submitted to the Chair of Entrepreneurial Risks in partial fulfillment of graduation requirements for the degree of
Master of Science
in Spatial development and infrastructure systems
September 2016
Master Thesis MSc SD&IS September 2016
Robert Kuert Cäsar Ritz Strasse 5 [email protected]
Abstract This study analyses results of real estate bubble indicators of fundamental based methods for eight OECD housing markets, using aggregate quarterly series from 1970Q1 to 2015Q4. Including up to five macroeconomic fundamental variables per country, a previously developed error correc-tion and cointegration vector autoregressive (CVAR) model are employed, which were formerly only applied to US data. Moreover, the collected property prices are investigated for a faster than exponential growth as a complementary bubble indicator. Results are aggregated and compared specification and country wise, using a binary cycle concordance indicator.
The results display high concordances between the estimated bubble indicators for France and the UK on the one hand, and New Zealand, Germany, Switzerland and the Netherlands on the other hand. Possible bubble regimes were found in Canada, New Zealand in recent years, and in Japan for past periods. However, data diagnostics showed problematic cases. Overall, the used methods showed a high sensitivity in small changes in data.
Keywords Housing, Bubble, Econometrics, Fundamentals, Cointegration, ECM, VAR
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Table of contents 1 When prices go over the roof Introduction to housing bubbles ............................. 1
1.1 Research in the field of housing bubbles .................................................................. 1
1.2 Research Focus ........................................................................................................ 2
2 Bubble indicators based on fundamentals ............................................................. 4
2.1 Cycle or bubble? Formal definition of a housing bubble ......................................... 4
2.2 Fundamentals ........................................................................................................... 5
2.3 Integration, Cointegration and their implications ...................................................... 9
2.4 Housing bubbles and cointegration ........................................................................ 11
3 Methodology ........................................................................................................ 14
3.1 Error correction modelling using price to rent and inverted demand benchmarks . 14
3.2 Cointegration Vector Error Correction Model ......................................................... 18
3.3 Model estimation ..................................................................................................... 19
3.4 Testing for super exponential growth ..................................................................... 20
3.5 Binary cycles: concordance of bubble indicators ................................................... 22
4 Data Description and temporal properties ........................................................... 24
4.1 Variable descriptions .............................................................................................. 24
4.2 Unit root tests .......................................................................................................... 37
4.3 Comparing price-fundamental benchmarks............................................................ 38
5 Results ................................................................................................................. 41
5.1 Altering the data for the United States .................................................................... 41
5.2 Cross country study ................................................................................................ 45
5.3 Concordance of binary cycles ................................................................................ 52
5.4 Robustness of long run coefficients and significance ............................................. 55
6 Discussion ........................................................................................................... 59
6.1 Comparing results to existing findings .................................................................... 59
6.2 Limitations ............................................................................................................... 61
7 Conclusions ......................................................................................................... 63
8 Acknowledgements .............................................................................................. 64
9 List of references ................................................................................................. 65
10 Appendix .............................................................................................................. 69
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A. Data Statistics and time series ............................................................................... 69
B. Order of integration test results .............................................................................. 78
C. Results for the single equation specification .......................................................... 83
D. Results for the cointegration vector autoregressive model .................................... 85
E. Concordance indices .............................................................................................. 87
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1 When prices go over the roof
Introduction to housing bubbles
1.1 Research in the field of housing bubbles
A particular interest in the development of housing prices grew in the aftermath of the US housing bubble and the following recession that spread around the world as a consequence. For many it seemed difficult to understand how defaults of mortgage borrowers could trigger distant effects like the collapse of investment banks such as Lehmann Brothers. Even more surprising seemed the subsequent government bail outs of AIG in the US or the one of UBS in Switzerland, institutions that were heavily exposed to mortgage backed financial products. People and eco-nomic researches alike therefore became more aware of the seemingly more intertwined finan-cial system and – this part being focus in this thesis –housing prices.
The relevance of housing in the context of Economics is high. The $26 billion of housing stock in the United States form maybe the biggest asset class in the world. Attached to it are around $11 billion in mortgage debt, from which $1 billion belong to lenders from abroad, altogether incorporating one of the most extensive concentrations of financial risks (The Economist 2016). Likely, this distribution can look very similar in other countries and some of the risks might not be revealed yet.
Therefore, it is not surprising, that various institutions, be it governmental, academic or private, strive to find appropriate risk metrics or, when analyzing price levels, bubble indicators. The Chair of Entrepreneurial Risks of ETH Zürich for instance investigates criticality within the housing market of prices in Switzerland using asking data on a district level and publishing bi-annual reports. Similarly, UBS presents a real estate bubble index1 for Swiss districts, and since 2015, for 15 selected cities worldwide. However, the debate about housing bubbles is far from being settled and research about appropriate measures is ongoing and conflicting. This work will shed light on some of the most recent econometric techniques that pioneer in the field, so called fundamental based approaches, and will explore the application of a promising specifi-cation onto a set of eight OECD economies. 1 Measure takes in to account housing only, not other types of real estate, although the name might suggest other-
wise. https://www.ubs.com/global/en/about_ubs/media/switzerland/releases.html
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Housing is especially relevant, because the asset involved is not only held by private, capital strong investors. This would be typical for the commercial real estate sector. In contrast, private single household’s account for a major share in the housing domain and connected to this is an outstanding sum of mortgage loans – household’s main liabilities. On top of that, if the legal environment and bank practices are securitization friendly, loans can be bundled and sold, ex-tending the dependencies of the loans – and therefore the risk of default from the owner. Isolated defaults and related foreclosures are not necessarily a problem. If, however properties are in general overvalued and the mortgage debt is by far bigger than market prices reflect, spillover effects are inevitable, as was seen in the US housing bubble before 2008. So it is in the interest of both property owners and investors that houses are fairly valued and prices reflect the current market situation.
For a brief time, a bubble in the housing market is characterized by a long period of irrational and unjustified price increases, followed by price correction. Real estate bubbles can have se-rious impacts on other markets or the economy as a whole. Reasons for the price regime shifts in housing markets can be various, but often they are related to speculation and high capital gain expectations. With increasing prices, demand (counter intuitively) is increasing as well, because people expect prices to inflate even further (Meen 1990, Jowsey 2011). These can then pass on shocks to the real economy, for instance when households withdraw equity from their mortgage for an increase in consumption, as happened in the early 2000s (Anundsen 2013). According to Black et al. (2006), house busts have a much stronger effect on the economy than stock busts. This is why understanding them better is also important for policy making.
1.2 Research Focus
The main interest of this study is to use the recently developed real time bubble indicator meth-odology by Anundsen (2013), which gave promising results for the United States (US), to as-sess price – fundamental relationships in other economies. This includes an analysis of the re-lated scientific contributions, the collection of appropriate and comparable time series data, reporting of the results and the comparison of the findings with other contributions. Further-more, it attempts to explore differences between the result of the fundamental based studies in comparison with the super exponential growth bubble diagnostic derived from the methodolog-ical framework from Zhou and Sornette (2006), who identified successfully the US housing bubble.
Within the focus on prices, the emphasis lies only on housing, which includes all residential property, regardless of dwelling types, e.g. whole houses, single flats or mixed use property. Excluded are land prices, which are generally difficult to measure, and all other classes of real
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estate, such as commercial, retail or logistics space. Once again it should be stressed, that hous-ing often forms the biggest asset class of economies, which leads to its price developments being so prominently relevant.
Since housing concerns macroeconomics and often high level policies, studies on residential property price developments are addressed on a national level and the associated economic research is conducted by big governmental or super governmental organizations, in particular central banks or bodies like the Bank of international settlement (BIS), the international mone-tary fund (IMF) or the organization of economic cooperation and development (OECD). This thesis follows related studies and therefore also puts the emphasis on a country level investiga-tion, relying on macroeconomic time series. The temporal resolution is quarterly. Historical values of housing prices are considered as far back as to 1970, therefore incorporating some identified bubble-bust cycles, allowing for possible ex-post diagnosis’. Also captured is the span of the housing bubble in the US, in order to investigate possible co-movements of prices in other countries.
After this introduction, the second chapter outlines the formal definitions of housing bubbles in the economic literature and reviews previously completed empirical studies for selected coun-tries. The role of fundamentals and the motivation for following the research line of Anundsen (2013) will also be discussed. In chapter three, the modeling approaches and their specifications are given, whereas chapter four describes the data set for the eight collected countries. Results are presented in chapter five, followed by a discussion and encompassing of the results within the literature in chapter six. Conclusions are drawn in the closing chapter.
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2 Bubble indicators based on fundamentals
Researches, regulators and industry alike are monitoring the housing market on a macroeco-nomic scale. However, there has been no consensus on how to spot overvaluation and “bubble”-like price developments as mentioned by Girouard et al. (2005) or Anundsen (2013). Nonethe-less since the 90ies there has been some consolidation of the formal definition of a bubble and in particular the link to macroeconomic fundamentals has become more evident through empir-ical research.
2.1 Cycle or bubble? Formal definition of a housing bubble
The most common definition of a bubble applied to the housing market is the one by Stiglitz (1990):
“If the reason that the price is high today is only because investors believe that the selling price is high tomorrow – when “fundamental“ factors do not seem to justify such a price – then the bubble exists.“
Very similar and expressing the same two components is the definition, by Schiller:
“An asset price bubble is a price acceleration that cannot be explained in terms of the underlying fundamental conditions (Case and Shiller 2003). The most important non-fundamental element driving price increases is the belief that prices will con-tinue to rise” Dreger and Zhang (2013).
These definitions combine the elements, that (a) fundamentals do not explain the price, and (b), that there is speculative behavior and (capital gain) expectations, meaning a price-price inter-action, involved. But an extraordinary upturn in housing prices does not necessarily indicate a bubble, as Case and Shiller (2003) state. Also it is noteworthy, that a bubble implies overvalu-ation but not vice versa. Conversely, even seemingly high prices can potentially be justified by current market conditions. For instance, the current pressure on investment due to low interest rates observed in Switzerland could represent such a regime. In this case, high prices could possibly be explained by the all-time low (and even negative) interest rates. Therefore, it is important, to analyze if price developments are somehow justified by movements in these so called “fundamentals”, namely macroeconomic variables that are connected to those prices.
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Economic theory dictates that they should be linked by a long term relationship to the prices of houses, representing a rational allocation of economic resources (Stiglitz 1990).
Furthermore and as seen by a ”long-term perspective, the equilibrium price a household is will-ing to pay for a house should be equal to the present discounted value of future services pro-vided by the property” (Glindro et al. 2011). “This financial approach implies exploiting the relationship between house prices and rents, as originally proposed by Case and Shiller (1989)” (Antipa and Lecat 2010). These mentioned methodologies sometimes appear combined and are not mutually exclusive, which is why both will be covered in the following sections. Neverthe-less, the empirical literature is mostly focused on one set of methods, depending highly on the availability and structure of data. The detailed functional forms and lags included also tend to be largely data determined (Muellbauer and Murphy 1997). It is hardly necessary to mention, that with these data driven macroeconomic approaches one enters the domain of econometrics, e.g. applying statistical methods on observational data (Wooldridge 2014).
Moreover, there is an ongoing discussion about the stochastic nature of bubbles in the economic literature of bubbles. For instance, Kim and Min (2011) state that bubbles are considered to be stochastic because they may survive or burst at each point in time. Still it is “decidedly difficult to know when or even if, a price bubble will collapse”. However mathematical rigorous research is pursued to look for such “tipping points”, for instance by Zhou and Sornette (2006) or Ardila et al. (2016). After such a peak, price corrections can be quick (in economic terms several con-secutive quarters or years) or, like historical trends show, deflate slowly over time, as observed in Switzerland during the late 90ies (Ambrose et al. 2013). Additionally, Helbling (2005) and other researchers pointed out, that booms are in general followed by busts. However it is not necessary that there is a quick price correction at all. Rather the focus switched to business cycles, introduced byBuckley and Ermisch (1982), whose applications of life cycle models spread in the research on housing markets, both theoretically and empirically. Most abundant in macroeconomic analyses up to date are econometric models in a time series context. Namely these are vector autoregressive (VAR) and error correction models (ECM), where in the latter cointegration tests, given first by Engle and Granger (1987) play a gradually improving role. Their applications and the of house prices shall be reviewed in the following chapters, however, first the key fundamental determinants of property prices are explored.
2.2 Fundamentals
To judge on a given price for real estate, it makes things a lot easier to consider the price in relation to its realizable rent or cash flow. If a property investment would pay off quickly, say in 5 years, it definitively is a good investment. This logic of ratios can be extended to the mac-roeconomic scale, allowing the construction of benchmarks, of which in particular the price-to-rent and the price-to-income approach have become very prominent. Girouard, Kennedy et al.
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(2005) already showed, how these ratios can help to assess overvaluations especially when comparing economies. Furthermore, studies like those from Cadil (2009) and Kim and Lim (2014)used these benchmarks as bubble indicators. They were able to compare actual and cal-culated price-to-rent ratios, which allowed them to make statements about overvaluation, in particular by extending the studies to compare different economies. However, alongside rents and income there are various other macroeconomic variables connected to property prices and the question still circulates, what particular fundamental metrics explain prices.
Also Stiglitz (1990), with his fundamental driven bubble definition, left open, what specific macroeconomic variables qualify in general or at best as fundamentals. Nevertheless, this topic has been covered extensively both theoretically and empirically for a large number of countries. Table 1 summarizes the most frequent fundamentals used in models in comparable empirical studies published within the last 10 years. Some of the determinants are now pointed out spe-cifically.
In general, the housing price index (PH) is the endogenous metric; however, the price-to-rent ratio (P/R) or the price-to-income ratio (P/I) are often included as explained variable. Alongside the rents, typical productivity measures connected to price levels are usually the gross domestic product (GDP) or disposable income, often standardized in terms of per capita. Population or demographics are taken into account in various ways, however mostly the crude population number serves as explanatory variable, but also taken in first differences it can proxy well for migration effects. Taxes and interest rates can simply be included as an explanatory variable or as a base variable for the user cost, a metric to proxy real costs of owning a house therefore summing up periodically returning expenses based on servicing mortgage loans which are linked to interest rates (IR), property taxes and value depreciation. Construction and the housing stock, which are both important supply side fundamental factors, are taken in to account in ten of the surveyed studies. Further fundamentals often used are the stock, urbanization or certain growth rates. It is not surprising to find a strong representation of OECD economies, since they commonly have good data pools available and the not yet dis-cussed models rely heavily on reliably and standardized data sources.
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Table 1 Fundamentals used to model housing prices in selected studies
Country First Author
Yea
r
Met
ric
GD
P or
Inco
me
CPI
Tax
es
IR
Pop
ulat
ion
Une
mpl
oym
ent
Con
stru
ctio
n Others
Australia Glindro 2011 PH X
X X
X *
Canada **Orsal 2014 PH X X
X X
Canada Kholidilin 2010 PH X X
X X
Urbanization
Czechia Cadil 2009 P/R, P/I X (X)
X X
X
China Glindro 2011 PH X
X X
X *
France Antipa 2010 PH
X X X X X
Germany Kholidilin 2010 PH X X
X X
Urbanization
Hong Kong Glindro 2011 PH X
X X
X *
Ireland Stevenson 2008 P/R X
X X
Expectations
Israel Dovman 2012 P/R X X
X
Expectations
Korea Glindro 2011 PH X
X X
X *
Korea Kim 2011 PH
X
X
Netherlands Kranendonk 2008 PH X X
X
Stock
New Zealand Glindro 2011 PH X
X X
X *
New Zealand Fraser 2008 P/I X X
Norway Jacobsen 2005 PH X X X X X X
Stock
Spain Antipa 2010 PH
X X X X X
Taiwan Peng 2011 PH X X X
Ownership
Thailand Glindro 2011 PH X
X X
X *
UK Black 2006 PH X
USA Anundsen 2013 P/R, P/I X
X X
USA Zhou 2010 PH X X
X
X
Frequently used fundamental macroeconomic variables to explain housing prices in country level studies from the past 10 years. GDP is the gross domestic product, CPI the consumer price index and IR the mortgage interest rates. Most frequent is GDP, followed by IR and population. Rents seem to be widely underrepresented and are only used in 8 studies because of data unavailability. Supply side metrics, like the housing stock, are also rarely used. The asterix (*) includes land supply, mortgage credit-to GDP ratio and other fundamentals2. ** For the sake of brevity, countries from Orsal 2014 were reduced to Canada3
Besides selecting the correct fundamentals connected to house prices, it is import to understand how they are linked. Model specifications and methods vary a lot throughout the literature. Nevertheless, of particular interest is the use of previously mentioned ECM’s, which account for long run relationships by pushing house prices back towards an equilibrium if they deviate
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too much from underlying fundamentals. Even more influential was the concept of cointegra-tion, first introduced by Engle and Granger (1987). Applying ECM’s and testing for cointegra-tion requires selected fundamentals to fulfill assumptions about the order of integration, which is discussed in the following.
2Glindro, Subhanij et al. (2011) used the following fundamentals: the effective exchange rates, stock price index,
business freedom, financial freedom, corruption, property rights. 3 The original study includes Australia, Austria, Belgium, Finland, Netherlands, New Zealand, Norway, Sweden,
Switzerland, UK and the US.
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2.3 Integration, Cointegration and their implications
In an econometric sense, fundamentals themselves should be “non-stationary economic time series” reflected by key supply and demand factors (Anundsen 2013). This requirement is nec-essary to sustain the validity of error correction frameworks.
