Is the increase in housing prices over the period 2008-2017 in Amsterdam a sign of a housing market bubble? : an appraisal of the current situation on the Amsterdam housing market.

Is the increase in housing prices over the period 2008-2017 in Amsterdam a

sign of a housing market bubble?

An appraisal of the current situation on the Amsterdam housing market.

Paul Boers

10562052

Supervisor: Drs. P.V. Trietsch, M.Phil.

Study programme: BSc Economie & Bedrijfskunde, Universiteit van Amsterdam Track: Financiering & Organisatie

Amount of credits for bachelor thesis: 12 ECTS Date: 31-01-2018

Statement of originality

This document is written by student Paul Boers who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

Abstract

This paper researches whether there is a bubble present in the Amsterdam housing market by analyzing the housing prices and its fundamentals over the period 2008 to 2017. There is not one clear definition for bubbles, but it is researched in stock markets as well as housing markets by several researchers. Following previous literature, the hypothesis of this thesis is that there is no bubble present in the Amsterdam housing market, focusing on the period 2008-2017. The statistical methods that are conducted in this paper show evidence that this null hypothesis can be rejected, stating that there is a possible bubble in the Amsterdam housing market for the period 2008 to 2017.

Table of Contents 1 Introduction ... 4 1.1 Motivation ... 4 1.2 Research question ... 5 1.3 Sub questions ... 5 1.4 Previous research ... 5 1.5 Data ... 5 1.6 Research method ... 6 1.7 Structure ... 6 2 Literature Review ... 7 2.1 Bubbles ... 7 2.2 Measuring a bubble ... 8

2.2.1 Bubbles in stock markets ... 9

2.2.2 Bubbles in housing markets ... 10

2.3 Fundamentals determining housing prices ... 12

2.3.1 Housing prices and rent ... 12

2.3.2 Housing prices and income ... 12

3 Data ... 14

4 Methodology ... 17

4.1 Step 1: Ratio-analysis ... 17

4.2 Step 2: Testing for unit root using the Phillips Perron test ... 18

4.3 Step 3: Johansen-Juselius test on co-integration ... 19

5 Results and Statistical Analysis ... 20

5.1 Step 1: Ratio-analysis using price-income and price-rent ratios ... 20

5.2 Step 2: Unit root test ... 22

5.3 Step 3: Testing for co-integration ... 23

6 Conclusion and possible further research ... 24

1 Introduction

UBS released their annual research on housing market bubbles in September 2017. The UBS Global Real Estate Bubble Index states that the bubble indicator for Amsterdam is at 1.59. Having a bubble indicator bigger than 1.5 means that there is bubble risk, meaning

Amsterdam is in bubble-risk territory (UBS, 2017).

There is not one clear definition on what a bubble is but Stiglitz (1990) states the most classic definition of a bubble. Stiglitz (1990) states that the definition of a bubble is that if the price is high today only because people believe that the asset can be sold for a higher price in the future, and when the “fundamentals” do not justify this high price, then a bubble exists. Furthermore, Case and Shiller (2003) state that during housing market bubbles

homebuyers will acquire a house, that would normally be considered too expensive for them, because they believe that the price will keep rising and they will get compensated for their more expensive purchase in the future. When housing prices are rising but this can’t be linked to fundamental factors that influence the housing market it can be the case that there is a bubble forming.

Research on bubbles has been conducted on stock markets (Diba and Grossman (1988); Froot and Obstfeld (1991); Philips, Shi and Yu (2015)) and on the housing market (Case & Shiller (2003); Arshanapalli & Nelson (2008); Kivedal (2013); Bourassa, Hoesli & Oikarinen (2016)). The previous researches find different results on the existence of bubbles. Also, the Amsterdam housing market has not yet been investigated extensively (Ambrose, Eichholtz & Lindenthal (2013); Droes, Houben & Lamoun, 2017).

Between March 2015 and March 2017, the housing prices in Amsterdam have increased with 46%, while for The Netherlands as a whole the housing prices increased with 5% (Droes, Houben & Lamoun, 2017). This difference between Amsterdam and The

Netherlands raises the question to what extend the housing prices in Amsterdam are rising due to its underlying fundamental variables. This paper aims to determine if the rise in residential housing prices in Amsterdam over the period 2008-2017 can be linked to its underlying fundamentals or that it can be classified as a bubble.

