Testing for bubbles in the housing market of The Netherlands : national vs regional price dynamics

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Abstract

Current sharp regional housing price increases in The Netherlands beg for posing the question whether exuberance has arisen. With the previous housing market bust in mind it is clear that an unstable housing market can harm The Dutch economy when it goes south. Recently new introduced asset bubble detection tests by Phillips et al.(2013, 2015) give an opportunity to test for exuberance and may give a signal to home-buyers, home-owners, banks, policy makers and Central banks whether their actions have resulted in regional unsustainable housing markets. This research will argue that irrational exuberance has unduly escalated housing prices in Amsterdam. Previous stake-holders should be aware that a bubble can be controlled when reflated.

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Testing for bubbles in the housing market

of The Netherlands

national vs regional price dynamics

MSc Finance Thesis

Rutger de Brauw

University of Amsterdam

[Date]

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Table of Figures

Figure 1 aggregated housing wealth Dutch households in billion euro... 9

Figure 2 mortgage debt The Netherlands ... 10

Figure 3 Netherlands Real Price Index compared to OECD countries ... 12

Figure 4 Dutch provinces index levels since 2010 ... 13

Figure 5 Urban areas Real Price Indices ... 13

Figure 7 Mortgage interest rate for new buyers ... 21

Figure 8 SADF and GSADF procedures: recursive unit root tests with rolling windows ... 22

Figure 9 The Netherlands Real Price anchored ... 25

Figure 10 annuity payment formula, calculated amount as percentage of principal mortgage ... 29

Figure 11 pre-tax affordability index The Netherlands ... 29

Figure 12 Affordability index The Netherlands ... 30

Figure 13 example Netherlands 42 year house price index GSADF test (2010=100) ... 32

Figure 14 22 year GSADF test The Netherlands ... 32

Figure 15 significant GSADF statistics indicating evidence of explosiveness per region per quarter ... 33

Figure 16 results relative difference GSADF tests price indices ... 34

Figure 17 GSADF tests Urban areas Real Price Indices relative to corresponding province ... 34

Figure 18 Significant GSADF statistics regional real price indices anchored to the corresponding regional real disposable household income index ... 35

Figure 19 regional indices anchored to GDP ... 36

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1. Introduction

Nobel Prize winner Robert Shiller states in his book “Irrational Exuberance”: “The word bubble creates a mental picture of an expanding soap bubble, which is destined to explode suddenly and irrevocably. But speculative bubbles are not so easily ended; indeed, they may deflate somewhat, as the story changes, and then reflate.” (Shiller, 2015).

Asset bubbles are large upward movements in asset values for a prolonged period of time that are considered not to be justified by fundamental drivers. Their existence have been recorded many times. The Netherlands have an infamous role in the history of bubbles with one of the earliest recorded bubble: “the Tulip mania”. At the peak of its height in 1637, a buyer of a rare tulip variety was willing to pay the equivalent of a house in the centre of Amsterdam for one unit (Garber, 1990). This time houses in the centre of Amsterdam have grown for 4 years, with an average annual growth rate of 10% per year. Therefore the question arises, how many thousand tulips would it take to buy a house in the centre of Amsterdam?

This thesis will focus on the Dutch housing market and the formation of asset bubbles over the past 22 years. It is a response to the recent housing price developments in the large cities of the Netherlands and takes a retroactive approach to conclude whether there may be regional bubbles forming on the Dutch housing market. The housing market of The Netherlands seems to be recovering from a low in 2013 with an upward trend in housing prices since then.

By using relative newly introduced tests developed by Phillips et al. (2015) to test whether asset value increases show evidence for explosive autoregressive characteristics in prices. Through decomposing the Netherlands in different regions this research can give an unique insight in the Dutch housing market. The central question is: Are there regional bubbles forming in the housing market in the Netherlands? This research fits in the literature regarding the discovery of housing value bubbles that in the past had enormous impact on economies when they busted (Pavlides et al. 2015). The conclusions could be useful for the Dutch Central Bank(DNB), Dutch Commercial Banks, Dutch Home-owners and starters on the housing market. Central banks have a longstanding discussion regarding asset bubbles in which detection and behaviour are discussed. With their current expanding monetary policy they may cause abnormal market dynamics due to low interest rates. Additionally Dutch Central Bank president Klaas Knot, stated in 2014 that the current unconventional expanding monetary policy, causing low interest rates, of the European Central Bank(ECB) could encourage excessively risky investment behaviour. There seems evidence for increased search for yield on financial market that is unstable and could deteriorate easily. According to Knot the ECB should constantly wake for potentially contributing to asset bubbles even when he argues that detecting the existence of an asset bubble is impossible to do with certainty. (DNB, 2014) This hunger for scarce yield may lead to exuberance behaviour.

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4 Dutch Commercial Banks have enormous mortgage portfolio’s outstanding in the Netherlands. With high loan-to-value ratio’s and decreasing interest rates, the results of losses as a consequence of potential asset bubbles on the housing markets, can hit banks severe and forms a systemic risk. All while Dutch Home-owners and starters may be encouraged at the current low interest rates and increasing housing prices to be highly leveraged, but can see their equity to be wiped out when they are the last person to hold the key.

The structure of this paper is along the following lines. The following section -Section 2 - discusses what has been researched and concluded within relevant areas for this study: Asset bubbles, the recursive unit root tests and the fundamental drivers of the Dutch housing market asset values. Section 3 goes deeper into major aspects of the Dutch Housing Market, reviewing housing index movements in the past and the present. Based on the literature of Section 2, 3 and 4 the hypotheses this thesis want to answer are formed, as specified in Section 5. The empirical data and methodology used to test these hypotheses are explained in Section 6 and 7. In section 8 the results are presented and the economic meaning is examined. Section 9 will discuss these results by focussing on the robustness of the findings. Section 10 will finish with the conclusion of this research and further research recommendations.

2. Literature Review

2.1. Asset bubbles

The bubble value of an asset is fragile by the lack of fundamentals and therefore the asset value can depreciate rapidly. The cycle of an asset bubble is divided in a boom and a bust period. During a boom period, the expectations of an assets’ future value are very optimistic, at the bust period these expectations tend to be pessimistic. The boom and bust periods of asset bubbles are related to big fluctuations in GDP cycles. The magnitude of these fluctuations depend on the drivers and size of the asset bubble. The most prominent example is the 2008 burst of the sub-prime mortgage bubble and the big magnitude it had on the world economy (Kobrak & Wilkins, 2011). These sub-prime mortgages were bundled and together deemed far less risky than time later would prove and thus were severely overvalued. This caused a major global financial crisis. Before this the dot-com bubble around the start of the current century comes to mind. During this cycle extremely optimistic expectations drove internet company-stocks to irrational heights before they crashed. The bust of this tech-bubble did not result in as much spill over to the economy as the sub-prime mortgage bubble did and the recession it caused was much milder. The major difference between the drivers of these previous two bubbles, credit driven bubbles, as the 2008 was, are far more damaging than equity financed bubbles (Brunnermeier & Schnabel, 2015).

This link between asset price movements and debt have been very well studied by the monetary policy makers. Former Federal Reserve President Ben Bernanke wrote in multiple papers about bubbles and

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5 the stance of Central Banks against it, or away from it. Bernanke described the negative effect bubbles can have on the real economy, especially during a bust of an asset cycle. It could weaken balance sheets, inducing financial distress, causing a further downward spiral and increase bond market spreads. Despite these multiple times articulated risks, Bernanke argued that it would be undesirable if Central Banks would have an active role in intervening in the asset markets to challenge these (Bernanke and Gertler 1999, 2001; Bernanke 2002, 2004).

The argument of Bernanke is considered as the cleaning side of the “lean vs clean” debate in respect to monetary policy (White, 2009). The debate focusses on the approach of central banks towards bubbles. The cleaning side is focussed on stabilizing inflation and output after the burst of the bubble, based on the belief that bubbles cannot be correctly assessed. The leaning side is the argument that Central Banks will “lean” against the bubble by slowing or ‘popping’ the bubble actively.

