Amsterdam housing market overheated or on the verge of a
bubble?
The correction of fundamental variables
UNIVERSITY OF AMSTERDAM
BSc Economics & Business
Specialisation Finance and Organisation
Author:
J.M.V. Kuijvenhoven
Student number:
10663940
Thesis supervisor: dr. J.J.G. (Jan) Lemmen
Finish date:
January 2017
Statement of Originality
This document is written by student Jetse Kuijvenhoven who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is 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
In this thesis the Amsterdam real estate market is tested for the current boom in housing prices. Prices are examined between 2008Q4-2016Q3. The current media focuses on the extremely low mortgage rate, the onward rising prices and the housing shortage as causes of the boom. The preliminary analysis combined with earlier published articles show an overheated market. To test whether it is just an overheated market or a bubble I did a trio of tests. The Augmented Dickey-Fuller test showed me that my variables where non-stationary in level and stationary in first differences. After this test the Johansen-Juselius test results in the conclusion that the variables are co-integrated. These two results were a necessity to work with the Vector Error Correction Model. This model shows whether the Price Index is corrected in the short-term by ECM𝑡−1 or that the price is in a new fundamental long-term
value. Four of the six variables showed that the housing price is corrected in the short-term. So four of the six variables say that there is not an ongoing bubble in Amsterdam. On the other hand, at least two of the six variables show signs of a bubble. Further research is needed to show that indeed only two, instead of more variables, result in deviating results.
Keywords: Amsterdam Real Estate Market, Co-integration, VEC-model, Housing bubble JEL-codes: R31, G01, C22, R22, G12
TABLE OF CONTENTS
ABSTRACT ... 3 TABLE OF CONTENTS ... 4 LIST OF TABLES ... 5 LIST OF FIGURES... 6 CHAPTER 1 Introduction ... 71.1 Newspapers and Reports... 7
CHAPTER 2 Theory and Literature Review ... 9
2.1 Price Determination ... 9
2.2 Bubbles ... 12
CHAPTER 3 Method ... 14
3.1 Augmented Dickey-Fuller test ... 14
3.2 Johansen-Juselius test ... 16
3.3 VECM ... 17
CHAPTER 4 Data ... 19
4.1 Data ... 19
4.2 Expected Influence Data ... 21
CHAPTER 5 Empirical Analysis ... 22
5.1 Testing 5.1.1. Augmented Dickey-Fuller test ... 22
5.1.2 Johansen-Juselius test ... 23
5.1.3. VECM ... 24
5.2 Lagrange-Multiplier test ... 26
CHAPTER 6 Conclusion & Discussion ... 27
LIST OF TABLES
[Continuous numbering throughout the thesis]
Table 1: Descriptive statistics of the variables in Amsterdam, 2008Q4-2016Q3 p. 19 Table 2: The variables, their indicator and their expected sign p. 21 Table 3: ADF tests of the variables of Amsterdam for 2008Q4-2016Q3 p. 22
Table 4: JJ-tests on co-integration p. 23
Table 5: VECM tests on error-correction term p. 24
LIST OF FIGURES
[Continuous numbering throughout the thesis]
Figure 1: Dutch Mortgage rates in percentages p. 8
Figure 2: Rise in Price Index p. 10
Figure 3: Amstedam Price index versus the Netherlands’ Price index p. 11 Figure 4: From 1995Q1 to 2016Q1 historical grow percentage versus grow percentage p. 13
CHAPTER 1 Introduction
1.1 Newspapers and Reports‘’Fear of new housing-bubble Amsterdam’’ (AD.nl, 2016), ‘’Housing bubble threatens to
Amsterdam’’ (Parool.nl, 2016), ‘’Housing market major cities boils dry; new supply remains off’’ (FD.nl, 2016). The latest concerns about a new housing bubble are to be seen in the headlines of the leading newspapers. Not only newspapers are worried about the development of a new housing bubble. Also, the investment bank UBS did a research about distressed housing markets. In their paper they conclude that Amsterdam is an overheated market.
Additional to this is the article of the FD in which they claim that in the first quarter of 2016 48% of the buyers in Amsterdam overbid the asking price. At the end of 2015 this was only 42%. Compared to the Netherlands, where there was 10% overbidding on average, a huge difference. This sign of positivity about the appreciated housing market in Amsterdam, is by Himmelberg et al. (2005) explained as a bubble. They explain a bubble as being driven by homebuyers who are willing to pay inflated prices for houses today because they expect unrealistically high housing appreciation in the future. The increased number of overbidding shows such a positive expectation.
Monika and Schneider (2009) show in their estimation that there is always a group who think it is a good time to buy a house because they believe the house price will rise further. They saw this group doubled towards the end of the crisis. Like Monika and Schneider saw a doubling of positive buyers in their survey, we can see an overoptimistically group of buyers who are willing to pay above the asking price.