Be reminded that stationarity means that the probabilistic character of a time series is time -invariant, or, formally expressed, that an equally spaced stochastic process{xt: t=1,2…}is iden-tically distributed and that correlation between two adjacent terms (xt, xt+1) is the same across all time periods (Wooldridge 2014) or generalized by the theorem of weak stationarity as in Binh (2013):
E[Xt] = μ ∀𝑡
Var[Xt] = σ2 ∀𝑡
Cov[Xt |Xt+k] = γ ∀𝑡 ∀𝑘
[ 1]
Stationarity or nonstationarity of a variable xt is assessed with established formal tests such as the augmented Dickey fuller test (ADF), following Dickey et al. (1984), the general formula of which reads
Δxt = μ + 𝜃xt−1 +∑𝑟𝑘Δxt−k
𝑛
𝑘=1
+ 𝑏𝑡 + 휀𝑡
[ 2]
Where Δ denotes the difference operator, defined as Δxt ≡ xt - xt-1, 휀t is the error term and 𝜃, 𝑟 and b are coefficients. Introducing n lagged terms allow to adjust for autocorrelation – meaning correlated error terms -, which leaves a purely random, e.g. stationary, process. Also note, that 𝜇 (drift) and bt (trend) are only introduced as restrictions if necessary, depending on xt, being a level or an already differenced variable. Economic time series are likely to inherit a trend and being ~I(1), meaning “trend-stationary”. This is why the generic assumption is H0: 𝜃 = 0 , im-plying xt, ~I(1), where xt is then called a unit root process. A variable is therefore called an ~I(d)-process (read integrated by the order d), if it becomes stationary after differencing d-times. So for finding xt,, for instance, the housing prices or related fundamentals are ~I(1), an ECM wont underlie spurious regression Wooldridge (2014). So this provisional formal test is critical for allowing economic time series to yield a valid error correction framework, why the former mentioned tests are widespread in literature.
Cointegration means that not a single, but a linear combination of two or more-time series is integrated by the order zero and therefore stationary. In economic theory, this describes the co-movements of variables in the long run (Engle and Granger 1987, Zhou 2010). This is mostly assessed by calculating the regression 𝑦𝑡 = 𝜇 + 𝛽𝑥𝑡 + 휀𝑡 and then testing the residuals ut, 𝑢t = 𝑦𝑡 − 𝛽𝑥𝑡 − 𝜇, for stationarity. Here [ 2] is applied on ut. However, the intercept μ can
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be removed, since calculated sample residuals have a mean of zero by design. Since more than one variable is involved now, ordinary t-values do not qualify and instead they depend on the number of variables included and the sample size4. Tests for cointegration in the context of vector based models rely mostly on the Johansen trace or eigenvalue test, allowing to assess the long run relationship between an endogenous and multiple other variables (Johansen 1991).
Since stationarity of the underlying series is a conditional assumption for any ECM, collected series are tested for unit roots (or higher order of integration) prior to inclusion with the estab-lished methods already mentioned and for a robustness check, with the framework given by Phillips and Perron (1988). Corresponding test results are given in Appendix B Order of inte-gration test results. As a robustness check, the Philipps-Perron test was also conducted. Never-theless, the assumption about integration relies on the ADF, since it is more consistent for small samples5.
So although cointegration is an appropriate measure for the long term relationship between property prices and fundamentals, it took the financial crisis of 2007 and 2008 for the finance and economic literature to become more aware of bubbles or, at least, overvaluation in property prices. Hence, the most notable contributions and their empirical results are pointed out.
4 A corresponding table with t-values was proposed by http://citeseerx.ist.psu.edu/viewdoc/down-
load?doi=10.1.1.456.4786&rep=rep1&type=pdf 5 See MacKinnon, James G. (2004). Econometric Theory and Methods
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2.4 Housing bubbles and cointegration
Empirical evidence for a formal long-term stability measure and the lack of it as a possible bubble indicator have been used in various empirical studies since the burst of the housing bubble in the US. Table 2 gives the summarized results for works assessing cointegration and overvaluation on a country level using aggregated time series.
In general, the studies include countries with good data availability (mostly OECD) and esti-mate ECM’s and in most of the cases a complementary cointegration test.The investigated sam-ples end up to four years earlier compared to the publication date, which is due to both the duration of the publication process and the lag in data publishing.
Noteworthy are in particular studies, which cover and compare results for different countries, such as the papers from Glindro, Subhanij et al. (2011) or Antipa and Lecat (2010), of whom the second authors found cointegration for Spain and France in part of the sample and overval-uation in successive periods. For nine Asia-Pacific Economies, Glindro, Subhanij et al. (2011) found fundamentals explaining prices and reject was a housing bubble, however the authors had problematic outcomes due to small sample sizes. Whereas them found no overvaluation in New Zealand, Fraser et al. (2008) reported high overvaluation using a present-value model in-stead of testing for a price-fundamental cointegration relationship. Correctly, the latter authors highlight the necessity for further work with more focus on other drivers, such as migration, which was not taken into account.
For their multinational survey, Hott and Monnin (2008) use three different cointegration tests for the housing markets of the US, UK, Japan, Switzerland and the Netherlands. Applied were the ADF, the PP and KPSS Test, whereby only the last consistently indicated cointegration for Japan and Switzerland. However, their overall testing results are in most cases contradictory. They conclude therefore, that a statistical inference on cointegration is in this case very difficult.
Moreover, Hott and Monnin (2008) found a complete disconnection between observed and fun-damental prices for the Netherlands, whereas Kranendonk (2008) rejects any overvaluation at all when using an ECM based on almost the same variables. However, the lather authors in-cluded the housing stock, what likely lead to the different outcome.
No cointegration was observed for Australia, Belgium, Finland, the Netherlands and New Zea-land by Orsal (2014), when employing a panel cointegration test based on GDP, Population and interest rates for a sample of 1989Q3 to 2010Q4. The author claimed however, that when global stochastic trends are included, cointegration could be made visible.
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Table 2 Bubble periods found for different housing markets
Country First Author Year Sample period
ECM Co-integration test
Bubble periods
Australia Glindro 2011 1993, 2006 X X
Canada **Orsal 2014 1989, 2010
X
Canada Kholidilin 2010 1975, 2009 X X
Czech Republic Cadil 2009 1998, 2006 X
China Glindro 2011 1993, 2006 X X
France Antipa 2010 1980, 2008 X X [2005, 2008]
Germany Kholidilin 2010 1975, 2009 X X
Hong Kong Glindro 2011 1993, 2006 X X [2005]
Ireland Stevenson 2008 1978, 2003 X X [1999, 2000]
Israel Dovman 2012 1996, 2010
Japan Hott 2008 1980, 2005 X X [1988, 1993]
Korea Glindro 2011 1993, 2006 X X
Korea Kim 2011 1986, 2003 X
[1986, 1997] [1999, 2003]
Malaysia Glindro 2011 1993, 2006 X X [1996] [2005, 2006]
Netherlands Kranendonk 2008 1980, 2007 X
Netherlands Hott 2008 1980, 2005 X X [2001, 2006]
New Zealand Glindro 2011 1993, 2006 X X
New Zealand Fraser 2008 1970, 2005 X
Norway Jacobsen 2005 1990, 2004 X
Spain Antipa 2010 1982, 2007 X X [2003, 2007]
Switzerland Hott 2008 1980, 2005 X X [1987, 1993]
Taiwan Peng 2011 1980, 2007
X [1992] [2000]
Thailand Glindro 2011 1993, 2006 X X
United Kingdom Black 2006 1973, 2004 X
[1987, 1990] [2001, 2004]
United Kingdom Hott 2008 1980, 2005 X X [1990] [2005, 2006]
USA Anundsen 2013 1975, 2010 X X [2000, 2007]
USA Zhou 2010 1978, 2007 X X
USA Hott 2008 1980, 2005 X X [1990] [2005,2006]
This table summarizes results from selected studies linking housing prices with fundamentals, displaying information about sample and model, such as error correction models (ECM) or cointegration test. A bubble period is given by rejecting cointegration or insignificant coefficients within a VAR framework. Note that the found bubble periods mostly coincide with each other between 2003 and 2007. ** For the sake of brevity, countries from Orsal 2014 were reduced to Canada 6.
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Several studies address the US housing market, since data availability is good and the market presents a relatively high cyclic behavior. Empirical research about the cointegration in the US housing market goes back to Malpezzi (1999) and Gallin (2006), of whom nobody found coin-tegration between house prices and fundamentals in 95 metropolitan areas over 22 years in the US7. They concluded that therefore the level of house prices did not have a sustainable long term relationship with fundamentals. This differs from the findings of Anundsen (2013), who found cointegration over the full sample period and for subsamples, except when the sample was sequentially expanded by the years 2002 to 2008. Interestingly, when including all quarters for 2009 and 2010, the null-hypothesis about cointegration is not rejected anymore, which could indicate the end of a “bubble regime”. Indeed, the use of recursive estimations in an ECM framework, add to the discussion, that the question of cointegration is crutial crucial for a bub-ble debate.
Whereas the presented bubble periods clearly coincide in the early 2000’s, the overvaluation values do not and in between methods used, the results are somewhat conflicting. However, testing for cointegration recursively, possible bubble regimes or regime shifts can be assessed, as proposed by Anundsen (2013). His work is based on a large sample in comparison to other studies, spanning from 1975Q1 to 2010Q4, a total of 144 observations. A concern of Granger (1981) was that too much data is necessary for practical use of cointegration analysis. However, as series get longer, this should motivate more empirical work like this thesis. Given that Anundsen (2013) not only contributed new empirical evidence for the US, but presented a seemingly stable real time bubble indicator, his methodology is subsequently introduced.
6 The original study includes Australia, Austria*, Canada* Belgium, Finland, Netherlands, New Zealand, Norway*,
Sweden*, Switzerland*, UK* and US*, for which Orsal, D. D. K. (2014). "Do the global stochastic trends drive the real house prices in OECD countries?" Economics Letters 123(1): 9-13. Table 5, country-by-country, where * indicates a matrix rank of one (cointegration).
7 The US is well represented in most of the reviewed studies in the literature due to availability of long series with good temporal and spatial resolution.
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3 Methodology
Property prices can be explained in terms of fundamentals, but their selection and the choice of an appropriate mathematical model are crucial. Building on the above mentioned price-funda-mental benchmarks and noteworthy results from literature, the framework of Anundsen (2013) is introduced. It consists of two different approaches, whereas the first includes the rent as a main component – named price-to-rent approach, and the second relates the price to income and the housing stock – called inverted demand approach, a term that will become clearer in the following subsection. These approaches are furthermore divided into their possible model specifications, on the one hand a single equation specification, and on the other hand the coin-tegration vector autoregressive model (CVAR). The CVAR consists of a system of equations and will be subdivided further in to two specifications, namely one including a trend and one only including constants. For comparison and further inference, all the methods are employed on each data set. This yields two single equation results as well as two CVAR estimates per approach, summing up to six different outcomes per data set for the fundamental based analysis. In addition, the results are complemented by an investigation of the price dynamics segregated from fundamentals in terms of super-exponential growth behavior. Finally, these eight results are assessed for concordance, both country wise and model wise.
3.1 Error correction modelling using price to rent and inverted demand
benchmarks
Following Anundsen (2013) two important links between housing prices and fundamentals can be drawn, summarized as the inverted demand and price-to-rent approach. These two relative benchmarks can be operationalized in an econometric sense to explain housing prices. For clar-ification it is necessary to start by the underlying life cycle model of housing, as derived from Meen (1990). It states that the following equilibrium has to be satisfied
𝑈𝐻𝑈𝐶= 𝑃𝐻 [(1 − 𝜏𝑦)( 𝑖 + 𝜏𝑝) − 𝜋 + 𝛿 −
𝑃�̇�
𝑃𝐻 ] [ 3]
whereas U𝐻U𝐶
is the marginal rate of substitution between housing, H, and a composite consump-
tion good C. In equilibrium, it follows that the marginal willingness to pay for housing services in terms of different goods equals the cost in terms of foregone consumption. Here, PH is the
15
real purchasing price of dwellings, commonly measured as an indexed time series, τy is the marginal income tax rate, i is the interest rate on current mortgage loans, τp is property tax rate, π describes the current inflation rate, δ is the depreciation rate and 𝑃�̇�
𝑃𝐻 accounts for the house
price inflation and (•) denotes the time derivative. The term on the right hand side gives the real user cost of capital for holding a dwelling such as a house or flat. Expectations could be modeled as a moving average-process of the house price inflation. This will not be the case in this study, since such expected capital gains would be too sensitive in terms of number of lags (Anundsen 2013). Instead expected capital gains will be contained by the coefficients of the lagged terms.
Since it is possible to equate U𝐻U𝐶 with Q, which is the imputed rent on housing services. The user
cost of some dwelling should be equal to the periodic rent for a dwelling of similar quality. However, current accounts and country statistics about the imputed rent are not published, why it is reasonable to follow Meen (1990) and replace Q by R - the observable rent. By measuring the real house price in terms of the rent, the user cost is now separated on the right hand side of the equation:
𝑃𝐻
𝑅=
1
[(1 − 𝜏𝑦)( 𝑖 + 𝜏𝑝) − 𝜋 + 𝛿 − 𝑃�̇�
𝑃𝐻 ]
[ 4]
By only focusing on the housing services, namely taking in to account the real direct user cost, e.g. omitting the expected capital gains 𝑃�̇�
𝑃𝐻, one gathers an operative measure for the user
cost.
Because the real user cost can be negative, the estimate of the linear relationship is taken in to semi-log form, meaning the log price is explained by the log of the actual rent and the levels of user cost. So one derives:
𝑃𝐻
𝑅= 𝛾𝑈𝐶𝑈𝐶 → 𝑙𝑛 (
𝑃𝐻
𝑅) = 𝛾𝑈𝐶𝑈𝐶 → 𝑙𝑛(𝑃𝐻) − 𝑙𝑛 (𝑅) = 𝛾𝑈𝐶UC
[ 5]
Writing in short form, with small letters indicating logarithmic form, the so called price-to-rent approach is derived:
𝑝ℎ = γr𝑟 + γUCUC [ 6]
Where for γr no predefined value such as γr =1 is defined. This retains the ability to test for the elasticity between ph and r as well as the effects of linear increase of UC. Also it needs to be
16
mentioned that considering a semi-elasticity model, the coefficients γ and intercepts are in general slightly overestimated (Wooldridge 2014). An assumption about strict exogenity is not given. The complete error correction representation for the price-to-rent approach as sin-gle equation specification is than expressed as:
Δpht = μ + αph (ph – γrr − γUCUC)t−1
+∑𝜌𝑝ℎ,𝑖
𝑝
𝑖=1
Δpht−i +∑𝜌𝑟,𝑖
𝑝
𝑖=0
Δrt−i +∑𝜌𝑈𝐶,𝑖
𝑝
𝑖=0
ΔUCt−i +∑𝜆𝑑,𝑙𝑑𝑙
3
𝑙=1
+ 휀𝑡
[ 7]
whereas ph – γrr – γuc UC is called the error correction term. Furthermore, lagged differences with up to p lags as well as seasonal dummies, dl, are introduced for the quarters l=1,2,3 while the 4th quarter seasonal effect is captured by μ. Note that the error correction term accounts for the lagged levels and not the differenced ones, describing the long term adjustment between ph and the fundamentals, whereby the hypothesis is given by
H0: αph = 0 (indicating no cointegration) HA: αph ≠ 0 (indicating cointegration)
[ 8]
The second approach, called inverted demand, considers the imputed rent Q as a function of the demand drivers’ income, Y, and the housing stock H.
𝑄 = g(Y, H) [ 9]
Again, a log – level approach then gives:
𝑝ℎ = �̃�𝑦𝑦 + �̃�ℎℎ + �̃�𝑈𝐶𝑈𝐶 [ 10]
This representation could also be interpreted as a demand equation similar to that pointed out in Meen (2002), which is why it is called (in the sense of Anundsen), inverted-demand. Assum-ing furthermore, that prices adjust to a long term equilibrium, an adequate representation is the single equation error correction which reads:
17
Δpht = μ + �̃�𝑝ℎ (ph – �̃�𝑦𝑦 − �̃�ℎℎ − �̃�𝑈𝐶𝑈𝐶)t−1+∑�̃�𝑝ℎ,𝑖Δpht−i
𝑝
𝑖=1
+∑�̃�𝑦,𝑖
𝑝
𝑖=0
Δyt−i +∑�̃�𝑈𝐶,𝑖
𝑝
𝑖=0
ΔUCt−i +∑�̃�𝑑,𝑙𝑑𝑙
3
𝑙=1
+ 휀𝑡
[ 11]
Where �̃�𝑝ℎ is the adjustment coefficient and (ph – �̃�𝑦𝑦 − �̃�ℎℎ − �̃�𝑈𝐶𝑈𝐶)t−1 is the error cor-
rection term, which represents the long term dynamics and is expected to be ~I(0), e.g. (trend-) stationary, whereas the sums of the first order and lagged differences give the short term dy-namics between the house price, the income and the user cost. To clarify, underbraces point out the expected order of integration:
Δpht = μ + �̃�𝑝ℎ (ph⏟ – �̃�𝑟𝑦⏟ − �̃�ℎℎ⏟ − �̃�𝑈𝐶𝑈𝐶⏟ )t−1
~𝐼(1) ~𝐼(1) ~𝐼(1) ~𝐼(1)⏟
~𝐼(0)
+ ∑ �̃�𝑝ℎ,𝑖Δpht−i
𝑝
𝑖=1⏟ +∑�̃�𝑦,𝑖
𝑝
𝑖=0
Δyt−i⏟
+∑�̃�𝑈𝐶,𝑖
𝑝
𝑖=0
ΔUCt−i⏟
+ 휀𝑡
[ 12]
~𝐼(0) ~𝐼(0) ~𝐼(0)
Obviously, the error correction term aggregates a linear combination of non-stationary variables to a stationary variable, which can be interpreted as an equilibrium, to which variables return after being disturbed or shocked. In terms of stationarity, the non-stationary components of the underlying fundamentals and ph cancel each other out, therefore generating a stationary term at t-1, which linearly influences Δpht by the adjustment speed �̃�𝑝ℎ.
Given the above equations, the major concern for assessing cointegration are the statistical sig-nificance and the sign of the adjustment coefficients, �̃�𝑝ℎ and 𝛼𝑝ℎ. The estimates for all long run coefficients, the elasticities β, only play a minor role.