2.2. Recursive unit root tests: housing market and other applications

With regards to asset bubbles; there is a great amount of academic discussion relating to both the plausibility as well as the identification method of bubbles.

Bubbles tested using traditional unit root test methods have been somewhat unfortunate. In 1991 Evans demonstrated that periodically collapsing bubbles were mostly not possible to detect in a unit root test. Therefore Phillips, Wu and Yu (2011) (PWY) introduced a sup Augmented Dickey–Fuller (SADF) which test repeatedly on a expanding sample sequence for structural change from a random walk towards explosive behaviour. This test shows time estimates of the period of a bubble existence. In their research, PWY returned on the remark of former fed president Alan Greenspan: “How do we know when irrational exuberance has unduly escalated asset values?” (Alan Greenspan, 1996), showing that a financial exuberance occurred on the Nasdaq from mid-1995, using the SADF test.

Later Phillips and Yu (2011) used the test to estimate the timeline of the financial bubbles during the subprime crisis. Their conclusion was that bubbles emerged in the housing market in February 2002 before collapsing with the subprime crisis. After that the bubble would have migrated from the housing market to certain commodity markets and the bond market as well.

Homm and Breitung (2012), compared multiple tests to detect rational bubbles. All tests were mainly focussing on a change from a random walk to an explosive regime to indicate bubble behaviour. Using the PWY test as reference, they compared the results and concluded it particularly effective as a real time bubble detection algorithm.

A limitation in the PWY methodology was that it is especially focussed on finding a single bubble period. Multiple bubbles collapses within a period were harder to detect, especially when the second bubble had a lesser magnitude. This is why Phillips, Shi and Yu (2013, 2015) (PSY) introduced a test that would be testing whether there are multiple bubbles in a time series. They proposed the generalized

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6 sup augmented Dickey–Fuller (GSADF, hereafter) test which has the advantage that detect multiple periodically collapsing bubbles instead of the PWY test.

Yiu, Yu and Jin applied the PSY method on the Hong Kong property market (Yiu, Yu, & Jin, 2013). They revealed bubbles on Honk Kong’s overall property market, the mass segment and the luxury segment in 1997, while pointing to another bubble at the start of 2011 in the overall market and in the mass segment.

Using the same technique on exuberance in the emerging markets economies, more lessons were learned by Wang (2014). These areas have experienced intense periods filled with asset values booms and surges of international capital flows. Wang (2014) found that the MSCI emerging markets overall index had two periods of explosiveness behaviour in the mid-2000s while fundamentals, such as dividends, did not show any comparable pattern. This led to the conclusion that multiple stock-bubbles occurred. Chen and Funke made a recursive calculation of the GSADF Test for the Netherlands and have shown that the test statistic did very decently in the previous housing booms. They also did it for many European countries and majority of the PSY GSADF statistics exceeded a 99% critical value in the build up towards the peak and inevitable bust (Chen & Funke, 2016).

Pavlidis, Yusupova, Paya, Peel, Martinez-Garcia, Mack, and Grossman (2013) used the Phillips et al. (2013, 2015) GSADF Test on the Dallas Fed International House Price Database, consisting of 22 countries, including The Netherlands. They found that the majority of the national indices showed highly significant GSADF statistics in the build-up before they showed a high decrease in value, both in the GSADF test of real price indices individual and the real price indices divided by their respective national disposable income indices.

For this research the paper of Pavlides et al.(2013) functions as starting point. Based on their findings for the Netherlands, which showed exuberance in the build up towards the bust, they concluded that there was evidence for bubble behaviour for the whole nation. Many different papers have only been limited towards national housing price indices. It would be interesting to go beyond these findings and examine how the different regions of The Netherlands behaved during the boom and bust period.

2.3. Fundamental drivers of the Dutch Housing market

Ambrose, Eicholtz and Lindenthal (2011) utilized a dataset of 355 years to examine the long term relation between house prices, rents and interest rates. By retrieving market data of the Netherlands through multiple sources they constructed two fundamental drivers; the “price-rent ratio” and the market interest rate. Furthermore they controlled for inflation. While they concluded that prices show mean-reversion around fundamentals, they also showed that deviations between house prices and fundamental drivers can be persistent and long-lasting, possible taking decades.

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7 Later Eichholtz, Huisman and Zwinkels (2014) concluded that housing market participants may behave different over time. House prices do relate to both fundamentals and recent price developments but the weight of each of these factors influencing house prices could vary over time. With a heterogeneous agents model they found that fundamentals are main drivers during an economic slowdown, while recent price momentum may have the upper hand during periods of economic booms. Since price momentum does not carry any fundamental value, it seems logical that an upward movement of asset value based on that, deviates from its fundamental value. Or as Case and Shiller concluded: when expectations of rapid and continuously rising price are crucial incentives for housing buyers, the market becomes inherently unstable (Case and Shiller, 2003).

With respect to which fundamental driver determines the housing price, Dröes & van de Minne (2015) analysed the determinants of house prices over time. Using an Amsterdam index dataset introduced by Eichholtz (1997), which Ambrose, Eicholtz and Lindenthal (2011) and Eichholtz, Huisman and Zwinkels (2014) also used. They estimated periodically the effect of seven known determinant of house prices for the Dutch index. They found that long-run cointegrating relationships differ over time. Growth in population, cost of construction and housing supply were the main determinants during the 19th century, after which at the start of the 20th_{century income began to be a more significant driver. This} change was reverted in the decades after World War II, the population growth and housing supply became again main determinants, in line with the post-war rebuilding period and the baby-boom that occurred in that period. Concluding with the end of the 20th_{century until now, the main determinants of} housing prices are believed to be personal income and mortgage interest rates. This reflects the increasing popularity to finance houses with mortgages in combination with financial innovation and liberalization.

This is in line with a paper from the Rabobank where the current housing prices increase is being studied. The authors attributed the sharp increases to growth in GDP and household income together with the decline of unemployment and further decreasing mortgage interest rates (Van Dalen, Aalders, & Giesbergen, 2016).

The Dutch Central Bank(DNB) recently brought out an Occasional Study that argued that according to the writers, there were signs of overheating in the urban areas but there would be no credit driven bubble behaviour. They argued that buyers increasingly funded their houses with own money and average loan-to-value(LTV) ratios were decreasing. But they also noted that surveys point out that Dutch home-owners’ expectations of house prices are optimistic, with on average an expected growth of 3.5%. This optimism was even greater in the Urban areas of the Netherlands (Hekwolter of Hekhuis, Nijskens, & Heeringa, 2016).

With respect to decreasing loan-to-value ratios, the DNB’s occasional Study shows that near to half of all mortgage loan-to-value rates at 100% or higher in both the Netherlands overall, as well as the four

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8 biggest cities. It should be argued that houses are still bought with an extreme high level of leverage. Although this top group (LTV>100%) is decreasing, so does the lowest group of LTV levels below 80%. All while the group of mortgages with LTV ratios between 90% and 99% is increasing proportionally of the total mortgages. Additionally Verbruggen et al. (2015) and Jansen, et al. (2017), points out that Dutch home buyers are likely to take mortgage LTV’s of 100% or more. Therefore this research concerning the current regional price developments in the Netherlands considers any evidence of price exuberance as credit driven and therefore potential dangerous.

Garretsen and Marlet (2017) did a research regarding the amenity of cities in the Dutch housing market. The Netherlands is a highly urbanized and small country in which commuting is a vital part of the labour market. People in the Netherlands can easily commute from one city to another which implies that a big city is not necessary existing due to the advantages, such as labour travel time considerations, as traditional literature would explain. More than 50% of the labour force lives in a different municipality from the municipally where it works. This gives an indication that housing in certain areas of the Netherlands are not a necessity but are bought based on a more cost-utility consideration.

In a comparison in effects of financial wealth and housing wealth, Case, Quigley and Shiller (2005) did find clear proof that an increase in housing wealth has immediate positive effect on consumption. They concluded in their research that changes in housing prices should be considered to be more affecting household consumption than changes in stock prices, both negatively as positive.

