Constructing an Early Warning System to Predict the Speculative House Price Bubble in the Current Western- European Housing Marke

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Nijmegen School of Management Master Thesis

Constructing an Early Warning System to Predict the

Speculative House Price Bubble in the Current Western-

European Housing Market

By JESSE PETERS (S4484096).

Abstract

In this paper, the author constructs an early warning system to predict speculative house price bubbles in the Netherlands, Slovenia, Belgium, and Slovenia in the period between 2011 and 2018. A speculative house price bubble is a situation where the actual house price index is structurally different from the fundamental house price index. First, the speculative bubble chronology is obtained, that is necessary to identify speculative bubble periods. The speculative bubbles are identified by combining two techniques, the fundamental and filter technique. The two techniques are used as criteria and only when both criteria hold, a speculative bubble is identified. Subsequently, the speculative bubbles are tested to see if they can be predicted. It is done by applying the random-effect logit and probit approaches. The results show that neither of the approaches has the required prediction accuracy for the early warning system to function as an accurate predictor of speculative bubbles in the housing market. In conclusion, the constructed early warning system cannot be used by policymakers to help to forecast future speculative house price bubbles.

Supervisor: Dr. Sascha Füllbrunn Department of Economics

Master: Economics (Business Economics) August 2019

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1. Introduction

1.1. Motivation

The housing market in the Netherlands is booming the last couple of years. The house prices kept rising and reached the highest level last year according to an article written by Jenda Terpstra in Trouw (2018). The Netherlands is not the only country. House prices in Belgium, Germany, and Slovenia also reached records in the last couple of years. These four countries were defined as Western-Europe in the rest of the paper. The current Dutch house price is even higher than before the credit crisis of 2008. Even though the house prices are at such a high level, Terpstra (2018) wrote that financial expert Robin Fransman does not expect a drop in the Dutch price as happened in 2008. Fransman said that we cannot know if we are in a bubble until it’s too late (Terpstra, 2018). His statement is supported by expert Paul de Vries. De Vries claimed that we cannot speak of a bubble at the moment. There is only a bubble when the price rises in the entire country, or when people borrow much more money than they can handle (Terpstra, 2018).

Housing market economist of the Rabobank Christian Lennartz was less optimistic. Lennartz claimed that there is a housing market bubble in the big Dutch cities, such as Amsterdam. Structurally, the selling price is above the asking price and people are expecting that the housing market will continue to rise. If something unexpected happens in the economy, such as when investors retreat, it can be devastating for the market (Terpstra, 2018). Lennartz’ s concerns are grounded according to Erik Ooms, advisor European spatial planning in Berlin. Ooms (2017) thought that people focus too much on making a profit in the housing market. Ooms (2017) said that the ECB, IMF, and OESO informed the Dutch government on the high private mortgage debt of the people in their country. ‘The problem is that the government did not do anything to limit this behavior and only looks at the positive side, such as economic growth. Now, it looks positive and everything is going well, but when the bubble pops, there will be a new crisis and that crisis might even be worse than the one in 2008’ (Ooms, 2017).

As already mentioned, the house prices in Belgium, Germany, and Slovenia are also increasing. According to Frank Knopers (2017), the German housing prices rose more than 40 percent on average between 2010 and 2017. The German government executed research in 2017 for 127 cities and found that housing prices were up to 30 percent overvalued. The rise in house prices was due to the low mortgage interest and strong economic growth. However, according to a board member

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of the Deutsche Bundesbank, Andreas Dombret, Germany does not have to worry about a house price bubble that can threaten financial stability (Knopers, 2017).

In 2018, house prices in Belgium showed record values. In a lot of countries, the house prices declined after the credit crisis, but not in Belgium. In Belgium, the house prices kept increasing. In fact, Belgium showed the biggest increase in house prices in Europe during the last15 years. In these 15 years, the house prices went up 80 percent (Luysterman, 2018). Vervaeke (2018) claimed that economists have warned the Belgian government for years that Belgian housing is overvalued. Belgian economists worry that if the mortgage and savings interest rise, the price correction will still come. The price correction could threaten the Belgian financial stability (Vervaeke, 2018).

A final country that seems to experience a real estate bubble is Slovenia. In 2016, the house price in Slovenia grew twice as fast as in the other European countries. The same happened in 2017 when the country reached an at that time record in prices and transactions. Again, Slovenia had the highest increase in house prices in Europe in 2018. However, the central bank did not see signs of risk to financial stability yet. According to Banka Slovenije, the risks in the real estate market do not increase, because the growth of housing loans is stable and moderate. Moreover, the central bank of Slovenia claimed that household debts are not too high. Also, the lending standards for the construction sector is higher than before the crisis, and this increases the resilience to possible shocks in the market (The Slovenia Times, 2018).

The situations described for each country suggest that the actual market house price might deviate from the fundamental value, as in a bubble would occur. Especially, in the Netherlands and Slovenia, there is a discussion regarding whether there is a housing market bubble or not. However, it is not known what the cause of the potential bubble might be. According to Levin and Wright (1997), a house price bubble might occur due to speculative behavior. When there is a so-called specuylative bubble, the results could be detrimental for a countries' economy when it pops (Edison, 2003). Therefore, it can be suitable to empirically test whether there is a speculative bubble in the Western- Europe housing markets or not.

Hu, Su, Jin, and Jiang (2006) decompose the actual house prices into two components, the fundamental and speculative component. There is no unique way to define fundamental value. Geographical variables, such as real income and real interest, and institutional factors, such as the loan-to-value ratio, are examples of measuring the fundamental value. The speculative component is determined based on the degree of speculation. House price speculation is defined as the purchase

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of a house motivated by the expectation of a real increase in the price of a house in the future. A speculative house price bubble only exists when the degree of speculation causes the house price to increase beyond the long-run equilibrium level (Hu et al., 2006).