Note, that in equations [ 7] and [ 11] the estimated γ coefficients allow the long run elasticities or β’s to be derived since simply 𝛽𝑣𝑎𝑟 =
𝛾𝑣𝑎𝑟
−�̃�𝑝ℎ with var ∈ {y, r, UC, h}. From theory, 𝛾𝑟 in equa-
tion [ 7] should be positive (and close to one). Or when considering the long run coefficient, housing prices at t ought to rise by 𝛽𝑟 percent, when rents in t-1, meaning the quarter before, increase by one percent. In equation [ 11], �̃�𝑟 is expected to be positive and �̃�ℎnegative. As for
18
all �̃�𝑣𝑎𝑟,𝑖, the significance and magnitude can differ with the number of lags, p. Taking in to account short term effects, such as price-to-price interactions or volatility within the payed wages, the observed market rents or the underlying direct user costs of housing.
Combining Stiglitz (1990) and the setup from Anundsen (2013), a bubble regime or regime shift could be indicated when the housing price is not cointegrated (anymore) with fundamen-tals. Extending this idea to the potential combinations of variables and fundamentals, the ad-justment coefficient α becomes a vector, representing all possible cointegration relationships. This broadens the approach and gives more hints about wider connections or disconnections between the property price and fundamentals.
3.2 Cointegration Vector Error Correction Model
After specifying the error correction models, those are now enhanced by the system based ap-proach from Johansen (1991), which relies on a re-parametrization of a p-th order VAR, taking in to account all possible cointegration relationships between the variables. Hence the equations for inference becomes a cointegration vector autoregressive model and takes the following form for the price-to-rent approach:
Δ𝒚𝑡 = ∏𝒚𝑡−1 +∑𝜞𝒊
𝑝−1
𝑖=1
Δ𝑦𝑡−1 +𝜱𝐷𝑡 + 휀𝑡
[ 13]
Here, yt is a k × 1 vector of the endogenous variables, 𝛷 being a k × d matrix of coefficients and Dt is a vector of d constants, including centered seasonal dummies and the intercept. Since there are several possible deterministic trends, they are included in Π. Now Π𝒚𝑡−1 is the error correction term and the error is given by εt ~ IIƝ(μ=0, σ=Ω), with Ω being diagonal. In detail Π and 𝛤𝑖 are defined as follows
Π = ∑Π𝑖
𝑝
𝑖=1
− 𝐼 = 𝛼𝛽⊺ = −(𝛪 − Π1−. . . −Π𝑝), 𝑖 = 1,… , 𝑝
𝛤𝒊 = − ∑ Π𝑗
𝑝
𝑗=𝑖+1
= −(Π𝑖+1−. . . −Π𝑝), 𝑗 = 𝑖 + 1,… , 𝑝
[ 14]
With I being the identity matrix and Π𝑖 being the coefficient matrix according to lag number i of the vector yt. Hence Π𝑖 represents a stability measure between the incorporated variables,
19
which technically all have a nearly independent character and Γi measures transitory effects (Pfaff 2008).
For the price-to-rent model, yt is 3 × 1, representing the housing price, rents and the user cost, all in real terms. For the inverted demand framework, yt is 4 × 1. However, for the housing stock is inelastic in the short run, yt is split up in to xt and zt, where zt is a scalar only containing the stock. yt on the left hand side is furthermore replaced by the exclusively endogenous varia-bles incorporated in the vector xt (3 × 1). The price-to-rent CVAR equation than reads:
Δxt = ∏𝑦𝑡−1 +∑𝛤𝑥,𝑖
𝑝
𝑖=1
Δ𝑥𝑡−𝑖 +∑𝛤𝑧,𝑖
𝑝−1
𝑖=0
Δ𝑧𝑡−𝑖 +𝜱𝐷𝑡 + 휀𝑡
[ 15]
where yt = (xt’, zt’). So zt represents the housing stock only, while xt contains the residential property price, income and user costs, again, all in real terms. Furthermore, the housing stock coefficient is considered constant in the short run, reflecting its inelasticity, which is why 𝛤𝑧,𝑖 = 𝛤ℎ,𝑖 = 0∀𝑖 is assumed.
The test for cointegration then follows then out of the rank r of the matrix Π. This is based on the trace test from Johansen (1991), where the hypothesis reads:
H0: r < r* r* = 1,2,3 ≤ k HA: r = r*
[ 16]
H0 gives the estimated 𝛱. The trace procedure therefore includes up to three tests per approach and henceGoing further, the case (2) allows Π to be rewritten as 𝛼𝛽⊺ both being k × r. α contains the r loading factors or adjustment vectors, whereas β holds the m cointegration vectors, mean-ing the long run coefficients respectivelyHence r is the count of stationary cointegration rela-tionships. A deterministic trend enters the space spanned by α. Note that after estimating rank and coefficient, further analysis is crucial. Critical model diagnostics are tests for autocorrela-tion, heteroscedasticity and non-normality of the error process, like pointed out by Pfaff (2008).
3.3 Model estimation
The implementation of the mentioned methods uses the Ox code and data provided by Anundsen (2013)8 with the software OxMetrics. The estimation of the equations [ 7] and [ 11],
8 Code and Data for the US are available at http://www.andre-anundsen.com/research.html
20
is done with a general-to-specific (Gets) procedure, in which a first general unrestricted model (GUM) is gradually reduced to fit the empirical data9. For the automatic variable selection in the Gets framework, the algorithm Autometrics, available in PcGive is employed. It allows to find the most appropriate simplified model. The number of lags is selected based on the AIC criterion.
In general, the significance level for the variable selection is set to 5% and the lagged levels, particularly the variables inside the error correction term, are restricted to enter the final speci-fication.
For both the single equation and CVAR approaches, [ 7], [ 11] as well as [ 13] and [ 15] respec-tively, the estimates are done recursively, meaning that the investigation sample is iteratively prolonged until the full sample is reached. This explicitly allows to make statements about spe-cific regime shifts, as proposed by Anundsen (2013). For the single equations, the last observa-tion T is sequentially added by one, and in the CVAR equations, by four, as the latter framework needs more observations to be stable. The starting point in the main sample 1970Q1 - T is selected according to valid model output, e.g. is not stopped by matrix singularities or lack of observations for the test for Heteroscedasticity. The exact sample depends on the country data, starting at the first set of cross-sectional available data points, including all the lagged variables. Used sample sizes will be outlined in the results section.
Noteworthy is that, for the t-values in the estimation of the adjustment coefficient in [ 7] and [ 11], no standard t-values can be used. Instead, critical t-values rom Ericsson (2002) are con-sidered, since they account for the left-skewed non-standard distribution. For the CVAR, the critical t-values origin from the tables provided by Doornik (2003). The significance level and connected cut-off point for adding one to r* and repeat the test is set to 10%, following both Anundsen (2013) and Stevenson (2008).
3.4 Testing for super exponential growth
In order to assess the price dynamics isolated from other macroeconomic determinants and compare them with the fundamental based results, the above presented methods are comple-mented by the faster then exponential growth diagnostic, outlined in Zhou and Sornette (2006). Assuming possible positive feedbacks, this gives rise to a power law singularity
𝑝ℎ𝑡 = 𝐴 + 𝐵(𝑡𝑐 − 𝑡)𝑚
9 See for an overview of gets: https://www.federalreserve.gov/pubs/ifdp/2005/838/ifdp838.pdf
[ 17]
1
Where pht is the log property price index at time t, and tc is the estimation of the end of a bubble, such that t < tc. A, B and m are coefficients. When m < 0, pht is singular when t → 𝑡𝑐− , B >
0 and Δpht > 0. If 0 < m < 1, pht is finite but its first derivative 𝑝ℎ ̇ is singular at tc and B < 0 ensuring that Δpht > 0. An extension of this power law follows the form of the log-periodic power law singularity (LPPLs) for the logarithm of the price
𝑝ℎ𝑡 = 𝐴 + 𝐵(𝑡𝑐 − 𝑡)𝑚 + 𝐶(𝑡𝑐 – t)
𝑚 cos[ 𝜔 ln(𝑡𝑐 − 𝑡) − 𝜙] [ 18]
where 𝜔 is the log frequency and 𝜙 is a phase constant. Hence the bubble indicator is a detected faster-than-exponential growth of PHt, (in levels) possibly extended by log periodic oscilla-tions10.
10 For the critical values of the (sup)PL and (sup)LPPLS fits please refer to Ardila, D., D. Sanadgol and D. Sornette
(2016). "Out-of-sample forecasting of housing bubble tipping points."
22
3.5 Binary cycles: concordance of bubble indicators
The former implied equations give six different fundamental based results and two for the LPPLs fit. In order to check for their synchronization the resulting metrics are aggregated to one single binary indicator, denoted as Sx,T, where x is the approach and T the last estimation period. For the single equation error correction framework, S is derived from the p-value of αph, and reads:
𝑆𝑥,𝑇 = {10
𝑝 − 𝑣𝑎𝑙𝑢𝑒 > 𝛼 𝑝 − 𝑣𝑎𝑙𝑢𝑒 ≤ 𝛼
[ 19]
With 𝛼 = 0.1 as pointed out above. In order to account for the CVAR, the bubble indicator is based on the test result of the matrix rank from the Johansen procedure, with again x denoting the approach and T the end period. The bubble indicator therefore reads:
𝑆𝑥,𝑇 = {10
𝑅𝑎𝑛𝑘(Π) = 0
𝑅𝑎𝑛𝑘(Π) > 0 [ 20]
After transforming the test results to a binary cycle Sx,t, a concordance indicator I is employed, as proposed by Harding and Pagan (2006), measuring the synchronization of the cycles 𝑆𝑥,𝑡 . Similar to a covariance or correlation matrix, but suitable for binary rather than continuous variables, it allows to summarize the concordance of the phase states, in this case defined as (a) a bubble or (b) a stable regime. The concordance indicator reads:
𝐼𝐾 = 1
𝑇[∑𝑆𝑥,𝑡 𝑆𝑦,𝑡
𝑇
𝑡=1
+∑(1 − 𝑆𝑥,𝑡)(1 − 𝑆𝑦,𝑡)
𝑇
𝑡=1
] ∀𝐾 [ 21]
The main advantage of this indicator is the anticipation of computing zero standard deviation values which invalidates the correlation coefficient 𝜌𝑆. However, as mentioned in Harding and Pagan (2006), there is still the following relationship between the concordance index I and the correlation 𝜌𝑆:
𝑖𝑆 = {
1 𝑇𝑜𝑡𝑎𝑙 𝑐𝑜𝑛𝑐𝑜𝑟𝑑𝑎𝑛𝑐𝑒 𝑜𝑟 𝜌𝑆 = 1(0,1) 0 𝑁𝑜 𝑐𝑜𝑛𝑐𝑜𝑟𝑑𝑎𝑛𝑐𝑒 𝑜𝑟 𝜌𝑆 = −1
[ 22]
The set K can either consist of the countries, whereas x and y would correspond to the ap-proaches, or K denotes the approaches and x and y are the countries respectively. In this study, both cases are of interest. The concordance indicator IK first calculated for all possible combi-
23
nations of binary cycles related to the six different model specifications granting (62) = 15 dif-
ferent relationships of interest in the 6 × 6 matrix. If the PL and LPPLs fit are also included, the matrix becomes 8 × 8. For the inter-country analysis, IK is an 8 × 8 matrix with (8
2) = 23 con-
cordance values. These are expected to coincide, meaning iS would be asymptotically 1, in order to consolidate the indication of a bubble or stable economic regime.
24
4 Data Description and temporal properties
Since this study includes different major economies, a high priority is given to consistency and comparability of the data, which amounts to a careful selection of sources. The chosen property price indices and fundamentals should measure as accurate as possible the wanted model input and representativeness is a major issue11.
The countries were chosen by (1) assessment in prior studies linking property prices and fun-damentals, (2) global economic relevance and reports of extraordinary price developments, (3) data availability and in particular length of necessary time series data. The general investigation sample size spans from 1970Q1 to 2016Q2, a total sample of 190 observations per series. How-ever, some series cover significantly smaller horizons, therefore reducing the corresponding country analysis as a whole.
4.1 Variable descriptions
For each of the eight assessed economies, twelve metrics were collected in total. The main measure and explained variable is the property price index (PH). The macroeconomic funda-mentals are the population (Pop), the rent (R), the income (Y), the housing stock (H; measured monetarily), and the user cost (UC). The User cost is constructed out of the following rates collected per country and if necessary, aggregated: depreciation, property tax, income tax, mort-gage interest, and inflation. Deflators are the consumer price index (CPI), once without housing components (CPI1), for deflating PH, R and Y, once measured for all items in order to account for the inflation in the user cost (CPI2). Additionally, the value of the housing stock is deflated by an appropriate metric, depending on the measure used for the stock (PJ). Table 3 summarizes the used variables and their main data sources.
The measure of the housing stock is used after comparisons with the metric for the US from Anundsen (2013), who used aggregated replacement values for all dwellings. It has to be noted that replacement values refer to the re-construction of dwellings, whereas the market value re-flects and estimates the current value of constructions and land12. In general, the re-construction
11 Consults https://www.bis.org/publ/qtrpdf/r_qt1409h.htm for the issue of representativeness 12 Compare page 10 for a discussion between different measures of property values:
http://www.are.admin.ch/dokumentation/publikationen/00016/00564/
25
value is lower than the market value, since the land price is included. This can lead to the over-estimation of coefficients for the housing stock compared to the original analysis with the model13. Table 3 Data and variable definition
Variable Description Dimension Deflation Main Source
PH Property Price Index Index by CPI2 BIS
Pop Population [Total residents] R Real housing rent Index by CPI2 OECD
Y Per capita disposable income [national currency/resident] by CPI2 and Pop AMECO
H Per capita Housing stock [national currency/resident] by PJ and Pop Oxford Economics
CPI1 CPI Less shelter Index CPI2 CPI All items Index UC User Cost (1-τy)(i+τp) - π + δ δ Housing depreciation rate [%] of property value τ p Property tax rate [%] of property value OECD
τ y Average income tax rate [%] of marginal income OECD π Inflation rate [%] Annual rate i Mortgage interest rate [%] Annual rate
Variables used to explain property prices PH. Fundamentals being the housing rent, R, the disposable income per capita Y, the housing stock, H, and the user cost, which is derived from the depreciation rate, the property tax rate, the income tax rate, the year-on-year inflation and annual mortgage interest rate. Where data was available, a single main source was preferred. Otherwise, data was selected based on prior reviewed surveys, or if more suitable, from various country specific sources available at the Thomson Reuters Data Base, FED St. Louis or Quandl.
Fundamental metrics were selected by (1) availability of countrywide comparable data, (2) samples used in former studies, and (3) length of the time series. Data sources from already investigated samples follow the presented literature from chapter 2 and mainly Girouard, Kennedy et al. (2005) and Kholodilin et al. (2010).
So except for PH, R and H, the sources are country specific, mostly coming from corresponding statistical institutions. For the property price index, PH and the residential capital stock, H, and Y central sources were chosen for best comparability. Current rent levels are often incorporated in a CPI and series only representing this component are available, why these indices are used throughout this study for the price to rent approach.
The following subsections describe the data country wise, starting showing exact sample sizes and summarizing statistics. The corresponding time series plots and unit root tests can be found
13 See http://www.emeraldinsight.com/doi/full/10.1108/14635780910993186# for a detailed discussion.
26
in the Appendix A and Appendix B respectively. If nothing about seasonal adjustment (SA) is stated in the following, the described series are considered not being SA. If interpolation was necessary for the collected data, e.g. Population, it refers to linear interpolation. The indexing mentioned in the presented tables refer to indexing after streaming from the database.
4.1.1 United States
For testing the effects of altering the data of the original model14, different property price indices were chosen. Of particular interest is the data from the BIS, already real and without SA. Figure 1 compares the data from Anundsen (2013), who used a repeated sales index from the FHFA, with the newly collected series from the BIS and a third source series from the FED Dallas.
Figure 1 US Property price series in levels and log returns from different sources
This figure shows the original quarterly time series used by Anundsen (2013) (source Federal Housing Finance Agency- FHFA) and two further collected time series in levels and log returns. Generic variable descriptions are to be found in Table 3. Note that the levels are all in real terms and indexed at 1990Q1=1.0. However, inflation adjustment depends on the source. Log returns of FHFA and FED Dallas series coincide closely, whereas the BIS series overshoots by up to 2 percentage points during the early 2000’s and undershoots up to 2 percentage points in the correction period, 2006Q4 to 2009Q1.
The time span is shorter compared with the original, spanning now from 1975Q4 to 20105Q4, which in combination with the fundamentals yields 140 observations for further analysis. The BIS index is based on economic data by the federal reserve (national level) and uses averaging
14 For original data see http://www.andre-anundsen.com/research.html
27
as the main method and does not include SA. In comparison, the original series from the Federal Housing Finance Agency (FHFA) is based on a repeated sales method. Still, they are correlated with a degree of 0.96 in levels, although only 0.65 in log returns. The different price series can alter up to 20% in terms of the 1990 level when it comes to the price peak around 2006 and several percentage points in the lags. On top of collecting other price series, an alternative housing stock measure from Oxford Eco-nomics is introduced. It represents the current market value of housing, allowing to explore its relationship with property prices and other fundamentals.
4.1.2 Canada
The residential property prices for Canada were gathered from the Federal Reserve (FED) of St. Louis and originate from the Bank of International Settlements (BIS) data. The series were available from 1970Q1, representing a national average and are already real. The population data was derived from CANSIM – Statistics Canada, is already quarterly and covers the whole investigation sample. Table 4 compiles the gathered data for Canada.