3. Dutch Housing Market

The European Commission notes that the Dutch market has been shaped by a wide array of policies combined with large fiscal incentives and the development of financing instruments. These policies together effectively increase the loan-to-values which causes that the Dutch house-owner is subject to high levels of leveraged housing wealth (Vandevyvere & Zenthöfer, 2012). With the high level of leveraged wealth, it is clear that a decrease in housing value can have a major effect for the Dutch economy.

In 2014 the Dutch households had an estimated aggregate total net wealth of 1118.6 billion euro1_{. At} the same time, they held an estimated 1045.7 billion euro of value in personal residences but 680.7 billion of mortgages (CBS data). With a net position of 365 billion euro of wealth coming from value of their own houses, nearly one third, but an equity risk of almost equal to the complete household wealth2_{it is clear how the European commission came to the previous stated conclusion. But even} though the Dutch house market is high leveraged and has the highest loan-to-value ratio’s in the world,

1_{Retirement rights are not included in these wealth calculations}

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9 Dutch households have a very low default rates on mortgages (Nederlandse Vereniging van Banken, 2014).

Figure 1 aggregated housing wealth Dutch households in billion euro.

Historically the Netherlands has had a high share of housing stock allocated to the rent market. In 1990 the majority of all houses were rented, 44% of all the houses was comprised under social rent (Boelhouwer, 2002). Currently 25% of all houses in the Netherlands are rented, of which 80% under the social rent policy. The social renters of the Netherlands are strongly protected by law (Huisman, 2016). This makes rent increases limited. The amount of leveraged household constitutes the majority of the population.

The sample period of the Dutch housing market that is covered in this research, 1995 till 2017, can be divided in three periods regarding the housing policies of the Netherlands: The home-ownership stimulus period from 1988 to 2000; The first reforms of the housing markets from 2001 to 2008; The reflection and revision of previous 30 years after 2008.

The start of the sample of this research lies in the privatisation and deregulation period that started around 1990. In 1988 The Memorandum of Heerma on Housing Policy introduced a change in the housing policy. The State Secretary for Housing Heerma pleaded for stimulus of home-ownership, the corporatization of national housing associations and most notable a reduction of the social housing policy (Heerma, 1988). The government at that time wanted to cut government spending and the financial support to public housing programs were a heavy burden (Priemus, 1998). More-over the popularity of the “Right to Buy” policy of the Thatcher government in the United Kingdom in the 1980s formed the start of many countries’ policies to support home-ownership and reduce public rental housing (Lux, 2003). Therefore the Dutch home-ownership was stimulated by liberalising the mortgage market and continuing the fiscal support for home-owners while the government housing made cuts in the housing supply policies; by cutting subsidies for social rental housing, selling social rented dwellings

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10 and increasing the annual social rent heavily (Priemus, 1995). As interest rates were tax deductible, the Dutch home-buyer was already more commonly keeping down payments as low as possible (Van Dijkhuizen, 2005). Originally the interest tax deductibility was countered by the tax on the estimated market value of renting a dwelling, but this replaced by the imputed rent tax which was the market value of the rent expressed as percentage of the estimated value of the dwelling and added to a persons’ personal income and thus taxed. But this imputed rent as percentage of the house was far behind the market value of the rent of a home and the net effect of the fiscal policy, from the 1970s onwards, was effectively subsidizing the home-ownership (Elsinga, Haffner, & Van der Heijden, 2006). Additionally the financial liberalisation introduced new mortgage products that maximized this subsidy (DNB, 2000). This maximization was mainly accomplished by not redeeming the principal amount of the mortgage debt until the end of the duration. Even interest-only mortgage loans were possible, in which no redeeming was agreed upon. In 2005 the Dutch Central Bank noted that since 1995, 90% of all mortgages loans that were extended were not repaid during the duration with one-third of those being interest-only (Van Dijkhuizen, 2005). Another big stimulus for the home-ownership was the adjustment of the mortgage criteria in 1993, in which the income of two persons of a household could be taken in account, instead of the preceding criteria in which only one income could count for admissibility of a mortgage. This latter criteria change increased the maximum possible amount of mortgage-loan for households. The effect of all the preceding stimulus for mortgage loans was in addition increased by decreasing mortgage interest rates and increasing incomes. These factors constituted an increase in the demand side of the Dutch housing market. In 2000 the Dutch Central Bank set out in a report that a relative normal two-earner household in 1998 was able to borrow 86% more in mortgage credit, in comparison to 1994 (DNB, 2000). Housing values were rapidly growing from the 90s until 2000, annually 11% on average in nominal terms, but so did the indebtedness of the Dutch society. (Verbruggen et al., 2005).

Figure 2 mortgage debt The Netherlands

100 150 200 250 300 350 400 100.000 200.000 300.000 400.000 500.000 600.000 700.000 1989 1995 2001 2007 2013 In d ex lev el Mo rtg ag e d eb t (m illi o n eu ro ) Year

Mortgage debt evolution The Netherlands

Total mortgage debt Dutch Home-owners (left axis) Total Mortgage debt lended by Dutch MFI's (left axis) Real Housing index Netherlands (1989=100) (right axis)

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11 Around the new century The Netherlands had a large reform of the tax policy. Due to the results of the previous decade in which the increased home-ownership was seen as an success, but also saw much criticism of the heavy subsiding, the policy makers started limited reforms (Goudswaard & Caminada, 1998; Caminada, 1999). This limitation was understandable, as effects of radical changes were known to could have serious consequences for the whole Dutch economy. The Dutch Central Bank pointed out that the housing market did add 1% in GDP growth in 1999 and 2000, while decreasing the GDP by 0.5% in 2001 after the Dutch Housing market slowed down heavily (DNB, 2002). Already introduced in 1997, a new law reduced the mortgage interest rate deductibility to only one dwelling. Additionally there were political efforts made to stimulate repayments of the mortgage debt. As from 2001 the period in which mortgage interest could be deducted, reduced from unlimited, to 30 years. In 2004 a new law obliged moving home-owners to invest the housing surplus of the previous home in the new home in order to maintain deductibility of mortgage interest (Dutch Government Agreement of 2002, de Mooij & Stevens, 2003). From 2005 the law-Hillen connected the imputed-rent tax to the mortgage interest rate deductibility by stating that the imputed rent tax was maximally equal to the mortgage interest deducted. Although this was a break from the previous period, the fiscal policy did not change much to the fiscal treatment of home-ownership for a person his own home (Vording, Goudswaard, & Caminada, 1999) During this period, 2001 to 2008, housing prices growth slowed down, annually around 3.5%, which was mostly attributed to reduction in income growth and less wealth accumulation from other income sources but helped by further decreasing mortgage interest rates (Verbruggen & Kranendonk, 2005).

The aftermath of the global financial crisis of 2008, was the start of the realisation of the impact of the government policies on the housing market. The economic recession, the stagnation of the Dutch housing market and the rapid price decreases of houses nationwide led to the perception that previous policy has resulted in an overleveraged and unhealthy housing market. The results were a nationwide drop in housing prices, with a total decline of nearly 25%. As a consequence of that value drop the economic growth was estimated to be 0.5% lower, in terms of the Dutch GDP, for the next years (Jansen, 2017).The results of this change in insight has led to multiple adjustments: mortgage markets are more regulated, tax adjustments are introduced, and housing policies have been changed. Introduced in 2011, a new Mortgage Code of Conduct was introduced to discipline the financial institutions that lend mortgage-loans. In 2013 a temporary set of rules was enacted to reduce the leverage of the Dutch Households. Later more rules were introduced and the assessments of borrowing capacity was no longer a principally private matter of the parties involved. The maximum loan-to-value ratios are set to be at 100% in 2018, the mortgage interest deduction is further restricted to only redeemable mortgages and the maximum tax tariff against which the mortgage interest rate is deducted for the highest earners (Mak, 2015). These measurements resulted in a reduction in the total mortgage debt for the first time in more than 3 decades, in 2013 and 2014. Albeit for a short period, in 2015, 2016 and 2017 the total mortgage debt further increased (De Vries et al., 2016).