A method that might predict if there is a speculative housing market bubble in a country is an early warning system. An early warning system, or EWS, is a model that predicts whether there is financial stress in a market within a specified period. If financial stress is defined as a speculative housing market bubble, an early warning system can predict and forecast whether there is a speculative bubble in the market. The problem, however, with a speculative housing market bubble is that it cannot be directly observed. Therefore, it is difficult to make a distinction between the growth of the house prices supported by the fundamental or the speculative component. The two effects need to be separated to extract the speculative component that can cause a speculative bubble. Hence, a speculative housing market bubble is a situation in which the actual house price index structurally differs from the fundamental house price index. Different early warning systems are each constructed for a different market, for example, for the currency, or equity market, or the banking sector (Davis & Karim, 2008; Edison, 2003). In this research, an early warning system specially designed for housing markets is applied to the housing markets of the Netherlands, Germany, Belgium, and Slovenia. This paper aims to construct an early warning system for the Western-European housing market to predict speculative house price bubbles. To examine this, a quarterly timeframe from Q1-2011 till Q2-2018 is chosen. This timeframe is chosen because 2011 was the first year since, the start of the global financial crisis, that the housing market prices of the Western-European countries showed signs of recovery. To include the entire recovery, 2011 is the first year in the dataset (Smulders, 2018). The second quarter of 2018 is the most recent quarter for which data is available. The timeframe is large enough so that the early warning system only works when there is a structural difference between the actual and fundamental value (Bucevska, 2011). Early warning systems are likely to inform policymakers as well as investors about the occurrence of financial stress shortly. An EWS can have substantial value to policymakers by allowing them to detect underlying economic weaknesses and vulnerabilities and taking pre-emptive steps to reduce the risk of experiencing financial stress if necessary. Noticing a speculative housing market bubble in time is important because the housing market plays a crucial role in the real economic performance of a country. Besides, housing busts bear the systematic risk for the whole economy and can have devastating effects if not predicted in time (Dreger & Kholodilin,

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2011). An example of a pre-emptive step that can be taken by policymakers is adjusting the tax rebate on mortgage interest. Lowering the interest might make buying a house less attractive and could slow down the speculative bubble. Early warning systems are useful in predicting speculative house price bubbles, but previous research suggests that they have to be interpreted with prudence. So, even when the constructed EWS in this paper shows significant results in predicting speculative bubbles, the findings have to be interpreted with caution (Bussiere & Fratzscher, 2006).

In this research, a speculative bubble chronology is formed to find the speculative bubble periods. The logit and probit approaches are used to predict the speculative bubble periods that were found in the speculative bubble chronology for Western-European countries. The logit and probit approaches do not show the required prediction accuracy for predicting speculative house price bubbles correctly. The too low prediction accuracy causes that the constructed early warning system does not have enough predictive power to function as a reliable and accurate forecaster of speculative house price bubbles.

1.2. Research question

The previous chapter made clear that the housing market plays a determinative role in the economic performance of a country. The occurrence of a speculative bubble can have detrimental consequences for a country. However, experts do not agree with each other on the existence of a speculative housing market bubble in Western- Europe. As earlier mentioned, to test and predict whether there is a speculative house price bubble in the current housing market, an early warning system is useful. But, there is no early warning system for Western- European yet. This research tries to determine the existence and occurrence of speculative house price bubbles to fill the research gap. The following research question is formed to fill the research gap: Can the constructed early warning system predict speculative house price bubbles in the current housing market in Western-European countries? To answer the research question, several sub-questions are formed and answered. First of all, it should be clear what an early warning system is and what it consists of. Secondly, the different parts of the early warning systems are analyzed and adjusted to improve and fit this research. Finally, it is clear what variables showed significant results in the early warning system. With the significant variables, the predictive power of the early warning system can be determined based on the prediction accuracy of speculative house price bubbles of the selected models.

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2. Literature Review

The main focus of this study is empirical, but before discussing the relevant empirical literature, the theoretical foundation of an early warning system is explained.

An early warning system is a tool that is designed to function as a forward-looking instrument that provides anticipatory signals of financial stress. Early warning systems are functional and data-driven approaches that alert policymakers of potential financial stress based on the analysis of past financial stress periods. Once financial stress emerges, its path and severity can be determined by the institutional and market microstructure. If not addressed by a liquidity lender of last resort, solvency problems can spread throughout the financial system due to contagion effects. Early warning systems are grounded in economic theories of the financial crisis and are specifically designed to provide risk alerts on an objective and systematic basis. The foundation of an early warning system is the causal relationship between factors that drive financial stress and the financial stress itself to predict the systematic risk on macro- and micro-level. Early warning systems can provide a basis for assessing the exposure of a market to systematic risk (Gramlich et al., 2010). Most theories of macro risk focused on currency crises, such as the publication of Kaminsky and Reinhart (1999).

Early warning systems exist in many possible combinations of elements, but there is a framework in which all elements are put together. The framework, shown in Figure 1, summarizes the steps policymakers take to construct an early warning system. The system starts with setting the objectives. According to Gaytán and Johnson (2002), there should be a tight correspondence between the output of the early warning system and the objectives of its user. Secondly, a risk measure that operationalizes the systemic risk is identified. Setting a risk measure incorporates defining financial stress. The next step is identifying the risk factors or indicators. It means choosing the variables that determine the risk of macro and micro-level (Gramlich et al., 2010). The fourth step is picking the right risk model. Berg, Borensztein, and Pattillo (2005) emphasize the importance of agreeing on a list of variables, defining signals and determining a reasonable period between signal and financial stress. If both the risk measure and risk model peak at the same time, the early warning system signals that there is financial stress and that pre-emptive steps are appropriate. The final step is setting measures to manage potential financial stress. Since this is an optional step, it is not considered in this research.

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Figure 1: Conceptual Framework of an Early Warning System

Notes: The figure shows the steps that are necessary to construct an early warning system that tries to predict and identify financial stress.

Early warning systems generated mixed results throughout the years they are used. Bell and Pain (2000) argue that an EWS provides a simplified form of modeling crises and that some variables seem to be rather coincidental than leading indicators. If financial crises are predictable at all, then the authors suggest that an EWS should capture the increasing complexity and transmission of changes in financial markets. On the other hand, Edison (2003) found that an early warning system can provide some helpful insights and meaningful results. But, the author also emphasizes the limitations of such an approach (Edison, 2003). In addition, an EWS might be regarded as a diagnostic tool for monitoring the relative direction of the financial system, rather than a measurement of definitive crisis signals. Berg, Borensztein, and Pattillo (2005) argue that it is very difficult to forecast financial stress reliably because in order to do so a model has to systematically outperform the market in predicting sudden changes. In-sample predictions are much easier to achieve than out-of-sample predictions because every financial stress period may be fundamentally different from the last. The out-of-sample performance of an early warning system also depends on the time horizon of the sample. The authors concluded that the short-horizon private sector models they examined performed poorly out of sample. However, they see little to no difference between nine months or two years horizon. In conclusion, researchers agree on the idea that an early warning system might provide useful insights, but the model is not accurate enough to be used as the sole method to anticipate crises (Berg, Borensztein & Pattillo, 2005).