Table 4 Data summary for Canada
Variable Start End Obs Indexed Min Max Mean Source
Pop 1970Q1 2016Q2 186
21180000 36160000 28500000 CANSIM - Statistics Canada
rPH 1970Q1 2015Q4 184 2010Q1 0.004 0.012 0.007 BIS Residential Property Prices
rR 1970Q1 2016Q2 186
1.023 2.517 1.481 CANSIM - Statistics Canada
rY 1981Q1 2016Q1 141
22810 28010 25470 CANSIM - Statistics Canada
CPI1 1970Q1 2016Q2 186 2010Q1 0.130 1.164 0.612 CANSIM - Statistics Canada
CPI2 1970Q1 2016Q2 186 2010Q1 0.175 1.115 0.673 CANSIM - Statistics Canada
rH 1980Q1 2016Q2 146
0.329 0.392 0.367 Oxford Economics
PJ 1981Q1 2016Q1 141 2010Q1 0.344 1.168 0.702 CANSIM - Statistics Canada
Table providing the sample windows, number of consecutive observations, indexing and summary statistics for the main variables of the model specifications. The lowercase r in front of the variable represents real/constant prices. Generic variable descriptions are to be found in Table 3. Note that indices are given in decimal numbers, and 1 reflects the indexing period. Variables related to the user cost, namely depreciation and tax rates, are in general held constant and that is why they are omitted in the table. For time series graphs and unit root statistics please refer to Figure A 1 or Table A 1 respectively.
28
For the user cost, which is based on five variables, the depreciation rate15 is represented by the corresponding measure from Statistics Canada, held constant at 2% before 1997 and after that at 1.5%. The property tax rate is held constant at 1.5%, like proposed in the working paper of the OECD, Girouard, Kennedy et al. (2005), reflecting simplification of the actual tax rates, which are levied partly on the national, provincial and municipal level. The average residential mortgage lending rates come from the Bank of Canada and were aggregated from monthly to quarterly series. They represent the necessary mortgage service payments on a yearly basis. The sum of these costs is multiplied with the tax free income share, assuming that the marginal personal income stays at the arithmetic mean of 24%. This value is derived by taking the arith-metic mean of the Federal Tax rates for individuals from the Canada Revenue Agency16. Finally, the user cost is obtained by subtracting the annual inflation rate, taking the CPI for all items. The household disposable income for Canada was only available in seasonally adjusted terms from the capital accounts of Statistics Canada. After deflating by population it is measured in Canadian Dollars (CAD) per Capita and is considered real. The real housing rent comes from the CPI dwelling component and was interpolated to quar-terly values.
The housing stock is based on the end of period market value, estimated by oxford economics. For standardization, the series was then deflated by population, yielding per capita (financial) housing stock values.
4.1.3 United Kingdom
For the residential property prices in the United Kingdom, the already CPI deflated series from the corresponding BIS database is used. The quarterly values reach from 1970Q1 to 2015 and are indexed at 2010Q1. Compare Table 5 for summarized statistics. Real housing rents are measured as a component of the Retail Price Index (RPI) from the Office for National Statistics (ONS) of the UK. The series is aggregated to quarters. Since the actual rent is in fact a part of the RPI, a measure for inflation, there is no deflation conducted on the series.
15 Compare http://www5.statcan.gc.ca/olc-cel/olc.action?ObjId=62F0014M2001015&ObjType=46&lang=en for
the measure 16 Compare http://www.cra-arc.gc.ca/tx/ndvdls/fq/txrts-eng.html
29
Table 5 Data summary for the United Kingdom
Variable Start End Obs Indexed Min Max Mean Source
Pop 1970Q4 2015Q4 181
55660000 65140000 58530000 Development Indicators - World Bank
rPH 1970Q1 2015Q4 184 2010Q1 0.20 1.10 0.60 BIS Residential Property Prices
rR 1987Q1 2016Q2 118
1.00 3.60 2.41 ONS - UK
rY 1970Q4 2015Q1 178
1579 4548 3105 ONS - UK
CPI1 1970Q1 2015Q1 181
0.09 1.12 0.63 Main Economic Indicators, OECD
CPI2 1970Q1 2015Q1 181 2010Q1 0.10 1.14 0.63 Main Economic Indicators, OECD
rH 1987Q1 2015Q4 116
33550 62930 48730 Oxford Economics
PJ 1987Q1 2016Q2 118 2010Q1 0.32 1.17 0.76 ONS UK Table providing the sample windows, number of consecutive observations, indexing and summary statistics for the main variables of the model specifications. The lowercase r in front of the variable represents real/constant prices. Generic variable descriptions are to be found in Table 3. Note that indices are given in decimal numbers, and 1 reflects the indexing period. Variables related to the user cost, namely depreciation and tax rates, are in general held constant and that is why they are omitted in the table. For time series graphs and unit root statistics please refer to Figure A 2 or Table A 2 respectively.
As before, the user cost includes measures for inflation, namely the housing depreciation, the council tax – an aggregated property tax rate for England – and the marginal income tax rate.
The rates are available from 1976 annually and were interpolated to quarterly values. A value of 3% per quarter would thus still represent an annual tax of 3%. For the mortgage lending rates, the already quarterly series from the actual interest rate of build-ing society mortgages, available from 1980 on, are used. They come from Oxford economics forecast survey.
4.1.4 France
Since the seasonally unadjusted property prices from the BIS only cover 1996Q1 to 2015Q4, instead the nominal data, covering the period back to 1957Q1, is used and deflated accordingly. For the summary of the data, have a look at Table 6.
For the metropolitan population of France, the data is given by the National Institute for Statis-tics and Economic Studies (INSEE) and reaches back to 1975 on a monthly basis without sea-sonal adjustment. Data is subsequently aggregated to quarters.
30
Table 6 Data summary for the France
Variable Start End Obs Indexed Min Max Mean Source
Pop 1975Q1 2016Q2 166
52620000 64590000 58270000 INSEE - France
rPH 1970Q1 2015Q4 184 2010Q1 0.50 1.10 0.70 BIS Residential Property Prices
rR 1990Q1 2015Q4 104
1.22 1.31 1.27 INSEE - France
rY 1975Q1 2016Q2 166
0.02 0.03 0.03 AMECO, European Commission
CPI1 1970Q1 2016Q2 186 2010Q1 0.13 1.09 0.65 Main Economic Indicators - OECD
CPI2 1970Q1 2016Q2 186 2010Q1 0.15 1.07 0.69 IMF - International Financial Statistics
rH 1980Q1 2016Q2 146
22890 51300 35580 Oxford Economics
PJ 1970Q1 2016Q2 186 2010Q1 0.16 1.06 0.69 Thomson Reuters Table providing the sample windows, number of consecutive observations, indexing and summary statistics for the main variables of the model specifications. The lowercase r in front of the variable represents real/constant prices. Generic variable descriptions are to be found in Table 3. Note that indices are given in decimal numbers, and 1 reflects the indexing period. Variables related to the user cost, namely depreciation and tax rates, are in general held constant and that is why they are omitted in the table. For time series graphs and unit root statistics please refer to Figure A 3 and Table A 3 respectively.
A rent metric is also available from INSEE, covering only 1990Q1 to 2015Q4 without SA. For the disposable income, the indexed nominal series from 1960Q1 to 2015Q4 by AMECO is interpolated and deflated by the population and the CPI respectively. The CPI deflator excluding housing comes from the OECD and gives the current price level from 1957Q1 to 2016Q4, whereas the all-items deflator is taken from the IMF covering the same time.
Quarterly Housing stock measured at market value in billions of Euros origins from Oxford Economics, which contains actual values from 1980Q1 to 2014Q4 and apart from there fore-casted values, which are excluded from the analysis. For correction of the housing stock at market value, the price deflator from Thomson Reuters, quarterly values from 1950Q1 up to date are used. However, the series was only available not SA.
Actual Interest rates on a quarterly basis come from Oxford Economics as well and reach from 1980Q1 to 2016Q2. As of 2016Q2, they are at an all-time low, namely at 5.15%, reflecting the current low yield regime.
Depreciation rate, property tax rate and income tax rate are held constant at 2.5, 1.7 and 30% respectively.
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4.1.5 Germany
For Germany, there is a markedly data issue. Some of the available data for Germany underlies a major distortion, namely due to the reunification (“Wiedervereinigung”) of 1989, which is reflected in the Population data, jumping in 1990 from around 60 to 80 Million. See Table 7 or Figure A 4.
Table 7 Data summary for Germany
Variable Start End Obs Indexed Min Max Mean Source
Pop 1970Q1 2016Q1 185
60710000 82080000 72220000 Federal Statistical Office, Germany
rPH 1970Q1 2015Q4 184
1.07 1.53 1.25 BIS Residential Property Prices
rR 1970Q1 2016Q2 186
0.76 1.04 0.91 Main Economic Indicators
rY 1970Q1 2016Q1 185
2667 5240 4290 Deutsche Bundesbank
CPI1 1970Q1 2016Q2 186
0.32 1.07 0.74 Deutsche Bundesbank
CPI2 1970Q1 2016Q2 186
0.32 1.07 0.74 Deutsche Bundesbank
rH 1980Q1 2013Q2 134
37360 63000 55750 Oxford Economics
PJ 1970Q1 2013Q2 174
0.32 1.24 0.80 Deutsche Bundesbank
Table providing the Sample windows, number of resulting observations, indexing and concrete values for the main variables of the model specifications. The lowercase r in front of the variable represents real/constant prices. Generic variable descriptions are to be found in Table 3. Note that indices are given in decimal numbers, and 1 reflects the indexing period. Variables related to the user cost, namely depreciation and tax rates, are in general held constant and that is why they are omitted in the table. For time series graphs and unit root statistics please refer to Figure A 4 or Table A 4 respectively.
Quarterly Population numbers come from the statistical federal authority destatis, spreading from 1961Q1 to 2016Q1. Personal disposable income was only available SA and origins from the Deutsche Bundesbank. Also the CPI as a continuous series was only available SA by the same source and is used as accounting for both price deflators, CPI1 and CPI2.
Although there is a housing stock measure available from Oxford Economics, an appropriate deflator for it is missing. As a proxy, the Construction price index is used, which is discontinued and ends at 2013Q2.
Values to construct the user cost rely on Girouard, Kennedy et al. (2005), assuming 2% for annual depreciation, 0.35% for the annual property tax and 42% as income tax rate.
32
4.1.6 Japan
Although it measures only working population (people over 15 years old), the series from the Statistics Bureau of Japan was preferred over others. The maximal number of 111 Mio in Table 8 is therefore lower than the actual 126 Mio residents17. The series contains annual values from 1953 to 2016 and is hence aggregated to quarterly values.
Table 8 Data summary for Japan
Variable Start End Obs Indexed Min Max Mean Source
Pop 1970Q1 2016Q2 186
78570000 111200000 99960000 Statistics Bureau Japan
rPH 1970Q1 2015Q4 184 2010Q1 0.97 2.15 1.45 BIS Residential Property Prices
rR 1970Q1 2016Q2 186 2010Q1 0.31 1.04 0.84 Statistics Bureau Japan
rY 1980Q1 2016Q2 146
412.6 727.6 633.6 Oxford Economics
CPI1 1970Q1 2016Q2 186 2010Q1 0.24 1.05 0.81 Main Economic Indicators, OECD
CPI2 1970Q1 2016Q2 186 2010Q1 0.32 1.04 0.87 Statistics Bureau Japan
rH 1980Q1 2016Q1 145
5767 25480 12260 Oxford Economics
PJ 1970Q1 2016Q1 185 2010Q1 0.32 1.90 1.17 JREI - Japan Real Estate Institute
Table providing the Sample windows, number of resulting observations, indexing and concrete values for the main variables of the model specifications. The lowercase r in front of the variable represents real/constant prices. Generic variable descriptions are to be found in Table 3. Note that indices are given in decimal numbers, and 1 reflects the indexing period. Variables related to the user cost, namely depreciation and tax rates, are in general held constant and that is why they are omitted in the table. For time series graphs and unit root statistics please refer to Figure A 5 and Table A 5 respectively.
Due to the insufficient time horizon of the real BIS data, instead the nominal series, spanning 1970Q1 to 2015Q4, is used and deflated by the CPI. Due to the deflation, previous peaks (and bubble periods) are partially even punctuated. A CPI less housing component and without SA is available from OECD. It covers quarterly values from 1970Q1 to 2016Q2 after aggregation. The total CPI is surveyed by the statistics bureau of Japan and is subject to the same aggregation, giving the equivalent time period. For deflating the housing stock at current market value, the interpolated AMECO price deflator is used. As a rent measure, the corresponding price index from the statistics bureau is used and
17 Actual total Population of Japan to date is an estimated 126 Mio, http://www.worldometers.info/world-popula-
tion/japan-population/
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aggregated from monthly to quarterly values, yielding a series from 1970Q1 to 2016Q2. Per-sonal income is available from Oxford economics spanning from 1980Q1 up to date.
4.1.7 Netherlands
Population was retrieved from the CBS Statistics Netherlands and interpolated to quarterly val-ues. Following the BIS source, the long nominal series from 1970Q1 to 2016Q1 was preferred to the real series, since the latter was available in only very limited extent. Compare Table 9 for the numerical values.
Table 9 Data summary for the Netherlands
Variable Start End Obs Indexed Min Max Mean Source
Pop 1970Q4 2016Q2 183
12960000 16940000 15150000 CBS - Statistics Netherlands
rPH 1970Q1 2016Q1 185
0.88 3.19 1.84 BIS Residential Property Prices
rR 1970Q1 2016Q2 186
0.64 1.17 0.91 Main Economic Indicators, OECD
rY 1980Q1 2016Q2 146
3049 4791 4040 Oxford Economics
CPI1 1970Q1 2016Q2 186
0.23 1.01 0.65 CBS - Statistics Netherlands
CPI2 1970Q1 2016Q2 186
0.23 1.01 0.65 CBS - Statistics Netherlands
rH 1980Q1 2015Q1 141
48070 106600 76390 Oxford Economics
PJ 1970Q2 2015Q1 180
0.12 1.00 0.56 AMECO, European Commission
Table providing the Sample windows, number of resulting observations, indexing and concrete values for the main variables of the model specifications. The lowercase r in front of the variable represents real/constant prices. Generic variable descriptions are to be found in Table 3. Note that indices are given in decimal numbers, and 1 reflects the indexing period. Variables related to the user cost, namely depreciation and tax rates, are in general held constant and that is why they are omitted in the table. For time series graphs and unit root statistics please refer to Figure A 6 and Table A 6 respectively.
The CPI housing from the main economic indicators from the OECD is proxying for rents and is aggregated to quarterly values. For the personal disposable income, an already real series without SA from Oxford Economics, time span 1980Q1 to 2016Q2 is collected. Since no spe-cific deflator excluding shelter was readily available, instead the CPI compromising all items is aggregated to quarterly values and used as a general deflator. The total market value of housing stock comes from Oxford Economics, does not cover histor-ical values after 2012Q4 though. This discontinuity shortens the overall sample size for the model specifications including the stock. Long term government bond yields proxy the current mortgage interest rates. The series is
34
available back to 1960 and comes from OECD. Necessary rates to construct the user cost were-held constant at 2.5 % for depreciation and 0.3 % for the property tax rate, as proposed by the OECD Girouard, Kennedy et al. (2005). The inflation depends on the CPI and the income tax rate was held constant at 42%18.
4.1.8 Switzerland
The Swiss population data comes from Eurostat and is interpolated from an annual to a quarterly series. Real Property prices for Switzerland come from the BIS and span 1970Q1 to 2015Q4. For the rent data, the CPI corresponding component is taken. It comes from the OECD main economic indicators and was available from 1970 to 2015Q4. The already quarterly index is not seasonally adjusted and takes into account housing services, repairs, maintenance and the imputed rent. To measure income, the quarterly per capita disposable income from annual macro-economic database from the European Commission (AMECO) is taken, covering 1983Q1 to 2016Q2. Compare Table 10 for the exact samples and summary statistics.
18 See source http://www.expatax.nl/tax-rates-2014.php
35
Table 10 Data summary for Switzerland
Variable Start End Obs Indexed Min Max Mean Source
Pop 1970Q4 2016Q2 183
6169000 8281000 6940000 EUROSTAT
rPH 1970Q1 2015Q4 184
0.72 1.21 0.91 Bank for International Settlements
rR 1970Q1 2016Q2 186 2010Q1 0.25 1.05 0.70 Main Economic Indicators,copyright OECD
rY 1983Q1 2016Q2 134
54970 81050 69430 AMECO, European Commission
CPI1 1983Q1 2016Q2 134 2010Q1 0.66 1.02 0.89 FSO - Federal Statistical Office, Switzerland
CPI2 1983Q1 2016Q2 134 2010Q1 0.66 1.02 0.89 IMF - International Financial Statistics
rH 1980Q1 2015Q1 141
1091 2133 1690 Quarterly National Accounts,copyright OECD
PJ 1983Q1 2016Q2 134 2010Q1 0.71 1.05 0.87 FSO - Federal Statistical Office, Switzerland
Table providing the Sample windows, number of resulting observations, indexing and concrete values for the main variables of the model specifications. The lowercase r in front of the variable represents real/constant prices. Generic variable descriptions are to be found in Table 3. Note that indices are given in decimal numbers, and 1 reflects the indexing period. Variables related to the user cost, namely depreciation and tax rates, are in general held constant and that is why they are omitted in the table. For time series graphs and unit root statistics please refer to Figure A 7 or Table A 7 respectively.
Deflators are the CPI excluding rent from the federal statistics office, which are aggregated to quarterly index values, and the CPI2 for all items, suggested by the IMF.
For the housing stock, no appropriate measure was available, why it will be omitted in the inverted demand approach19. Nevertheless, the author experimented with asset formation values from the OECD as a proxy (see table). These have not been included in the final models.
For the mortgage interest rate, the series from Switzerland Mortgage New of the Zürcher Kan-tonalbank (ZKB)20, was chosen, being one of the only available from 1970. It is averaged to quarterly values.