1.2 Research question

The central question for this thesis is: Is the increase in housing prices over the 2008-2017

period a sign of a housing market bubble in Amsterdam? 1.3 Sub questions

How can a bubble be measured? What are the fundamentals driving the housing market? 1.4 Previous research

For bubbles in stock markets Diba and Grossman (1988), Froot and Obstfeld (1991) and Philips, Shi and Yu (2015) apply an econometric framework to identify a bubble. Using an econometric framework to identify a bubble on the housing market has been conducted by Case and Shiller (2003) Arshanapalli and Nelson (2008) and Kivedal (2013). Subsequently, Bourassa, Hoesli and Oikarinen (2016) compare the most common tests and conclude that a ratio-analysis is the most effective for identifying a bubble.

When conducting research on the housing market there are certain underlying fundamental variables that explain housing prices. Adams and Füss (2010) examine the dynamics and impact of macroeconomic variables on housing prices. Case and Shiller (2003), research the impact of income on the housing prices. Ambrose, Eichholtz and Lindenthal (2013) examines whether the rental prices can explain the increase in house prices.

1.5 Data

The data that is used in this paper consists of housing prices in Amsterdam from 1995 to 2017, which will be tested against its underlying fundamentals income and rent. Data on transaction prices of houses sold in Amsterdam is obtained through the Centraal Bureau voor de Statistiek (CBS). Data on income is obtained through Datastream. The average transaction prices and income are both obtained on quarterly basis. Furthermore, the average rent price per m2 _{per month is obtained through Pararius.nl, also quarterly, from}

1.6 Research method

Following the framework of Bourassa et al. (2016) the price-to-income and price-to-rent ratio-analysis is analyzed. Furthermore, the method conducted by Arshanapalli and Nelson (2008) is used, by analyzing if housing prices and its underlying fundamental variables income and rent are non-stationary and co-integrated.

1.7 Structure

The structure of this paper is as follows. In chapter 2 the known literature about bubbles in general, bubbles in housing markets and the housing market fundamentals will be reviewed. Chapter 3 provides an explanation about the data that is used in this paper. Chapter 4 describes the methodology. In chapter 5 the results of the statistical test are presented and analyzed. Finally, in chapter 6 a conclusion and a recommendation for possible further research is given.

2 Literature Review

The term “bubble” is a term that is widely used but there is not one main definition on what a bubble is exactly. The most common used definition of a bubble is defined by Stiglitz (1990). Stiglitz (1990) states that a bubble can be defined by the following basic intuition: “if the reason that the price is high today only because investors believe that the selling price will be higher tomorrow, when fundamental factors don’t seem to justify such a higher price, then a bubble exists”. So, when people only think that the price will be higher tomorrow, but there are no fundamentals supporting this higher price, the market is pursuing bubble-like behavior. Case and Shiller (2003) conduct research on the housing market and ask if there was a bubble in the United States during the 2000s. They believe that the term “bubble” refers to a situation where prices are temporarily elevated due to excessive public

expectations of future price increases. Case and Shiller state that for the housing market this means that a homebuyer will buy a house that they would consider to be too expensive for them at that moment, but they buy it anyway because the homebuyer thinks they will get compensated in the near future by a significant further price increase. Another important aspect of a housing market bubble that Case and Shiller mention is that homebuyers worry that if they do not buy now, they will not be able to afford the house in the future which creates an unstable environment with even more unstable prices. Finally, Abreu and Brunnermeier (2003) and Stiglitz (1990) state that during a bubble typically the market will eventually collapse, the bubble bursts. This is one aspect that makes identifying a bubble difficult as in a lot of research on bubbles this collapse has not yet taken place.

The following section will review the different statistical methods that can be used to identify a bubble to get a better understanding on how to recognize a bubble before the eventual collapse takes place. This paper focuses solely on the housing market, but the methods that are used on the stock market are also relevant. The stock market and housing market share characteristics and to get a broader framework the stock market analysis is incorporated in this paper.

2.2 Measuring a bubble

To identify a bubble there exist multiple statistical methods. These methods have been implemented on the stock market and the housing market. First of all, the bubbles on stock markets are reviewed and thereafter the methods to identify a housing market bubble are reviewed. Both the stock market as the housing market are included in this paper because the stock market and housing market share characteristics when conducting research on a bubble. By including both methods more insight can be gained into how bubbles can be investigated using a method that not only works in the housing market. Below a table is added with an overview that summarizes all the major literatures that are relevant for this paper:

Table 1: Literature on bubbles

Authors Research Method Market Conclusion

Diba and

Grossman (1988)

Unit root test and co-integration test

Simulated data on stock markets

No clear evidence for a bubble

Froot and Obstfeld (1991)

Linear asset-pricing model and unit root test

U.S. stock market Bubble period present

Phillips, Shi and Yu (2015)

Unit root test U.S. stock market Bubble period present

Case and Shiller (2003)

Regression analysis U.S. housing market Bubble present in housing market

Arshanapalli and Nelson (2008)

Unit root test and co-integration test

U.S. housing market Bubble present in housing market

Kivedal (2013) Unit root test U.S. housing market Bubble present in housing market

Bourassa, Hoesli and Oikarinen (2016)

Comparison of methods that can identify a bubble Housing market of multiple metropolitan cities Ratio-analysis most effective method to identify a bubble

2.2.1 Bubbles in stock markets

Diba and Grossman (1988) conduct an empirical test on the existence of rational bubbles in the stock market. They construct an econometric model that identifies a bubble by

examining if stock prices diverge significantly from market fundamentals. The fundamental Diba and Grossman (1988) use to test against the stock prices is defined as the present value of all expected dividends and the sum of an unobservable variable, discounted at a constant rate. They state that a rational bubble occurs when the stock prices diverge from the

fundamental value. To test whether the stock prices are diverging or are stationary a test on unit-root using the Dickey-Fuller test is used. Diba and Grossman (1988) find that both stock prices and the underlying dividends are non-stationary. Knowing this they investigate whether the stock prices and the market fundamental they constructed is co-integrated. To test this the co-integration test suggested by Engle and Granger (1987) is applied. Testing for co-integration identifies if there is a long-term relationship between the stock prices and underlying fundamental and also tests if the stock price deviates from this long-term equilibrium (Engle and Granger, 1987). Following this test, they find mixed results and conclude that the results do not state that a rational bubble was present. They conclude that the mixed results are probably due to the low power of the tests.

Froot and Obstfeld (1991) investigate United States stock prices and research whether the behavior of the stock prices can be explained by the movement of the

dividends. They propose a test that depends only on exogenous fundamentals, it introduces no extraneous sources that influence the variance of the model, they refer to this as being an intrinsic bubble. The motivation for this is that intrinsic bubbles have a property that the fundamentals lead to under- or overvaluations that are stable and persistent. The model they use to identify a bubble in the U.S. stock market is a linear asset-pricing model that identifies a bubble by finding an alternative price path being taken on that is a nonlinear function of the fundamentals. Following this method Froot and Obstfeld (1991) find that the hypothesis that there is no bubble can strongly be rejected.

Phillips, Shi and Yu (2015) construct an econometric framework to test for multiple bubbles. They examine historical episodes of explosive price increases and crashes in the S&P500 over the period from January 1871 to December 2010 and research whether the explosive price deviations can be identified as a bubble.

To identify if there was a bubble present they apply a generalized version of the sup

augmented Dickey-Fuller (ADF) test on unit root constructed by Phillips and Hansen (1990). The S&P500 price-dividend ratio is examined from 1871 to 2010 and Philips et al. (2015) examine multiple peaks and falls of the ratio, a movement that suggests that there could be a bubble present. Applying the tests on unit root Philips et al. (2015) find that there is evidence for bubble existence in the periods they expected to be a bubble.

2.2.2 Bubbles in housing markets

As this paper focuses on the possible housing market bubble in Amsterdam the literature on housing market bubbles is highly relevant. Using the methods that are also applied in stock markets, multiple researchers find ex-post and ex-ante proof for the existence of bubbles in housing markets.

Case and Shiller (2003) investigate the United States housing market on state-level and research whether there was a bubble present. Using a linear and log-linear regression model they find that in forty states the income growth alone explains the trend that the housing prices follow in the investigated period. Case and Shiller conclude this from the resulting R2_{, finding 96% to 99% explanation on relationship between housing prices and}

income in the most stable states. In contrast for the states where housing prices are most volatile, they find that income explains the variance of the housing prices for only 45% to 83%. From this Case and Shiller (2003) conclude that for the eight states that show a higher variance in housing prices this can’t be explained by the income patterns. To gain more insight in why the housing prices have changed Case and Shiller add more fundamentals into the regression. From this they find that adding more variables like employment, housing starts, unemployment and mortgage rates adds explanatory power significantly.

But, when adding these variables, they also find that the housing prices get significantly under forecasted by the added fundamentals. Also taking the pattern of the price-to-income ratio into an account, Case and Shiller (2003) conclude that the hypothesis that a bubble exists in the states with the most volatile housing prices can’t be rejected.

Arshanapalli and Nelson (2008) examine the rising housing prices in the United States over the period 2000-2007.To identify a bubble in the housing market they conduct the unit-root test by Perron and Phillips (1988) and the co-integration test formulated by Johansen

This paper can be seen as an extension of the research Case and Shiller (2003) conducted and supports the findings that were found. Using the co-integration test Arshanapalli and Nelson (2008) find evidence for the presence of a housing bubble in the United States during the 2000s by examining the relationship between housing prices and seven fundamental economic variables. The variables that are used are mortgage rates, unemployment, debt/income, housing affordability, home builder stock index and income, stating that income is the most important of the seven variables. The findings of this paper state that using the co-integration test can act as a detection system for early forming bubbles.

Kivedal (2013) tests for a rational bubble in the period prior to the 2007 subprime mortgage crisis. To test whether a bubble in the United States housing market was present the relationship between the rent and housing prices, the price-rent ratio, is analyzed. The price-rent ratio is analyzed using multiple econometric tests. The results from these empirical tests suggest that there was a bubble present in the housing market prior to the subprime mortgage crisis in 2007. Kivedal (2013) concludes that the econometric tests that are conducted in his paper can be used to monitor the housing market and timely detect significant deviations from fundamentals.

Bourassa, Hoesli and Oikarinen (2016) use data on six metropolitan housing markets in three different countries and compare different methods to identify a bubble. This article is the first that provides a comparison of methods that can identify a bubble. The methods Bourassa et al. (2016) examine can be divided into three categories: a ratio-analysis that compare house price to rents or incomes, a regression analysis and a focus on the growth-rate of housing prices following a method drawn from physics. The ratio-analysis and the regression analysis are consistent with the bubble definition stated by Stiglitz (1990). The bubble periods are found using an asset pricing approach and they compare the results of the asset pricing approach with the results provided by the methods they want to test for effectiveness. The asset pricing model states that the sum of the present value of future rents should be equal to the value of the asset. Using the asset pricing model as a benchmark to compare with the examined methods, Bourassa et al. (2016) find that the price-rent ratio approach can identify a bubble correctly recursively in 84.1% of the cases. Also, the price-income ratio identifies a bubble correctly recursively in 80% of the cases. From this, Bourassa et al. (2016) conclude that the most effective method to identify a

2.3 Fundamentals determining housing prices

To gain insight on housing market bubbles and the dynamics of housing prices, there also needs to be investigated what fundamentals variables drive the housing market and its prices. For this, several papers on housing market bubbles and house price dynamics that make use of the relevant variables to identify a bubble are reviewed in the following section. 2.3.1 Housing prices and rent

Ambrose, Eichholtz and Lindenthal (2013) investigate the Amsterdam housing market over a period of 355 years and research if they can find periods that can be defined as a bubble. In order to identify whether there was a bubble present they investigate the price-to-rent ratio. Stating Ambrose et al. (2013), several studies have used the price-rent ratio and found evidence supporting that housing prices can deviate from fundamentals significantly,

implying that there is a bubble. Ambrose et al. (2013) follow the approach that builds on the fact that rent captures fundamentals like demographics, technological change, economic developments and wars or other disasters. Assuming that the rent-price ratio is stationary they conduct a test on co-integration and find that house prices and rents are co-integrated. The conclusion from this states that the same underlying fundamentals affect both housing prices and rent. Knowing this Ambrose et al. (2013) conclude that both house prices and rent correct deviations from the fundamental equilibrium and therefore rent can be used as a prime fundamental driving the housing prices.

2.3.2 Housing prices and income

Adams and Füss (2010) examine the impact of macroeconomic variables on international housing prices. They conduct a panel-data research consisting fifteen countries over a period of thirty years to examine the long-term interactions between macroeconomic variables and housing prices. Especially the relationship between housing prices and economic activity they find is relevant for this paper. An indicator for economic activity that is used widely is disposable income or Gross Domestic Product (GDP) (Adams and Füss, 2010). But, as

homebuyers have incomes that are generally above the population mean they state that this indicator might not gain insight in the effect on housing prices. Therefore, Adams and Füss (2010) construct an indicator for economic activity based on real money supply, real

Subsequently, to find out the statistical relationship between housing prices and economic activity Adams and Füss (2010) conduct a test on stationarity and co-integration. From this they find that in the long run a change in economic activity of 1% implies an increase in housing prices by 0.6%, concluding income, among the other variables that constitute economic activity, has a positive effect on housing prices.

Following the multiple researches conducted on housing market bubbles and papers on housing price dynamics the variables that will be researched in this thesis are rent and income. As previous research stated, income and rent can be used to gain insight in housing price dynamics and can be seen as fundamentals driving the housing market. Also previous researches on housing bubbles use rent and income as fundamental underlying variables and find evidence for bubbles through the relationship between housing prices, rent and income. Therefore, these variables are assumed to correctly measure whether a bubble is present in the Amsterdam housing market.

In accordance with the previous literature, the hypothesis of this thesis is that there is no bubble present in the Amsterdam housing market, focusing specifically on the period 2008-2017.

3 Data

In this section the used data and corresponding time-frames will be explained. For an overview a table with the used variables and an explanation is provided below:

Table 2: Researched variables explained

Variable Label Unit Source Explanation

Housing Prices

HPi Euro (€) Centraal Bureau

voor de Statistiek (CBS.nl)

Average transaction price paid for houses sold to private home owners in

Amsterdam.

Disposable Income per capita

Yi Euro (€) European Central

Bank (ECB)

National disposable income for The Netherlands divided per capita. Measure to indicate the income available for final consumption.

Gross Domestic

Product

GDPi millions, Euro

(mln €)

OxfordEconomics Gross Domestic Product (GDP), the

value of all finished goods and services produced by The Netherlands in a year.

Rent Ri per m2, Euro

(€)

Pararius.nl Average rent price per m2 _{per month in}

Amsterdam

This paper focuses on the possible bubble in Amsterdam for the period 2008 Q1 to 2017 Q3. In total, 39 quarters are observed and analyzed. This period is investigated because during this timeframe the housing prices in Amsterdam have risen significantly. To observe the Amsterdam housing market the quarterly average transaction prices of houses in

Amsterdam are obtained through the Centraal Bureau voor de Statistiek (CBS). The average transaction prices are obtained from 1995 Q1 to 2017 Q3. This is a much longer period than the period that is researched, because by using this period a long-term average housing price can be examined that is useful for the ratio-analysis. The data is observed quarterly because for Amsterdam there is no monthly data available.

For income two indicators are examined. Firstly, because focusing on two indicators makes the estimation more robust. And secondly, because the National Disposable Income is a better measure to be used in the ratio-analysis, whereas GDP is more suitable for the unit root and co-integration tests.

The income indicator Gross Domestic Product (GDP), is defined as the total value of all finished goods and services produced (CBS StatLine, 2017). The CBS concludes that it is not the most accurate measure of national economic activity, but it is the closest they can get to obtain such an indicator. Furthermore, the National Disposable Income per capita is

obtained from the database of the European Central Bank (ECB). The National Disposable Income (NDI) is defined as the measure to indicate income available for final consumption (OECD, 2018). The ECB constructs a per capita measure by dividing the total NDI by the population, which gives an average per person. GDP is obtained quarterly from 1995 Q1 to 2017 Q3, whereas NDI per capita is obtained from 2000 Q1 to 2017 Q2 as this was the broadest time-frame for quarterly data. Corresponding with the period used for housing prices, a longer period is examined for income as well. By using a longer period than the period that is researched, a long-term average can be constructed that is applied in the ratio-analysis.

Lastly, the rental prices of houses in Amsterdam are obtained through Pararius.nl which is a website that aggregates all houses for rent in Amsterdam. In November 2017 they conducted research on the free –sector rental prices in Amsterdam and the average rent price per m2 _{per month is obtained quarterly from this article (Pararius.nl, 2017). The rental}

prices are obtained from 2010 Q1 to 2017 Q3, which can be seen as a relatively short period. Nevertheless, this period gains insight in the house price-rent dynamics and can be used in the ratio-analysis. This period can also be used in the unit-root and co-integration test as this still corresponds with the period that is researched for a possible bubble in Amsterdam. To conclude this section a table with the descriptive statistics on all variables used is provided on the next page.

Table 3: Descriptive Statistics

Variable Observations Mean Standard

deviation Minimum Maximum

Housing Prices (HP) 91 243977 71591.82 94401 417652

Gross Domestic

Product (GDP) 91 136780.5 30013.77 80008.4 183760.2

National Disposable

Income per capita (Y) 70 17699.23 1425.814 14288.44 20001.7

Rent (R) 31 19.22452 2.144413 16.08 22.34

Note: Housing prices and GDP are examined from 1995Q1 to 2017Q3, National Disposable Income per capita is examined from 2000Q1 to 2017Q2 and rental prices are examined from 2010Q1 to 2017Q3.

4 Methodology

The method constructed by Bourassa et al. (2016) who conduct research on ratios is used to get an insight in the price trends in Amsterdam over the period 2008 Q1 to 2017 Q3. The price-income and price-rent ratio are conducted for Amsterdam and are analyzed for deviations from the long-term average. The ratio-analysis finds a simple insight into the housing price dynamics and how these are behaving with respect to its fundamentals. If the housing prices are presumably showing bubble-like behavior, the tests constructed by Arshanapalli and Nelson (2008) will be used to find out if there is statistical evidence for a bubble in the Amsterdam housing market. Identifying a bubble will be done by using the test on unit root constructed by Phillips and Perron (1988) and the test on co-integration.

4.1 Step 1: Ratio-analysis

The price-income and price-rent ratio are analyzed to gain insight into the Amsterdam housing market. Following Bourassa et al. (2016) the ratio-analysis is constructed using the steps in the following section.

The first step is calculating the price-income ratio. The formula for the price-income ratio is: Price-to-Income ratio = /01

21 (1)

With HPt being housing prices and Yt being National Disposable Income per capita at time t.

For each quarter that is part of the dataset the price-income ratio is calculated. The long-term average price-income ratio is calculated by aggregating all price-income ratios and dividing this by the total number of quarters N. The formula for the long-term average price-income ratio is:

Average Price-to-Income ratio = ₇6∑/01

21 (2)

From this the relative price-income ratio can be constructed by dividing the price-income ratio of each quarter by the long-term average price-income ratio. By calculating the relative ratio a measure is constructed that shows whether the price-income ratio is deviating relatively to its long-term average. The formula for the relative price-income ratio is calculated as:

Relative Price-to-Income ratio = P/I-ratio1

The rent ratio is calculated using the same method, below the formulas for the price-rent ratio are provided.

Price-to-Rent ratio = /01 <1 (4) Average Price-to-Rent ratio = ₇6∑/01 <1 (5) Relative Price-to-Rent ratio = P/R-ratio1 Average P/R-ratio (6)

By graphically presenting the relative price-income and price-rent ratios combined with a bubble threshold at 1.10 (10%) and 1.20 (20%) there can be investigated whether the relative price-income and price-rent ratio is above the bubble threshold. The bubble

threshold is constructed in accordance with the paper of Bourassa et al. (2016). This method gives a simple insight into the situation on the Amsterdam housing market over time. When the simple graphical analysis, using the bubble thresholds of 10 and 20 percent, concludes that there is a possible bubble period present there is tested for unit root and co-integration. This method is explained in the following section.

4.2 Step 2: Testing for unit root using the Phillips Perron test

Following the statistical framework of Arshanapalli and Nelson (2008) there is tested

whether house prices, income and rent have non-stationary and are co-integrated. The first step in this framework is the test on unit root as this is a necessary condition for

co-integration. Concerning stationarity and unit root Arshanapalli and Nelson (2008) state the following. When a time series fluctuates around a mean with a constant variation it can be identified as stationary. A variable that is stationary also has the property to revert back to the mean. When the variable is far away from the mean it should move back towards the mean instead of further away. Since a variable that is stationary reverts back to its mean it exhibits no trend and therefore only non-stationary variables can be co-integrated. To test whether housing prices, income and rent are non-stationary the Phillips Perron test on unit root is used. This test constructed by Phillips and Perron (1988) is built upon the augmented Dickey-Fuller test and tests whether ρ = 1 in the following regression:

The Phillips Perron test on unit root tests for the following hypotheses for non-stationarity: 𝐻I: 𝜌 = 1

𝐻₆: 𝜌 < 1

The variable is non-stationary when the null hypothesis can’t be rejected. 4.3 Step 3: Johansen-Juselius test on co-integration

When housing prices, income and rent are assumed to be non-stationary the test on co-integration can be applied. The co-co-integration test by constructed by Johansen and Juselius (1990) estimates the following regression:

𝐻𝑃?= 𝑎 + 𝑏𝑥?+ 𝑢? (8)

With HPt again being the housing prices and in this case xt representing the fundamental

underlying variable being either income or rent. Arshanapalli and Nelson (2008) argument that (8) may be rewritten as:

Δ𝐻𝑃_? = 𝑎 + (𝑏 − 1)𝑥_?E6+ 𝜇_? (9)

The housing prices and its underlying fundamental variable are co-integrated when the slope term, b, equals 1. The hypotheses that are tested using the Johansen-Juselius co-integration test are therefore:

𝐻_I: 𝑏 = 1 𝐻₆: 𝑏 < 1

When the null hypothesis can’t be rejected in this case the variables are co-integrated. A long-term relationship exists when the housing prices and its underlying variables are co-integrated, meaning that the variable and the underlying fundamental are in a long-term equilibrium. But, when no co-integration is found this could mean that housing prices is deviating from its fundamental underlying variable thus implying that a bubble may be present.

5 Results and Statistical Analysis

In this section the results of the statistical methods are shown and analyzed. First of all, the ratio-analysis is conducted to get a simple and effective insight into the housing price dynamics in the Amsterdam housing market over the period 1995 to 2017. Thereafter, the test on stationarity is conducted by using a test on unit root. Lastly, the Johansen-Juselius test on co-integration is conducted to find out if housing prices are deviating significantly from its fundamental variables income and rent.

5.1 Step 1: Ratio-analysis using price-income and price-rent ratios

The first step on identifying a bubble is the ratio-analysis using the relative price-income and price-rent ratios. The relative price-income ratio for 2000 Q1 to 2017 Q2 is presented in Figure 1. The relative price-rent ratio for 2010 Q1 to 2017 Q3 is presented in Figure 2.

Figure 1: Relative Price-to-Income ratio for the period 2000Q1 to 2017Q2

.8 .9 1 1 .1 1 .2 1 .3 1999q3 2001q3 2003q3 2005q3 2007q3 2009q3 2011q3 2013q3 2015q3 2017q3 Quarter

Relative Price-to-Income Ratio Bubble threshold 10% Bubble threshold 20%

Figure 2: Relative Price-to-Rent ratio for 2010Q1 to 2017Q3

From Figure 1 the conclusion can be drawn that from the end of 2015 the relative price-income ratio shows bubble-like behavior, using the 10% bubble threshold. Also with the 20% threshold there is evidence that the housing prices are departing from disposable income, suggesting that a bubble is present or forming on the Amsterdam housing market. This holds for 2016 Q3 and further.

From Figure 2 the conclusion that the Amsterdam housing market is showing bubble-like behavior can also be drawn. The relative price-rent ratio suggests that the bubble is forming from 2016 Q3, using the 10% bubble threshold. Compared to the graphical analysis on the price-income ratio, it seems that the price-rent ratio is more restrained whether there is a bubble. This can be the result of the less broad time-frame that is used for the price-rent ratio.

To conclude, through the ratio-analysis signs for the presence of a bubble or a forming bubble can be found. Therefore, in the next section a statistical test is conducted to back the findings of the ratio-analysis.

.9 1 1 .1 1 .2 2010q1 2011q1 2012q1 2013q1 2014q1 2015q1 2016q1 2017q1 2018q1 Quarter

Relative Price-to-Rent Ratio Bubble threshold 10% Bubble threshold 20%

5.2 Step 2: Unit root test

The second step on identifying a possible bubble in the Amsterdam housing market is the unit root test to conclude whether housing prices, income and rent are stationary or non-stationary. The method that is used for this is the Phillips Perron test on unit root. This statistical test states that the variable needs to be non-stationary in level and stationary in first differences to be integrated in order one, thus the null hypotheses should not be rejected for the variable in level and should be rejected in first differences. The statistical results of the Phillips Perron test on unit root is provided below in Table 4.

Table 4: Results of Phillips Perron test for housing prices and fundamentals for the Amsterdam housing market from the period 2008Q1 to 2017Q3

Variable Test on Test Statistic Conclusion

HP Level 0.372 I(1) dHP 1st _{difference -8.823* I(0)} GDP Level -1.062 I(1) dGDP 1st _{difference -4.451* I(0)} Y Level -0.536 I(1) dY 1st _{difference -8.361* I(0)} R Level -2.765 I(1) dR 1st _{difference -5.773* I(0)}

Note: 1. * indicates 99% significance; 2. I(0) means stationary, I(1) means integrated and non-stationary; 3. The first differences generated for the variables using STATA are denoted as dHP, dGDP, dY and dR.; 4. R is

observed from 2010Q1 to 2017Q3 and Y is observed from 2008Q1 to 2017Q2.

Concluding from the results of the Phillips Perron test, the null hypothesis that the variable is non-stationary can’t be rejected for all variables in level and can be rejected in first

difference, with a 99% significance level. Following from this, all variables are non-stationary in level and stationary in first difference. Knowing this, the Johansen-Juselius test for co-integration can be conducted.

5.3 Step 3: Testing for co-integration

The final step in the process of identifying a possible bubble in the Amsterdam housing market is conducting the Johansen-Juselius test on co-integration. The Johansen-Juselius test conducts research on the long-term relationship between housing prices and its underlying fundamentals income and rent. The Johansen-Juselius test for co-integration uses a null hypothesis of no co-integration in STATA and tests multiple co-integration hypotheses through ranks. The first rank states that there is no co-integration, the second rank in the statistical analysis supposes that there is at most one relationship with co-integration. The results found using the Johansen-Juselius test are provided in Table 5 below.

Table 5: Co-integration tests on housing prices and underlying fundamentals for period 2008Q1 to 2017Q3

Variable Co-integration hypothesis Trace statistic 5% critical value 1% critical value Conclusion

Housing Prices and GDP Rank = 0 Rank = 1 14.1686 0.5949 18.17 3.74 23.46 6.40 No co-integration

Housing Prices and Disposable Income Rank = 0 Rank = 1 11.4265 0.5922 18.17 3.74 23.46 6.40 No co-integration

Housing Prices and Rent Rank = 0 Rank = 1 9.1809 0.1039 18.17 3.74 23.46 6.40 No co-integration

Note: 1. R is observed from 2010Q1 to 2017Q3 and Y is observed from 2008Q1 to 2017Q2.; 2. Rank = 0 uses hypothesis that there is no co-integration, rank = 1 uses hypothesis that there is at most one co-integration relationship.; 3. For all variables the trace statistics concludes that there is no co-integration.

Using the Johansen-Juselius test for integration the null hypothesis that there is no co-integration can’t be rejected for housing prices and all underlying fundamentals that are researched. This means that the housing prices are deviating from its fundamental variables, proposing that the housing prices are showing bubble-like behavior.

The results that are found show evidence that can reject the null hypothesis that there is no bubble in the Amsterdam housing market over the period 2008Q1 to 2017Q3. Concluding from the statistical tests, there is possibly a bubble present in the Amsterdam housing market, or at least a bubble is forming. The result that is found for a possible bubble should

6 Conclusion and possible further research

The intention of this paper is to gain insight in the situation of the Amsterdam housing market and identify whether there is a bubble present. Using the methods conducted by Bourassa et al. (2016) and Arshanapalli and Nelson (2008) a tentative conclusion can be drawn that the Amsterdam housing market during the period 2008 to 2017 is showing bubble-like behavior. Further research has to be conducted to contribute to the evidence that there is an actual bubble in the Amsterdam housing market.

The methods that are applied are a ratio analysis which focuses on the price-to-income and the price-to-rent ratio, following the framework of Bourassa et al. (2016). Furthermore, the Phillips Perron test on unit root is conducted to research whether housing prices, income and rent are non-stationary. Finally, the Johansen-Juselius test on

co-integration is applied to analyze the underlying relationship between housing prices and its fundamentals, income and rent in this case. This is in correspondence with the research Arshanapalli and Nelson (2008) conducted.

The ratio analysis finds a simple identifies graphically whether a bubble is present by comparing the current ratios with their long-term averages. The ratio analysis shows that from 2015 and upon the relative price-ratio for the Amsterdam housing market is above the 10% bubble threshold, which could imply that housing prices are deviating from its

fundamentals. Furthermore, the statistical tests that are conducted show that all variables are non-stationary. Also, housing prices and all underlying fundamentals that are taken into an account in this paper are found to be not co-integrated as the test on co-integration states. The fact that housing prices and its fundamentals are not co-integrated could state that the housing prices are rising due to other factors that are not observed, which implies that the null hypothesis that there is no bubble in Amsterdam can be rejected.

Further research has to be conducted to contribute to the evidence that there is an actual bubble in the Amsterdam housing market. This paper only focused on Amsterdam. Comparing the statistical results with for instance Rotterdam, Utrecht or big cities like London and Paris could gain more insight in the housing market characteristics.

Furthermore, on the fundamental variables, there should be looked at more fundamentals and fundamentals that are specifically for Amsterdam. This paper focuses on income for The Netherlands as a whole for instance. For further research it can be more effective to use

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