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12 While the National index is still below 2010 and some regions are slowly recovering from pessimism, other areas may be subdued to new unrealistic levels of optimism. The upward trend is asymmetric divided across regions (Dutch Central Bureau of Statistics(CBS) data). According to data from the Organisation for Economic Co-operation and Development(OECD) (shown below). The Netherlands real housing price index is lagging behind the Eurozone, since 2010, having seen a far greater decrease during 2012 and 2013.

Figure 3 Netherlands Real Price Index compared to OECD countries

Although the Netherlands is small and compact, it is very diverse. Brounen and Huij (2004), concluded that the Dutch Housing Market does not exist. Not only do different regions diverge in housing value developments, they also react completely different on economic factors. They stated that global statements of the Dutch housing market are hollow and recommended that discussions about the housing market would need deepening and refinement.

Using data of CBS to differentiate the Dutch market in order to show how parts of the Netherlands move, the graph below shows the current divergent index levels of the provinces since 2010. The western provinces have recently seen a steady increase in housing price indices, while the other areas are slowly recovering. The three darkest areas are Noord-Holland(northwest), Utrecht(province; middle) and Zuid-Holland(West below Noord-Holland). These three also contain the 4 biggest urban areas with Amsterdam in Noord-Holland, Utrecht(city) in Utrecht(province) and The Hague and Rotterdam in Zuid-Holland. 40 60 80 100 120 Q1-1995 Q1-1998 Q1-2001 Q1-2004 Q1-2007 Q1-2010 Q1-2013 Q1-2016 iN DE X L EVE L

Real house price indices CBS & OECD data

(Index, 2010=100)

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13 Figure 4 Dutch provinces index levels since 2010

The 4 biggest Urban areas of the Netherlands: Rotterdam, Utrecht Den Haag and Amsterdam have recovered almost all, with the index level of housing prices above the peak of 2008 for Amsterdam and Utrecht. These Urban areas were traditionally aligned with the national housing market index, but in the latest upward movement they diverge heavily from the index and show a steep increase (CBS data). Figure 5 Urban areas Real Price Indices

Especially Amsterdam has seen an increase far greater than the national index. With the historical closer levels between national and local indices, this may give an indication that an exuberance arises in the local market, Amsterdam.

4. Rational bubbles

The question arises whether and when an upward movement in value qualifies as a bubble, and how dangerous it can be. The most accepted idea among economist is that a bubble is defined as a situation where an asset price exceeds the fundamental value of that asset. This does not mean that it will

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14 definitively crash, but that it the price is more liable to crash as there is no fundamental driver to maintain the value of the asset at its current price. Problematic is obviously that the fundamental value of an asset is regarded as a representation of a claim on the present value of a set of uncertain future payments that the asset will produce (Lucas Jr, 1978). Taking this in regard, a fundamental value is arbitrary and under no essence an objective assertion or quantifiable without exhaustive assumptions.

With respect to the theory that the fundamental value of an asset is regarded as a representation of a claim on the present value of future payments that the asset will produce (Lucas Jr, 1978), Blanchard & Watson (1982) discussed how bubbles may arise. Using the major assumption that people have rational expectations. Using a theoretical model consisting of an equation that relates an asset value at the current period, to both the present value of an asset value next period and the present value of the cashflows from the current period.

This leads to the following no Arbitrage condition (Blanchard & Watson, 1982): The return of an asset:

Equation 1 return of an asset

𝑅𝑡 =

𝑝𝑡+1− 𝑝𝑡+ 𝑥𝑡+1

𝑝𝑡

The expected return given the information that is available: Equation 2 conditional expected market return

𝐸𝑡(𝑅𝑡|Ω𝑡) = 𝒓

Gives the one period expected return to an asset equal to the market return: Equation 3 expected return asset

𝐸(𝑝𝑡+1 |Ω𝑡) − 𝑝𝑡+ 𝐸[𝑥𝑡+1] = 𝒓𝑝𝑡

𝑝𝑡 is the price of an asset at period t. 𝑝𝑡+1is the price of an asset at one period after t. Ω𝑡 is the information

at time t. 𝑥𝑡 is some type of direct return, it could be dividend or rent for example. 𝑅𝑡 is then the rate of

return on holding the asset. 𝒓 is the expected market return. Extending t+1 to t+T gives

Equation 4 rational price of an asset

𝑝𝑡∗= 𝐸𝑡[∑ 1 (1 + 𝑟)𝜏𝑥𝑡+𝜏 𝑇−𝑡 𝜏=1 ] + 𝐸𝑡[ 1 (1 + 𝑟)𝑇−𝑡𝑝𝑡+𝑇]

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15 Equation 5 infinite time resale value

lim

𝑇→∞𝐸𝑡[

1

(1 + 𝑟)𝑇−𝑡𝑝𝑇] = 0 𝑖𝑓 𝑟 > 0

And the unique solution of the price of an asset, 𝑝𝑡∗:

Equation 6 infinite time price asset

𝑝𝑡∗= 𝐸𝑡[∑ 1 (1 + 𝑟)𝜏𝑥𝑡+𝜏 𝑇−𝑡 𝜏=1 ] 𝑖𝑓 𝑟 > 0

Hence the idea that the fundamental value of an asset is regarded as a claim on the present value of future payments that the asset will produce. However, 𝑝𝑡∗ is not an unique solution if time is not infinite.

If time is not infinitive any 𝑝𝑡 that carries the next form also provides a solution:

Equation 7 finite time asset price solution

𝑝𝑡 = 𝑝𝑡∗+ 𝐵𝑡 with 𝐵𝑡 = (1 + 𝒓)𝐵𝑡−1+ 𝜀𝑏,𝑡 and 𝐸[𝐵𝑡+1 |Ω𝑡] = (1 + 𝒓)𝐵𝑡 , 𝐸[𝜀𝑏,𝑡+1]= 0

Such that expected return is still 𝐸𝑡(𝑅𝑡|Ω𝑡) = 𝒓

Therefore the price of an asset could be a fundamental part 𝑝𝑡∗ that fulfills previous equations, and a

component that deviates the price from its fundamental part 𝐵𝑡 , assumed to be a bubble component.

Because this bubble component can be persistent over long periods of times this implies that buyers are willing to pay the premium upon the fundamental value. If they are willing to pay the premium it can be concluded that investors in the housing market expect the non-fundamental component of the price of houses to be continuing and growing. Given that the expected return on an asset is equal to 𝒓, it indicates that the expected return on the bubble component is also to be 𝒓. This behaviour is consistent with the rational expectation theory, hence the name ‘rational bubbles’.

Since bubbles initiate and terminate, the previous solution of 𝑝𝑡 consisting of a deterministic deviation

from the fundamental value, does not hold. The bubble component would persist forever. Therefore Blanchard & Watson (1982) proposed a model with a stochastic bubble. The probability that a bubble will remain in a period is 𝜋; probability (1- 𝜋 ) that it will crash. With this probability, the expected returns of the bubble would be higher while still being consistent with rational expectations.

Equation 8 rational bubble component 𝐵𝑡 = (

(1+𝒓)𝐵_𝑡−1

𝜋 )𝜋 + 𝜀𝑏,𝑡 with 𝜀𝑏,𝑡 a sub martingale difference and 𝐸[𝜀𝑏,𝑡+1]= 0

In this stochastic explanation, the expected return of the bubble component of 𝑝𝑡 during the bubble is

much higher, and thus asset value 𝑝𝑡, will show explosive behaviour. When the probability of a

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16 expected rate. When π decreases, the higher probability of a crash leads to an acceleration of the value 𝐵𝑡 , thus 𝑝𝑡, while the bubble lasts.

For this research it therefore takes that the variables regarding the valuation show explosive behaviour, tested by adjusted right tail variants of the Augmented Dickey Fuller test.