In order to approximate the Swiss income tax for individuals, two tables from the federal tax authority are used. One is indicating tax revenues from the direct federal tax, which was used to average the unweighted tax revenue divided by the gross income per municipality. The sec-ond table with progressive tax rates on a municipal and cantonal level allowed to calculate an
19However different measures were tried as a proxy, like the Gross Fixed Capital Formation by Asset for Dwell-
ings, given by the OECD (values in Table 10 refer to this metric). 20 For the motivation to use this series, see http://ir.mobimo.ch/mobimo2014/download/de/immo-
bilien_schweiz_studion_bank_vontobel_2009.pdf
36
unweighted average for the different income levels per municipality and lastly the unweighted average over these values. Summing these tax values gives the aggregated tax rate for Switzer-land, used to correct the income for tax deductions in the user cost formula. The result is a constant value of 34%21. Property taxes are held constant at 1.5% annual rate
4.1.9 New Zealand
Population data was available from AMECO and is interpolated to quarterly values giving a consistent series from 1960Q1 to 2016Q4 (including forecast). Already real series for the prop-erty prices for 1979Q4 to 2015Q4 were taken from BIS. Since the rent proxy CPI housing was only available as discontinued series, namely from 1960Q1 to 2004Q1 and 1999Q2 to 2016Q4, splicing through average was used to combine them22. Personal disposable income was gathered from Oxford economics. The time span is 1987Q1 to 2015Q4 after removing forecast values. A CPI less shelter series could be found from the OECD, an all component CPI series from the IMF, whereas both reach back before 1970Q1, therefore covering the full investigation time horizon. An appropriate metric for the housing stock was not found, why the inverted demand specifi-cations excludes this metric.
The rates underlying the user costs are 2.5% for depreciation and 30% for the income tax rate23. The property tax is held at zero, since there are no property taxes in New Zealand24.
21 Tables can be found on http://www.bfs.admin.ch/bfs/portal/de/index/themen/18/02/blank/key/steuerbelas-
tung_kantone.html 22 See http://www.tandfonline.com/doi/pdf/10.1080/07350015.1997.10524716 for the proposed splicing method
used. 23 See http://www.ird.govt.nz/how-to/taxrates-codes/rates/itaxsalaryandwage-incometaxrates.html 24 See http://www.globalpropertyguide.com/Pacific/New-Zealand/Taxes-and-Costs and Girouard, N., M.
Kennedy, P. van den Noord and André C. (2005). "Recent House Price Developments." Economics Department Working Papers No. 475.
37
Table 11 Data summary for the New Zealand
Variable Start End Obs Indexed Min Max Mean Source
Pop 1970Q2 2016Q2 185
2828000 4584000 3653000 AMECO, European Commission
rPH 1979Q4 2015Q4 145
0.36 1.31 0.70 BIS Residential Property Prices
rR 1970Q1 2016Q2 186
0.07 1.63 0.77 Main Economic Indicators, OECD
rY 1987Q1 2016Q1 117
4692 7127 5815 Oxford Economics
CPI1 1970Q1 2016Q1 185
0.06 1.09 0.59 Main Economic Indicators, OECD
CPI2 1970Q1 2016Q2 186
0.07 1.09 0.60 International Financial Statistics - IMF
rH 1970Q2 2016Q2 185
21.81 35.36 27.89 None
PJ 1970Q1 2016Q2 186
0.53 31.07 8.71 None Table providing the Sample windows, number of resulting observations, indexing and concrete values for the main variables of the model specifications. The lowercase r in front of the variable represents real/constant prices. Generic variable descriptions are to be found in Table 3. Note that indices are given in decimal numbers, and 1 reflects the indexing period. Variables related to the user cost, namely depreciation and tax rates, are in general held constant and that is why they are omitted in the table. For time series graphs and unit root statistics please refer to Table A 8 and Figure A 8.
4.2 Unit root tests
As outlined in the methodology section, collected economic series are expected to be unit root processes, e.g. xt ~I(1) with trend and Δxt ~I(0) without trend. The necessary ADF test and a complementary PP test were performed for all series. The supporting tables with corresponding results are to be found in Appendix B, Order of integration test results.
For the provided US data from Anundsen (2013), these requirements were already tested and found for all variables, except for the housing stock ht, which is apparently Δ2ht ~I(0)25. How-ever, the collected housing stock time series from Oxford Economics deviate in that manner, by often being unit root processes already.
For Canada, the unit root expectations match all gathered data except for the rent in levels, which is already stationary with 5% significance (not for 1%).
Surprisingly, for the UK, rents and the user cost are already trend stationary in levels, both on the 1% significance level. ht is integrated of order one, all the other variables are in accordance with the assumptions.
25 Δ2
is the two lags (shifts) operator: Δ2xt = Δ (Δ xt) = Δxt - Δxt-1
38
France is completely in line with expectations, apart from the rent, which is Δrt ~I(0) only on the 5%, but not the 1% level. Also for the housing stock, Δht ~I(0) can be rejected on 5% (not 1%), in spite of clearly being Δ2ht ~I(0) for all significance levels.
Concerning rents, Germany shows the same pattern and ht is ~I(0) in levels, which is due to the earlier mentioned inconsistencies in the reunification at 1990. Anyhow, any subsample after 1990 will yield the expected order of integration.
For Japan, the diagnostics are somewhat concerning. On the one hand user costs are signifi-cantly trend stationary, whereas real rents are rt ~I(2)26, which stems from the slow rise until 2000’s and weak consecutive deflation afterwards. On the other hand, the housing stock, ht can be represented as a unit root process, not a second order integrated series. However, it is as-sumed that in the price-to-rent approach, user costs and rents, and in the inverted demand ap-proach, the housing stock, will cancel out problematic effects, leading to an error correction term ~I(0).
For the Netherlands, all variables are unit root processes, including the housing stock. This makes an error correction model and a CVAR seem appropriate.
Also the data for Switzerland is in accordance with all the unit root assumptions. The PP-test statistics support this information.
Data for New Zealand is in line with the unit root assumptions, however Δrt ~I(1) is only sig-nificant at the 5% level and Δht is ~I(1) instead of ~I(2).
4.3 Comparing price-fundamental benchmarks
In the following, benchmarks relating the price to rent, income and the current market value of housing are presented. By introducing the last, it is possible to measure, if market valuation is in line with current transaction prices (which are used for the BIS index construction). Figure 2 displays the developments of the benchmarks from 1980Q1 to 2015Q4, indexed at 2000Q1 for the eight economies.
When tracking the ratios, eye-catching is that five of the assessed countries faced severe price corrections after 2008, which amount to 20 to 30% in terms of 2000 constant prices. Although this is not the case for Germany, Switzerland and Japan, this concordance is striking. The price-to-income ratio exceeds long term averages in France and Netherlands. For the rest, however, values lie below the P-R trajectory and inherit only minor cycles. For the P-R and the P-H27,
26 With ADF Statistic of -9.17 (only constant; not tabled in Appendix) 27 P-R and P-H are strongly correlated (+0.98), why they move in tandem. Apparently the estimation of the market
value from Oxford Economics was based on the rents. Further information was not available.
39
Canada distinctively outpaces the long term average since the early 2000’s and still seems to gather momentum, with being at around 240% of 2000. In New Zealand there is a markedly increase since 2012, reaching almost pre-crisis levels of around 140 and 150% in terms of 2000 constant prices. For the other countries, the ratio is not volatile.
Prices in relation to the market value of housing stock seem to exceed in Canada, what could indicate that prices paid in transactions are too high compared to appraisals, or the estimated market values by appraisal are too low. In other economies, namely the UK and Japan, the market values even seem to undervalue the actual price level.
For scrutiny, the displayed ratios were inspected about matching with the current available benchmarks from the OECD28, finding correlations between 0.95 and 1 except for the P/R ratio New Zealand and the UK. Those correlations tend to be lower, being between 0.55 and 0.81, which might reflect the use of different price deflators as well as SA.
Japans price-to-rent and price-to-income ratios are still on an all-time low, hovering around 70% of the benchmark values from 2000 without showing signs of increase.
28 Quarterly available at http://www.oecd.org/eco/outlook/focusonhouseprices.htm
40
Figure 2 Price-to-rent, Price-to-Income and Price-to-Housing-Stock benchmarks for selected countries a
Figures display the real price- fundamental benchmarks for the eight selected countries, where P-R is the price to rent ratio, P-Y the price-to-income ratio and P-H the price-to-housing stock (market value) ratio, all indexed at 2000Q1. The values origin from nominal-over-nominal series. Fluctuations in the P-Y ratio reflect seasonality effect in the income. For Switzerland and New Zealand, no housing stock market value was available, that is why the P-H benchmark is omitted. Note the evident price corrections after 2007Q3 for all countries except Germany, Switzerland and Japan.
41
5 Results
Subsequently the results are reported in the following manner: (1) facing the presented specifi-cations for the US with alternative data as a robustness check of the methodology and (2) ap-plying the models to the eight gathered, country specific data sets. (3) Computing the concord-ance among models as well as among countries and (4) exploring the model estimates in terms of sign, magnitude and statistical significance.
5.1 Altering the data for the United States
To start with, Figure 3 presents the single equation results obtained by alteration of the estima-tion period, price inflators and the main property price metric. The estimation periods were set to start earlier, namely 1990Q4, what provides a longer window in which the long run stability of the resulting p-values, especially of the inverted demand approach, can be assessed.
Using the BIS property prices, cointegration cannot be found for 36 consecutive quarters in both approaches. With the original FHFA price series, the duration was 16 for the price-to-rent and 32 quarters for the inverted demand approach. Unlike with the BIS series, the inverted demand equation returns p-values rejecting the H0: αph = 0 pledging for cointegration in 2010. However, this signal is weak. A similar picture is displayed, when the housing stock is removed from the equation, therefore restricting γh = 0, see center right (labeled “no H”).
42
Figure 3 Results for the United states with the single equation specifications
The shown graphs indicate the change in the statistical significance of the adjustment coefficients αph from the pair of single equation specifications (see [ 7] and [ 11]) when variables are changeg step-wise. The recursive estimation and data is derivded from Anundsen (2013). The left y-axis represents the p-value, the right y-axis gives the house price index in levels. Red represents the inverted demand, blue the price-to-rent approach. The dashed line at 0.1 represents the significance level for αph. P-Values above could indicate a bubble regime. Top: original data, expand-ing the x axis, revealing instability of the inverted demand approach for small samples prior to 1995; Center left: the explained house price index PH is replaced by the real property prices from the BIS; which reduces the bubble period to significantly lower p-values after 2007, nevertheless there is no cointegration even before 2000 for the inverted demand approach; Center right: The housing stock, H, is omitted. As a consequence, p-values more resemble the price-to-rent approach and rejecting H0 prior to 1995. Bottom-left: H is replaced by the market value of housing stock series from Oxford Economics, leading to rejection of H0 throughout the whole subsamples. Bottom-right: the original housing stock is replaced by the market value of housing stock and PH by the BIS prop-erty price series, gathering results closer to the original recursive estimates.
43
Noteworthy is the behavior of the p-values, when the endogenous variable of housing prices is replaced by the BIS series. The hypothetical bubble period is markedly more punctuated, namely between 2002 and 2007, although the cointegration relationship is only finally rejected by 2009. Especially notable is the consistency of the results for the price-to-rent approach when PH or H is altered. P-values only change small numerically. For the inverted demand approach, p-values between 1998 and 2003 are volatile compared to the estimates with the unaltered data, implying a less clear signal. Important to note is, that altering PH and H separately changes the outcome for the inverted demand approach, not so though, when PH and H are changed in tandem. This empirical indication could possibly speak for higher model validity, when the BIS price series are combined with the housing stock data from Oxford Economics.
On top of the single equation, the CVAR tells a similar story when applied to the original data, shown in Figure 4, where the two approaches with their corresponding specifications are dis-played. Since most of the property price series inherit a visually detectable trend, this corre-sponding qualified specification is preferred over others. As displayed in the graphs on the left hand side, the results oppose each other for the whole sample when the trend is excluded. The inverted demand indicates a bubble regime, whereas the price-to-rent approach yields signifi-cant cointegration ranks of 2 and 3.
Figure 4 CVAR Results for the United States
The four graphs show the results for the recursively estimated CVAR, where a red shaded ribbon represents matrix rank zero, indicating a rejection of cointegration between prices and fundamentals and therefore a bubble regime (see [ 13] for the price-to-rent (ptor) and [ 15] for the inverted demand (invdem) equation). The numbers give the resulting rank of the matrix; the black time series is the explained property price in levels. All specifications and variables from Anundsen (2013) left unchanged. Most valid are the outcomes on the right hand side (with trend), pointing towards a bubble regime starting in 2001 or 2002 and ending in 2008 and 2009 respectively. Note that without a trend, the two approaches give opposite results.
44
Before applying the model specifications from equation [ 13] and [ 15], the BIS data is com-bined with the existing fundamentals in the original US data. The results are given in Figure 4 and indicate, that there are only minor changes compared to the original outcome. After chang-ing the explained variable, the CVAR, other than the single equations, give longer cycles of rank zero, indicating longer bubble regimes as seen on top-right of Figure 5.
Figure 5 Results for recursively estimated CVAR (qualified by a linear trend) and the aggregated bubble indicator for the United States with BIS property prices
Cointegration matrix rank estimates and aggregated bubble indicator for the US from 1977Q2 to 2010Q4 with data from Anundsen (2013) with altered property price series from BIS (in black, indexed 1980Q1) . Top: recursively estimated CVAR; using the inverted demand approach from equation on the left and the price-to-rent approach on the right, given by equation [ 13] and [ 15], both including a trend; Numbers above represent the Rank(Π) = r of the matrix, estimated with the Johansen procedure (see [ 16]) indicating the number of cointegration relationships. Red shaded ribbons represent r = 0, indicating a bubble regime. Stable relationships are only given in periods before and after the surge and fall in prices for the inverted demand, and only in 1998 and 99 for the price to rent approach, showing the high sensitivity of the bubble indicator, when a price series with higher log returns is chosen. Bottom: bubble indicators are combined specification wise to a single signal by summing the estimated ranks of the matrices and averaging the p-values for both single equation approaches.
Subsequently, an aggregated bubble indicator was formed by summing up the estimates of the matrix ranks r in the case of the CVAR’s and computing the average p-value for the single equation specifications, which allows to aggregate the signals and visualize them in connection
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with the property price index, as presented on Figure 5 below. The resulting graph displays a missing relationship until 2008, where after a strong decline in prices, cointegration can be found again for both specifications. Apparently higher log returns in the endogenous house prices series lead to more cases of rejecting cointegration, therefore triggering the bubble re-gime alarm in general more likely.
5.2 Cross country study
Subsequently all assessed economies were faced with both the CVAR with trend and single equation specifications for the pair of approaches. Figure 6 gives the results for the aggregated bubble indicators, but only for six out of eight countries as no housing stock fundamental was available for Switzerland and New Zealand. Figure 7 includes the results for all countries, there-fore excluding the housing stock. The de-aggregated results for the single equations and the CVAR can be found in the appendix on Figure A 10 and Figure A 11 respectively.
On the whole, the aggregated single equation and the CVAR bubble indicators do not markedly coincide when considering the equations with included housing stock. However, there are syn-chronic rejections of cointegration in subsamples of several years in the price series from Can-ada and Japan. In detail, Canada shows coincidence of the bubble indicators for a period of 10 yearly recursive estimates, namely from 2004Q4 to 2013Q, in both the matrix rank estimates and the single equations. However, the single equation p-values do not reject H0 αph= 0 through-out the whole sample which complicates inference about particular episodes. But since the ma-trix rank estimate is maximally 1, the cointegration relationship seems very weak after all.
Both the UK and France show opposite results for the specifications. However, a stable long term relationship cannot be rejected prior to 1997 for the UK in the two specifications.
Within the CVAR inverted demand framework, Germany does not exhibit cointegration after 2001, reverting the trend of p-values towards a rejection of H0 αph= 0. This is happening in a regime of falling prices, which possibly indicates that housing and income do not move along with the property price level, whereas rents do – indicated by a rank of one for the CVAR.
Japan does not show stability in the early recursive estimations in the couple of CVAR ap-proaches, in particular until 2000 and 2001 respectively. The single equation results point away from cointegration throughout the whole sample, also in the period of stagnating prices after 2009, when a return to equilibrium could be expected. The same is observed when the housing stock is removed from the sample.
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Figure 6 Aggregated bubble indicators for selected countries
This graphs report the aggregated results of the recursive estimates from the CVAR specification including a trend by Equations [ 13] and [ 15], and the single equation specification by [ 7] and [ 11] respectively. The bubble indicators are combined in a single plot, summing the ranks of the matrix test for the CVAR and averaging the p-values for both single equation approaches (dashed line). Black series are the BIS property price indices. Sample periods all end in 2015Q4, except for GER29, and start at CAN:1981Q2, UK:1987Q2, FRA: 1990Q2, GER:1990Q2, JAP 1980Q2, NL 1980Q2. Red shaded ribbons represent matrix rank zero, indicating a bubble period. For the results of New Zealand and Switzerland refer to Figure 7.
29 housing stock series only spans to 2013Q2 and therefore terminates the estimation earlier than 2015Q4.
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Figure 7 Aggregated bubble indicators when housing stock is excluded from the inverted demand approach for Canada, UK, France and Germany (other four countries on next page; see Figure 8)
These graphs report the aggregated results of the recursive estimates from the CVAR specification by equations [ 13] and [ 15], and the single equation specification by [ 7] and [ 11] respectively. The bubble indicators are combined in a single plot, summing the estimated ranks of the cointegration test for the CVAR and averaging the p-values for both single equation approaches (dashed red line). The dotted line at 0.1 is the chosen significance level α. Black series represent the BIS property price index. Sample periods all end in 2015Q4 and start at CAN:1981Q2, UK:1987Q2, FRA: 1990Q2, GER:1990Q2. Red shaded ribbons represent the matrix rank zero, indicating a bubble period.