On top of that is the prediction that this will go on for a few more years, due to the low mortgage rate (FD.nl, 2016). Monika and Schneider (2009) show that credit conditions always have been a major drive for the rise in housing prices. Just like what’s happening in Amsterdam. Among others, NVM and MVA claim that now is still a good time to buy considering the low mortgage rates.
Figure 1: Dutch Mortgage rates in percentages
Source: De Nederlandsche Bank
Himmelberg et al. (2005) say that when the mortgage interest rate is near zero, homeownership is relatively attractive because mortgage payments are low and alternatives do not yield much. Additional to this, they claim that an unexpected rise in the long-term real interest would cause a disproportionately large percentage decline in the price people would be willing to pay. Like the graph above shows, we are in an all-time low with mortgages. A small rise in the rate, at the end of 2016, could be the beginning of a larger rise. Wheaton and Nechayev (2008) also give the example of a positive shock in credit supply, which encourages people to buy. The risen mortgage rate then is a much overlooked or forgotten variable, but the expansion in buying is therefore a potential bubble.
Another concern is the inelasticity of the supply side of housing. Glaeser et al. (2008) say that when housing supply is elastic, new construction comes on line as prices rise, which causes the bubble to quickly unravel. They also claim that when housing supply is more inelastic, the bubble will have a larger impact on price and a smaller impact on the housing stock. Considering that the Dutch housing market has a relatively inelastic supply, a potential bubble would make an even greater impact (Rabobank, 2013).
This thesis is laid out as follows: section 1 is an introduction, section 2 is a literature review on price determination and other papers on bubbles. The method used to test for the bubble is described in section 3. In section 4 the data will be described. In section 5 the empirical analysis will be done and the last section shows a discussion and a conclusion.
0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Ja nua ry 2 00 8 M ay 2 00 8 Se p-0 8 Ja nu ar y 20 09 M ay 2 00 9 Se p-0 9 Ja nu ar y 20 10 M ay 2 01 0 Se p-1 0 Ja nu ar y 20 11 M ay 2 01 1 Se p-1 1 Ja nua ry 2 01 2 M ay 2 01 2 Se p-1 2 Ja nu ar y 20 13 M ay 2 01 3 Se p-1 3 Ja nu ar y 20 14 M ay 2 01 4 Se p-1 4 Ja nu ar y 20 15 M ay 2 01 5 Se p-1 5 Ja nua ry 2 01 6 M ay 2 01 6 Se p-1 6
Interest rates new house mortgages
CHAPTER 2 Theory and Literature Review
2.1 Price DeterminationIf we believe Fama (1970), there couldn’t be a possibility of a bubble because of the theory of efficient markets. Hereby proclaiming that in efficient markets prices fully reflect all available information. Some people say that prices are too high compared to the fundamental variables. According to the theory, they are wrong. Following the theory, if prices are too high, investors will start selling. The other way around, if prices are too low, they will invest in the particular asset. This will result in a price that always moves back to the mean. This holds for high-frequent traded assets like stocks. For real estate the information costs are high, there is a lower level of transactions and the product is quite heterogeneous. As a result, it is much harder for investors to set the right prices (Capozzo et al., 2004). Genesove and Mayer also claim that the housing market is inefficient. They show that prices do not fully incorporate predictable events such as for forecasted changes in interest rates (2001). Additional to this is the claim by Case and Shiller that the housing market isn’t driven by fundamentals such as income, demographic changes, national economic conditions and so forth. Making the housing market an irrational market (1990).
For a bubble it is about a deviation of the actual housing prices compared to the fundamental value of properties. To determine if there are bubbles in real estate markets, we first need to know more about the valuation or price determination of the housing market. The method used most, also by Hui and Yue (2006), is the comparison of price and market fundamentals. A common used
determinant for the housing price is the market value.
Market value is the estimated amount for which an object on the date of taxation would be submitted by a willingly seller to an accommodating buyer. This is in combination with a competitive market, after substantial marketing, where both parties are fully informed and acted without coercion. It is the best price for which the buyer is willing to pay and the most profitable price a seller can accomplish (Berkhout and Hordijk, 2008). The market value is often the asking price for a house. As told before, the transaction-price is in 48% of the cases higher than the asking price.
Nevertheless, to assess whether house prices are consistently higher, observers use growth in housing price. The housing prices used for this analysis are asking prices. Asking prices are based on the actual value of a house, so usually the market value. Figure 2 shows that the Dutch housing price index is higher than in the period of the crisis. The numbers used are from the CBS using 2010 as the base year. All the prices are normalised using the 2010 value.
Figure 2: Rise in Price Index
Source: Quarterly data from CBS.nl
Other measures to assess housing prices are the price-to-rent ratio and the price-to-income ratio. The first one is a metric calculating the cost of buying versus renting a home. So, when house prices are too high relative to renting, homebuyers will start renting instead of buying. The rise in demand on houses for rent subsequently results in a lower demand of houses for sale. This then results in a lower price for homebuyers. An argument used is that when the price-to-rent ratio stays high for a longer period, the prices are supported by unrealistic expectations of price increases rather than the rental value and therefore could contain a bubble. In contrast to the price-to-rent ratio, where the cost of renting relative to the cost of owning is shown, the price-to-income ratio shows the ability to pay relative to the housing costs (Himmelberg et al., 2005).
A lot of models of housing price movements focused on macroeconomic variables like income, interest rate and national demographic trends. But history shows us that most dramatic examples of price booms have taken place in specific demographic areas. Areas with a larger GDP or income like Amsterdam. These while prices in the rest of the country weren’t rising, or were rising in a lower degree. Causes of these specific booms are still not understood, but booms are essentially driven by expectations instead of fundamental factors (Case and Shiller, 1990). Figure 3 shows the same trend of higher prices in Amsterdam than in the rest of the country. Suggesting that the macroeconomic variables offer only a partial explanation of the price rises.
85 90 95 100 105 110 115 120 125 Q4 20082009Q2 2009Q4 2010Q2 2010Q4 2011Q2 2011Q4 2012Q2 2012Q4 2013Q2 2013Q4 2014Q2 2014Q4 2015Q2 2015Q4 2016Q2
Rise in Price index
Figure 3: Amstedam Price index versus the Netherlands’ Price index Source: CBS.nl 80 85 90 95 100 105 110 115 120 125 Q4 20082009Q2 2009Q4 2010Q2 2010Q4 2011Q2 2011Q4 2012Q2 2012Q4 2013Q2 2013Q4 2014Q2 2014Q4 2015Q2 2015Q4 2016Q2
Price Index Amsterdam vs Netherlands
2.2 Bubbles
There is no real agreement about what a bubble is. There are some behavioral characteristics which you could call a notion of a bubble: expectations about price increases in the future, the low assumed risk of falling prices and people’s worries about missing out if they don’t buy right away. The term refers to the situation in which the public’s excessive future expectations results in a rise in which the prices are temporarily elevated. During a bubble, people think they can afford a, normally too
expensive, house because of the compensation in the future. They don’t have to save a lot, because the future price increases do the saving for them. Also, a lot of first-time buyers feel the pressure to buy as soon as possible because they are afraid they can’t afford it in the future (Case & Shiller, 2003).
A lot of homebuyers see a home as an investment. An investment in where the willingness to pay depends on the perceived risk of the investment. Research by Case and Shiller (1990) show that not much homebuyers think the housing market as being risky. They also saw that the perception of risk was the lowest in the boom markets. Rising prices seem to dampen fears, and they may well enlarge the boom. This same perception of risk is shown on the Amsterdam housing market, resulting in the idea that buying a house is profitable. You would expect significant knowledge of market fundamentals with the strong investment motive. But as said earlier, and shown by the survey of Case and Shiller, it reveals the little real knowledge and agreement of the underlying causes of the price movement.
On top of this, the paper of Genesove and Mayer (2001) shows a research about loss aversion. The data shows large indications for the support of loss aversion. Resulting in sellers who set their asking price between 25 and 35 percent higher than other sellers when the expected selling price is below the original purchase price. Resulting in asking prices that are too high and disturb the market equilibrium. So it’s likely that Amsterdam housing prices are too high with investors who don’t have enough knowledge or understanding of the market. Case and Shiller also prove through their survey that a housing market bust can result from an event or a sequence of events. What’s even more frightening is the fact that this event often isn’t observed by investors or homebuyers resulting in a possible unexpected bust (1990). In other words, the burst of the bubble.
Prices are driven a lot by credit availability. The U.S. saw a rise in availability and resulting from this a growth in housing prices. This combined with second-home buyers could be a sign of an overvalued market. The investors, buying a second home, subtract with their purchases directly to the vacancy degree and therefore the supply. Many studies show that prices are sensitive to small
movements in vacancy and trading volume. If the credit supply and the willingness of investors to buy rise temporarily, it will result in higher housing demand and prices. If the reverse is happening, housing demand and prices will lower. This will mean that excess appreciation is driving demand,
Figure 4: From 1995Q1 to 2016Q1 historical grow percentage versus grow percentage
Source: CBS.nl
Zhou and Sornette (2008) define a bubble as qualified by a super-exponential growth. One way to look at super-exponential growth is the historical growth rate. This thus means that the historical growth percentage needs to be lower than the actual grow percentage. Figure 4 shows that, like around 2007/2008, the grow percentage of housing prices is since about the beginning of 2014 again bigger than the historical growth percentage of 1.7%.
Himmelberg et al. think of a housing bubble as being driven by homebuyers who are willing to pay inflated prices for houses today because they expect unrealistically high housing appreciation in the future. Resulting in the believe of future gains, thereby perceive a too low user cost and thus pay a too high a price for a house. If the reason that the price is high today only because people think the price is high tomorrow, when ‘fundamental’ factors do not justify this price, then a bubble exists (2005). -4.00 -2.00 0.00 2.00 4.00 6.00 8.00 10.00 12.00 Q 1 19 95 Q 1 19 96 Q 1 19 97 Q 1 19 98 Q 1 19 99 Q 1 20 00 Q 1 20 01 Q 1 20 02 Q 1 20 03 Q 1 20 04 Q 1 20 05 Q 1 20 06 Q 1 20 07 Q 1 20 08 Q 1 20 09 Q 1 20 10 Q 1 20 11 Q 1 20 12 Q 1 20 13 Q 1 20 14 Q 1 20 15 Q 1 20 16
Historical Grow percentage vs. Grow percentage
CHAPTER 3 Method
3.1 Augmented Dickey-FullerIn this thesis, I will be testing whether there is a bubble in Amsterdam or not. Testing this will be done over-time ranging from 2008 Q4 to 2016 Q3. 2008 Is included because in that time-period the
Amsterdam housing market saw a formation and burst of a real estate bubble (CBS), which gives a good insight in the rise of the prices. Testing for bubbles is not a common test to be done. Diba and Grossman (1988), Arshanapalli and Welson (2008) and Hui and Yue (2006) apply the methodology of co-integration to test for the long-term relationship. Diba and Grossman for the equity market,
Arshanapalli & Welson and Hui & Yue for the real estate market.
When housing prices are co-integrated with an economic variable and a bubble develops it is important to test for the long-term relationship between variables. The Johansen and Juselius test (1990) will test if there is a long-term relationship. The first step of testing for co-integration is to test whether the variables are stationary or non-stationary.
A stationary variable has the tendency to return to the mean. When it moved far from the mean, it is more likely to return to the mean rather than to move further away. Since a stationary variable has the tendency to move back to the mean, it exhibits no trend. Because a trend is a necessity for co-integration, only non-stationary variables may be co-integrated (Arshanpalli and Nelson 2008). Like Diba and Grossman (1988), I will be testing non-stationarity by the Augmented Dickey-Fuller. The test is obtained as the t-statistics of 𝛿 in the following regression. Where 𝛿 is: ρ-1 (Engle and Yoo, 1987).
∆𝑦𝑡 = 𝑎 + 𝛿𝑦𝑡−1+ ∑𝑁𝑖=0𝛽𝑖∆𝑦𝑡−𝑖 + 𝑢𝑡 (1)
Hypothesis for non-stationary are therefore:
𝐻0 ∶ 𝛿 = 0 (2)
𝐻1∶ 𝛿 < 0 (3)
This means that when the null-hypothesis is not rejected, the variable follows a random walk and the data is non-stationary. Otherwise the data is stationary and the co-integration test can’t succeed. This means that if 𝛿 is statistically negative, the null hypothesis can be rejected and the data is likely to be stationary. Engle and Sam (1987) say that a vector of time series, all of which are stationary only after
claiming that time series are integrated of order one I(1) when the level of the time series are non-stationary, but stationary after first differencing. Therefore, first differences will also be tested for being stationary.
3.2 Johansen & Juselius
When test results are sufficient, the Johansen & Juselius (1990) test of co-integration can be done. This test estimates the following co-integration regression.
𝑌𝑡 = 𝑎 + 𝑏𝑥𝑡+ 𝑢𝑡 (4)
This test is to be done in stata per hypothesized variable to have an influence on housing prices. So 𝑥𝑡
represents a fundamental variable, a and b are regression parameters and 𝑢𝑡 is the error term.
(1) Can be rewritten as the following equation.
∆𝑦𝑡 = 𝑎 + (𝑏 − 1)𝑥𝑡−1 + 𝑢𝑡 (5)
Hypothesis for co-integration are:
𝐻0 ∶ 𝑏 = 1 (6)
𝐻1∶ 𝑏 < 1 (7)
If variables are not co-integrated anymore, housing prices could move far from fundamentals. If the variables are co-integrated, then b equals one. So, the magnitude of the estimated b coefficient is very important for the test. If the null hypothesis b=1 is not rejected, then equation (5) is a stable
autoregressive equation and the data are inconsistent with co-integration. This thus means that if b isn’t 1 the variables are likely to be non-co-integrated (Hui and Yue, 2006).
If the variables are co-integrated, which is hypothesized, then there is a long-term relationship. This long-term relationship is needed to perform a VECM test and so testing for a bubble.
3.3 VECM
Like Hui and Yue did, I will be testing for bubbles using VECM (2006). Using the Johansen-test we can find out if there are any long-term relationships between variables, so called co-integrated
relationships. The VEC Model shows, using the error-correction term, whether there is a change in the fundamental long-term value or is corrected in the short-term.
The VECM, Vector Error Correction Model, is a model with an error-correction term incorporated. The idea is that a proportion of the disequilibrium from one period is corrected in the next period. 𝜆 Is the error-correction parameter, which measures how y and x react to deviations from long-run equilibrium. (Engle and Granger, 1987)
The classic error-correction formulation begins by positing long-run relationships between a dependent variable (here Price index), lagged values of the dependent variable, one or more
independent variables (for example GDP) and an error-term (Malpezzi, 1999). The VEC Model is formatted as follows:
∆𝑌𝑡 = 𝛿0+ ∑ 𝛿𝑖Δ𝑋𝑡−1+ ∑𝑘𝑗=1𝜇𝑗Δ𝑌𝑡−𝑗+ 𝜆(𝑌𝑡−1− 𝛼 − 𝛽𝑋𝑡−1) + 𝜀𝑡 𝑝
𝑖=0 (8)
∆𝑌𝑡 = 𝛿0+ ∑𝑖=0𝑝 𝛿𝑖Δ𝑋𝑡−1+ ∑𝑘𝑗=1𝜇𝑗Δ𝑌𝑡−𝑗+ 𝜆𝐸𝐶𝑀𝑡−1+ 𝜀𝑡 (9)
∆𝑌𝑡 is for the price-index and is the first difference of this variable. Δ𝑋𝑡−1 is for each dependent
variable in the research. Going from i=0 to p, resulting in the possibility of first differences or lagged differences. For the dependent variable it is of importance to have the possibility to check for lagged differences, that’s why j starts from 1. These first three are the ones that have an effect on the short-term. In the ECM part of the equation both first differences of 𝑌𝑡−1 and 𝑋𝑡−1 are used.
The 𝜆 in the equation is the ‘speed’ in which it adjusts disequilibrium. In other words, the
coefficient 𝜆 (which is assumed to be negative) shows the amount of correction since period (t-1). For example if 𝜆 is 0.5, then one halve of the gap between 𝑌𝑡−1 and the equilibrium value tend to be
reversed in period t. In this ceteris paribus is assumed. The ECM term shows the long-term and is the co-integrating part of the equation.
Verbruggen et al. (2005) assume in their model that the error-correction mechanism functions symmetric. This means that the adjustment to a higher long-term value happens with the same speed as the adjustment to a lower long-term value. They also find it reasonable to think that potential buyers would be willing to pay more when they have the idea that the long-term value in the previous period was lower than the actual value. This is a result of their confidence and speculation about a higher future price. As said earlier, this expectation is one of the most-used definitions of a bubble. If this is the case, then ECM will be positive or not significant. Resulting in an equilibrium value that will not
be restored and a larger chance on a bubble. The same accounts for small coefficient because it isn’t big enough to reverse to equilibrium. This points to a bubble.
CHAPTER 4 Data
4.1 DataAs mentioned before, I will use the dataset from 2008 Q4 until 2016 Q3. Like Hui and Yue, I involve a crisis period. This period shows a moment of no co-integration, the housing bubble in 2008, and maybe the development of a new bubble. Just like Hui and Yue took Hong Kong as a test case, I will be using the last bubble as my control variable in testing with the Johansen-Juselius test. Reason for this is the additional test of reliability, because we know that a bubble was present in 2008.
Reliability of housing prices depends on the quality and appropriateness of the data. CBS gives you the possibility to obtain two different types of data. The average selling price and the housing price index. The average selling price represents the average value paid in a period for existing homes that have been purchased by a private individual. The disadvantage of this method is that is doesn’t display the progression of the price development of all existing homes. For this the home price index is needed. The price index selling price presents the price-change of the stock of existing houses, and has to be sold to a private buyer (CBS.nl). For the city of Amsterdam only quarterly data is available.
Table 1: Descriptive statistics of the variables in Amsterdam, 2008Q4-2016Q3
Variable
Average
Standard
Deviation
Maximum Minimum
Amsterdam Housing price Index (P)
99.01
7.10
119.30
88.30
Amsterdam Quantity Residential Units (Q)
6351.51
1817.46
9484.33
3016.67
National Personal disposable nominal income
(Billions Euro) (DI)
78.60
2.27
82.88
73.80
The national nominal GDP (Billions Euro)
(GDP)
162.39
5.16
173.05
153.12
The 10 years NL mortgage rate (in %) (R)
4.62
0.78
5.60
3.03
Unemployment rate (in %) (U)
7.28
1.42
9.50
4.40
Household Debt Ratio (HDR)
18.97
0.52
19.70
17.80
Note: abbreviations used here will be used in the rest of the tables.
Another important variable is the number of dwellings available for sale. The data on the
number of vacant dwellings is available monthly, but I converted it to quarterly to match the
other data. Vacant dwellings are an important variable for the supply side. Important to say is that the descriptive statistics in table 1 show a broad range between maximum and minimum. This large maximum and minimum should be seen in the Price index, because Quantity Residential units are expected to influence the Price Index. In section 4.2 more on that. The rest of the variables are important for the demand side of housing. One of these variables is (nominal) disposable income
work with. The same accounts for the GDP (OxfordEconomics, Q3 2016), which will be studied using the nominal values as well.
Furthermore, the mortgage rate is one of the more important determinants of the housing price. I will be using 10-year fixed mortgage (DNB). 30-Year fixed mortgage rates weren’t available at the DNB, so this will have to do. Quarterly unemployment rate is also given by OxfordEconomics and is also one of the variables that has an influence and will be used for the test.
Last but not least, I will be using Household Debt Ratio. This is the amount of debt
households have. It includes consumer debt and mortgage loans. Because not many people can buy a house without a mortgage, the amount of mortgages to households is an important variable. Household Debt Ratio, further on HDR, is given quarterly by the Bank for International Settlements.
4.2 Expected Influence Data
With a higher supply prices will go down, because of the interaction between the forces of demand and supply. If the supply goes up, and the demand stays the same, housing prices will lower. So will the prices in Amsterdam. If there will be less supply vice versa will happen. If the personal disposable income goes up, people have more money to buy and to invest. This will result in a positive effect on the housing prices. The same holds for GDP.
The 10-years mortgage loan is the amount people have to pay interest over. If the mortgage rate, and therefore the loan, is going up, people will be taking a lower mortgage. And a lower mortgage means lower demand and will end up in falling prices. So does the unemployment rate. If the rate is to be going up, fewer people will have a job. This will result in falling amount of people who have an income, and therefore less people who will be willing to buy a house. Both have negative effects if going up.
The household debt ratio shows the amount of debt people have. If this amount of debt, and therefore the amount of mortgage, goes up, people are buying more. With more demand, prices will rise. But this is variable is also the variable which showed to be of great contribution during previous crises.
Table 2: The variables, their indicator and their expected sign
Variable Indicator Expected sign
P The housing price as an index, base year: 2010 1
Q Quantity residential units for sale _
DI Personal disposable nominal income (Billions Euro) +
GDP The national nominal GDP (Billions Euro) +
R The 10 years NL mortgage rate (in %) _
U Unemployment rate (in %)
_
HDR Household Debt Ratio +
CHAPTER 5 Empirical Analysis
5.1.1 Results Augmented Dickey-FullerAs told before, to perform the Johansen-Juselius test we need to have non-stationary variables and they have to be stationary after first differencing. If this is the case, then the variables are integrated I(1). This assumption/result is needed to perform a further research on housing bubbles. Table 2 shows the results of the Augmented Dickey-fuller test.
Table 3: ADF tests of the variables of Amsterdam for 2008Q4-2016Q3
Variable
Test on
Trend
No trend
Conclusion
Name
Intercept
Intercept
P
Level
0.047
-1.00
I(1)
DP
1
stdiff
-4.21**
-2.78*
I(0)
Q
Level
-1.15
-1.13
I(1)
DQ
1
stdiff
-4.70***
-3.83***
I(0)
DI
Level
-2.60
-0.18
I(1)
DDI
1
stdiff
-4.58***
-4.29***
I(0)
GDP
Level
-1.01
1.01
I(1)
DGDP
1
stdiff
-3.66**
-3.89***
I(0)
R
Level
-1.10
0.06
I(1)
DR
1
stdiff
-3,85**
-3.59**
I(0)
U
Level
-0.72
-1.47
I(1)
DU
1
stdiff
-3.14*
-2.95**
I(0)
HDR
Level
-2.11
0.30
I(1)
DHDR
1
stdiff
-7.31***
-5.91***
I(0)
Note: 1. *, ** and *** indicates 10%, 5% and 1% significance level respectively; 2. Number of lags in the unit root tests is determined by the AIC; 3. I(1) means non-stationary and I(0) means stationary; 4. DP, DQ, DDI, DGDP, DR, DU and DHDR are the first differences of the variables.
The results show that all variables are non-stationary in levels and most of them are stationary
after first differencing with a significance level of 1%. The significance level of 5% or 1%
means that the null hypothesis is rejected with a confidence level of 95% or 99% respectively.
This thus means that the variables are integrated of order one and we can move on with the
Johansen test.
5.1.2 Results Johansen Test
The next step is to test for co-intregation between the variables. For this I will be testing Priceindex and the independent separately to see if there is a long-term relationship. Say, Priceindex and Quantity we tested with a lagged difference of 8. The lagged difference is given by AIC and is backed by other tests using stata. These tests keep on adding lags until the error term is white noise. This means that the error term has a mean of zero and there is no more correlation with the values of the variable at different times. The r in the table shows the rank. A rank of r=0 has a null hypothesis saying that there is no co-integration. A rank of r=1 says that there is at most 1 co-integrated relationship. The results show, both using the trace test and the maximum-eigenvalue test, that all independent variables are co-integrated with Price index. Income aside, each variable shows a co-integration with a 1% significance level.
Table 4: Johansen_Juselius-tests on co-integration
Variables
Lagged
Trace test
Max-eigenvalue
test
Results
Differences
r=0 r=1 r=0 r=1
PI & Q
8
32.09** 4.57 27.24** 4.57
1
PI & DI
7
18.24* 3.53 14.71* 3.53
1
PI & GDP
7
26.67** 0.17 26.50** 0.17
1
PI & R
7
26.52** 1.21 25.31** 1.21
1
PI & U
8
33.30** 1.30 31.99** 1.30
1
PI & HDR
8
30.90** 2.47 28.42** 2.47
1
Note: 1. *, ** indicates 5% and 1% significance level respectively; 2. Number of lags in the tests is determined by the AIC; 3. R=0 means no co-integration, R=1 means co-integration; 4. 1 Means that the variables are co-integrated.
5.1.3 VECM
The augmented Dickey-Fuller test and the Johansen-Juselius test show both the results needed for a VEC-model. The results show that the variables are integrated of the order I(1) and there is a long-term relationship shown by the co-integration of the variables. As said before, the VECM, and
especially the error-term, shows if there is a change in the fundamental long-term value or is corrected in the short-term. Again, a bubble will show no correction in the short-term. This correction is done by the error-correction term ECM𝑡−1. The coefficient is shown in table 4 and thereby indicated if the term
is significant or not.
Table 5: Vector Error Correction Model on error-correction term
Variables Amsterdam Q42008-Q32016
ECM𝑡−1 Z-ratio P-value Obs. Chi-squared R-squared
Error Correction D(PI)
CointEq1 DQ 0,897* 1,83 0,067 24 61.14 0.88 CointEq1 DDI -0,199** 2,25 0,024 24 37.67 0.79 CointEq1 DGDP -0,089*** 3,72 0,000 24 81.42 0.89 CointEq1 DR -0,156*** 2,69 0,007 25 67.99 0.86 CointEq 1 DU 0,306 1,19 0,233 25 105.56 0.91 CointEq 1 DHDR -0,744** -2,23 0,026 22 37.28 0.86
Note: 1. *, ** and *** indicates 10%, 5% and 1% significance level respectively; 2. ECM𝑡−1 Shows the error-correction term; 3. Number of lags is the same as in the Johansen test; 4. Z-ratio and P-value show the significance level of the coefficient; 5. Chi-squared and R-squared show how well the test fits; 6. DQ stands for first difference Quantity Residential units, DDI stands for first difference Disposable Income and so on.
Equations 10-15 show the translation of the error-correction term into the VECM. Equations 10 and 14 show a positive result, which means there is a possible disturbance of the long-term equilibrium.
∆𝐷𝑃𝐼 = 𝛿0+ ∑ 𝛿08 1𝐷𝑄 + ∑ 𝜇81 1Δ𝐷𝑃𝐼𝑡−𝑗+ 0.897
𝜆
+ 𝜀𝑡 (10) ∆𝐷𝑃𝐼 = 𝛿0+ ∑ 𝛿07 1𝐷𝐷𝐼 + ∑ 𝜇71 1Δ𝐷𝑃𝐼𝑡−𝑗− 0.199𝜆
+ 𝜀𝑡 (11) ∆𝐷𝑃𝐼 = 𝛿0+ ∑ 𝛿07 1𝐷𝐺𝐷𝑃 + ∑ 𝜇71 1Δ𝐷𝑃𝐼𝑡−𝑗 − 0.089𝜆
+ 𝜀𝑡 (12) ∆𝐷𝑃𝐼 = 𝛿0+ ∑ 𝛿07 1𝐷𝑅 + ∑ 𝜇71 1Δ𝐷𝑃𝐼𝑡−𝑗− 0.156𝜆
+ 𝜀𝑡 (13) ∆𝐷𝑃𝐼 = 𝛿0+ ∑ 𝛿08 1𝐷𝑈 + ∑ 𝜇81 1Δ𝐷𝑃𝐼𝑡−𝑗+ 0.306𝜆
+ 𝜀𝑡 (14) ∆𝐷𝑃𝐼 = 𝛿 + ∑ 𝛿8 𝐷𝐻𝐷𝑅 + ∑ 𝜇8 Δ𝐷𝑃𝐼 − 0.744𝜆
+ 𝜀 (15)lower significance. Only 3 of the 4 show a relatively large coefficient. This thus means that the Mortgage rate, Disposable Income and Household Debt Ratio are the ones that can correct the price index in the short-term. So does GDP, but it is the question if the equation goes back fast enough to the equilibrium due to the small coefficient. Quantity Residential units and Unemployment both show a positive coefficient and are not, or at a low level, significant. These two outcomes could be a signs of a bubble. Because the other four are significantly negative, four of the six variables seem to correct in the short-term.
For the test to be functioning well, results shouldn’t be independent. In this test the null-hypothesis states independence and each outcome of chi-squared shows that this can be rejected. Furthermore almost all the tests show a R-squared of 0.85 or higher which means that the results are explained by 85% of the variables used. Better to see if the test is a good fit is to use the adjusted R-squared but this is not available in STATA when testing for VECM.
5.2 Lagrange-multiplier test
For an econometric model it is important that there is no serial correlation. Serial correlation, also called autocorrelation, is correlation with itself in different periods of time. If autocorrelation is the case, data is possibly distorted. So, I will be testing this using the Lagrange-multiplier test. The null-hypothesis in this test is that there is no serial correlation.
Table 6: Lagrange-multiplier test on auto-correlation
Variables Lagged Lags
Differences 1 2 PI & Q 8 0.285 0.002*** PI & DI 7 0.937 0.896 PI & GDP 7 0.525 0.827 PI & R 7 0.509 0.929 PI & U 8 0.938 0.810 PI & HDR 8 0.308 0.180
Note: 1. *, ** and *** indicates 10%, 5% and 1% significance level respectively; 2. When not significant, there is no autocorrelation.
Table 6 shows the results of the LM-test. The results show that in first differences there are no autocorrelations between the variables. In second differences there is significant proof that there is correlation between PriceIndex and Quantity Residential. This corresponds to off results in the descriptive statistics and the VEC-model. The rest of the variables seem to be well fitted.
Chapter 6 Conclusion & Discussion
In this thesis, I tried to test whether there is an ongoing housing bubble in Amsterdam. This was done by quarterly data from 2008 until 2016. This was done by a Vector Error Correction Model which tests for an error-correction term. To be able to do a VEC-Model, non-stationary, co-integrated variables are needed. To test for non-stationarity, I did an Augmented Dickey-Fuller test and checking for co-integration was done by the Johansen-Juselius test. The preliminary analysis, done by graphics and descriptive statistics, shows some evidence of a housing bubble, in the form of deviating values.
First the ADF-test was done. This results of this first test show that the variables are non-stationary in level form, non-stationary after first-differencing and are therefore integrated I(1). Because of these results, the Johansen-Juselius test can be performed. This test shows that the PriceIndex is co-integrated with all separate variables. This co-integration proofs that there is a long-term relationship between, for instance, housing price and disposable income. To see if this proven long-term
relationship is a new fundamental long-run equilibrium, or is corrected in the short-term, a VECM was done. Four of the six variables show a significant negative correction term. This thus means that the Price Index is corrected in the short-run by Disposable income, GDP, Mortgage rate and Household Debt Ratio. Those variables correct enough and seem to well-behave. The residual two show a positive or not even significant error-correction term
.
In contrast to the four well-behaving variables, these two won’t correct and therefore it is possible that the Price Index shows unusual movements resulting in a bubble. So, to conclude it’s quite hard to make a statement whether there is a bubble or not. On the one side. You can say there are no signs of a bubble, while on the other side you can say there is high probability of a bubble because at least two variables do not correct.
That is also one of the first points of discussion. If at least two variables show possible bubble movements, then how much more variables show this same deviating behavior? At this point, it looks like the market is compensated by the other four variables. But would there also be more
compensating than decompensating variables if all influencing variables are used? One of these missing variables is Household Disposable income. These values were not available for me. I think that this is an important variable because a lot of homebuyers in Amsterdam are couples who work both, in other words households. For further research this should be included.
Another difficulty about this thesis is that it is a research about a demographic specific area. This is because of two reasons. Amsterdam data came from all areas of Amsterdam, so including neighborhoods outside the ring like: Amsterdam New-West and Southeast. These areas show much less alarming housing prices and are included in the testing. This could also result in a deviation in the results. Additional to this is that not all data is available pure for Amsterdam or this data is only given annually. Input like GDP and Mortgage rate is data which accounts for all the Netherlands and not
may result in distorted input. The Quantity Residential for sale could produce additional distorted input. As said before, the descriptive statistics show large deviations between maximum and
minimum, while this movement cannot be seen in the Price Index. This should be taken into account if there would be further research.