5. Hypotheses

Taken into respect all previously discussed literature and data, this research will take place along the answering of three hypotheses. Recent heavy regional upward trends in housing prices in The Netherlands suggest that the expectations of the value of houses have increased. Although current government policy is doing a big effort to reduce the fiscal-support from the past, certain regional prices show trends toward previous heights. Therefore the start of the research at issue is testing the behavioural characteristics of the price indices for explosiveness, as the rational bubble theory suggests that any suddenly occurring bubble will show explosive characteristics.

Hypothesis 1: Explosive price behaviour occurs on the Dutch housing market.

Nonetheless as the literature from sections 2, 3 and 4 point out, the Dutch housing market has been subject to many different stimuli. Since a bubble is not fundamentally explainable, the important question is whether the upward movements are fundamental justifiable.

Hypothesis 2: Dutch regions diverge from its fundamental drivers.

Even though the literature makes clear that previous asset bubbles did do harm, the question remains why any evidence for an asset bubble on the Dutch housing should raise an eyebrow. In the end the boom of a bubble is only worth any consideration when the expected result is a bust. Since bubbles are rational during a period when a holders can expect to sell the asset in the next period while earning the market interest rate, problems only occur when that is not possible and the market will not pay that price. Hypothesis 3: Irrational exuberance has unduly escalated Dutch regional housing prices to unaffordable levels.

6. Data

In order for conducting this research, this section will show descriptive statistics of the data and explain certain output variables as well as important variables used as core fundamental drivers. Further explanation of the use of the data is found in section 7, the methodology.

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17

6.1. Housing indices: National and Regional

Originally housing price indices based on existing housing prices used the weighted repeat sales(WRS) method as introduced by Case and Shiller (1987)3_{. Important aspect of the WRS method is that it filters} out noise in comparison to indices based on median prices of houses sold. The problem with the latter is that the composition of the houses sold can differ and therefore that median prices paid at one time for houses can be very different to prices at another time due to the category of the houses that are sold given the different times (i.e. median housing prices based indices can increase by disproportionate amount of high priced houses). Therefore, the houses that are being sold that already have been sold are used in the WRS method. This controls accurately for the characteristics of individual houses as the true appreciation for the same house is observed. But major reliability issues can occur when the repeated sold houses are not representative for the whole housing market, causing a selection bias. Another bias occurs when houses’ characteristics change. The sample could contain the majority of the lemons of the market and therefore show lower values of appreciation, or the houses could have been upgraded which unfairly increases the appreciation of an index that measures the historical housing prices development. Eichholtz (1997) criticized this method for these reason in his paper “A long run house price index: The Herengracht index, 1628–1973”. In this paper the author built an index for the housing value next to one of the major canals of Amsterdam: “de Herengracht’, using an appraisal method that captured the true index levels better.

In line with this, Bourassa, Hoesli and Sun (2006) introduced the sale price appraisal ratio (SPAR) method. This process uses ratios of transaction prices and previous appraised values to construct a price index that produces similar results to the hedonic indices, while it reduces the selection bias. In addition this method is much easier to administer. The selection bias is reduced by using all the sales that are occurring, instead of only the recurring sales, while estimating the basis prices on a base period. This base appraisal is continuously updated to reflect the value of any subsequent improvements, by using data of house adjustments that require building permits. Consequently the measure is controlling for building improvements. The Dutch Central Bureau of Statistics(CBS) housing price index data for all Dutch regions uses this SPAR method.4

Equation 9 Index value based on SPAR method

3_{Also used for the well-known Standard & Poor's Case–Shiller Home Price Indices}

4_{Explained on the CBS website:}

https://www.cbs.nl/en-gb/our-services/methods/surveys/korte-onderzoeksbeschrijvingen/price-index-existing-own-homes

𝐼

_𝑡

=

𝑆

𝑗𝑡 𝑛𝑡 𝑗 =1

𝑛𝑗 =1𝑡

𝐴

𝑗𝑝

𝑆

𝑖𝑡 𝑛𝑝 𝑖=1

𝐴

𝑖𝑝 𝑛𝑝 𝑖=1

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18 It should be noted however that the CBS data does not adjust for inflation. Therefore in the research at issue, the index values are adjusted by the author using the HCPI index, also supplied by the CBS. Table 1: descriptive statistics of adjusted Indices

Descriptive Statistics of adjusted Indices

The Netherlands Amsterdam (City) Rotterdam (City) The Hague (city) Utrecht (City) MEAN 175 211 177 175 232 MEDIAN 183 222 188 186 252 MAXIMUM 215 298 212 218 309 MINIMUM 100 99 100 100 100 STD. DEV. 33 50 33 35 60 OBS 90 90 90 90 90 Provinces: Noord Brabant Noord Holland Zuid Holland Utrecht (province) Overijssel Drenthe MEAN ₁₈₀ ₁₈₇ ₁₇₀ ₁₈₂ ₁₇₁ ₁₇₁ MEDIAN ₁₈₆ ₂₀₁ ₁₇₇ ₁₉₂ ₁₇₉ ₁₇₇ MAXIMUM ₂₂₃ ₂₃₄ ₂₀₈ ₂₂₇ ₂₀₇ ₂₁₁ MINIMUM ₁₀₀ ₁₀₀ ₁₀₀ ₁₀₀ ₉₈ ₁₀₀ STD. DEV. ₃₆ ₃₈ ₃₁ ₃₅ ₃₂ ₃₃ OBS ₉₀ ₉₀ ₉₀ ₉₀ ₉₀ ₉₀

Provinces: _Limburg _Gelderland _Groningen _Friesland _Zeeland _Flevoland

MEAN ₁₄₉ ₁₇₇ ₁₆₇ ₁₈₄ ₁₇₅ ₁₅₃ MEDIAN ₁₅₆ ₁₈₆ ₁₇₁ ₁₈₇ ₁₈₁ ₁₅₉ MAXIMUM ₁₇₅ ₂₁₉ ₂₁₀ ₂₃₃ ₂₁₈ ₁₈₂ MINIMUM ₁₀₀ ₁₀₀ ₁₀₀ ₁₀₀ ₁₀₀ ₉₉ STD. DEV. ₂₂ ₃₄ ₃₃ ₃₈ ₃₆ ₂₆ OBS ₉₀ ₉₀ ₉₀ ₉₀ ₉₀ ₉₀

Descriptive statistics for real price indices used for this research. Quarterly index levels start at first quarter of 1995 (1995q1=100), ending at the end of the second quarter of 2017 (2017q2). All nominal index levels have been adjusted for nationwide inflation using HICP (Harmonised Index of Consumer Prices) retrieved from the CBS database. Rows contains the mean, median, maximum, minimum, standard deviation(std. Dev.) and number of quarterly observations(OBS) of the real national index of the Netherlands and the real index levels of the four biggest urban areas. The second and third table contain the real index levels of the provinces with the same statistics.