Turning to the results when the inverted demand is qualified by removing the housing stock, the aggregated bubble indicators do not strongly deviate in comparison to the prior estimates. Canada still displays a considerably long phase of no cointegration for all indicators, which in particular coincide from 2005 to 2014. The UK and France did also not change drastically com-pared with the results with included housing stock. The indicators still give opposing signals. In the other set of four countries, displayed in Figure 8, Japan shows irregular and alternating rejections of cointegration for the CVAR and no cointegration at all for the single equation specification. The Netherlands and Switzerland both show stable cointegration relationships for the CVAR, but not for the single equation specification, whereas New Zealand gives a bubble signal for both indicators in 2015 and contrary results else. In the CVAR, New Zealand’s prop-erty prices do not show cointegration for the recursive periods from 2014Q4 and 2015Q4 for the inverted demand, and just rank 1 for the price-to-rent approach.
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Figure 8 Aggregated bubble indicators when housing stock is excluded from the inverted demand approach for Japan, Netherlands, Switzerland and New Zealand
These graphs report the aggregated result of the recursive estimates from the CVAR specification by equations [ 13] and [ 15], and the single equation specification by [ 7] and [ 11] respectively. The bubble indicators are combined in a single plot, summing the estimated ranks of the cointegration test for the CVAR and averaging the p-values for both single equation approaches (dashed red line). The dotted line at 0.1 is the chosen significance level α. Black series represent the BIS property price index. Sample periods all end in 2015Q4 and start at JAP: 1980Q2, NL: 1980Q2, CH: 1983Q2, NZ: 1987Q2. Red shaded ribbon represents matrix rank zero, indicating a bubble period.
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When investigating property prices detached from fundamentals for super exponential growth patterns, power law regimes are identified for all countries, displayed by blue shaded ribbons in Figure 9. The diagnosed rates occur in small subsamples of just 1 but also reach periods of 30 to 40 consecutive quarters. Canada, the UK and France show similar patterns, short samples of super-exponential growth shortly before the nineties with durations of 6, 8 and 6 consecutive years. This trend is reversed by 2008 for Canada and France and by 2006 for the UK. Figure 9 Results of the PL fit for the collected property price series.
This graphs report the results from the power law (PL, compare equation [ 19]) fit for all the selected property price series. Grey shaded areas map the investigated sample; blue colored ribbons represent a regime of super-exponential growth.
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Whereas Japan only inherits one distinct and connected power-law phase, visible from 1989 to 1991, Switzerland and the Netherlands exhibit an unsustainable bubble for the periods of 1976 to 1978 and 1986 to 1990 respectively. Other successive periods occur from 1995 to 2003 and 2009 to 2014. Apart from that, regimes tend to be irregular for those two price series. New Zealand also does not provide clear-cut regimes, but bubble indications are given for 2003 to 2007 as well as in the end of the sample. Turning to the LPPLs fit, irregular single periods disappear, leaving consecutive time windows. Figure 10 gives the results for all countries. For the series of Canada, UK and France, the former super-exponential growth regimes from the early 2000’s are confirmed, but all start later, namely in 2003, 2000 and 2003 respectively. Japan now inherits two determinable periods ac-cording to the LPPLs, one after 1983 and one in the beginning of the 90ies. The Netherlands and Switzerland still contain irregularities, however the unsustainable price developments in Switzerland around 1990 point clearly towards a bubble. New Zealand displays three phases of super-exponential regimes, the last one reported in the very last quarters of the sample, 2015Q3 and Q4, which, however, does not coincide with the above mentioned evidence from the ECM and CVAR specifications.
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Figure 10 Results of the LPPLs fit for the collected property price series.
This graphs report the results from the log period power law singularity fit (LPPLs, see equation [ 18) for all selected property price series. Grey shaded areas map the investigated sample; red colored ribbons represent regimes of super-exponential growth with periodic oscillations. Note that all the countries inherit clear-cut unsustainable regimes, coinciding in the early 2000’s for half of them.
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5.3 Concordance of binary cycles
The previously presented results are transformed in to binary cycles as proposed by [ 19] and [ 20], yielding the 8 × 8 concordance matrices per country and six 8 × 8 concordance matrices for every approach. Table 12 presents the averaged concordances among all the countries, when housing is excluded from the specification.
Table 12 Average of Cross-country Concordance for all model specifications
CAN CH FRA GER JAP NL NZ UK
CAN 1.00 0.36 0.50 0.54 0.68 0.52 0.59 0.41
CH 0.36 1.00 0.77 0.61 0.54 0.57 0.66 0.71
FRA 0.50 0.77 1.00 0.62 0.62 0.69 0.76 0.91
GER 0.54 0.61 0.62 1.00 0.69 0.71 0.80 0.62
JAP 0.68 0.54 0.62 0.69 1.00 0.55 0.69 0.54
NL 0.52 0.57 0.69 0.71 0.55 1.00 0.72 0.66
NZ 0.59 0.66 0.76 0.80 0.69 0.72 1.00 0.75
UK 0.41 0.71 0.91 0.62 0.54 0.66 0.75 1.00
Mean 0.57 0.65 0.73 0.70 0.66 0.68 0.75 0.70 This table reports the concordance indicators (see [ 21]), a measure of coincidence for binary bubble cycles. 0 indicates no synchronization, 1 represents synchronization over the total common sample. The country wise pairs are averaged over all used model specifications. The results with the calculated median (see Table A 9) tend to higher values in general due to a multiple 1.00’s, but allow the same conclusions.
High in-between country concordances over 0.9 can be found for France and the UK. Also highly concordant, in between 0.8 and 0.9, is New Zealand in connection with Germany and Switzerland and the Netherlands. This can be explained with the overlap of fundamentals in line with house prices for the CVAR specification and absence of cointegration with the single equation approaches. Rather low synchronizations are found for Canada, with a mean close to 0.5, which also seems to be highly asynchronous in comparison with France, UK and Switzer-land. This is due to Canada also not being cointegrated in the context of the CVAR, which becomes clearly, when considering the specification wise concordances for Canada, shown in Table 14. Notable are the evident strong synchronizations between the different price-to-rent specifications (1.00 values between ptor), which coincide for every period, suggesting high consistency.
Turning to the specification wise concordances, Table 13 presents the resulting matrix for the US with the unaltered data and methodology from Anundsen (2013). Markedly high synchro-nizations are found between the CVAR specifications without trend and the different single equation specifications, e.g. the CVAR and the single equation. Apart from that, the single equation results for the US do not move in tandem (Ix,y ≤ 0.50). When the trend is excluded from
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the CVAR equation, the overlap seems to disappear completely (Ix,y = 0.05) which was already visible in Figure 4.
Table 13 Cross-country Concordance matrix for the United States
cvar invd noT cvar invd cvar ptor noT cvar ptor sing ptor sing invd
cvar invd noT 1.00 0.48 0.05 0.43 0.24 0.67
cvar invd 0.48 1.00 0.57 0.86 0.76 0.71
cvar ptor noT 0.05 0.57 1.00 0.62 0.81 0.29
cvar ptor 0.43 0.86 0.62 1.00 0.81 0.67
sing ptor 0.24 0.76 0.81 0.81 1.00 0.48
sing invd 0.67 0.71 0.29 0.67 0.48 1.00 This table reports the concordance indices (see [ 21]), a measure of coincidence for bubble cycles, specification wise for the recursive estimations for the United States using the data provided by Anundsen (2013). CVAR refers to equation [ 13] for the ptor and [ 15], for invdem, whereas sing represents the single equation specification [ 7] and [ 11] respectively. noT indicates, that no Trend is included in the equation specification.
In order to investigate an example which shows coincident signals model between specifica-tions, the concordances for Canada are presented in Table 14. Starting with the CVAR specifi-cations, concordances of 1.00 can be found between the price-to-rent approach (with or without trend) and the inverted demand approach without trend. Also, the price-to-rent CVAR results do coincide fully with the corresponding single equation specification output. Less so with the inverted demand single equation, which is, however, with a degree of 0.83 still high.
The analysis detached from the fundamentals, namely the power law and log periodic power law fits, display high concordances with Ix,y =0.89 among each other. After that, these power law fits overlap up to two thirds of the sample (Ix,y = 0.67) with all the price-to-rent specifica-tions and the CVAR from the inverted demand approach. Low synchronizations can be found between the PL and the inverted demand CVAR including a trend.
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Table 14 Concordance matrix for Canada
cvar invd noT
cvar invd
cvar ptor noT
cvar ptor sing ptor sing invd LPPLs PL
cvar invd noT 1.00 0.56 1.00 1.00 1.00 0.83 0.67 0.67
cvar invd 0.56 1.00 0.56 0.56 0.56 0.39 0.44 0.33
cvar ptor noT 1.00 0.56 1.00 1.00 1.00 0.83 0.67 0.67
cvar ptor 1.00 0.56 1.00 1.00 1.00 0.83 0.67 0.67
sing ptor 1.00 0.56 1.00 1.00 1.00 0.83 0.67 0.67
sing invd 0.83 0.39 0.83 0.83 0.83 1.00 0.72 0.83
LPPLs 0.67 0.44 0.67 0.67 0.67 0.72 1.00 0.89
PL 0.67 0.33 0.67 0.67 0.67 0.83 0.89 1.00 This table reports the concordance indices (see [ 21]), a measure of coincidence for bubble cycles, specification wise for the recursive estimations of Canada. CVAR refers to equation [ 12] for ptor and [ 15], for invdem, whereas sing represents the single equation specification, [ 7] and [ 11] respectively. noT indicates, that no Trend is included in the equation specification. PL represents the power law fit after [ 18] and LPPLs is log periodic power law fit following [ 19]. A 0 indicates no synchronization, a 1.00 represents synchronization over the total overlapping sample. Like for Canada, the concordances are high among the approaches for Switzerland, France and UK. See Appendix E for the corresponding tables. But this is not the case for Germany, dis-played in Table 15. The CVAR’s give opposing results and show very low coincidences with values ranging from 0 to 0.15. However, the common pattern of high concordances is still there for both the single equation specification and the power law fits with Ix,y = 0.77 and Ix,y = 1.00 respectively.
Table 15 Concordance matrix for Germany with excluded housing stock
cvar invd noT
cvar invd
cvar ptor noT
cvar ptor
sing ptor
sing invd
LPPLs PL
cvar invd noT 1.00 0.85 0.00 0.00 0.92 0.85 0.85 0.85
cvar invd 0.85 1.00 0.15 0.15 0.77 0.85 0.69 0.69
cvar ptor noT 0.00 0.15 1.00 1.00 0.08 0.15 0.15 0.15
cvar ptor 0.00 0.15 1.00 1.00 0.08 0.15 0.15 0.15
sing ptor 0.92 0.77 0.08 0.08 1.00 0.77 0.77 0.77
sing invd 0.85 0.85 0.15 0.15 0.77 1.00 0.69 0.69
LPPLs 0.85 0.69 0.15 0.15 0.77 0.69 1.00 1.00
PL 0.85 0.69 0.15 0.15 0.77 0.69 1.00 1.00
This table reports the concordance indices specification wise. The concordance (see [ 21]) is a measure of coincidence for bubble cycles. A 0 indicates no synchronization, a 1.00 represents synchronization over the total estimated sample. CVAR refers to equation [ 13] for ptor and [ 15], for invdem, whereas sing represents the single equation specification, [ 7] for ptor and [ 11] for invdem respectively. noT indicates, that no deterministic trend is included in the equation. PL represents the power law fit after [ 18] and LPPLs is the log periodic power law fit following [ 19].
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First, the results showed, that binary bubble cycles between countries are synchronized with a degree of over 0.80 in four cases, namely for the UK, France, Germany and New Zealand. Second, that the models do in most of the cases support each other specification wise, e.g. single equation with single equation and so on. An example was Japan (see Table A 12). Approach wise, meaning inverted demand with inverted demand etc., they only are concordant in some cases, like in the above explained example of Canada. However, in the case of Germany, the concordances were completely absent.
5.4 Robustness of long run coefficients and significance
In order to investigate the gathered results in accordance with economic theory, the signs and magnitudes of the adjustment coefficients αph are presented. Consider Figure 11 for the country comparison. For the price-to-rent approach they all exhibit the expected negative values close to zero. For Canada, the estimates are in the range of -0.1 and -.35, which indicates instability and a too strong reaction in terms of changes in the housing stock and income. But since the CVAR does not give significant values, this result is questionable. An exception to the in gen-eral negative values is France, where the estimates are around +0.04, which could be explained by Δrt being only weakly or not ~I(0) as well as the falling (not rising) prices and the relatively short sample30. Nevertheless, the magnitudes and signs seem valid. Also most of the estimates for the inverted demand approach are in line with expectations, however Japan displays mostly zeros despite of having several positive values, which is due to the fact, that the underlying series rt and uct have both been tested to be stationary, therefore likely invalidating the CVAR. Also notable for Japan are the first falling and then stagnating price levels. To model them adequately would demand adjustments of the model equation and the trend component.
Figure 11 gives the distributions of p-values, when testing H0: Rank(Π) = r* < 1 and HA: Rank(Π) = 1 respectively. The critical cut off point, above which r* is increased by 1, is selected at a significance level of 10%. A non-rejection leads to the conclusion of missing cointegration, expressing a possible bubble regime, clearly observed for Canada in the whole sample and for the Netherlands in the majority of recursive subsamples. As addressed before, Japan and New Zealand show somewhat inconsistent results with p-values just distributed in between the crit-ical area of 5 and 10%. For Japan this could be related to the fall in prices and the following stagnation, somewhat making the use of a trend unjustifiable. Significance for HA: r* = 1 is high for UK, France, Germany and Switzerland throughout all subsamples, indicating there is at least one or more stable cointegration relationships.
30 Below 100 observations when including lag order of five for the price-to-rent approach
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In the inverted demand framework, including the housing stock, highly significant results are observed for UK, France and New Zealand. The lack of cointegration however disappeared for Canada and the Netherlands, where the fundamentals, housing stock and income now seem to bear the price levels. Japan shows a similar pattern for the price-to-rent approach, neither be-having asymptotically towards rejection or non-rejection, possibly due to the reasons stated above. Germany’s p-values for the CVAR are not exclusively significant as well, which could be explained with the long period of deflating real prices.
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Figure 11 Error correction adjustment coefficients when estimating the CVAR
Boxplots showing the numerical estimates for the adjustment coefficient α per country in the CVAR framework (see [ 13] and [ 15]). Top results for the price-to-rent approach; Center: the inverted demand including housing stock Bottom: giving the inverted demand approach excluding housing (“noH”). Note that α is expected to be negative, representing a regime with slowly increasing prices. For the price-to-rent approach, coefficients are con-sistent with theory, except for France and the UK, where unit root assumptions are violated for rt and uct. The inverted demand approach yields expected signs and magnitudes; however, Canadas values are insignificant when ht is included. Japans estimates are biased due to stationarity of both rt and uct.
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Figure 12 p-value distributions for the trace test in the CVAR with trend specification
Resulting distributions of p-values for the recursive estimation of the CVAR with trend per country, for both the price-to-rent, inverted demand with and without housing stock (h). P-values represent the significance of the first step of the trace test (see [ 16]), H0: Rank(Π) < 1 and HA: Rank(Π) = 1, where a dashed line indicates the 10% significance level, serving as cut off point for rejecting H0 and increasing the tested rank consequently. A non-rejection of H0 therefore indicates a rank of zero, no-cointegration and a possible bubble regime. Canada and the Netherlands show no cointegration relationship for the whole sample in the inverted demand approach. Japan’s estimates are only partially significant for 10%. In the other cases, statistical insignificance is most likely due to stationarity of both rt and uct.
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6 Discussion
The results for the United States revealed some instability when the real property prices from the BIS replaced the former endogenous variable in the inverted demand approach for both the CVAR and the single equation specification. In general, using the series provided from the BIS lead to higher p-values for the single equations and lower rank estimates of the matrix in the CVAR within the trace test procedure. This might be explained in terms of the higher log returns. Since the BIS series are more punctuated in phases of rise (or fall respectively) the single equa-tion and in particular the CVAR approach seem to trigger the bubble regime alarm more likely. This has to be considered not only for the US, but also for the results of the other countries.
When the housing stock is excluded from the equation for the US, p-values for the inverted demand are more consistent with the price-to-rent approach, reducing the p-values in particular in 1992 to 1994 leading to a rejection of H0 and no cointegration. This mentioned, the exclusion of the housing stock is justified when performing the cross country study, especially because the lack of appropriate measures to adjust for inflation. Nevertheless, the inclusion of different housing stock or even construction metrics, e.g. in volumes or housing unit completions respec-tively, could improve the outcome of the proposed inverted demand approach.
Clearly, the concordances are higher when the housing stock was excluded from all the coun-tries, indicating more consistent results, when a price-to-income equivalent is used. Moreover, results for Canada and other countries suggest a higher robustness of the price-to-rent approach.
6.1 Comparing results to existing findings
Subsequently the found results are compared with findings in the literature. Hereby the focus lies on the bubble regime periods, that showed absolute concordance, (Ik = 1.00) both for the CVAR and the single equation specifications. Such binary cycles were found for a period of ten years in Canada, namely from 2004 to 2014 and for Japan in both unevenly distributed time spans and in distinct periods, in particular spanning from 1995 to 1998. For New Zealand such a cycle was exclusively identified in the year 2015.