Now, the earlier mentioned framework for early warning systems is applied to the housing market. The first step in the conceptual framework is setting the objectives (Gramlich et al, 2010). In this research, the intended users of the early warning system are the policymakers. Therefore, the objective is to construct an early warning system that might help to predict financial stress in the housing market. The constructed system might contribute to making decisions regarding the housing market. The second step in constructing an early warning system is formulating a clear

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definition of financial stress (Gramlich et al, 2010). In this case, financial stress is defined as a speculative housing market bubble. In turn, a speculative housing market bubble is defined as the structural difference between the actual and fundamental value of a house. In line with Terpstra (2018), a speculative bubble only arises when speculation drives up the house price beyond the long-run equilibrium level. To extract the speculative component, the fundamental and speculative component needs to be separated. An increase in housing prices is normal. It is natural and justified if it occurs as a result of fundamental factors (Edison, 2003). Fundamental factors include changes in the institutional features and macroeconomic and demographic conditions. If an increase in house prices cannot be linked to one of these factors the market might experience a speculative bubble. In other words, a speculative house price bubble is the occurrence of an increase in prices that are not justified by changes in the market fundamentals (Brzezicka & Wisniewski, 2014). According to Kholodilin, Michelsen & Ulbricht (2018), there are three major approaches to identify the existence of a speculative house price bubble empirically. The first approach detects boom and busts periods in housing prices as deviations from a trend, such as can be defined through a Hodrick- Prescott filter (Dreger & Kholodilin, 2011). A second approach identifies house price misalignments by comparing actual prices with a price that is estimated through fundamental factors, as was done by Kholodilin and Ulbricht (2015). Finally, Phillips, Wu, and Yu (2011) developed an empirical test to identify unusually strong increases in asset prices, the so-called explosive roots. These three approaches can be used to obtain a speculative bubble chronology for each country, and the speculative chronology represents the potential speculative bubble periods. This is essential because the speculative bubble chronology will be tested later in the early warning system to see whether there is a speculative bubble in the market (Dreger & Kholodilin, 2011).

During the last global financial crisis, it was easy for speculators to enter the market due to the high availability of credit provision. In addition, homeowners overleveraged themselves by using innovative financial products to buy larger houses. Finally, a bubble emerged because the short-term imbalances between supply and demand led to overshooting of prices. The consequences of housing asset bubbles can be rather large for a country. According to Goodhart and Hofmann (2008), speculative house price shocks have significant repercussions on economic activity and aggregate price inflation. Economic activity for example of private consumption and residential investment. The largest liability of households are housing loans and they also account for a large share of bank lending. House price bubbles can trigger massive production losses when they burst,

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may constitute differences in business cycles and can limit the prospects of a common monetary policy in the euro area (Dreger & Kholodilin, 2011).

Allen and Carletti (2013) claim that housing market prices cannot be modeled by standard valuation principles in a time of a bubble because house prices tend to rise and decline very quickly in a short amount of time. The authors found that high loan-to-value in combination with low-interest rates can trigger a bubble. In contrast, Muellbauer and Murphy (2008) examined the housing markets and the economy and acknowledge that macroeconomic stability and the stability of the financial system can cause house prices to overshoot their fundamentals. However, the authors claim that the way of pricing houses remains the same. Dreger and Kholodilin (2011) based their research on the results of Muellbauer and Murphy (2008). They claim that the real, or fundamental, house price dynamics depend on institutional features and macroeconomic and demographic conditions and that this does not change in bubble periods. Speculation is not a part of the house price dynamics because it does not reflect the fundamental value. Put differently, this is the third step Gramlich et al. (2010) categorized as identifying the risk factors or indicators. The most notable aspects of institutional features and macroeconomic and demographic conditions are disposable income, the housing stock, inflation, interest rates, bank credit, changes in equity prices and population growth. Also, monetary growth might support the emergence of house price bubbles, but there is no supporting evidence for this. The reasoning is that a rise in liquidity affects the quantity and marginal utility of money holdings relative to the housing and other assets. Alessi and Detken (2011) claim that liquidity is a very important performance indicator of growing financial imbalances because the indicator performed well in predicting asset price booms.

The first example of macroeconomic conditions is interest rates. Interest rates are important because lower interest rates decrease the opportunity cost of capital to invest in housing. Interest rates also reduce the servicing cost of mortgage credit and raise the present value of future household earnings (Dreger & Kholodilin, 2011). Secondly, real house prices affect private consumption through two channels, housing wealth and collateral. Even though a permanent increase in house price could have a positive effect on homeowners because of more purchase power, it also harms tenants because they pay higher rents. If winners win more than the losers lose, the house price has a positive impact on housing wealth. However, this is less likely to occur because many households do not take housing wealth into account in their consumption decisions. The collateral effect of house prices exists because houses are widely used as security for loans.

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The response of aggregate demand to house price shocks is exponentially improved by collateral effects (Dreger & Kholodilin, 2011).

The first example of differences in institutional conditions is the loan-to-value ratio. Almeida, Campello, and Liu (2006) found that the sensitivity of house prices and mortgage borrowings to income shocks is lower in countries with lower loan-to-value ratios. Furthermore, the difference in bank-based and market-based financial systems is important in-house price dynamics, according to Ludwig and Sløt (2004). A final example is the tax environment. Tax reliefs and subsidies can affect the development in the housing sector, and income tax systems appear to be contributory to house price volatility (Dreger & Kholodilin, 2011).

In the fourth step, the operationalization of systemic risk, or risk measures, and the selection of relevant risk factors, or risk indicators, are combined to form a risk model. In this step, the early warning system gets more shape because a methodological approach is chosen (Gramlich et al, 2010). Two general approaches are used to develop early warning system models. According to Bucevska (2011), the first is the econometric approach, or logit and probit approaches, that estimates limited dependent variable probability models for prediction of the outbreak of financial stress. These models estimate a probability relationship with a discrete dependent variable. A discrete variable has a value of either 1 or 0. Econometric approach models can detect what explanatory variables have predictive power and can show the probability of future financial stress. Logit and probit models differ from each other in the shape of the distribution. Probit models are based on the standard normal probability density function, whereas in logit models an S-shaped logistic function to constrain the probabilities within the [0,1] interval is used (Bucevska, 2011). Ari (2012) created an early warning system for Turkey to illustrate the recent history of currency crises of the Turkish economy. Based on the logit and probit approaches, the author found that the Turkish crises are mainly caused by high money supply growths, sharp rises in short-term external debt, excessive fiscal deficits, external adverse shocks and growing risk in the banking system (Ari, 2012).

The second approach Bucevska (2011) distinguishes is the signal extraction approach, that is defined as a non-parametric method to ascertain the risk of financial stress. In the extraction approach, a variable is triggered when it goes beyond a certain threshold level, that is specially set for each variable. The higher the threshold the fewer financial stress periods are identified, but this also triggers less false alarms. The optimal threshold is where there is a balance between correctly

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identifying the financial stress periods and producing the least false alarms. When several indicators exceed the threshold values, it can be considered as a signal of approaching or ongoing financial stress (Bucevska, 2011). Davis and Karim (2008) used both the logit and signal extraction approach for a worldwide dataset to find the robust leading indicators of banking crises. They found strong evidence that real GDP growth and terms of trade can cause a banking crisis (Davis & Karim, 2008). Appendix B gives an overview of the approaches the authors used and the respective results.

Alexandrova (2017) noticed that besides Dreger and Kholodilin (2011) there is little literature of early warning systems that focuses on the housing market. Dreger and Kholodilin (2011) created an early warning system by applying both the logit and probit approaches and the signal extraction approach to a worldwide dataset. In both approaches, the speculative bubble chronology that was found for each country was tested. They found that early warning systems can be useful in predicting and forecasting future speculative bubbles in the housing market. The conclusion was that their early warning system could be considered as an important tool and can be used by policymakers to try to timely detect the speculative house price bubbles and attenuate their devastating effects on the domestic economy. Furthermore, Alexandrova (2017) tried to create an early warning system in the US housing market that incorporated buyers’ and sellers’ behavior and signals. The author found that signals and behaviors can explain the variability in the housing stress index. In other words, the author found that stress periods can be predicted by signals and behaviors. Additionally, informed seller expectations of the market and housing market variables have statistically significant explanatory power (Alexandrova, 2017).

As summarized in Appendix B, the literature review suggests that an early warning system is arbitrary and that it is not enough to predict financial stress on its own, but it also shows that such a model can provide useful insights. Also, when such a system is constructed, it is fairly accurate and can, therefore, function as an important tool (Alexandrova, 2017; Dreger & Kholodilin, 2011). Hence, the hypothesis of this research is: it is possible for the constructed early warning system to predict speculative housing market bubbles in the current Western-European housing markets. The hypothesis is tested by producing a speculative bubble chronology for each country. After the speculative bubble chronology, the potential speculative bubble periods are clear and then tested by using the general approaches that are a part of the early warning system. In summary, in this paper, the speculative bubble chronology and the approach to test the speculative bubble

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chronology are both parts of the early warning system. Consequently, the results will be compared to the literature.

3. Methodology

In this chapter, the most suitable early warning system found in the literature is discussed, explained and adjusted in such a way that it fits this research. Going back to the EWS framework, the first two steps of Figure 1 has already been defined in the previous chapter. Firstly, the objective of this paper is to construct an early warning system that might help policymakers to predict financial stress. Secondly, in this paper financial stress was defined as a speculative housing market bubble that is the structural difference between the actual and fundamental value of a house. However, another decision is made in the second step because Kholodilin et al. (2018) identified three approaches to identify the existence of a speculative house price bubble empirically. In this research, it was chosen to detect boom periods in housing prices as deviations from a trend by using a Hodrick-Prescott filter, because it is the most used approach. Therefore, the first approach designed by Agnello & Schuknecht (2011) is the most suitable approach for obtaining a speculative bubble chronology. The early warning system that Agnello & Schuknecht (2011) constructed, was refined by Dreger and Kholodilin (2011). The refined early warning system of Dreger & Kholodilin (2011) is used as a reference point in this paper and adjusted in such a way that it fits this research. As this study uses a reference paper, chapter 4.3 focuses on the reflection of the results of Dreger and Kholodilin (2011) to put the results more into context.

Obtaining the speculative bubble chronology is the first part of the early warning system analysis. The speculative bubble chronology separates the speculative and fundamental component of the house price. The potential speculative bubbles are the periods where the actual house price index is higher than the fundamental value. The speculative bubble chronology is described in more detail below. The potential speculative bubble periods are then tested by using the most suitable approach. The coefficients of the variables that result from the approach are then graphed and compared to the potential speculative bubble periods. If the potential bubble periods match with the graph that results from the approach, the hypothesis can be accepted because in that case, the early warning system can accurately predict speculative housing market bubbles.

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3.1. Speculative Bubble Chronology

As mentioned earlier, the fundamental and speculative component of the house price need to be separated to predict speculative housing bubbles. This can be done by obtaining a speculative bubble chronology, that is based on an algorithm. Dreger and Kholodilin (2011) created a speculative bubble chronology algorithm that consists of two alternative techniques, the fundamental technique, and the filter technique. In the fundamental technique, the speculative component of the house price is extracted by estimating the deviations of the actual house price index from the fundamental house price index. The filter technique is based on estimating the deviations of the actual house price index from the trend regardless of the fundamentals. The reason for using both techniques is justified as follows. The speculative bubbles are the periods when the actual house price index is higher than is supported by the fundamental component. However, not each positive deviation can be treated as a speculative bubble because the deviations might be too short or minor. Instead, it is assumed that a speculative bubble only occurs when the deviation is positive and above the trend. Therefore, the speculative bubble chronology is the one that is confirmed by both techniques (Dreger & Kholodilin, 2011).

Following Dreger and Kholodilin (2011), the speculative bubble chronology starts with a time-series regression of the real house price index on a set of fundamental factors. This technique is necessary to identify the potential speculative bubble periods. There are several assumptions made in the time-series regression of the fundamental factors. The first assumption is that the series is stationary. In other words, the series is normally distributed and the variance and mean are constant over time. Secondly, the error term is randomly distributed and the variance and mean are constant over time. It is also assumed that the series does not have outliers because outliers may lead to misleading coefficients and results. If there are shocks in the model, it is assumed that they are randomly distributed with constant variance and a mean of zero. A further assumption is that the selected fundamental factors are the only factors that determine the actual and fundamental house price indices. The last assumption is that observations are independent of each other (Velicer & Fava, 2003).

According to Dreger & Kholodilin (2011), the fundamental factors are real GDP per capita, population size, urbanization and the own lag of the dependent variable given the strong time persistence of the house prices. Real GDP per capita looks at the GDP per person and functions as a measure of a country’s standard of living (OECD, 2019). Population size looks at the number of

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residents a country has (OECD, 2019). Urbanization refers to the move of the population from rural to urban areas (OECD, 2019). The real house price index measures the price change of residential housing as a percentage change from the starting year 2015 (OECD, 2019). All variables, except for urbanization, are expressed in logarithms. The expectation is that only urbanization negatively affects housing prices. High urbanization means that fewer people migrate from rural to urban areas, and therefore can have a negative impact on housing prices. For the other variables, the higher the income and population, the more people need houses and the higher the price they are willing to pay (Dreger & Kholodilin, 2011).

The regression of the fundamental factors gives the following formula for each country: RHPIit = α0 + α1RHPIi,t-1 + α2RGDP_PCit + α3POPit + α4URBANit + εit (1)

Where RHPIit is the logarithm of the real house price index in country i in period t. RGDP_PCit

is the real GDP per capita, POPit is the population, and URBANit is the urbanization rate (Dreger

& Kholodilin, 2011).

In the determination of the fundamental house price index, the coefficients (α) of the variables are kept constant based on the coefficients of the real house price index regression. The variables are the same, 𝛼̂ represents the constant coefficients and the same dataset is used for the regression. But, the error term disappears because the estimation of the actual house price index is already known.

The fundamental house price index is defined as: 𝑅𝐻𝑃𝐼

̅̅̅̅̅̅̅_𝑖𝑡_{= 𝛼̂}₀_{+ 𝛼̂}₁_RHPI_i,t-1_{+ 𝛼̂}₂_{RGDP_PC}_it_{+ 𝛼̂}₃_POP_it_{+ 𝛼̂}₄_URBAN_it ₍₂₎

Equation 1 and Equation 2 represent the first technique of the speculative bubble chronology and identify the deviations of the fundamental value from the actual value. To clarify the first technique, the two equations are combined to define the difference between the actual and fundamental house price index. The combination of the equations is shown in Equation 3.

Δit = RHPIit - 𝑅𝐻𝑃𝐼̅̅̅̅̅̅̅𝑖𝑡 = RHPIit – [𝛼̂0 + 𝛼̂1RHPIi,t-1 + 𝛼̂2RGDP_PCit + 𝛼̂3POPit + 𝛼̂4URBANit] (3)

A positive value of Δit is treated as a potential speculative bubble. In other words, when the

actual house price index is bigger than the fundamental house price index it is viewed as a potential speculative bubble period, but this is not necessarily the case. There is only a speculative bubble when the second technique of the algorithm, which is explained next, holds (Dreger & Kholodilin, 2011).

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The second technique of the algorithm is used to identify the house price booms, in which the booms do not necessarily represent a speculative bubble. The technique looks at the deviation from the trend of the actual house price index. This can be done by using the Hodrick-Prescott filter and by different thresholds determining the growth intensity of house prices. The Hodrick-Prescott, or HP, filter assumes that the observed time series is a sum of a cyclical and a growth component. The method is widely used in economic research and decomposes an observed variable into a trend and a cycle by following an algorithm. In other words, the HP filter removes the cyclical component of a times series from raw data to determine the long-term trend. The outcome is a smoothed time series that reveals rather the long-term than short-term fluctuations. The filter is known to suffer from an end-of sample problem, but it is still the most popular method in econometrics (Reimers, 2012). In the case of quarterly data, the default λ in the Hodrick-Prescott filter is 1600 and it is applied to the logarithm of the real house prices index. λ is a smoothing parameter that represents the ratio of variances of the cyclical component and change in the growth of the trend component. The larger the λ, the smoother the series will be (Hodrick & Prescott, 1997).

The Hodrick-Prescott filter and different thresholds for each country give the following inequality:

CYCLEit = RHPIit – TRENDit > ϕ𝜎_𝑖𝑐 (4)

In Equation 3, TRENDit is the Hodrick-Prescott trend obtained from the real house price index,

and ϕ is the price boom threshold factor that determines the growth intensity. 𝜎_𝑖𝑐 is the standard deviation of the cyclical component in country i, CYCLEit. The standard deviation of the cyclical

component is country-specific. The threshold value of ϕ is chosen in such a way that the difference between the HP cyclical component of the actual house price index and the potential speculative bubble period is the highest. There is only a house price boom if CYCLEit is bigger than ϕ𝜎_𝑖𝑐. In

words, if the cyclical component of a country is bigger than the threshold factor multiplied by the standard deviation of a country’s cyclical component, it is treated as a boom. The boom periods, in combination with the potential speculative bubble periods from the first technique, determine the speculative bubbles periods (Dreger & Kholodilin, 2011).

The final speculative bubble chronology consists of the combination of the potential speculative bubble periods and the house price booms. Based on the two above explained techniques, a speculative bubble only occurs when two conditions are met. The first condition is that Δit must be

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it coincides or partially overlaps with a house price boom. In other words, the second criterion holds when the cyclical component of the actual house price index is bigger than the threshold value times the standard deviation. The expectation is that every country shows periods where neither, both or one of the two criteria hold (Dreger & Kholodilin, 2011). The early warning system is designed to correctly identify and predict these speculative bubble periods by using the right risk model, as was summarized in Figure 1. If the speculative bubble chronology and risk model are correctly identified and give a speculative bubble, or peak, at the same time, the EWS signals financial stress and that pre-emptive regulation are appropriate. The early warning system does give a signal if the speculative bubble chronology identifies a speculative bubble period and the risk model does not, and vice versa. There is also no signal when neither the speculative bubble chronology nor the risk model identifies a speculative bubble or peak period. The assumption in this paper is that a signal of the early warning system is always equally strong (Gramlich et al., 2010). Figure 2 represents the speculative bubble chronology and summarizes the two criteria that have to be met for a speculative bubble period to occur.

Figure 2: Criteria Speculative Bubble Periods

Notes: The figure summarizes the two criteria that have to be met to identify speculative bubble periods. The first criterion says that the deviation, Δit, between the actual house price index from the fundamental index values should be positive and higher than 0.5

standard deviations (σ) of the deviations (Δit). The second criterion says that the cyclical component of the actual house price index

should be bigger than the threshold value times the standard deviation. The criteria are applied to every separate country and the equation as a whole represents the speculative bubble chronology.-

3.2. Prediction of Speculative Bubbles

Now, the appropriate research method to predict speculative bubbles, or risk model, can be selected, which is the fourth step in the EWS framework of Gramlich et al. (2010). In the previous chapter the two main approaches to developing an early warning system were discussed, the econometric and signal extraction approach. Dreger and Kholodilin (2011) used both approaches to create an early warning system and found that the logit and probit approaches are more accurate in predicting speculative bubbles than the signal extraction approach and is, therefore, a more suitable approach for an early warning system. There are more advantages to the logit and probit

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models. First of all, the approaches provide a framework for statistical testing of the magnitude and statistical significance of each of the independent variables. Secondly, the approaches consider the correlation between regressors. Finally, the probability of occurrence of financial stress can be estimated given projected values of the independent variables. Because of these advantages and the higher accuracy, this paper uses only the econometric approach or logit and probit approaches to design an early warning system for speculative bubbles in the Western-European housing market (Bucevska, 2011).

A logit or probit model allows determining the sign and significance of the influence of each of the relevant variables. The logit and probit techniques can be formulated as:

Pr(Rit = 1|Xit) = F (Xitβ + εit) (5)

Rit is equal to 1 in case of a speculative bubble and 0 when there is not a speculative bubble. For

each country, this is based on the speculative bubble chronology described above. Pr is the conditional probability of the speculative bubble. Xit represents the selected set of variables that

are necessary to determine the house price in a country. The variables are selected and explained in the third step of the EWS framework in the following paragraphs. F is a cumulative probability function and ε is a disturbance term (Dreger & Kholodilin, 2011).