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19

6.2. Housing indices: National vs Regional & Regional vs Local

Table 2: descriptive statistics relative indices compared to national level and corresponding provinces

Descriptive Statistics of Relative Divergence

Relative difference regional index levels to the national index of the Netherlands Amsterdam (City) Rotterdam (City) The Hague (city) Utrecht (City) Zuid Holland (province) Utrecht (province) Noord Holland (province) Mean 19% 0% 7% 1% 9% 4% -3% Median 20% 0% 8% 0% 6% 4% -3% Maximum 63% 11% 19% 13% 35% 10% 0% Minimum -4% -9% -1% -5% -3% -2% -6% Std. Dev. 15% 4% 4% 4% 10% 3% 1% Obs 90 90 90 90 90 90 90

Relative difference urban index levels to province

Amsterdam (City) relative to Noord Holland Rotterdam (City) relative to Zuid Holland

The Hague (city) relative to Zuid Holland Utrecht (City) relative to Utrecht (province) Mean 11% 4% 5% 3% Median 11% 2% 3% 3% Maximum 37% 15% 23% 12% Minimum -4% -5% -1% -3% Std. Dev. 9% 4% 4% 7% Obs 90 90 90 90

Descriptive statistics for relative regional comparisons used for this research. All nominal index levels have been adjusted for inflation using nationwide HICP (Harmonised Index of Consumer Prices) retrieved from the CBS database. First table is the relative difference of Quarterly Index level of the selected regions compared to The Netherlands

(𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒕𝒐 𝒕𝒉𝒆 𝑵𝒆𝒕𝒉𝒆𝒓𝒍𝒂𝒏𝒅𝒔𝒕=

𝒓𝒆𝒈𝒊𝒐𝒏 𝒊𝒏𝒅𝒆𝒙 𝒍𝒆𝒗𝒆𝒍𝒕

𝑵𝒆𝒕𝒉𝒆𝒓𝒍𝒂𝒏𝒅𝒔 𝒊𝒏𝒅𝒆𝒙 𝒍𝒆𝒗𝒆𝒍𝒕− 𝟏 ) index levels start at first quarter of 1995

(1995q1=100), ending at the end of the second quarter of 2017 (2017q2). Rows contains the mean, median, maximum, minimum, standard deviation(std. Dev.) and number of quarterly observations(obs) of the selected regions relative to The Netherlands. The second table contains the relative difference of Quarterly Index level of the Urban areas compared to the province is located

(𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒕𝒐 𝒑𝒓𝒐𝒗𝒊𝒏𝒄𝒆𝒕=

𝑼𝒓𝒃𝒂𝒏 𝒊𝒏𝒅𝒆𝒙 𝒍𝒆𝒗𝒆𝒍𝒕

𝑷𝒓𝒐𝒗𝒊𝒏𝒄𝒆 𝒊𝒏𝒅𝒆𝒙 𝒍𝒆𝒗𝒆𝒍𝒕− 𝟏 )

6.3. Fundamental drivers

Data on fundamental drivers of the Dutch housing market are described in the next sub-sections. The use of this data is explained in the Methodology, section 7.

6.3.1. National GDP per capita

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20

6.3.2. National Rent index

The OECD supplies a nominal rent index for the Netherlands, ranging from 1960 to 2017Q2. The data is adjusted using an inflation index retrieved from DataStream. Normalized at 1995, the values are adjusted by the author using the Harmonised Consumer Price Index series.

6.3.3. Household disposable income

An index is created of the household disposable income for every regions using various data points of the CBS databases regarding average disposable household income per year, The Netherlands Household Personal Disposable Income index from Ycharts, The Netherlands Personal Disposable Income index and the Dutch Harmonised Consumer Price Index series.

For every region there is data available of the average annual household disposable income in the years 1994 to 2000 and the years 2005 to 2015. For the provinces and The Netherlands the years 2000 to 2005 are also available. To produce quarterly data points the national index growth rate is used with a factor to compensate the difference in growth rate to the region. The period of 2015 to 2016 is extended with relative difference in personal disposable income that was available for all regions. The remaining 2 quarters of every region is predicted using the quarterly Dutch national Disposable Income Index from the International House Price Database supplied by the Federal Reserve Bank of Dallas.

The household disposable income is defined as the sum of wages and salaries, mixed income, net property income, net current transfers and social benefits other than social transfers in kind, less taxes on income and wealth and social security contributions paid by employees, the self-employed and the unemployed.

6.3.4. Mortgage interest rate for new buyers

The interest rates as the cost of borrowing mortgage-loans for households for a house purchase. The data is constructed via multiple sources. First for the sample period 2003 to 2017 the quarterly cost of borrowing for new households for house purchase in the Netherlands is available from the Statistical Data Warehouse of the European Central Bank, supplied by the Dutch Central Bank. In order to expand the dataset for the period 1995 to 2003, the Dutch Central Bureau of Statistics(CBS) provides a quarterly weighted average available mortgage interest rate for Dutch home-owners from 1994 till 2003. The data is nearly identical for the common months in 2003 of the two datasets. Over the whole period the interest rate was generally declining. This data is used for the newly introduced affordability index, further explained in the methodology.

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21 Figure 6 Mortgage interest rate for new buyers

7. Methodology

7.1. PSY

This research uses the test introduced by Phillips, Shi and Yu (PSY). As explained in section 2.2, it is considered a useful test for asset bubble discovery. The PSY method use a right tail variation of the Augmented Dickey-Fuller unit root test wherein the null hypothesis is a unit root of a variable and the alternative is of a mildly explosive process in the test.

Starting with their equation: Equation 10 PSY method ADF equation

𝑦𝑡 = 𝜇 + 𝛿𝑦𝑡−1+ ∑ ∅∆𝑦𝑡−𝑖+ 𝜀𝑡 𝑝

𝑖=1

Where

𝑦𝑡 is the value of the tested variable at time t, could be the price index or the fundamental adjusted price

index, 𝜇 is a constant(intercept), 𝑦𝑡−1 the value of the dependent variable one period ago, ∆𝑦𝑡−𝑖

difference of lag i,∅ difference lag coefficient, 𝜀𝑡is the error term 𝜀𝑡 𝑁(0, 𝜎𝑟1,𝑟2

2 ₎

~

𝑖𝑖𝑑 _.

𝛿 is the variable of interest. This is the autoregressive coefficient that is tested based on a right-tail variation of the standard ADF unit root test.

𝐻0∶ 𝛿 = 1 𝐻1∶ 𝛿 > 1 0 1 2 3 4 5 6 7 8 9 1993 1998 2003 2008 2013 2018 A n n u al mo rtg ae r ate (% ) Period

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22 Which can be rewritten as ∆𝑦𝑡 = 𝜇 + 𝛽𝑟1,𝑟2𝑦𝑡−1 with 𝛽 = 𝛿 − 1

Hypothesis would be:

𝐻0∶ 𝛽 = 0

𝐻1∶ 𝛽 > 0

The stochastic process of the corrected asset price follow a unit root under the null hypothesis. Under the alternative hypothesis, the price process follows an explosive process (characteristic of bubble formation). The levels of dependent variables can be tested using supremum ADF (SADF) (Phillips, Wu, and Yu, 2011) and generalized SADF (GSADF) (Phillips, Shi, and Yu, 2015). The corresponding exact finite sample critical values will be simulated via Monte Carlo methods. The GSADF, is deemed superior in the case of multiple bubbles by Phillips, Shi and Yu (2015).

Crucial part of the used tests is that not the whole sample is used for the calculation of the Dickey-Fuller statistic. Using a whole sample would reduce the extreme values of the autoregressive coefficient when asset bubbles both occur and collapse. Instead the PSY method use supremum values of the Dickey Fuller statistics based on rolling sample windows at different starting dates. This has been graphically shown below:

Figure 7 SADF and GSADF procedures: recursive unit root tests with rolling windows

Phillips, Wu, Yu (2011) Phillips, Shi, Yu (2013, 2015)

This recursive estimation procedure utilizes all information within the available time period (comparable with a rolling window procedure). Therefore it performs better compared to tests that only use the full time window (especially in presence of multiple bubbles).