Overall, there is no striking overlap of identified regimes with those, diagnosed by other con-tributions. However, it has to be noted that the samples from literature end on average seven years earlier and that sample sizes differ in general. Nevertheless, there is some evidence of
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common results, namely for periods in the cases of Canada, Germany and partially the Nether-lands. Table 16 Found bubble regime cycles in comparison with other studies
Country First Author
Year Sample Literature
Sample Thesis
Bubble Periods Literature
Bubble Periods Thesis
Canada Kholidilin 2010 1975, 2009 1981, 2015
Canada Orsal 2014 1989, 2010 1981, 2015
France Antipa 2010 1980, 2008 1987, 2015 [2005, 2008]
Germany Kholidilin 2010 1975, 2009 1990, 2015
Japan Hott 2008 1980, 2005 1980, 2015 [1988, 1993] [1995, 1998] [2000] [2015]
Netherlands Kranendonk 2008 1980, 2007 1980, 2015
Netherlands Hott 2008 1980, 2005 1980, 2015 [2001, 2005]
New Zealand Glindro 2011 1993, 2006 1987, 2015
[2015]
New Zealand Fraser 2008 1970, 2005 1987, 2015 [2005] [2015]
Switzerland Hott 2008 1980, 2005 1983, 2015 [1987, 1993] [1997, 2005]
United Kingdom Black 2006 1973, 2004 1987, 2015 [2001, 2004]
United Kingdom Hott 2008 1980, 2005 1987, 2015 [1990] [2005, 2006]
Table comparing samples and bubble cycles between the literature reviewed and this thesis. The cited displayed articles from literature were restricted to those which performed fundamental based ECM approaches. The thesis bubble period only represent full coincidence between the used CVAR (see equations [ 13] and [ 15]) without trend and single equation specifications as a robustness check ( [ 7] and [ 11]). Note that for the US, the data from Anundsen (2013) was altered in terms of the price series and the housing stock.
Although there was a bubble regime found by Fraser (2008) in 2005, this is not supported by the findings in this work. Instead, a possible regime is found in 2015.
Triggers like those used by Antipa and Lecat (2010) showed possible bubble regimes in France, however when the authors added a measure for households borrowing capacity, the overvalua-tion could be explained. Actually, this result also could have achieved with including income in the framework, as proposed by the results in this study. However, the selection of appropriate variables and underlying data remains an open and non-trivial topic.
In particular, comparing the results for the Netherlands, the housing stock inclusion in the in-verted demand framework could not lead to evidence of cointegration, in contrast to Kranendonk (2008), who found cointegration. Instead the single equation price-to-rent ap-proach coincides with Hott and Monnin (2008), who identified a bubble period from 2001 to 2005. Moreover, the rents seem not to explain the rise in prices after 2012 in the Netherlands.
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When it comes to the coefficient estimates of the CVAR, the results coincide with Kholodilin, Menz et al. (2010), who found significant adjustment speeds except for Japan and Switzerland. This estimates were partially confirmed here, by finding values statistically insignificant from zero for both approaches in the case of Japan and only for the inverted demand approach in the case of Switzerland. The author moreover agrees with Kholodilin, Menz et al. (2010) about the assumption, that the estimates can possibly be invalidated through the bust of bubbles in the 90’ies and the subsequent fall in prices for these economies.
The periods diagnosed by Black, Fraser et al. (2006) and Hott and Monnin (2008) were not confirmed by this study, although the price-to-rent approach alone showed the loss of a stable long term relationship after 1997 (see Table A 10 in the supporting material).
Results as given by the literature do in general not coincide with the found bubble cycles, when restricting bubble periods to the absolute coincidence of the different approaches. In that case the calculated bubble indicator seems to become rather conservative, therefore reducing poten-tial false positives.
6.2 Limitations
Also in line with Kholodilin, Menz et al. (2010), it has to be pointed out, that institutional factors and the legal environment can play a key role in the development of bubbles and studies only taking into account economic fundamentals might mask these factors. A rejection of cointegration can simply mean, that better fitting fundamentals could have been used to explain the housing prices. In particular this was obvious, when the housing stock was excluded for the US, therefore leaving user costs and income explaining property prices more significantly.
For the single equation specifications, the duration and signal strength of the bubble regimes seemed to be largely overestimated. Besides being explained by typical model draw-backs, such as small sample sizes or heteroscadicity, this could be due to the cross-country heterogenity of housing markets, which are domestic by nature, therefore making the transfer of a model that looked promising for the US ques-tionable for other economies.
The trend component incorporated in the CVAR plays an important role when estimating price series. When changing the sample recursively, the coefficients can vary and depending on the cyclic behavior of the property price series, estimations for the rank can be somewhat flawed.
When considering the econometric model assumptions in terms of order of integration, it was expected, that all the included time series are ~I(1), which makes the pair of a single equation ECM and a CVAR feasible. However, for Japan and UK these assumptions are violated, since the conducted unit root tests could not reject: uct,JAP ~I(0), rt,JAP ~I(2) and uct,UK ~I(0), rt,UK ~I(0) respectively. As a consequence, the error terms are likely to be correlated which could lead to spurious regression. This is supported by the performed tests for both heteroscedasticity and autocorrelation in the single equation specifications,
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which could not reject the corresponding hypothesis’. However, this is not concerning both specifica-tions. The CVAR still finds cointegration relationships, therefore relaxing the strict assumptions about order of integration by iterating between the variables. For Japan, the diagnostics clearly reject the hy-pothesis’ of no autocorrelation and no heteroscedasticity throughout almost all of the subsamples in the pair of approaches. This reveals the strong importance of selecting series that fulfill the unit root as-sumption. Alternatively, for the UK, the trend stationary series uct,UK and rt,UK could be inserted in to a model based on levels, rather than first differences. Nevertheless, this would require an appropriate trend-stationary property price measure.
Throughout the iterative work of collecting data, testing for unit roots and assess model outputs, collec-tion appropriate deflation measures were especially relevant. The use of inadequate inflation adjustment can affect the outcome significantly. In particular, this was evident for the housing stock ht that could be spuriously correlated31 with the explained property price. This problem can be solved, by deflating with an appropriate inflation adjustment metric, like the one proposed by Anundsen (2013) for the US. However, for the assessed economies such comparable deflators were too short, had a different under-lying methodology or were simply not available. Related to that and noteworthy is that the removal of the housing stock as a fundamental in the inverted demand model leads to higher concord-ances among specifications – which favors the use of the equivalent of a price-to-income, rather than the one of an inverted demand approach, when comparing different country sets. Such diagnostic problems for this approach were already detected by Stevenson (2008), especially when extreme price movements occur, what the author reported for Japan and Switzerland. This was confirmed for Japan in this study, where prices were falling, what likely lead to question-able results. Nevertheless, the discussion of an appropriate inverted demand or price-to-income framework remains mainly a data issue. The inclusion of an appropriate inflation adjusted hous-ing stock measure, as presented by Anundsen (2013) , is also likely to lead to a valid results in other economies, given that the sample size is large enough and price regimes are not to extreme.
31 A correlation between two variables that is not due to causality, but perhaps to the dependence of the two
variables on another unobserved factor Wooldridge, J. M. (2014). Introduction to Econometrics. Hampshire, United Kingdom, CENGAGE Learning..
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7 Conclusions
This thesis used the models and data from a previously developed econometric fundamental framework based on the work from Anundsen (2013), who performed diagnostics for the US market. In order to explore the sensitivity of the models, they were extended by alternative data. Moreover, the author collected comparable price and fundamental series for eight OECD econ-omies, which range from as early as 1970Q1 to 2015Q4. These were faced with all possible model specifications, gathering comparable results for both error correction models (ECM) and cointegration vector autoregressive models (CVAR). Additionally, the collected price series were investigated for super-exponential growth, detached from the fundamentals. Out of the total of these eight results, binary bubble regime cycles were identified and checked for syn-chronization with a concordance index, both among countries and among specifications.
The results indicated high concordances between France and the UK as well as for the set of Germany, Netherlands, Switzerland and New Zealand. Synchronic bubble regimes could be found in subsamples for Canada, New Zealand and Japan. New Zealand seems to pass through a period, in which fundamentals explain property prices only irregularly and both the crude price-fundamental ratios as well as the model results signify a major disconnection of the prop-erty prices from fundamentals. Another finding was, that the models do in most of the cases support each other specification wise, e.g. CVAR with CVAR and so on, which was different for the approach wise comparison. However, it also has to be mentioned, that the results for Canada underlie poor model diagnostics and that the rent and user cost fundamentals of the UK and Japan are no unit root processes, questioning the use of ECM.
The comparison of clearly identified bubble regimes, measured by all methods pointing towards no cointegration, do in general not coincide with the assessed literature. First, this could be explained by a too restrictive bubble criterion (only considering full concordance of all meth-odologies), or second, the variation in variables and sample sizes lead to opposite findings. Actually, the empirical evidence explored that the presented single equation and CVAR speci-fications show high sensitivity when exposed to different fundamental time series and conclu-sions can differ, even when the changes in the underlying data are small.
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8 Acknowledgements
I would like to thank all people who supported me in writing this thesis, in particular my super-visors Diego Ardila Alvarez and Dr. Dorsa Sanadgol. Their understanding and openness for questions was remarkable. Also, I would like to thank Professor Didier Sornette for providing a great working environment. His breakfast meetings always were an inspiration and motivated me throughout the time of investigating real estate bubbles.
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9 List of references
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Books
Jowsey, E. (2011). Real Estate Economics. London, PALGRAVE MACMILLAN.
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(2016). Comradely Capitalism. The Economist. Aug 20th.
Under publication
Ardila, D., D. Sanadgol and D. Sornette (2016). "Out-of-sample forecasting of housing bubble tipping points."
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10 Appendix
A. Data Statistics and time series
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Figure A 1 Time series for Canada
This plots show the real measures derived from the collected data, where rPH is the real property price index, rR, the real rent (CPI housing), rY is the real per capita disposable income, rH is the real housing stock in monetary terms per capita, UC the real direct user cost, CPI1, the consumer price index without housing, CPI2 is for all items, Pop is population in total residents, PJ is the deflator for the housing stock and I are the (mortgage) interest rates.
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Figure A 2 Time series for the United Kingdom
This plots show the real measures derived from the collected data, where rPH is the real property price index, rR, the real rent (CPI housing), rY is the real per capita disposable income, rH is the real housing stock in monetary terms per capita, UC the real direct user cost, CPI1, the consumer price index without housing, CPI2 is for all items, Pop is population in total residents, PJ is the deflator for the housing stock and I are the (mortgage) interest rates.
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Figure A 3 Time series for France
This plots show the real measures derived from the collected data, where rPH is the real property price index, rR, the real rent (CPI housing), rY is the real per capita disposable income, rH is the real housing stock in monetary terms per capita, UC the real direct user cost, CPI1, the consumer price index without housing, CPI2 is for all items, Pop is population in total residents, PJ is the deflator for the housing stock and I are the (mortgage) interest rates.
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Figure A 4 Time series for Germany
This plots show the real measures derived from the collected data, where rPH is the real property price index, rR, the real rent (CPI housing), rY is the real per capita disposable income, rH is the real housing stock in monetary terms per capita, UC the real direct user cost, CPI1, the consumer price index without housing, CPI2 is for all items, Pop is population in total residents, PJ is the deflator for the housing stock and I are the (mortgage) interest rates.
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Figure A 5 Time series for Japan
This plots show the real measures derived from the collected data, where rPH is the real property price index, rR, the real rent (CPI housing), rY is the real per capita disposable income, rH is the real housing stock in monetary terms per capita, UC the real direct user cost, CPI1, the consumer price index without housing, CPI2 is for all items, Pop is population in total residents, PJ is the deflator for the housing stock and I are the (mortgage) interest rates.
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Figure A 6 Time series for Netherlands
This plots show the real measures derived from the collected data, where rPH is the real property price index, rR, the real rent (CPI housing), rY is the real per capita disposable income, rH is the real housing stock in monetary terms per capita, UC the real direct user cost, CPI1, the consumer price index without housing, CPI2 is for all items, Pop is population in total residents, PJ is the deflator for the housing stock and I are the (mortgage) interest rates.
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Figure A 7 Time series for Switzerland
This plots show the real measures derived from the collected data, where rPH is the real property price index, rR, the real rent (CPI housing), rY is the real per capita disposable income, rH is the real housing stock (proxied by capital formation, measure from OECD), UC the real direct user cost, CPI1, the consumer price index without housing, CPI2 is for all items, Pop is population in total residents, PJ is the deflator for the housing stock and I are the (mortgage) interest rates. The housing stock H and PJ were not included in the final model estimation.
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Figure A 8 Time series for New Zealand
This plots show the real measures derived from the collected data, where rPH is the real property price index, rR, the real rent (CPI housing), rY is the real per capita disposable income, UC the real direct user cost, CPI1, the consumer price index without housing, CPI2 is for all items, Pop is population in total residents, PJ is the deflator for the housing stock and I are the (mortgage) interest rates. Note that the housing stock, H, is represented by building permits and was not included in the final model specifications.
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B. Order of integration test results
Table A 1 Test statistics for order of differencing for Canada
Variable Sample size
t-ADF t-crit 5%
t-crit 1%
k-ADF Type t-PP Bandwidth
ph 184 -1.45 -3.43 -4.01 5 trend -1.82 5
r 186 -3.71 -3.43 -4.01 4 trend -2.55 5
y 141 -1.83 -3.44 -4.02 4 trend -1.85 4
uc 182 -3.19 -3.43 -4.01 5 trend -3.44 5
h 146 0.01 -3.44 -4.02 5 trend -1.43 4
Dph 183 -4.65 -2.88 -3.46 5 drift -12.01 5
Dr 185 -3.80 -2.88 -3.46 5 drift -11.81 5
Dy 140 -4.65 -2.88 -3.47 3 drift -13.11 4
Duc 181 -5.70 -2.88 -3.46 4 drift -9.44 5
Dh 145 -2.47 -2.88 -3.47 5 drift -8.44 4
DDh 144 -10.86 -2.88 -3.47 4 drift -20.00 4 Table showing the results for the unit root test statistics for the collected time series in levels, the first differences (D=Δ) and second difference (DD=Δ2) for the housing stock. The column -ADF refers to the test-statistic for the augmented dickey fuller test and PP for the Philips-Perron Test (zτ). The critical t-values count for both test specifications (Ericsson 2002). k denotes the ideal lag truncation for the ADF, starting with a maximal value of 5 and testing down with AIC. Type drift refers to the inclusion of a constant; trend refers to a trend and a constant.
Table A 2 Test statistics for order of integration for the United Kingdom
Variable Sample size
t-ADF t-crit 5%
t-crit 1%
k-ADF Type t-PP Bandwidth
ph 184 -2.61 -3.43 -4.01 5 trend -2.43 5
r 118 -4.66 -3.45 -4.03 4 trend -3.30 4
y 178 0.04 -3.43 -4.01 4 trend -2.03 5
uc 141 -4.93 -3.44 -4.02 4 trend -5.64 4
h 116 -1.83 -3.45 -4.04 1 trend -1.63 4
Dph 183 -5.23 -2.88 -3.46 4 drift -8.02 5
Dr 117 -1.26 -2.88 -3.48 3 drift -13.34 4
Dy 177 -4.52 -2.88 -3.46 4 drift -36.59 5
Duc 140 -4.49 -2.88 -3.47 5 drift -13.18 4
Dh 115 -6.96 -2.88 -3.48 0 drift -6.10 4
DDh 114 -6.97 -2.88 -3.48 5 drift -21.95 4 Table showing the results for the unit root test statistics for the collected time series in levels, the first differences (D=Δ) and second difference (DD=Δ2) for the housing stock. The column -ADF refers to the test-statistic for the augmented dickey fuller test and PP for the Philips-Perron Test (zτ). The critical t-values count for both test specifications (Ericsson 2002). k denotes the ideal lag truncation for the ADF, starting with a maximal value of 5 and testing down with AIC. Type drift refers to the inclusion of a constant; trend refers to a trend and a constant.
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Table A 3 Test statistics for order of integration for France
Variable Sample size t-ADF t-crit 5% t-crit 1% k-ADF Type t-PP Bandwidth
ph 184 -2.22 -3.43 -4.01 5 trend -1.80 5
r 104 -3.29 -3.45 -4.04 4 trend -2.47 4
y 166 -2.50 -3.43 -4.01 5 trend -1.72 4
uc 146 -3.15 -3.44 -4.02 5 trend -2.57 4
h 146 -2.26 -3.44 -4.02 4 trend -1.59 4
Dph 183 -4.37 -2.88 -3.46 5 drift -9.34 5
Dr 103 -2.96 -2.89 -3.49 4 drift -13.33 4
Dy 165 -4.14 -2.88 -3.47 4 drift -9.62 4
Duc 145 -3.78 -2.88 -3.47 5 drift -7.82 4
Dh 145 -3.24 -2.88 -3.47 3 drift -9.08 4
DDh 144 -8.82 -2.88 -3.47 4 drift -25.92 4 Table showing the results for the unit root test statistics for the collected time series in levels, the first differences (D=Δ) and second difference (DD=Δ2) for the housing stock. The column -ADF refers to the test-statistic for the augmented dickey fuller test and PP for the Philips-Perron Test (zτ). The critical t-values count for both test specifications (Ericsson 2002). k denotes the ideal lag truncation for the ADF, starting with a maximal value of 5 and testing down with AIC. Type drift refers to the inclusion of a constant; trend refers to a trend and a constant.
Table A 4 Test statistics for order of integration for Germany
Variable Sample size t-ADF t-crit 5% t-crit 1% k-ADF Type t-PP Bandwidth
ph 184 -1.86 -3.43 -4.01 4 trend -2.76 5
r 186 -2.09 -3.43 -4.01 5 trend -1.29 5
y 185 -2.71 -3.43 -4.01 2 trend -3.02 5
uc 106 -3.24 -3.45 -4.04 4 trend -2.94 4
h 134 -2.74 -3.44 -4.02 1 trend -2.09 4
Dph 183 -4.06 -2.88 -3.46 3 drift -11.12 5
Dr 185 -2.90 -2.88 -3.46 4 drift -13.88 5
Dy 184 -8.54 -2.88 -3.46 1 drift -15.11 5
Duc 105 -6.39 -2.89 -3.49 3 drift -10.58 4
Dh 133 -9.92 -2.88 -3.48 0 drift -10.29 4
DDh 132 -7.84 -2.88 -3.48 5 drift -36.12 4 Table showing the results for the unit root test statistics for the collected time series in levels, the first differences (D=Δ) and second difference (DD=Δ2) for the housing stock. The column -ADF refers to the test-statistic for the augmented dickey fuller test and PP for the Philips-Perron Test (zτ). The critical t-values count for both test specifications (Ericsson 2002). k denotes the ideal lag truncation for the ADF, starting with a maximal value of 5 and testing down with AIC. Type drift refers to the inclusion of a constant; trend refers to a trend and a constant.