In the logit and probit models, several assumptions are made. The first assumption is very important in this paper and states that it is possible to identify and predict speculative bubbles with the logit and probit models. Furthermore, the selected variables (Xit) are the only variables that

affect the occurrence of a speculative bubble. In other words, no important variables are omitted and no unnecessary variables are included. Another assumption about the variables is that the independent variables are measured without error and. Additionally, the independent variables are not linear combinations of each other and are not cointegrated. A fifth assumption of the logit and probit models is that the observations are independent of each other. The final assumption is that the error terms are independent and normally distributed, and is only applicable to the probit model (Statistics Solutions, 2019).

Setting the variables is the third step in the EWS framework of Gramlich et al. (2010). The variables are mainly selected based on the conclusions of Muellbauer and Murphy (2008), who concluded that house prices, in particular, depend on macroeconomic and demographic conditions, and institutional features. In addition, the money supply is taken into account and hereby completes the selection of the following set of variables: nominal and real money market rate, money supply,

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nominal and real money supply growth, spread, lending-to-GDP ratio, real effective exchange rate, rent price index, house price-to-rent index, investment-to-GDP ratio, general government balance to-GDP-ratio, growth rate of real GDP per capita and property taxation. The set of variables is similar to the variables as were used by Dreger and Kholodilin (2011) in their early warning system. The next paragraph discusses the operationalization of the variables.

Property taxation includes taxes on the use, ownership, or transfer of wealth. The taxes on the use or ownership of property is determined by looking at the value of the property at a particular time but accrues continuously. Taxes on the transfer of wealth are recorded at the time that the transfer takes place. Property taxation is taken as a share of the real GDP (IMF, 2014). The money supply is operationalized as the money amount that is in circulation plus the overnight deposits, expressed in millions of euros (IMF, 2016).

GDP, or gross domestic product, is defined as the added value created through the production of goods and service and does not include import. As is the case in all variables, real values, such as real GDP, are adjusted for inflation and nominal variables, such as nominal GDP, are not (IMF, 2014). Nominal and real GDP are not included in the set of variables that are used in the logit and probit approaches but are necessary to calculate other variables that are included. The real growth rate of GDP per capita, for example. GDP per capita looks at the GDP per person and functions as a measure of a country’s standard of living (IMF, 2014). The real growth rate of GDP per capita looks at the GDP growth per person compared to the same quarter of the previous year and is adjusted for inflation. The variable is calculated by dividing the GDP growth of a country by a country’s population.

Other variables that are measured both in real and in nominal terms are money supply growth and money market rate. The money supply growth of a period looks at the country’s growth in money supply compared to the same period of the previous year (IMF, 2016). In this paper, the period is a quarter. The money market rate, or term interest rate, is the rate at which short-term borrowings are effected between financial institutions, such as banks. The real money market rate is based on a three-month average of the short-term interest rate (OECD, 2019). The nominal money market rate is adjusted for inflation. The real money market rate, or short-term interest rate, is also used to determine the spread between long-term and short-term interest rates. The long-term interest rate refers to the interest rate on government bonds that mature in ten years (OECD, 2019). The spread represents the difference between long-term and short-term interest rates.

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The real effective exchange rate is the weighted average of a country’s currency concerning an index or basket of other major currencies. The relative trade balance of a country’s currency is compared to each country within the index to determine the weights (OECD, 2019). The rent index is the indexed measure of the change in prices that households pay for housing rentals (OECD, 2019). The rent index is also necessary to determine the house-to-rent index. The house price-to-rent index of a period is calculated by indexing the division of the house price index of a period by the rent index of the same period. The house price-to-rent index estimates whether it is relatively cheaper to rent or own property (OECD, 2019). The investment-to-GDP ratio indicates the share of GDP that is used for nominal investments. It is calculated by dividing the nominal investment by the nominal GDP (OECD, 2019). The lending-to-GDP ratio represents the loans to households, for house purchase and new business in a country relative to the total real GDP of a country (ECB, 2019). The final variable that is operationalized is the general government balance-to-GDP ratio. The general government balance is the central and local government revenues minus expenditures excluding interest payments on consolidated government liabilities. The general government balance-to-GDP ratio in every period is then calculated by dividing the general government balance in every period by the real GDP in the same period (IMF, 2014).

Agnello and Schuknecht (2011) also added a mortgage market deregulation dummy variable in their dataset of the early warning system. The authors identified the deregulation dummy variable because until the mid-1980s the mortgage market was highly regulated. The regulation made it very difficult for households to obtain credit. To include the deregulation, a dummy variable was added to define two different periods (Agnello & Schuknecht, 2011). However, this research does not include data from the 1980s, so the dummy variable is dropped. An overview of the variables and their sources is displayed in Table 7 in Appendix A.

The data preparation steps for the logit and probit approaches are summarized in Figure 3. The first step in preparing the data for the logit and probit models is smoothing the variables for every country by using the Prescott filter. Instead, of using the original data, the Hodrick-Prescott trend data is used. Secondly, the smoothed series are standardized by subtracting the mean and then divided by the country-specific standard deviation. The country-specific standard deviation is defined as the standard deviation of the Hodrick-Prescott trend of each variable. Finally, the smoothed and standardized variables of each country are stacked over each other to

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create a panel dataset. In addition, the country-specific speculative bubble periods that are found in the speculative bubble chronology are added to the panel dataset (Dreger & Kholodilin, 2011).

Figure 3: Data Preparation Steps for the Logit and Probit Approaches

Notes: The figure summarizes the steps that are necessary to create a panel dataset that can be used in the logit and probit approaches.

After the data preparation, the logit and probit approaches are applied to the panel dataset. Similar to the data preparation, there are steps necessary to eventually determine the predictive power of the constructed early warning system. Figure 4 summarizes the essential steps to determine the predictive power. In the panel logit and probit approaches, it is important to choose between random-effects and fixed-effects model while working with panel data. In order to decide, a Hausman test is done. It is a test to see if the results of a fixed-effects model differ systematically from the random-effects model. If there are systematic differences, a fixed-effects model is preferred (Nelson, 2007). On the one hand, if the chi-squared does not show a significant difference a random-effects model is suitable, in which the standard panel logit and probit approaches can be used. On the other hand, when there is a significant difference, the fixed-effects model should be used. In that case, a hybrid method of the fixed-effect model should be used, because a normal fixed-effects logistic model cannot be applied to a probit model (Allison, 2009). The results of a logit or probit approach cannot be interpreted directly because the results represent the marginal effect of log odds. Therefore, the marginal effects at the means are taken because then the 1-unit change in an independent variable represents the amount of change in the dependent variable. With marginal effects at the means, the marginal effect is calculated by keeping the independent variables at their means. Both the random effects logit and probit models with the marginal effects at the means are displayed in the next chapter (Williams, 2012).

The last step to test whether the models are suitable for predicting speculative house price bubbles is by taking the respective predicted probabilities and test the prediction accuracy of a speculative bubble. This is the last step in the early warning system and will determine the predictive power of the system. With the predicted probabilities, it can be tested when the logit and probit approaches find a speculative bubble. If the predicted probability is above 0.5 then the

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approach finds a speculative bubble. If the estimation is in concordance with the speculative bubbles found in the speculative bubble chronology, the prediction accuracy of the logit and probit models can be determined. The more often the approach finds a speculative bubble in the same quarter as the speculative bubble chronology, the better the prediction accuracy of the approach, and the higher the predictive power of the early warning system (Bucevska, 2011).

Figure 4: Predictive Power of the Early Warning System

Notes: The figure shows the methodological steps that are necessary to find and test the prediction accuracy of the logit and probit models, and the predictive power of the early warning system. If the predicted probability is above 0.5 then the approach finds a speculative bubble. The speculative bubbles that are found with the predicted probabilities are compared to the speculative bubble periods from the speculative bubble chronology. With the comparison of the prediction accuracy of the approaches, the predictive power of the early warning system is determined.

3.3. Data

The main differences between this research and the research of Dreger and Kholodilin (2011) are the timeframe and examined countries. The timeframe in this paper is from Q1-2011 till Q2-2018, in comparison to the research of Dreger and Kholodilin (2011) where the timeframe is from Q1-1969 till Q4-2009. The selected countries in this research are Slovenia, Germany, Belgium, and the Netherlands, which is different from the reference paper that examined OECD countries worldwide, such as Australia, the US, Japan, and France.

Dreger and Kholodilin (2011) mainly depended on Datastream as a data source. After they gathered the data from Datastream, they used the values of those variables to calculate the missing values of the remaining variables. Due to the unavailability of Datastream, Eikon is used as the main source to collect the data. Like Dreger and Kholodilin (2011), some variables are calculated by using the gathered data. For example, the data for the investment-to-GDP rate is calculated for every quarter by dividing nominal investment by nominal GDP. An overview of the used variables and how they are retrieved can be found in Appendix A.

It is tried to gather all data quarterly to increase the reliability, but the data was not available for all variables. The variables lending to households, real effective exchange rate, general government balance, and money supply are only available monthly. Nevertheless, these variables are included

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in the method by transforming them into quarterly data. According to Cociuba, Prescott, and Ueberfeldt (2009), it is possible to convert monthly into quarterly data. In their conversion, they denote mi as monthly data to be converted into quarterly data.

Define:

d = min⁡(𝑚1,⁡𝑚2,⁡𝑚3)⁡⁡

𝑎𝑣𝑒𝑟𝑎𝑔𝑒⁡(𝑚1,⁡𝑚2,⁡𝑚3) (6)

Then the quarterly data over those three months, q, is calculated as follows: q = {

3∗⁡𝑎𝑣𝑒𝑟𝑎𝑔𝑒⁡(𝑚1,⁡𝑚2,⁡𝑚3)−min(𝑚1,⁡𝑚2,⁡𝑚3)

2 , if⁡d⁡ < ⁡0.95

𝑎𝑣𝑒𝑟𝑎𝑔𝑒⁡(𝑚₁, ⁡𝑚₂, ⁡𝑚₃), if⁡d⁡ > ⁡0.95 (7)

In words, the value for the respective quarter is the average of all values when no particular value of the monthly data deviates too much from the average of those monthly data. If this does not hold, the minimum value is ignored, and the quarterly data is the average of the two highest monthly values (Cociuba, Prescott & Ueberfeldt, 2009). The conversion is a proper solution but does not predict the quarterly value accurately, so it is considered in the discussion.

Other variables, property taxation, and urbanization were only available yearly. To still include these variables into the model, it is assumed that they do not change during the year. In other words, the yearly value that is retrieved from Eikon remains constant every quarter (Jacobs, Kroonenberg & Wansbeek, 1989). The assumption results in an overestimation of the coefficient of the variables but is considered in the discussion.

4. Results

Before the results will be discussed, the two criteria of the previous chapter will be discussed since they are the guidelines of this chapter. First of all, there will only be a potential speculative bubble period when the deviation of the actual house price index from the fundamental values, or Δit, is positive and higher than 0.5 standard deviations (σ) of the deviations. Secondly, for a boom

period to occur the cyclical component (CYCLEit) must be bigger than the country-specific

threshold value times the standard deviation (ϕ𝜎_𝑖𝑐). These conditions are visualized in Figure 2 and only when both conditions hold a speculative bubble occurs. The logit and probit approach then try to predict these speculative bubbles (Dreger & Kholodilin, 2011).

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4.1. Speculative Bubble Chronology

To start, the results of the first technique in the speculative bubble chronology, based on Equation 3, are shown. The fundamental factors that were identified in the previous chapter, real GDP per capita, population size, urbanization and the own lag of the dependent variable, are regressed against the real house price index. Following Dreger & Kholodilin (2011), all variables except for urbanization are expressed in logarithms. The time-series regressions are done for each country separately. Performing time-series analysis can cause concerns in the estimation of the standard errors. With the use of the Huber-White sandwich estimators, the robust standard errors could be predicted. The robust standard errors deal with the concerns about normality, heteroscedasticity, large residuals, leverage or influence. The estimation coefficients do not change, only the standard errors are affected by the Huber-White sandwich estimators. Adjusting for the concerns improves the reliability and validity of the estimations (UCLA, 2019). The results of the actual house price index regression are summarized in Table 9 in Appendix C.

The estimation coefficients of each variable are then used as alphas to calculate the fundamental house price index of each country. The actual and fundamental house price index of each country is presented in Figure 8 in Appendix D. As can be seen in the graph, the actual and fundamental house price index differ from each other. The difference between the lines is calculated for every country to test whether it is positive and higher than 0.5 standard deviations of the difference. If that is the case then it is seen as a potential speculative bubble period. The potential speculative bubble periods of every country that were identified by using this technique are visualized in Figure 5. The orange shaded areas represent the periods in which there is a potential speculative bubble, hence, the periods in which the first criterion of the speculative bubble chronology holds.

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Figure 5: Potential Speculative Bubble Periods in Each Country

Notes: In the figures, the log real house price index is shown for each country. The orange shaded areas represent where the first criterion holds and shows the potential speculative bubble periods. The figures represent the first, or fundamental, technique of the speculative bubble chronology.

Figure 5 shows that every country has several periods in which there might be a speculative bubble. The Netherlands has one potential speculative bubble period that lasts four quarters, from the last quarter of 2015 till the third quarter of 2016. Slovenia has several periods where there might be a speculative bubble for one or two quarters, such as is the case in the last quarter of 2011 and 2014. Belgium has the least potential bubble speculative periods, but still shows quarters in which there might be a speculative bubble, such as in the first quarter of 2017. Finally, Germany shows a similar picture as Slovenia. The country has several periods in which there might be a speculative bubble for one or two quarters. For example, Germany shows that the housing market might have experienced a speculative bubble in the first and second quarter of 2014 and the last two quarters of 2016 and 2017. Another thing that the graph seemingly shows is that the orange shaded areas

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overlap with the peaks in the graph. Belgium shows this in particular. In most cases when there is a clear peak, there is also a potential speculative bubble period, such as in the last quarter of 2014 and the first quarter of 2017. However, the other countries also show this tendency only the peaks are less clear. The potential speculative bubble periods are combined with the boom periods to form the speculative bubble chronology and to identify the speculative bubbles.

Therefore, the next step in creating the speculative bubble chronology is identifying the boom periods. As can be seen in Equation 3, three things are essential in identifying the boom periods in every country. The first part is using the Hodrick-Prescott filter to determine the cyclical component of the real house price index. This can be done by subtracting the trend of the real house price index that the Hodrick-Prescott filter finds from the real house price index. The HP cyclical component, CYCLE, is shown in Figure 9 in Appendix E. As can be seen in the figure, the Netherlands and Slovenia have a more volatile HP cyclical component than Belgium and Germany. This is because the Netherlands and Slovenia have less of a trend in the actual house price index, as can be seen in Figure 9. This causes a larger difference between the actual house price index and the trend of the actual house price index, and consequently a more volatile cyclical component of the house price. The second part of Equation 3 includes determining the standard deviation of the cyclical component of every country and can be done by taking the standard deviation of the cyclical component. Finally, a threshold has to be set for every country. As earlier mentioned, the threshold value is chosen in such a way that the difference between the HP cyclical component of the actual house price index and the potential speculative bubble period is the highest. The difference between the HP cyclical component of the actual house price index and the potential speculative bubble are visualized in Figure 9 in Appendix E. Next to the HP cyclical component, the potential speculative bubble periods that were found earlier are graphed. The country-specific maximum difference between the lines is the threshold of a country. An overview of the thresholds that were set for each country is given in Table 10 in Appendix F. A threshold level represents a countries’ growth intensity. The higher the value of the threshold the faster a countries’ actual house price index grows. As a result of the higher volatility of the cyclical component in the Netherlands and Slovenia, the threshold levels are also higher in these countries. Now that the three parts that determine the boom periods are known, it is possible to identify them. The orange shaded areas in Figure 6 show the boom periods that were identified through the inequality of Equation 3.

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The orange areas represent the periods in which the second criterion of the speculative bubble chronology holds, as was summarized in Figure 2.

Figure 6: Boom Periods in Each Country

Notes: In the figures, the log real house price index is shown for each country. The orange shaded areas represent the boom periods. The figures represent the second, or filter, technique of the speculative bubble chronology and are the second criterion of Figure 2.

The Netherlands show boom periods in the first five and in the last eight quarters of the timeframe. In the period between the second quarter of 2012 and the third quarter of 2016, the cyclical component was not larger than the threshold multiplied by the standard deviation. A similar pattern can be seen in Slovenia. There are also two periods of multiple quarters at the beginning of the timeframe and at the end. The second quarter of 2013 is an exception because this quarter also shows a boom period. Belgium and Germany show more dispersed boom periods. As was the case in the potential speculative bubble periods, the boom periods in Belgium overlap with the clear peaks of the real house price index. Since the peaks last only one quarter, the boom periods

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are also shorter than in the Netherlands and Slovenia. Finally, Germany has a similar pattern to Belgium. In most periods where there is a peak in the real house price, there is also a boom period, such as is the case in the last two quarters of 2012 and in the second quarter of 2013.

Now, that both the potential speculative bubble and boom periods are clear, the final speculative bubble chronology is created. The speculative bubble chronology represents the periods in which there is a speculative bubble in a country. There is a speculative bubble when both criteria of Figure 2 hold. In other words, if in the same quarter there is both a potential speculative bubble and a boom period, as are shown by the orange shaded areas in Figure 5 and Figure 6, then there is a speculative bubble.

Figure 7: Speculative Bubble Periods in Each Country

Notes: In the figures, the log real house price index is shown for each country. The orange shaded areas represent the speculative bubbles and will be used as the dependent variable in the logit and probit approaches. In the orange shaded areas, both criteria of Figure 2 that are derived from the techniques of the speculative bubble chronology hold.

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Again, in every country, the log real house price index is graphed against the year and the orange shaded areas represent the speculative bubble periods. As Figure 7 shows, there is a speculative bubble in the Netherlands in the first quarter of 2011, the first and second quarter of 2012 and the third quarter of 2016. In Slovenia, there is a speculative bubble in the first quarter of 2011, the second and third quarter of 2012, the second quarter of 2013 and the second quarter of 2017. Further, Belgium experiences a speculative bubble in the first quarter of 2013, the last quarter in 2014, the first quarter of 2017, and in the third and last quarter of 2017. Germany has a speculative bubble in the first quarter of 2011, the third and fourth quarter of 2012, the second quarter of 2013, the third and fourth quarter of 2016, and in the third and fourth quarter of 2017. What is striking is that in none of the countries a speculative bubble lasts more than two quarters. Furthermore, the Netherlands, Slovenia, and Germany have similar periods in which there is a speculative bubble. The produced speculative bubble chronology finalizes the first part of the methodology. The number of periods in which both criteria of the speculative bubble chronology hold, and therefore are identified as a speculative bubble is shown and discussed in Table 1. Next, the logit and probit models will be applied to try and predict the speculative bubbles.

4.2. Prediction of Speculative Bubbles

The prediction of speculative bubbles starts with the selection of the appropriate variables. As already explained in chapter 3.2, the following variables are selected: nominal and real money market rate, money supply, nominal and real money supply growth, spread, lending-to-GDP ratio, real effective exchange rate, rent price index, house price-to-rent index, investment-to-GDP ratio, general government balance to-GDP-ratio, growth rate of real GDP per capita and property taxation. A summary of the variables and the way they are retrieved can be found in Table 7 in Appendix A. The data for every country is gathered, smoothed with the HP filter, standardized by subtracting the mean and dividing by the standard deviation, and then stacked over each other to create a panel data set. Before the logit and probit approaches can be done, it has to be clear if a fixed or random-effects model is appropriate. This can be decided by applying the Hausman test. It is a test to see if results from a fixed-effects model differ systematically from the random-effects model. The Hausman test showed no significant results, so it is not the case. Therefore, a random-effect model is most suitable, which means that it is not necessary to hold time-invariant variables constant.

Constructing an Early Warning System to Predict the Speculative House Price Bubble in the Current Western- European Housing Marke