The normal right tail ADF for a period statistic would be calculated as 𝐴𝐷𝐹_𝑟𝑟₁2₌ 𝛽̂𝑟1,𝑟2

𝑠.𝑒.(𝛽_𝑟1,𝑟2)

Then the test hypothesis is 𝑈𝑛𝑖𝑡 𝑟𝑜𝑜𝑡: 𝐻0∶ 𝛽 = 0 against mildly explosive behaviour: 𝐻1∶ 𝛽 > 0

Sample interval 𝑟𝑤= 𝑟0 0

𝑋

SADF procedure 𝑟𝑤= 𝑟2− 𝑟1 𝑟1 Sample interval 𝑟𝑤= 𝑟2− 𝑟1 0

𝑋

GSADF test 𝑟1 𝑟1 𝑟2 𝑟2 𝑟2

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23 The SADF(PWY) uses the supremum ADF statistic for different periods. With 𝑟2varying from to the

initial window to the whole sample 𝑆𝐴𝐷𝐹(𝑟0) = 𝑠𝑢𝑝 𝐴𝐷𝐹0

𝑟2

𝑟2 ∈ [𝑟𝑤, 1]

𝑈𝑛𝑖𝑡 𝑟𝑜𝑜𝑡: 𝐻0∶ 𝛽 = 0 against single periodically collapsing bubble price behaviour: 𝐻1∶ 𝛽 > 0

𝐺𝑆𝐴𝐷𝐹(𝑟0) = 𝑠𝑢𝑝 𝐵𝑆𝐴𝐷𝐹𝑟𝑟₁2

𝑟2 ∈ [𝑟0, 1], 𝑟1∈ [0, 𝑟2− 𝑟0]

𝑈𝑛𝑖𝑡 𝑟𝑜𝑜𝑡: 𝐻0∶ 𝛽 = 0 against multiple periodically collapsing bubble periods: 𝐻1∶ 𝛽 > 0

To set initial window size 𝑟0 the rule of thumb of Phillips et al. (2015) is used.

𝑟0= 0.01 + 1.8 √𝑇

This equals in this study for al Dutch indices to 18 observations.

Under the null hypothesis, the limit distribution of the GSADF statistic is as shown below:

sup 𝐴𝐷𝐹𝑟1 𝑟2 𝑟2∈ [𝑟0, 1], 𝑟1∈ [0, 𝑟2− 𝑟0] { 1 2𝑟𝑤[𝑊(𝑟2) 2_{− 𝑊(𝑟} 1)2− 𝑟𝑤] − ∫ 𝑊(𝑟)𝑑𝑟[𝑊(𝑟2) − 𝑊(𝑟1) ] 𝑟2 𝑟1 𝑟𝑤1 2⁄ {𝑟𝑤∫ 𝑊(𝑟)2𝑑𝑟 − [∫ 𝑊(𝑟)𝑑𝑟 − 𝑟2 𝑟₁ ] 2 𝑟2 𝑟₁ } 1 2⁄ } With 𝑟𝑤= 𝑟2− 𝑟1

For the Monte Carlo simulation of the ADF critical values for the GSADF test 3000 simulations were used.

Regarding the dates, Phillips et al.(2015) recommend a date stamping strategy for identification of origination and termination of evidence of exuberance behaviour. If the null hypothesis of a unit root is rejected, the sequence of GSADF statistic is used to show at which time the exuberance occurred. The procedure of origination date, 𝑟̂𝑒 as fraction of sample, and termination date, 𝑟̂𝑓, as fraction of sample is

shown below. 𝑟̂𝑒 = 𝑖𝑛𝑓 {𝑠 ∶ 𝐴𝐷𝐹𝑠> 𝑐𝑣𝐵𝐴𝐷𝐹_𝑛 (𝑠)} 𝑠 ≥ 𝑟0 and 𝑟̂𝑓= 𝑖𝑛𝑓 {𝑠 ∶ 𝐴𝐷𝐹𝑠< 𝑐𝑣𝐵𝑛 𝐴𝐷𝐹_(𝑠)} 𝑠 ≥ 𝑟̂𝑒

𝑐𝑣𝐵𝐴𝐷𝐹_𝑛 is right-side critical value of 𝐴𝐷𝐹𝑠 , corresponding with significance level 𝐵𝑛. In general, these

critical values are computed at each point in time. If the test statistic exceeds the critical values, bubble formation is detected. If the test statistic drops below the critical value, the bubble formation ends. GSADF Tests will be done for real price index levels individual, regional index levels relative to the national index, and urban areas against corresponding provinces.

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24

7.2. PSY on real indices

Considering previous equation 𝑦𝑡 = 𝜇 + 𝛿𝑦𝑡−1+ 𝑝𝑖=1∅∆𝑦𝑡−𝑖 + 𝜀𝑡

In line with (Blanchard & Watson, 1982) it is a reasonable assumption is that the economic return on housing, follow a general autoregressive process of order 1 as below:

𝑦𝑡 = 𝜇 + 𝛿𝑟₁,𝑟₂𝑦𝑡−1+ 𝜀𝑡

∆𝑦𝑡 = 𝜇 + 𝐵𝑟1,𝑟2𝑦𝑡−1+ 𝜀𝑡

𝑦𝑡 is the log of real index at time t. ∆𝑦𝑡 is the difference between the log of real index at time t and the

log of real index at time t-1, so equal to the log of the quarterly real price return. 𝜇 would be the fixed rate of return, as explained by (Blanchard & Watson, 1982), the normal expected rate of return. 𝜀𝑡 is a

white noise process.

Long term equilibrium relation for which 𝑝𝑡is integrated to order 1:

Log(𝐸[𝑝𝑡+1 |Ω𝑡]) = log ((1 + 𝑅𝑡) ∗ 𝑝𝑡) =log (1 + 𝑅𝑡) + log (𝑝𝑡) and 𝐸[𝛿] = 1

so that ∆𝑝𝑡 is integrated to order 0:

𝑙𝑜𝑔 (𝐸[𝑝𝑡+1 |Ω𝑡]

𝑝𝑡 ) = log (1 + 𝑅𝑡) and 𝐸(𝛽) = 0

The 𝛽 therefore should be zero and 𝛿 should be 1 under long term circumstances. But when bubbles occur, this relation is distorted and people may have excessive expectations.

When 𝑝𝑡 = 𝑝𝑡∗ + 𝐵𝑡 with 𝑝𝑡∗ = (1 + 𝑅𝑡)∗ 𝑝𝑡−1+ 𝜀𝑝_𝑡∗,𝑡 and 𝐵𝑡 = (1 + 𝑅𝑡) ∗ 𝐵𝑡−1+ 𝜀𝑏,𝑡

1+𝑅 with

𝐸[𝐵𝑡+1] = (1 + 𝑅𝑡) ∗ 𝐵𝑡−1 because the sub martingale difference: 𝐸[𝜀𝑏,𝑡]= 𝐸[𝜀𝑏,𝑡−1] =0

While long term equilibrium returns under null hypothesis are still:

𝑙𝑜𝑔 (𝐸(𝑝𝑡+1 )

𝑝𝑡 ) = log((1 + 𝑅𝑡)) + log (

𝐸[𝜀𝑝,𝑡+1] = 0 +𝐸[𝜀𝑏,𝑡+1] = 0

(1 + 𝑅𝑡)𝑝𝑡

+ 1) = log((1 + 𝑅𝑡))

The returns become distorted short run.

7.3. PSY method on Relative indices to National index

The expectations of the price development of a regional index relative to the national index is assumed to be influenced by a attractiveness versus cost consideration . Since all the price indexes are controlling for quality improvements of houses by the SPAR method and as the total area of The Netherlands is small, a deviation would not be expected explosive. As previous discussed, Garretsen and Marlet (2017) did find that 50% of the labour force lives in a different municipality from its occupation so the

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25 substitution of expensive regions to less expensive regions should result in a regional index relative to the index of its outer area to follow a mean-reversing relation. For the main research 1 lag is used.

7.4. Fundamentals

Fundament drivers can account for periods that show high exuberance in housing prices. Therefore the results of tests using fundamental drivers are crucial to see whether any deviation qualifies as fundamental. To use all the main drivers that Dröes & van de Minne (2015) found for the current period (1970 to now), the housing indices are anchored to the regional household disposable income index, national rent index and national GDP per capita index.

𝐻𝑜𝑢𝑠𝑖𝑛𝑔 𝑖𝑛𝑑𝑒𝑥 𝑡𝑜 𝑛𝑎𝑡𝑖𝑜𝑛𝑎𝑙 ℎ𝑜𝑢𝑠𝑒ℎ𝑜𝑙𝑑 𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑏𝑙𝑒 𝑖𝑛𝑐𝑜𝑚𝑒 𝑎𝑛𝑑 𝐺𝐷𝑃 𝑝𝑒𝑟 𝑐𝑎𝑝𝑖𝑡𝑎

By dividing the real housing index by the real disposable income index, the deviation in the average number of years a worker has to work for the cost of a house is expressed numerical. This ratio is meant to capture partly the demand dynamics for the majority of the home-owners in the Netherlands. By testing this ratio using the GSADF test, the hypothesis that this follows a normal mean-reversing relationship is tested against the alternative of an explosive increasing deviation of the number of years needed per house.