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Table A 5 Test statistics for order of integration for Japan
Variable Sample size t-ADF t-crit 5% t-crit 1% k-ADF Type t-PP Bandwidth
ph 184 -2.08 -3.43 -4.01 5 trend -2.29 5
r 186 -2.86 -3.43 -4.01 5 trend -4.88 5
y 146 -1.75 -3.44 -4.02 5 trend -2.49 4
uc 146 -4.28 -3.44 -4.02 4 trend -3.86 4
h 145 -2.04 -3.44 -4.02 2 trend -3.28 4
Dph 183 -5.01 -2.88 -3.46 4 drift -6.61 5
Dr 185 -1.40 -2.88 -3.46 4 drift -8.63 5
Dy 145 -5.80 -2.88 -3.47 3 drift -15.63 4
Duc 145 -7.90 -2.88 -3.47 3 drift -11.22 4
Dh 144 -3.50 -2.88 -3.47 5 drift -15.42 4
DDh 143 -10.25 -2.88 -3.47 5 drift -55.96 4 Table showing the results for the unit root test statistics for the collected time series in levels, the first differences (D=Δ) and second difference (DD=Δ2) for the housing stock. The column -ADF refers to the test-statistic for the augmented dickey fuller test and PP for the Philips-Perron Test (zτ). The critical t-values count for both test specifications (Ericsson 2002). k denotes the ideal lag truncation for the ADF, starting with a maximal value of 5 and testing down with AIC. Type drift refers to the inclusion of a constant; trend refers to a trend and a constant.
Table A 6 Test statistics for order of integration for Netherlands
Variable Sample size t-ADF t-crit 5% t-crit 1% k-ADF Type t-PP Bandwidth
ph 185 -2.64 -3.43 -4.01 5 trend -1.72 5
r 186 -1.71 -3.43 -4.01 5 trend -3.40 5
y 146 -1.56 -3.44 -4.02 4 trend -11.26 4
uc 182 -1.87 -3.43 -4.01 4 trend -1.79 5
h 141 -1.63 -3.44 -4.02 5 trend -1.16 4
Dph 184 -3.61 -2.88 -3.46 5 drift -9.27 5
Dr 185 -4.80 -2.88 -3.46 4 drift -23.45 5
Dy 145 -5.84 -2.88 -3.47 3 drift -47.88 4
Duc 181 -8.27 -2.88 -3.46 3 drift -12.55 5
Dh 140 -3.63 -2.88 -3.47 4 drift -4.69 4
DDh 139 -5.19 -2.88 -3.47 4 drift -20.58 4 Table showing the results for the unit root test statistics for the collected time series in levels, the first differences (D=Δ) and second difference (DD=Δ2) for the housing stock. The column -ADF refers to the test-statistic for the augmented dickey fuller test and PP for the Philips-Perron Test (zτ). The critical t-values count for both test specifications (Ericsson 2002). k denotes the ideal lag truncation for the ADF, starting with a maximal value of 5 and testing down with AIC. Type drift refers to the inclusion of a constant; trend refers to a trend and a constant.
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Table A 7 Test statistics for order of integration for Switzerland
Variable Sample size t-ADF t-crit 5% t-crit 1% k-ADF Type t-PP Bandwidth
ph 184 -2.37 -3.43 -4.01 4 trend -1.64 5
r 186 -1.34 -3.43 -4.01 3 trend -1.68 5
y 134 -2.56 -3.44 -4.02 5 trend -2.70 4
uc 181 -3.27 -3.43 -4.01 5 trend -3.07 5
h 141 -2.13 -3.44 -4.02 4 trend -11.04 4
Dph 183 -3.60 -2.88 -3.46 3 drift -11.68 5
Dr 185 -3.66 -2.88 -3.46 2 drift -10.28 5
Dy 133 -5.20 -2.88 -3.48 4 drift -8.83 4
Duc 180 -8.00 -2.88 -3.46 3 drift -10.36 5
Dh 140 -5.11 -2.88 -3.47 3 drift -26.17 4
DDh 139 -14.28 -2.88 -3.47 3 drift -38.20 4 Table showing the results for the unit root test statistics for the collected time series in levels, the first differences (D=Δ) and second difference (DD=Δ2) for the housing stock. The column -ADF refers to the test-statistic for the augmented dickey fuller test and PP for the Philips-Perron Test (zτ). The critical t-values count for both test specifications (Ericsson 2002). k denotes the ideal lag truncation for the ADF, starting with a maximal value of 5 and testing down with AIC. Type drift refers to the inclusion of a constant; trend refers to a trend and a constant.
Table A 8 Test statistics for order of integration for New Zealand
Variable Sample size t-ADF t-crit 5% t-crit 1% k-ADF Type t-PP Bandwidth
ph 145 -2.27 -3.44 -4.02 1 trend -2.18 4
r 186 -1.36 -3.43 -4.01 5 trend -0.77 5
y 117 -2.48 -3.45 -4.03 5 trend -1.66 4
uc 182 -2.20 -3.43 -4.01 4 trend -2.72 5
h 185 -2.81 -3.43 -4.01 1 trend -2.00 5
Dph 144 -6.01 -2.88 -3.47 0 drift -6.21 4
Dr 185 -3.10 -2.88 -3.46 4 drift -6.80 5
Dy 116 -3.47 -2.88 -3.48 5 drift -6.49 4
Duc 181 -10.08 -2.88 -3.46 3 drift -10.16 5
Dh 184 -3.29 -2.88 -3.46 0 drift -3.25 5
DDh 183 -13.23 -2.88 -3.46 0 drift -13.63 5 Table showing the results for the unit root test statistics for the collected time series in levels, the first differences (D=Δ) and second difference (DD=Δ2) for the housing stock. The column -ADF refers to the test-statistic for the augmented dickey fuller test and PP for the Philips-Perron Test (zτ). The critical t-values count for both test specifications (Ericsson 2002). k denotes the ideal lag truncation for the ADF, starting with a maximal value of 5 and testing down with AIC. Type: drift refers to the inclusion of a constant; trend refers to a trend and a constant.
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C. Results for the single equation specification
Figure A 9 Results for the Single equation specifications when housing stock
This graphs report p-values for the single equation specification, given by [ 7] and [ 11], recursively estimating subsamples corresponding to the displayed window. Black series are the BIS property price indices. Sample periods all end in 2015Q4 and start at CAN:1981Q2, UK:1987Q2, FRA: 1990Q2, GER:1990Q2, JAP 1980Q2, NL 1980Q2, CH 1983Q2, NZ 1987Q2.
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Figure A 10 Aggregated bubble indicators when housing stock is excluded from the inverted demand approach
This graphs report p-values for the single equation specification, given by [ 7] and [ 11], recursively estimating
subsamples corresponding to the displayed window. Sample periods all end in 2015Q4 and start at CAN:1981Q2, UK:1987Q2, FRA: 1990Q2, GER:1990Q2, JAP 1980Q2, NL 1980Q2, CH 1983Q2, NZ 1987Q2.
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D. Results for the cointegration vector autoregressive model
Figure A 11 Results for all countries when recursively estimating the CVAR (qualified by a linear trend)
Graphs reporting the resulting rank estimates of the CVAR specification qualified by a trend for the inverted demand (invdem) and price-to-rent (ptor) approach (see equations [ 13] and [ 15] respectively). Shaded areas correspond to the recursively estimated periods, red shaded ribbons indicate an estimated rank of 0, therefore giving an unsustainable bubble regime. Sample periods all end in 2015Q4 and start at CAN:1981Q2, UK:1987Q2, FRA: 1990Q2, GER:1990Q2.
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Figure A 11 (continued) results for all countries when recursively estimating the CVAR (qualified by a linear trend)
Graphs reporting the resulting rank estimates of the CVAR specification qualified by a trend for the inverted demand (invdem) and price-to-rent (ptor) approach (see equations [ 13] and [ 15] respectively). Shaded areas correspond to the recursively estimated periods, red shaded ribbons indicate an estimated rank of 0, therefore giving an unsustainable bubble regime. Sample periods all end in 2015Q4 and start at JAP 1980Q2, NL 1980Q2, CH 1983Q2, NZ 1987Q2.
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E. Concordance indices
Table A 9 Cross-country Concordance index matrix for all model specifications excluding housing stock
CAN CH FRA GER JAP NL NZ UK
CAN 1.00 0.30 0.50 0.62 0.67 0.56 0.72 0.42
CH 0.30 1.00 1.00 0.66 0.58 0.38 0.77 0.75
FRA 0.50 1.00 1.00 0.66 0.62 0.84 0.81 1.00
GER 0.62 0.66 0.66 1.00 0.85 0.70 0.88 0.71
JAP 0.67 0.58 0.62 0.85 1.00 0.48 0.75 0.62
NL 0.56 0.38 0.84 0.70 0.48 1.00 0.68 0.66
NZ 0.72 0.77 0.81 0.88 0.75 0.68 1.00 0.83
UK 0.42 0.75 1.00 0.71 0.62 0.66 0.83 1.00
Mean 0.60 0.68 0.80 0.76 0.70 0.66 0.80 0.75
This table reports the concordance indicators (see [ 21]), a measure of coincidence for binary bubble cycles. 0 indicates no synchronization, 1 represents synchronization over the total common sample. The country wise pairs are averaged over all used model specifications.
Table A 10 Concordance matrix for United Kingdom with excluded housing stock
cvar invd noT
cvar invd
cvar ptor noT
cvar ptor
sing ptor
sing invd
LPPLs PL
cvar invd noT 1.00 1.00 1.00 1.00 0.25 0.25 0.33 0.42
cvar invd 1.00 1.00 1.00 1.00 0.25 0.25 0.33 0.42
cvar ptor noT 1.00 1.00 1.00 1.00 0.25 0.25 0.33 0.42
cvar ptor 1.00 1.00 1.00 1.00 0.25 0.25 0.33 0.42
sing ptor 0.25 0.25 0.25 0.25 1.00 1.00 0.92 0.67
sing invd 0.25 0.25 0.25 0.25 1.00 1.00 0.92 0.67
LPPLs 0.33 0.33 0.33 0.33 0.92 0.92 1.00 0.75
PL 0.42 0.42 0.42 0.42 0.67 0.67 0.75 1.00
This table reports the concordance indices specification wise. The concordance (see [ 21]) is a measure of coincidence for bubble cycles. A 0 indicates no synchronization, a 1.00 represents synchronization over the total estimated sample. CVAR refers to equation [ 13] for ptor and [ 15] for invdem, whereas sing represents the single equation specification, [ 7] for ptor and [ 11] for invdem respectively. noT indicates, that no deterministic trend is included in the equation. PL represents the power law fit after [ 18] and LPPLs is log periodic power law fit following [ 19].
88
Table A 11 Concordance matrix for France with excluded housing stock
cvar invd noT
cvar invd
cvar ptor noT
cvar ptor
sing ptor
sing invd
LPPLs PL
cvar invd noT 1.00 0.92 0.92 0.92 0.08 0.08 0.31 0.31
cvar invd 0.92 1.00 1.00 1.00 0.00 0.00 0.38 0.38
cvar ptor noT 0.92 1.00 1.00 1.00 0.00 0.00 0.38 0.38
cvar ptor 0.92 1.00 1.00 1.00 0.00 0.00 0.38 0.38
sing ptor 0.08 0.00 0.00 0.00 1.00 1.00 0.62 0.62
sing invd 0.08 0.00 0.00 0.00 1.00 1.00 0.62 0.62
LPPLs 0.31 0.38 0.38 0.38 0.62 0.62 1.00 1.00
PL 0.31 0.38 0.38 0.38 0.62 0.62 1.00 1.00
This table reports the concordance indices specification wise. The concordance (see [ 21]) is a measure of coincidence for bubble cycles. A 0 indicates no synchronization, a 1.00 represents synchronization over the total estimated sample. CVAR refers to equation [ 13] for ptor and [ 15] for invdem, whereas sing represents the single equation specification, [ 7] for ptor and [ 11] for invdem respectively. noT indicates, that no deterministic trend is included in the equation. PL represents the power law fit after [ 18] and LPPLs is log periodic power law fit following [ 19].
Table A 12 Concordance matrix for Japan with excluded housing stock
cvar invd noT
cvar invd
cvar ptor noT
cvar ptor
sing ptor
sing invd
LPPLs PL
cvar invd noT 1.00 0.67 0.62 0.57 0.81 0.81 0.81 0.81
cvar invd 0.67 1.00 0.48 0.62 0.48 0.48 0.48 0.48
cvar ptor noT 0.62 0.48 1.00 0.48 0.62 0.62 0.62 0.62
cvar ptor 0.57 0.62 0.48 1.00 0.48 0.48 0.48 0.48
sing ptor 0.81 0.48 0.62 0.48 1.00 1.00 1.00 1.00
sing invd 0.81 0.48 0.62 0.48 1.00 1.00 1.00 1.00
LPPLs 0.81 0.48 0.62 0.48 1.00 1.00 1.00 1.00
PL 0.81 0.48 0.62 0.48 1.00 1.00 1.00 1.00
This table reports the concordance indices specification wise. The concordance (see [ 21]) is a measure of coincidence for bubble cycles. A 0 indicates no synchronization, a 1.00 represents synchronization over the total estimated sample. CVAR refers to equation [ 13] for ptor and [ 15] for invdem, whereas sing represents the single equation specification, [ 7] for ptor and [ 11] for invdem respectively. noT indicates, that no deterministic trend is included in the equation. PL represents the power law fit after [ 18] and LPPLs is log periodic power law fit following [ 19].
89
Table A 13 Concordance matrix for Netherlands with excluded housing stock
cvar invd noT
cvar invd
cvar ptor noT
cvar ptor
sing ptor
sing invd
LPPLs PL
cvar invd noT 1.00 0.43 0.00 0.00 0.43 1.00 0.33 0.48
cvar invd 0.43 1.00 0.57 0.57 0.62 0.43 0.71 0.67
cvar ptor noT 0.00 0.57 1.00 1.00 0.57 0.00 0.67 0.52
cvar ptor 0.00 0.57 1.00 1.00 0.57 0.00 0.67 0.52
sing ptor 0.43 0.62 0.57 0.57 1.00 0.43 0.62 0.67
sing invd 1.00 0.43 0.00 0.00 0.43 1.00 0.33 0.48
LPPLs 0.33 0.71 0.67 0.67 0.62 0.33 1.00 0.86
PL 0.48 0.67 0.52 0.52 0.67 0.48 0.86 1.00
This table reports the concordance indices specification wise. The concordance (see [ 21]) is a measure of coincidence for bubble cycles. A 0 indicates no synchronization, a 1.00 represents synchronization over the total estimated sample. CVAR refers to equation [ 13] for ptor and [ 15] for invdem, whereas sing represents the single equation specification, [ 7] for ptor and [ 11] for invdem respectively. noT indicates, that no deterministic trend is included in the equation. PL represents the power law fit after [ 18] and LPPLs is log periodic power law fit following [ 19].
Table A 14 Concordance matrix for Switzerland with excluded housing stock
cvar invd noT
cvar invd
cvar ptor noT
cvar ptor
sing ptor
sing invd
LPPLs PL
cvar invd noT 1.00 0.62 0.62 0.62 0.38 0.38 0.77 0.62
cvar invd 0.62 1.00 1.00 1.00 0.00 0.00 0.69 1.00
cvar ptor noT 0.62 1.00 1.00 1.00 0.00 0.00 0.69 1.00
cvar ptor 0.62 1.00 1.00 1.00 0.00 0.00 0.69 1.00
sing ptor 0.38 0.00 0.00 0.00 1.00 1.00 0.31 0.00
sing invd 0.38 0.00 0.00 0.00 1.00 1.00 0.31 0.00
LPPLs 0.77 0.69 0.69 0.69 0.31 0.31 1.00 0.69
PL 0.62 1.00 1.00 1.00 0.00 0.00 0.69 1.00
This table reports the concordance indices specification wise. The concordance (see [ 21]) is a measure of coincidence for bubble cycles. A 0 indicates no synchronization, a 1.00 represents synchronization over the total estimated sample. CVAR refers to equation [ 13] for ptor and [ 15] for invdem, whereas sing represents the single equation specification, [ 7] for ptor and [ 11] for invdem respectively. noT indicates, that no deterministic trend is included in the equation. PL represents the power law fit after [ 18] and LPPLs is log periodic power law fit following [ 19].
90
Table A 15 Concordance matrix for New Zealand with excluded housing stock
cvar invd noT
cvar invd
cvar ptor noT
cvar ptor
sing ptor
sing invd
LPPLs PL
cvar invd noT 1.00 0.12 0.06 0.19 1.00 0.75 0.75 0.75
cvar invd 0.12 1.00 0.81 0.81 0.12 0.38 0.25 0.25
cvar ptor noT 0.06 0.81 1.00 0.88 0.06 0.31 0.31 0.31
cvar ptor 0.19 0.81 0.88 1.00 0.19 0.44 0.44 0.44
sing ptor 1.00 0.12 0.06 0.19 1.00 0.75 0.75 0.75
sing invd 0.75 0.38 0.31 0.44 0.75 1.00 0.75 0.88
LPPLs 0.75 0.25 0.31 0.44 0.75 0.75 1.00 0.75
PL 0.75 0.25 0.31 0.44 0.75 0.88 0.75 1.00
This table reports the concordance indices specification wise. The concordance (see [ 21]) is a measure of coincidence for bubble cycles. A 0 indicates no synchronization, a 1.00 represents synchronization over the total estimated sample. CVAR refers to equation [ 13] for ptor and [ 15] for invdem, whereas sing represents the single equation specification, [ 7] for ptor and [ 11] for invdem respectively. noT indicates, that no deterministic trend is included in the equation. PL represents the power law fit after [ 18] and LPPLs is log periodic power law fit following [ 19].