Figure 8 The Netherlands Real Price anchored

7.5. Affordability index: Housing index, mortgage interest rate, household

disposable income and taxes

The mortgage interest rate is a vital consideration for Dutch home-owners to buy a home due to their high loan-to-value(LTV) ratio’s, which are currently possible to be 101% of the housing value, therefore

40 80 120 160 200 240 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016

real price index The Netherlands

The Netherlands price index vs Real Disposable Income The Netherlands price index vs GDP

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26 decreases in the mortgage rates can explain upward movements as costs of financing decreases. To capture the demand dynamics for the majority of the new home-buyers in the Netherlands an index is created that tries to show how expensive it has become for new entrants to buy a house.

The start of this model is the annuity mortgage. It is the mortgage variant in which the borrower has equal payments over the full period of the mortgage. The three biggest mortgage lenders in The Netherlands -ABN-AMRO, Rabobank and ING- all have indicative mortgage calculation tools on their websites and use this type of mortgage to show the borrower an indication of his mortgage payments.

𝑎𝑛𝑛𝑢𝑖𝑡𝑦 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 = 𝑚𝑜𝑟𝑡𝑔𝑎𝑔𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑝𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 ∗ (𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑚𝑜𝑟𝑡𝑔𝑎𝑔𝑒) 1 − (1 + 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝑚𝑜𝑟𝑡𝑔𝑎𝑔𝑒 𝑝𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑)−𝑝𝑒𝑟𝑖𝑜𝑑𝑠

As an example: A person with an income of EUR 37.000,- wants to buy a house of EUR 160.000,- , according to the websites of ABN-AMRO, Rabobank and ING the next table is applicable.

HOUSE COST ASSUMED ADDITIONAL COSTS ANNUAL INTEREST RATE (10Y FIXED) (MAX) MORTGAGE OWN MONEY NEEDED MORTGAGE ANNUITY PAYMENT PAYMENT FORMULA ABN AMRO 160.000 € 8,072 1.93% € 161,600 € 6,472 592 592

RABOBANK 160.000 N/A 1.75% € 161,600 N/A 577 577

ING 160.000 € 10,251 1.79% € 161,600 € 8,651 580 580

As shown above a person can borrow € 161,600 on a house of 160.000. Additionally there are added costs to buy a house, such as transfer tax and bank fees. Therefore ABN-AMRO gives an indication of €6,472 to be brought by the buyer and ING suggests this needs to be € 8,651. The mortgage annuity of the banks are equal to those calculated with the formula. This shows how a 100% of housing value as mortgage is possible, since own money is required for the total costs above the home value. More-over the research of Jansen, et al. (2017), concluded after analysing DNB (Dutch Central Bank) Household Survey Data that 70% of the LTV ratios for first-time buyers in the Netherlands was 100% or higher (N=1900). The research department of the Dutch Central Bank itself concluded that a typical LTV ratio at time a home was bought in the Netherlands was 100% (Verbruggen et al., 2015).

ABN AMRO and Rabobank also supply an indicative net payment. This value is based on the deductibility of mortgage interest and the added imputed rent tax. For this example the interest on the mortgage can be deducted of an income that is taxed 40.4%. The imputed rent tax in 2017 is 0.75% of the WOZ(“waardering onroerende zaken”; “valuation of real estate”) value of a home. The WOZ value is the valuation of the home by the government and is periodically adjusted. For 2017 this value is set at the valuation of the home at 1 January 2016. Since ABN-AMRO and Rabobank do not have this value for this example, they assume the value of the WOZ which has been set at 1 January 2016. By recursive calculation this assumed WOZ value can be subtracted.

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27 HOUSE COST MORTGAGE MORTGAGE ANNUITY PAYMENT NET MORTGAGE ANNUITY PAYMENT ASSUMED WOZ VALUE ABN AMRO € 160,000 € 161,600 € 592 € 522 € 142,658 RABOBANK € 160,000 € 161,600 € 577 € 517 € 140,575

The Affordability index model proposed in this research level sets the value of the 160.000 home in 2017Q2 at the index level at 2015Q4. Using the index the presumed WOZ value of the model was €145.116,- a bit higher than the two banks do. By setting the mortgage to 100% to the home value the comparison can be done in the next.

HOUSE COST MORTGAGE INTEREST RATE

MORTGAGE ANNUITY PAYMENT AS PERCENTAGE OF HOUSE COST (MONTHLY) NET MORTGAGE ANNUITY PAYMENT AS PERCENTAGE OF HOUSE COST (MONTHLY) ABN AMRO €160,000 €160,000 1.93%* 0.366%* 0.323%* RABOBANK €160,000 €160,000 1.75%* 0.357%* 0.320%* ING €160,000 €160,000 1.79%* 0.359%* N/A AFFORDABILITY MODEL 100 100 1.93% 0.366% 0.324% 100 100 1.75% 0.357% 0.321% 100 100 1.79% 0.359% 0.321%

This shows that the model is fairly close to estimating the after tax costs of a 100% home-value mortgage for a new home-owner, earning a median income.

Over the 22 years this research covers, the tax rates, imputed rent percentage, WOZ valuation dates all have changed drastically. Therefore all the different input has been summarized in the next table:

* ACCORDING TO WEBSITE, BASED ON INPUT OF EXAMPLE PREVIOUS STATED

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28 YEAR YEARLY IMPUTED RENT TAX AS PERCENTAGE OF WOZ VALUE MEDIAN INCOME MARGINAL TAX RATE WOZ VALUE ESTIMATION DATE 2017 0.75% 40.80% 1-1-2016 2016 0.75% 40.40% 1-1-2015 2015 0.75% 42.00% 1-1-2014 2014 0.70% 42.00% 1-1-2013 2013 0.60% 42.00% 1-1-2012 2012 0.45% 42.00% 1-1-2011 2011 0.40% 42.00% 1-1-2010 2010 0.40% 42.00% 1-1-2009 2009 0.40% 42.00% 1-1-2008 2008 0.40% 42.00% 1-1-2007 2007 0.40% 42.00% 1-1-2005 2006 0.55% 42.00% 1-1-2003 2005 0.60% 42.00% 1-1-2003 2004 0.85% 42.00% 1-1-1999 2003 0.80% 42.00% 1-1-1999 2002 0.80% 42.00% 1-1-1999 2001 0.80% 42.00% 1-1-1999 2000 1.25% 50.00% 1-1-1995 1999 1.25% 50.00% 1-1-1995 1998 1.25% 50.00% 1-1-1995 1997 1.25% 50.00% 1-1-1995 1996 2.29% 50.00% 60% of value on 1-1-1996 1995 2.29% 50.00% 60% of value on 1-1-1995

Table containing the taxes, WOZ valuation estimation dates and imputed rent tax used as affordability index inputs.

Normal period of repaying a mortgage is 30 years, 12 times a year a payment is made. The interest rate mortgage per period is the yearly interest rate divided by 12. The present value of the mortgage is equal to the total sum the mortgage loan. The interest rate is the cost of borrowing for households for house purchase retrieved from the CBS and OECD databases. But because mortgage interest rate is tax deductible in the Netherlands, the interest rate is multiplied with (1-median tax rate).

Instead of using the principal amount in euro’s for the present value of mortgage, the nominal index value is used. Since 100% of the value of a house is the normal amount borrowed, and the index value replicates the true increase in housing costs, the outcome of the variable payment shows the development of the affordability over the time as percentage of the home value with regards to price appreciation, interest rates and household disposable income development.

Without multiplying with the indices, the payment variable shows the percentage of the mortgage value, equal to housing value in this model, that has to be payed, shown below: