**Master’s Thesis - May 15**

^{th}

### , 2017

**Thomas Fiskerstrand** **Sondre Riise Kjelstrup**

**MSc. Finance & Investments**

Supervisor: Jørgen Bo Andersen
### Are we currently experiencing a bubble in the Norwegian housing market?

### Copenhagen Business School

### Abstract

The Norwegian housing market has experienced an extreme growth in prices between 1990-2017.

With this growth in mind, and the great amount of attention the topic receives from both the media and the general public, the Norwegian housing market has become a favorite among experts with regards to predicting and explaining current and future developments. Our goal with this master’s thesis is to investigate whether the recent price development can be supported by fundamental factors. Simply stated, are we currently experiencing a bubble in the Norwegian housing market?

For our thesis, we have chosen to use previously made housing price models to conduct a comparative empirical analysis of the housing price development. The models we have chosen to use are the Hodrick- Prescott Filter (HP filter), the Price-to-Rent ratio and Tobin’s Q. For all these models we have also compared our results with Denmark and Sweden to be able to better explain if the development in Norway is abnormal. We also re-estimated the widely-used Jacobsen & Naug model to investigate if it still explains the development in prices and how the many variables have changed in terms of how they affect housing prices. All these housing price models include specific fundamental factors both on the supply and demand side of housing. The magnitude of these fundamental factors are further analyzed to investigate the underlying factors of the housing price development.

Interestingly enough, all housing price models except for the HP filter applied on Norway, point to bubble tendencies in the Norwegian housing market. This is also concluded from Case & Schiller’s seven criteria for a housing bubble at the end of our thesis. However, when investigating the fundamental factors on both the supply and demand side of the housing market the price growth is supported. This is mostly led by a record low key rate, the large deviation between supply and demand in housing, a low and stable unemployment rate, steadily increased disposable income, population growth and positive expectations about future housing prices. With that said, while housing prices have increased, the debt burden among the general public has also continued to increase, making politicians extremely weary of the situation. This is shown by the recent regulations the government has put on the banks’ lending policies. In conclusion, our investigation for this master’s thesis leads us to believe that there is currently no bubble in the Norwegian housing market.

**Table of Contents **

**1. ** **Introduction... 5 **

1.1. Motivation ... 5

1.2. Problem Statement ... 6

1.3. Methodology ... 7

1.4. Delimitation ... 7

1.5. Data ... 8

1.6. Thesis Structure ... 9

**2. ** **Historical Development of the Norwegian Housing Market... 10 **

**3. ** **Bubble Theory ... 14 **

3.1. Case & Shiller’s Market Characteristics ... 15

3.2. Euphoric and Non-Euphoric Bubbles ... 16

**4. ** **Supply and Demand in the Housing Market ... 18 **

4.1. Supply and Demand Theory ... 18

4.2. Supply and Demand in the Housing Market ... 18

4.2.1. Supply ... 19

4.2.2. Demand ... 22

**5. ** **Comparative Empirical Analysis ... 27 **

5.1. Hodrick-Prescott Filter ... 27

5.1.1. Limitations ... 28

5.1.2. Empirical Testing ... 29

5.1.3. Comparison ... 32

5.2. Price-to-Rent Ratio ... 37

5.2.1. Assumptions ... 41

5.2.2. Data Material ... 42

5.2.3. Empirical Testing ... 43

5.2.4. Fundamental vs. Real P/R Ratio ... 45

5.2.5. Limitations ... 47

5.2.6. Comparison ... 47

5.2.8. Empirical Testing – Sweden ... 49

5.3. Tobin’s Q ... 52

5.3.1. Marginal and Average Q ... 53

5.3.2. Tobin’s Q and the Housing Market ... 54

5.3.3. Limitations ... 55

5.3.4. Data ... 56

5.3.5. Empirical Testing ... 57

5.3.6. Comparison - Denmark ... 59

5.4. Conclusion ... 61

**6. ** **House Price Models ... 62 **

6.1. MODAG ... 62

6.2. Jacobsen and Naug ... 63

6.2.1. Weaknesses and Discussion ... 66

**7. ** **Fundamental Analysis of Supply Side ... 68 **

7.1. New builds ... 68

7.2. Building costs ... 71

7.3. Cost of land ... 73

7.4. Bank Regulations ... 75

7.4.1. Collateral in real estate ... 75

7.4.2. Loan-to-value ratio ... 75

7.4.3. Interest rate increases and Interest-only mortgages ... 76

7.5. Conclusion ... 77

**8. ** **Fundamental Analysis of Demand Side ... 78 **

8.1. Disposable income ... 78

8.2. Unemployment ... 80

8.3. Interest Rate ... 81

8.4. Population growth ... 83

8.5. Demographics ... 84

8.6. Housing Taxation ... 86

8.6.1. Tax on Housing Capital ... 86

8.6.2. Property Taxes ... 87

8.6.3. Tax Deductions on Interest Expenses ... 87

8.6.4. Tax on Sale Profit ... 87

8.6.5. Tax on Rental Income ... 88

8.7. Expectations ... 88

8.8. Conclusion ... 90

**9. ** **Correlation Analysis ... 91 **

9.1. Analysis ... 91

**10. ** **Re-estimation of the Jacobsen and Naug model ... 94 **

10.1. Expectation Variable ... 94

10.2. Re-estimation of Jacobsen and Naug model ... 98

10.3. Testing the model ... 100

10.3.1. Testing for Stationarity ... 101

10.3.2. Testing for Autocorrelation ... 104

10.4. Interpretation of the Coefficients ... 106

10.5. Discussion of model ... 108

10.6. Conclusion ... 111

**11. ** **Case and Schiller’s Seven Criteria for a Housing Bubble ... 112 **

11.1. See housing as an investment ... 112

11.2. Widespread agreement of an increase in prices ... 113

11.3. Exaggerated expectations, excitement and word of mouth ... 113

11.4. Sense of urgency in buying a home ... 113

11.5. Simple or simplistic theories ... 114

11.6. The occurrences of sales above asking prices ... 114

11.7. Perception of risk ... 115

11.8. Conclusion ... 116

**12. ** **What do the Experts and Professionals Say? ... 117 **

**13. ** **Conclusion ... 119 **

**14. ** **References ... 121 **

**15. ** **Appendix A ... 133 **

### 1. Introduction

Since the beginning of the 1990’s, housing prices in Norway have increased by 500% (Holberggrafene, 2017). In this 25-year timespan we have experienced a continuous increase in the housing market, only stagnated by minor corrections. Last time we saw a similar growth pattern was in the early 80’s, which resulted in a major crash. With this in mind many experts and professionals are debating whether the growth we are experiencing now can backed up by fundamental factors, or if we are experiencing a housing bubble that is ripe to burst.

The development of housing prices is a hot topic for the media, analysts as well as the people in general.

The reason for this is fairly obvious. It is said that around 95% of the population in Norway will some time in their life own their own dwelling (Eiendom Norge, 2013). Since the purchase of a dwelling is most likely the largest investment one will make, it is understandable that the housing market receives so much attention. It is almost viewed as a human right to own your own dwelling in Norway, and therefore the governing body in Norway will do what they can to keep it as attractive as possible to own your own dwelling. With 82% of the population over 16 years old owning a dwelling, Norway is amongst the very top in the world (SSB, 2016a). However, although the Norwegian government continues to upkeep the benefits, there are many regulations one must overcome before even being able to purchase a dwelling, making the market very stable compared to other countries. Considering all these aspects and the importance of a well-functioning housing market, this lays the foundation for an extremely interesting thesis for us.

### 1.1. Motivation

Our master thesis is a long investigation about the current market conditions for housing in Norway.

This is a topic that has received more and more attention in recent years as many people believe what we are experiencing now in housing prices cannot be fundamentally backed up.

Our motivation with this master thesis is to use the tools we have available and what we have learned through our master’s degree to give analytic and descriptive feedback regarding our topic. We will also use previously made models and try to use the data we have available today to see if they are still

applicable for today’s market conditions. Also, we wish to investigate the different driver’s effect on housing prices and how this has changed.

Both of us are students who are just about to start new jobs in Oslo. Therefore, the process and findings of this master thesis will to a large degree affect us in the near future as we are both planning to purchase an apartment. This clearly creates an even larger motivation for us to find out if we are planning to buy at a price peak, or if we can safely invest our money in housing for the years to come.

### 1.2. Problem Statement

As stated in the beginning of this section, Norway has experienced a continuous growth in housing prices the last 25 years. It seems as if the longer this development continuous the more people are going to write, discuss and analyze whether we are experiencing a housing bubble or not. This can to some extent become a self-fulfilling prophecy as they will only continue to state this until one day housing prices will decrease for a longer period. Our goal is therefore to investigate if these statements about today’s housing market are accurate. This has led us to the following problem statement:

*“Are we currently experiencing a bubble in the Norwegian housing market?” *

To be able to reach the conclusion of this problem statement we will answer other sub-questions throughout the thesis:

➢ Is the housing price level and development unique for Norway when looking at other comparable countries?

➢ Is it possible for the fundamental factors on the supply and demand side of the housing market to explain the recent price growth?

➢ Can previously made housing price models precisely predict and explain the current market situation?

### 1.3. Methodology

In this thesis, we have mostly used a quantitative research approach. Quantitative research is an approach for testing objective theories by examining the relationship among variables (Creswell, 2014). However, in the fundamental analysis we utilize a mixed approach. In a mixed approach, a mix between qualitative and quantitative research design is used. We will use quantitative research data, but analyze it in a more qualitative way where we make interpretations of the meaning of the data. The worldview and framework for conducting the thesis stems from a post-positivistic approach. By worldview, we mean the basic set of beliefs that guide action. A post-positivistic approach assumes an objective reality, but the absolute truth about it can never be found. Evidence from research is always imperfect and fallible. Thus, we never confirm a hypothesis, we can only reject (or fail to reject) the alternative hypothesis. Being objective is another key assumption of this approach. Validity and reliability in the data is therefore of high importance. We have a deductive approach to our analysis, where we have specific theories that we want to test with the collected data in order to test our hypothesis about the Norwegian market. This thesis does not seek to create new theories or models, but more to analyze and discuss the possibility of a housing bubble in Norway, and the drivers behind the increase. We therefore have a descriptive approach in this thesis, where we seek to describe more than explain.

### 1.4. Delimitation

The Norwegian housing market can be considered very regional. This is to a large extent because of the extreme urbanization in Norway. Areas with large cities will in general experience a higher volatility in housing prices than rural areas. Also, if one region is highly correlated with an industry it will be more affected here than other areas. For our master thesis, we have chosen to look at the housing market as one. We will refer to certain regional examples, however the overall thesis will focus on Norway as one housing market. This is also true for dwelling types, when referring to “housing” and “house” it will entail houses, apartments, and other residences. Both these assumptions are indeed a simplified version of reality; however, we believe that it will not affect our final conclusion.

The time horizon we have chosen to focus on is primarily from 1980 until today. In the historical section, we will go further back, as this is only to get a picture of the historical development. However, all

analysis will be conducted using data from at the latest 1980. This is true for Norway and for the other comparative countries. For the comparable countries data availability has set the frame for how far back we could go.

The latest collected data we have chosen to include dates back to May 1^{st}, 2017. All data and articles
published beyond this date have not been considered.

### 1.5. Data

The statistical and theoretical background for this thesis is based on secondary data. Our topic is a common subject for articles, theses and literature. The Financial Crisis of 2007 that erupted due to a housing bubble in the United States sparked even more discussion and published research on the topic.

Not only does this make it easier to find information and data, but also to find good and reliable data.

Using primary data would in this case neither be possible nor feasible, as we are not able to get better and more reliable data than what a large and well-known organization can. As we have used data from renowned statistics banks and researchers for our statistical tests, it makes us confident that our data has both high validity and reliability.

A weakness that comes from the plethora of articles and sources on our topic of interest is that it becomes harder to differentiate the reliable sources from the unreliable ones. We have therefore chosen to stick to well-known authorities on the subject for the theoretical foundation, as well as the dataset for the re- estimation. Most of the data used for our analyses is gathered from well-known statistical databases such as Statistics Norway (SSB), Statistics Sweden (SCB), Statistics Denmark (DST), Husbanken and the Norwegian Central Bank (NCB). Using these sources, we get stronger and more reliable results from our tests. We also back up our results and discussion with comments and thoughts from leading industry experts, including analysts, real estate agents and economists. This helps us see the current situation from multiple angles, as their different backgrounds makes them see the situation with different eyes.

For the re-estimation of Jacobsen and Naug’s house price model, we got the updated time series directly from Bjørn E. Naug himself (Naug, 2017). In the email, he also told us that some of the time series’ have

been revised since Jacobsen and Naug did their analysis back in 2004, so we will not be able to replicate their results. Getting data directly from NCB and Bjørn E. Naug strengthens our analysis, and it also helps us avoid mistakes that can happen when transforming or changing data to make it fit to a specific model or time period.

The Norwegian house price index has been gathered from NCB, and thus is the most reliable measure of the historic price development in Norway. In order to find the real house price development, we deflate it with the consumer price index (CPI), also downloaded from NCB.

In order to see the Norwegian market in comparison with other markets, we have chosen to compare some key figures with other markets. Due to the differences in the housing markets across borders the most relatable countries are the other Scandinavian countries, Sweden and Denmark. These countries are similar to Norway in population, culture, tax structure and the credit market. This way we can get a good indication to whether the Norwegian house price development is abnormal compared to relatable markets.

### 1.6. Thesis Structure

The structure of this thesis is build up by four distinct sections. First, we will take the reader through the historical development of the Norwegian housing market. From this we will introduce the theories behind market bubbles, as well as the macroeconomic theory behind supply and demand in the housing market. Second, we will conduct an empirical comparative analysis using three well-known housing price models. Each model is explained in detail before the empirical test is conducted. Third, we will investigate many of the fundamental factors on both the supply and demand side of housing which are used in the various housing price models. From this we will look at how each of these fundamental factors can affect the housing market. In this section, we will also see how the fundamental factors in Jacobsen and Naug’s model have changed. In the end, we will tie all conclusions from the conducted analyzes together and interpret the results as well as state our final conclusion.

### 2. Historical Development of the Norwegian Housing Market

To understand the different aspects of today’s market, we believe it is helpful to analyze the historical context. By looking at the Norwegian housing market from a historical point of view, we seek to identify both normal and abnormal periods. Using data from the NCB we can analyze the real prices from the time the first prices were recorded by the NCB in 1819, all the way up until 2015. As the NCB has not published the CPI for 2016, we cannot calculate the real house price for 2016. Comparing past situations to the one we have today is believed to make our conclusions stronger, as we have a historical perspective and backing behind our conclusions.

At the end of the 19th century, Oslo (at the time called Kristiania) experienced a population-boom as more and more people moved to the capital in order to gain from the higher wages in the city. All these new inhabitants needed housing, which resulted in an overestimated building-boom. After a few years this led to over 5000 empty dwellings in the capital. Deregulation in the lending market coupled with a massive demand for housing and mortgages resulted in no less than six new banks in 1897 alone. These banks specialized in mortgages with stocks as security and loans to construction firms, and they offered their clients liberal conditions. The rapid growth soon turned to speculation, which led to a bubble that burst on June 11th, 1899. All six banks went bankrupt in the years following the crash. The stock market crash had a direct impact on the housing market as a lot of the mortgages were directly tied to the stock market (Søbye, 2000). After 5 years, the market was again back to more normal price levels, but it would take almost 100 years before the real price of houses again returned to the level it was in 1899, which is found in figure 1.1. Real prices are nominal prices adjusted for inflation, which is done to make house prices comparable over time.

As the First World War came to an end, the Norwegian market experienced a boom in demand for consumer goods. Suppliers were not able to meet the new level of demand, which resulted in a massive price increase, high inflation, trade deficits, currency depreciation and an overheated economy (Grytten, 2002).

Figure 1.1

*Source: NCB 2017; Own calculations *

The Great Depression hit Norway harder than most countries. As a small open economy, it was affected more heavily by changes in trading partners, especially Great Britain and Sweden (Grytten, 2002). The opposite monetary policies introduced during the war and right before the Great Depression also made the situation worse. High inflation coupled with a banking crisis that led to a shortage in mortgages, caused a drop in the price growth for the housing market.

After World War II, the housing market stabilized and saw little growth in real prices. Structural changes to the credit market, more generous lending policies and a less regulated housing market all contributed to a tremendous rise in housing prices during the 1980's. In order to control the credit expansion, stricter regulations were introduced at the beginning of 1986. A drop in the oil price and an increased key rate led to a notable drop in housing prices, resulting in heavy losses for the banks. The stock market also went through a recession at that time, making the situation even worse. After the bubble burst and Norway went into a recession, housing prices decreased until it reached the bottom in 1992 (Torsvik, 1999).

0 50 100 150 200 250 300 350

1819 1824 1829 1834 1839 1844 1849 1854 1859 1864 1869 1874 1879 1884 1889 1894 1899 1904 1909 1914 1919 1924 1929 1934 1939 1944 1949 1954 1959 1964 1969 1974 1979 1984 1989 1994 1999 2004 2009 2014

### Real house price index

The growth in the real estate market has been outstanding ever since prices started increasing again in 1992. The Financial Crisis only put a slight stop to the phenomenal growth in prices, and even though the government has tried to regulate the market and experts have said every year that the growth is going to stop, 2016 saw the largest growth yet with over 12.3% increase in total, and a 24% increase in Oslo.

The only region that seems to be heavily affected by the low oil prices is Stavanger, the oil capital of Norway.

Figure 1.2

*Source: NCB 2017 (2015 prices); Own calculations *

The largest cities in Norway the last 200 years have experienced different development in prices, this can be seen in figure 1.2 above. Oslo has throughout the period had the highest price per square meter, and the Kristiania Crisis is clearly visible with the peak in 1899. For Oslo, it took 106 years before prices per square meter again rose above the real prices in 1899. After 1950 it seems like the cities started to have more similar developments, and that they more started following the same trends. During the late 70’s the price difference per square meter between the different cities decreased, giving more similar price levels. This was mainly caused by an increase in prices in Bergen, Trondheim and Kristiansand.

0 10000 20000 30000 40000 50000 60000

1819 1824 1829 1834 1839 1844 1849 1854 1859 1864 1869 1874 1879 1884 1889 1894 1899 1904 1909 1914 1919 1924 1929 1934 1939 1944 1949 1954 1959 1964 1969 1974 1979 1984 1989 1994 1999 2004 2009 2014

### Real price per square meter

Oslo Bergen Trondheim Kristiansand

Comparing the average square meter price of Oslo to the average square meter price of Bergen, Trondheim and Kristiansand, the gap becomes evident. From 1992 to 2005 the average difference was about 6,044 NOK, while from 2006 until 2015 it became more than twice that, about 12,329 NOK.

Kristiansand, being geographically close to Stavanger, felt the repercussions from the oil crisis that hit Stavanger hard, and therefore experienced a fall in real prices in 2014/2015.

The incredible growth in prices has made it lucrative for existing house owners, while young people looking to establish themselves in the market have experienced greater and greater difficulties. With housing prices, both in real and absolute terms being the highest they have ever been, the debate is raging whether these high prices can be explained by fundamental factors in the economy and whether the price level is sustainable. Will we continue to see record-breaking growth, or will we experience a bursting bubble? History has shown us that periods of high growth most often are followed by periods of declining prices.

### 3. Bubble Theory

Defining a financial market situation as a "bubble" has no clear and unified definition. One definition that is used by this thesis and other analyses is the one put forward by Stiglitz (1990):

*"If the price is high today only because investors believe the selling price will be high tomorrow, when *
*the fundamental factors do not seem to justify such a price, then a bubble exists." (Stiglitz, p. 13, 1990) *

Following the theoretical foundation of Grytten (2009), a housing bubble, or any speculative bubble, can be expressed like this:

Equation 3.1

𝑏𝑡 = ( 1

1 + 𝑟) 𝐸𝑡(𝑏_{𝑡+1})

𝑏_{𝑡} is the value of the bubble, t is time, 𝐸_{𝑡} is expectations and r is the expected rate of return.

The equilibrium condition in a financial market can be written as:

Equation 3.2

𝑝𝑡 = ( 1

1 + 𝑟) 𝐸𝑡(𝑑𝑡+1+ 𝑝_{(𝑡+1)})

This expression shows that price p for period t equals expected E rate of return d plus expected price on the financial object in the next period t+1, discounted with the required rate of return r.

Over time, the price on the financial object will accumulate in line with this expression:

Equation 3.3

𝑝𝑡 = ∑ ( 1 1 + 𝑟)

𝑗

𝐸𝑡(𝑑_{𝑡}+ 1) + ( 1
1 + 𝑟)

𝑛

𝐸𝑡(𝑝𝑡+𝑛)

𝑛

The first part of the equation is the sum of discounted expected return for the entire period, while the other part of the equation shows the expected price at the end of the period.

Present value of the price on the financial object will therefore be:

Equation 3.4

𝑝𝑡 = ∑ ( 1 1 + 𝑟)

𝑗

𝐸𝑡 (𝑑𝑡+1) + 𝑏_{𝑡}

𝑛

𝑗=1

𝑏𝑡 is a stochastic process satisfying equation 3.1. We get the following equation explaining the value of a bubble by rearranging equation 3.4:

Equation 3.5

bt= 𝑝𝑡− ∑ ( 1 1 + r)

j

Et (dt+j)

∞

𝑗=1

Through equation 3.5 we see that the value of a bubble is the asset’s market price minus the discounted sum of future returns, or the assets fundamental value. If the fundamental value is less than the market price of the asset, there is a positive bubble value. As both the annual return on housing and the capital gain in previous periods are unknown sizes, the fundamental value is a relative theoretical term that has to be estimated. Comparing market value with the fundamental value is a common theme in bubble theory. This will therefore be tested in several ways throughout this thesis.

### 3.1. Case & Shiller’s Market Characteristics

A bubble most often refers to a situation where public expectations of a future increase in price causes the price to be temporarily and artificially high. With housing bubbles, people tend to spend more and save less, as they believe they will be duly compensated by the expected price increase in the future.

They see their investment in real estate as a way of saving, as the price increase in itself is considered saving.

Case & Shiller (2004) use seven market characteristics to analyze whether a housing bubble is present.

These characteristics are based on surveys they performed in 1988 and 2003. Seeing as these characteristics predicted both the bubble at the end of the 1980's and the Financial Crisis, we see them as useful indicators for predicting bubbles. Case and Shiller’s characteristics are:

• People see housing as an investment

• Widespread agreement of continuing rise in prices

• Exaggerated Expectations, Excitement, and Word of Mouth

• Sense of urgency in buying a home

• Simple (or simplistic) theories

• The occurrence of sales above asking prices

• Perception of risk

### 3.2. Euphoric and Non-Euphoric Bubbles

Grytten differentiates between two main types of bubbles: euphoric and non-euphoric bubbles. Euphoric bubbles are closely related to the seven characteristics, as these bubbles are driven by psychological factors in the market. The market participants believe that the prices will increase and therefore they are willing to spend more in order to enter the market. Non-euphoric bubbles are driven by fundamental factors, but the growth is not stable in the long run. The Kristiania Crisis is for example best described as a non-euphoric crisis. People back then used many of the same factors that are being used today in order to explain the price increase; urbanization, housing demand and increased income. Still the market crashed hard, and it took a long time for it to fully recover. Grytten also points at four factors that can help explain the recent increase in prices, but that are not stable in the long run:

• Not enough building

• Strong pressure from work immigration

• Low interest rate

*"I believe this is a long-lasting state of emergency, and therefore people see this as the new normal. But *
*I don't think this is normal." – Ola H. Grytten (Dagens Næringsliv, 2016a). *

Speculation is often a clear indication of a bubble. When people buy to invest and not to live, it causes prices to increase even further. This also attracts investors with more money than those looking for a place to live, which in turn intensifies the competition for the more affordable dwellings. As the market in Oslo is the one that has experienced the most extreme increase, the Norwegian government has tried to stop these speculative investors by introducing new (temporary) regulations. Until June 2018, there is a 40% equity demand when buying a second dwelling in Oslo, and banks have a lot less freedom to give loans above 5 times total debt ratio (Regjeringen, 2016).

### 4. Supply and Demand in the Housing Market

In this section, we will investigate the supply and demand theory of the housing market, which ultimately lays down the basis of how housing prices are determined in theory. It is important to distinguish between the short and the long-run when looking at the supply in the housing market, therefore we will present both situations and how the equilibrium is found. By using the theoretical procedure set by Jacobsen and Naug (2004) and Hendry (1984) in their articles, we will be able to shed light upon some of the explanatory factors within the supply and demand theory in housing.

### 4.1. Supply and Demand Theory

The law of supply and demand is a fundamental economic principle that applies to all products. The principle states that, holding all else equal, if the supply of a product increases, the price will decrease.

If the supply of a product decreases, the price will increase. Alternatively, if the demand of a product increases, the price will increase. If the demand of a product decreases, the price will decrease.

### 4.2. Supply and Demand in the Housing Market

With regards to the housing market the supply is the housing stock available and the demand is the consumers who are looking to buy. The supply can be considered relatively flat, or fixed, in the short- run, as it takes time for new builds to be completed and the amount of construction per year is low considering the total housing supply. The supply could therefore be considered inelastic in the short-run.

An oversupply in housing would result in what is called a “buyer’s market”, as the buyers will have many objects to choose from, which will ultimately drive prices down. An undersupply in housing would alternatively result in a “seller’s market”, where the supply of housing is scarce and the consumers fight to “win” each object available. This would result in a price increase.

The demand is continuously changing to the consumer’s preferences, which makes the demand elastic.

A large increase or decrease in the consumer’s demand will therefore affect housing prices quickly and drastically. Consequently, in the short-run, housing prices fluctuate with the demand. In the medium to long-run, is it assumed that the supply will adapt to the demand, reaching its equilibrium.

### 4.2.1. Supply

The supply within the housing market consists of two factors, (1) depopulation, demolition or renovation and (2) new builds. These two factors can be considered the total housing supply. New builds only comprise of about one percent of the total housing mass available each year and therefore have a very little effect of the supply curve in the short-run (NOU, 2002). New builds take time to complete mainly because of all the preparation that comes into play for the build to start. The more tangible aspects are for example land acquisition, workforce, materials, machines and tools, but also more importantly is the bureaucracy aspect which includes city council approval to build and other regulations. Because of all these factors the supply is generally deemed fixed in the short-run, or in other words perfectly inelastic.

However, in the very long-run we can assume that real estate developers will adapt to the demand of the market and supply what is needed, therefore in this time horizon we can assume the supply is perfectly elastic. Worth mentioning is that vacant land in the big cities is scarce and in rural areas less so, but still not infinite, therefore this assumption of perfect elasticity is not theoretically sound.

Figure 4.1 Figure 4.2

Short-run equilibrium Long-run equilibrium

*Source: Own creation * * Source: Own creation*

As written above, the housing supply can be viewed in the short-run and in the long-run. To describe the housing supply both in the short and long-run we can use Hendry’s model (Hendry, 1984).

Equation 4.1

𝐻_{𝑡} = (1 − 𝛿_{𝑡})𝐻_{𝑡−1}+ 𝑐_{𝑡}

Where,

𝐻𝑡 = Housing supply, period t

𝛿 = Depreciation rate of present housing supply 𝐻𝑡−1 = Housing supply, period t-1

𝑐_{𝑡} = Number of new builds, period t

As we can see from equation 4.1, the housing supply is described as the housing supply in the previous
period 𝐻_{𝑡−1}, adjusted for the depreciation (1 − 𝛿_{𝑡})𝐻_{𝑡} and the number of new builds 𝑐_{𝑡}. As concluded
by Hendry, since 𝑐_{𝑡} is small relative to the total housing supply, it is assumed that the housing supply is
fixed in the short-run. In other words, the housing supply is constant to the previous period 𝐻𝑡−1

(Rødseth, 1987).

### 4.2.1.1. Supply in the Short-run (Short-run equilibrium)

With regards to what is written above, by definition, in a perfect market the equilibrium price for housing
is found where the supply and demand curve intersect. Therefore, in the short-run when the supply curve
is completely inelastic, the price is adjusted by changes in the demand. In figure 4.3, we can see how the
supply is fixed in the short-run at point 𝐻_{𝑡−1}. The demand curve, defined as 𝐷_{1}, intersects with 𝐻_{𝑡−1} and
creates an equilibrium price at 𝑃_{1}. As the price is only subject to change from the demand in the short-
run, we can see that a shock where demand goes to 𝐷_{2}, makes the new equilibrium price go up to 𝑃_{2}.
Here it is easy to see that any change to the demand, either up or down, will have large effects in the
short-run.

Figure 4.3

*Source: Own creation *

### 4.2.1.2. Supply in the Long-run (Long-run equilibrium)

Following an increase in demand for housing, it is natural to assume that real estate developers will supply more housing for the market, as the market is willing to pay more for each unit. Therefore, within the medium- to long-run, new supply has been released to the market. Over the long-run horizon, one could assume the supply to be fully elastic and horizontal. According to Hendry, the long-run equilibrium could therefore correspond to a steady state in which real estate developers are earning normal profits and new builds exactly match the depreciation in the housing supply (Hendry, 1984). As the supply curve is horizontal, any price increase within the housing market will correspond to the inflation, holding all else equal.

As seen in figure 4.4, the price, 𝑃^{∗}, stays constant because the supply curve, 𝑆_{𝐿𝑅}, is horizontal in the
long-run. This is shown as the demand, 𝐷_{1}, moves to 𝐷_{2}. The price stays the same.

Figure 4.4

*Source: Own creation *

### 4.2.2. Demand

As written many times above, in the short-run the demand in the market will always be the main reason for price movements for housing. In the following section, we will use Jacobsen and Naug’s aggregate demand model to explain the demand side of the housing market.

First, it is important to distinguish between the two types of demand as explained by Jacobsen and Naug (Jacobsen & Naug, 2004).

1) Household demand for owner-occupied housing, i.e. demand for housing with the intention to live in.

2) Demand for housing as a pure investment instrument, i.e. demand where the sole goal is future capital gains either in the form of rent or by realized gain by sale.

We can assume that the first group is much larger than the second, and therefore it is the main focus both for Jacobsen and Naug’s article and our thesis. (Jacobsen & Naug, 2004).

The aggregate demand function is as follows,

Equation 4.2

𝐻^{𝐷} = 𝑓(𝑉
𝑃, 𝑉

𝐻𝐿, 𝑌, 𝑋)

𝑓_{1} < 0, 𝑓_{2} < 0, 𝑓_{3} > 0,
where

𝐻^{𝐷} = Housing demand

*V * = Total housing costs for the general owner

*P * = Index of prices for goods and services other than housing
*HL * = Total housing costs for a general tenant (rent)

*Y * = Households’ real disposable income

*X * = Vector of other fundamentals that affect housing demand
𝑓𝑖 = The derivative of 𝑓(*) with respect to agreement i

From equation 4.2 we can conclude that the demand for group number one will increase if income increases and will decrease if housing costs of ownership increase in relation to house rents or prices.

According to Jacobsen & Naug, “the vector X represents various observable variables which capture
*the effects of demographic conditions, banks’ lending policies and household expectations concerning *
*future income and housing costs” (Jacobsen & Naug, p. 31, 2004). This vector will be further explained *
later in this section.

The next equation explains the housing cost for a dwelling owner. “The housing cost measures the value
*of goods in which the owner relinquishes by owning and living in his own dwelling” (Jacobsen & Naug, *
p. 31, 2004).

The real housing price for owners (𝑉/𝑃) may be defined as:

Equation 4.3

𝑉 𝑃≡𝑃𝐻

𝑃 𝐵𝐾 =𝑃𝐻

𝑃 [𝑖(1 − 𝜏) − 𝐸𝜋 − (𝐸𝜋^{𝑃𝐻} − 𝐸𝜋)]

where

*BK * = Housing cost per real krone (NOK) invested in a dwelling
*PH * = Price for an average dwelling (in NOK)

𝑖 = Nominal interest rate

𝜏 = Marginal tax rate on capital income and expenses

𝐸𝜋 = Expected inflation (expected rise in P and HL, measured as a rate)
𝐸𝜋^{𝑃𝐻} = Expected rise in PH (measured as a rate)

The first expression in the bracket [𝑖(1 − 𝜏) − 𝐸𝜋] shows the real after-tax interest rate. In other words,
this is the direct cost of a mortgage. Jacobsen and Naug explains it as follows, “It measures the real
*interest costs associated with a housing loan and the real interest income lost by investing in a house” *

(Jacobsen & Naug, p. 31, 2004). From this we can see that an increase in the real interest rate will both
increase the interest cost and the return when money is deposited in the bank, which ultimately increases
the cost of living and decreases the demand. The second expression in the bracket [𝜋^{𝑃𝐻} − 𝐸𝜋] shows
the expected real dwelling price growth. If this expression increases, the real housing costs will fall and
conclusively the expected dwelling wealth will increase. From this one can say that relatively speaking,
it will become more beneficial to own a dwelling than renting, and demand for housing increases. To
sum equation 4.3 up, it shows the difference between the real interest rate after tax and the real price
increase for housing. Jacobsen and Naug further simplify equation 4.3 into the following equation:

Equation 4.3*

𝑉 𝑃=𝑃𝐻

𝑃 𝐵𝐾 =𝑃𝐻

𝑃 [𝑖(1 − 𝜏) − 𝐸𝜋^{𝑃𝐻}]

Looking back at equation 4.3 once again, Jacobsen and Naug have also created a function for the variable
*Y, which represent the real disposable income. The equation for Y is as follows: *

Equation 4.4

𝑌 = 𝑌𝑁

𝑃^{𝑎1}𝐻𝐿^{𝑎2}𝑃𝐻^{𝑎3}

𝑎_{1}+ 𝑎_{2}+ 𝑎_{3} = 1, 𝑎_{1} < 𝛽_{1}, 𝑎_{2} < 𝛽_{2},

where

*YN * = Nominal disposable income

From observing equation 4.4, we can see that there are three factors in the denominator that will reduce the purchasing power of households and conclusively the demand. These factors are as mentioned;

*P * = Index of prices for goods and services other than housing
*HL * = Total housing costs for a typical tenant (rent)

*PH * = Price for an average dwelling (in NOK)

The last term of the aggregate demand function 4.2 of Jacobsen and Naug is the variable *X. As stated *
above the vector *X represents various observable variables which capture the effects of demographic *
conditions. Jacobsen and Naug show to examples such as migrations patterns, population size and strong
urbanization, as significant demographic factors which can increase the demand for housing (Jacobsen

& Naug, 2004). One of the most powerful explanatory factors in the variable *X explains the impact of *
the banks’ lending policies. As most dwelling purchases are financed through mortgages the availability
of credit for the consumer will without doubt affect the demand. Especially in Norway, where in 2016
the Financial Supervisory Authority of Norway (FSAN) presented numbers which stated that Norway
had a ratio of household debt to disposable income of 297% (FSAN, 2016a). As concluded previously,
lower interest rates will affect the housing demand in a positive way. Since the bank’s credit offerings
can have such an impact on the housing market, Jacobsen and Naug created a function for this factor as
well.

The banks credit offerings to households (𝐿^{2}) is as follows:

Equation 4.5

𝐿𝑠 = ℎ [𝑂, 𝑅𝐸𝐺, 𝑌, 𝑈,𝑃𝐻 𝑃 ]

ℎ_{1} > 0, ℎ_{2}< 0, ℎ_{3}> 0, ℎ_{4}< 0, ℎ_{5} > 0,
where

𝐿_{𝑠} = Bank’s supply of credit to households
𝑂 = Bank’s profitability

𝑅𝐸𝐺 = Measure of government regulation of bank lending

𝑈 = Unemployment rate

ℎ𝑖 = The derivative of h(*) with respect to argument 𝑖

From observing equation 4.5 we can see that the bank’s credit offering will decline with stricter regulations, if the bank’s profitability decreases, and if there is an increase of unemployment. An increase in unemployment will ultimately decrease the expectation of future income and solvency.

### 5. Comparative Empirical Analysis

In this section, we will use well-known models such as the Hodrick-Prescott filter, Price-to-Rent ratio, and Tobin’s Q to investigate the current development in housing prices in Norway. Using these results, we will be able to better conclude whether the Norwegian housing market is in fact facing a housing bubble or not. Also, to gain a better understanding of the Norwegian housing market we will look at Sweden and Denmark to compare our results. This is to further conclude if there are any abnormalities in the price development.

### 5.1. Hodrick-Prescott Filter

The Hodrick-Prescott filter (HP filter) was first proposed by E.T. Whittaker in 1923, however it was
further developed by Hodrick and Prescott in the 1980’s (Hodrick & Prescott, 1981). It quickly became
a popular tool in the field of economics and is for example used by the Norwegian government and NCB
(NCB, 2013). The HP filter is a mathematical tool used to remove the cyclical component of a time series
from the raw data (Hodrick & Prescott, 1997). In a memo written by NCB they explain the use of the
HP filter as follows, “the basic idea is that when the deviation between the indicator and trend is large
*i.e. the cycle is high, this may signal a financial crisis a few years ahead and should therefore trigger a *
*response from policymakers to increase banks’ resilience to adverse shocks” (NCB, p. 2, 2013). *

We assume that the original series 𝑦_{𝑡} is composed of a trend component (𝜏_{𝑡}) and a cyclical component
(𝑐_{𝑡}). This is presented in equation 5.1:

Equation 5.1

𝑦_{𝑡} = 𝜏_{𝑡}+ 𝑐_{𝑡}, 𝑡 = 1, 2, 3 … , 𝑇

Hodrick and Prescott suggest a way to isolate 𝑐_{𝑡} from 𝑦_{𝑡} by the following minimization equation;

Equation 5.2

𝐻𝑃𝑡 = {min ∑(𝑦𝑡− 𝜏𝑡)^{2}+ 𝜆 ∑[(𝜏𝑡+1− 𝜏𝑡) − (𝜏_{𝑡}− 𝜏𝑡−1)]^{2}

𝑇−1

𝑡=2 𝜏

𝑡=1

} , 𝑡 = 1, 2, 3 … , 𝑇

The residual 𝑦𝑡− 𝜏𝑡 (the deviation from the trend) is commonly referred to as the business cycle component. The deviations are squared to give equal weights to both positive and negative deviations.

The second part of the equation measures the change in the trend from one period to the next and includes the smoothing parameter 𝜆, which penalizes the acceleration in the trend relative to the business cycle component (Ravn & Uhlig, 2002). As 𝜆 approaches 0, the trend component becomes equivalent to the original series. This would be considered the optimal condition, as the deviation between the actual data and trend is zero. However, this is highly unrealistic as it would imply that business cycles do not exist.

When 𝜆 gets close to infinity, the trend component approaches the linear trend. (Kim, 2004). This is also unrealistic, as this implies that the trend is 100% linear with constant growth.

One of the most discussed aspects of the HP filter is the determination of the smoothing parameter 𝜆.

Many choose to follow Hodrick and Prescott’s value of 1600, however this value is mostly used for
quarterly data (Hodrick & Prescott, 1997). The question that arises is, what value should one use when
looking at annual data. Backus and Kehoe (1992) use a value of 100, where Correia, Neves, and Rebelo
(1992) suggest a value of 400. Even more recent is the conclusion from (Ravn and Uhlig, 2002), where
they suggest a 𝜆 of 6.25, which is found by ^{1600}

4^{4} .

### 5.1.1. Limitations

Although the HP filter is widely used in the world of economics, there are many potential weaknesses due the simplicity of the model. Here are some of the weaknesses that can be mentioned:

*Choosing the smoothing parameter. As we just wrote above, there is no clear value that one must use *
for the parameter 𝜆. It is set subjectively and can affect the results of the model greatly. Studies have
been made to find the best fitted smoothing parameter, however one can never be certain that the model
will produce the best fitted trend for the time series.

*Equal weight of up- and downturns. As there are both up- and downturns in an economy the HP filter *
must deal with these fluctuations in the best manner. However, the HP filter equally weights the up- and

However, research has concluded that this is not the case. Cristina Romer concluded in her research that economic upturns are longer lasting than economic downturns (Romer, 1999).

*End-point problems. The HP filter uses previous, current, and future data points to determine the trend *
in a given time period. This is a problem for both end points, beginning and ending, as there are no data
from before the start point and no data from after the end point. Hence, the trend at both end points will
be estimated from current and future data and previous and current data, respectively. Consequently, the
trend-estimates at these two end-points will be more affected by current observations than the rest of the
series.

*Real-time problems. This problem makes the last-mentioned end-point problem even more severe, and *
it is arguably the most critiqued aspect of the HP filter. It is well known that current data in time series
are often uncertain, and can be changed after some time. Therefore, the end-point problem becomes even
bigger as these trend-estimates are given more weight than the rest of the time series.

Professor at UC San Diego, James Hamilton has recently written an article where he heavily critiques
the HP filter. His arguments are very much in line with the problems we have mentioned. His arguments
are as follows: “(1) The HP filter produces series with spurious dynamic relations that have no basis in
*the underlying data-generating process. (2) A one-sided version of the filter reduces but does not *
*eliminate spurious predictability and moreover produces series that do not have the properties sought *
*by most potential users of the HP filter. (3) A statistical formation of the problem typically produces *
*values for the smoothing parameter vastly at odds with common practice, e.g. a value for 𝜆 far below *
*1600 for quarterly data” (Hamilton, p. 1, 2017). *

### 5.1.2. Empirical Testing

Before we can go forth with applying the HP filter we must conclude which smoothing parameter we will use for 𝜆. As stated above, Hodrick and Prescott concluded in their paper that a smoothing parameter of 1600 would give the best fit for their quarterly data. Our analysis considers annual data; therefore, we must take this into consideration. The annual data we have collected for our analysis goes back to 1819.

One of the reasons for why we have chosen to look so far back, rather than only looking from 1980 and out is to pick up the historical development. Also, another positive side of having so many data points is that we are able to eliminate some of the end-point problems that occur with the HP filter, at least from the start point. It will be difficult to properly analyze the current situation; however, we will be able to analyze previous bubbles and see whether the model fits or not. If previous bubbles are captured, then we can write about the results with higher confidence.

There are many aspects to think about before choosing the value for 𝜆. A level of 100 has been considered
for annual data (Hodrick & Prescott, 1997). The recent development in the Norwegian housing market
may pose a challenge for having a low 𝜆 since the trend will follow the current extreme values, which in
turn will underestimate a potential bubble. Another problem is highlighted by the European Central
Bank, “the smoothing parameter does not only effect the cycle but the volatility of trend growth and well
*– a consequence of the fact that the HP filter does not contain an explicit model of the cycle.” (ECB, p. *

9, 2005). This is why many economists argue to use high values for 𝜆 when analyzing annual data, because they feel that when using lower values, it would give rise to implausible volatile trend growth rates. Also, using a higher smoothing parameter will ultimately provide more volatility, which also makes a larger portion of the fluctuations a result of temporary disturbances.

To be able to capture both aspects of previous academic conclusions we will use one low and one high smoothing constant. We have chosen to use a newer and an older conclusion of the best fitted value for 𝜆. We will use Ravn and Uhlig’s smoothing parameter for annual data of 6.25 and Correia, Neves, and Rebelo’s smoothing parameter for annual data of 400. Hence, we will be able to see some changes in the results and investigate both sides of the discussion of which value for 𝜆 to use.

Figure 5.1 shows the development of the real house prices for Norway in general and both trend components, using 6.25 and 400 as the smoothing parameter from 1819-2015. When looking at the smoothing parameter of 6.25, the trend moves very close to the real house price, as expected. Therefore, the real house prices only show to be overpriced for a short window in five distinct time periods, which we have already previously have mentioned. That is, the Kristiania Crisis, World War I, the Great

is that the real house prices showed signs of being underpriced at the bottom of the crash. Interestingly enough, if we look at the recent development it actually seems as if real house prices are undervalued.

In 2014, real house prices experienced a minor drop, which is not too surprising considering the recent oil price drop. Here it must be mentioned, that our data only includes data up to 2015, as NCB has not released the most recent data. Therefore, the model does not include 2016’s leap in housing prices.

Figure 5.1

*Source: NCB, 2017; Own calculations*

Next, we look at the smoothing parameter of 400. As the trend becomes more linear with constant growth as 𝜆 increases, it becomes more evident to observe the financial turmoil’s that we have previously mentioned. It becomes clearer that real house prices have been overpriced in these periods, as well as underpriced when the bubbles hit bottom. The gap between the trend and the real house prices during the Norwegian Banking Crisis is the largest gap viewed in our data. After this, the trend seems to have followed the real house prices. Conclusively, given the data we have available, the model indicates that Norway is currently experiencing an underpricing.

The conclusion changes when looking at figure 5.2, which shows the development of the real house prices for Oslo, with both trend components using 6.25 and 400 for 𝜆 from 1841-2015. The data for Oslo looks fairly similar to the data for Norway in general. It could be argued that the data is more volatile in

0 50 100 150 200 250 300 350

1819 1834 1849 1864 1879 1894 1909 1924 1939 1954 1969 1984 1999 2014

### Real house prices with trend lines, Norway (1819-2015)

Real House Prices HP - 6.25 HP - 400

Oslo. Also, the magnitude of the Kristiania Crisis in 1899 is much larger, which is expected as this was primarily experienced in Oslo. The main characteristic we want to point out from this graph is the fact that both trends using smoothing parameters of 6.25 and 400 are below the real house prices from 2014 and out. From this we can conclude that both trends imply that the real house prices in Oslo are overpriced.

Figure 5.2

*Source: NCB, 2017; Own calculations *

We have observed that we currently have two different scenarios in Norway. For Norway in general today’s real house prices are below the estimated HP filters, both when using smoothing parameter’s 𝜆 = 6.25 and 𝜆 = 400, suggesting undervalued prices. However, when looking at Oslo by itself, the real house prices are above the estimated HP filter, which implies overvalued housing prices. From this we can conclude that there could exist a bubble in Oslo, but not for Norway in general.

### 5.1.3. Comparison

To be able to fully evaluate the results for Norway it would be beneficial to have some relevant comparisons. From this one could with more confidence conclude whether the results from Norway are abnormal. As previously mentioned we will look to the other Scandinavian countries.

0 50 100 150 200 250 300 350

### Real house prices with trend lines, Oslo (1841-2015)

Real House Prices HP - 6.25 HP - 400

The first country we will use the HP filter and compare the results from Norway with is Sweden. As the historical data available for Sweden is much shorter than Norway the time horizon here will be 1975- 2016. Nonetheless, it is within this period the largest growth rate has occurred for all Scandinavian countries. Therefore, this window should be sufficient enough to be able to conduct the analysis with good results.

*Sweden *

Sweden went through its own banking crisis as Norway, between 1990-1995 (NCB, 2011). This is clearly seen in figure 5.3 which shows that the housing market was overpriced and not long after corrected to its average mean. Since then the housing market has grown, but the growth rate has not surpassed the trend line significantly. There are two periods where this happened and it was during the Financial Crisis, and now in recent times. Therefore, unlike Norway, one can conclude that given this data the Swedish housing market is in general overpriced.

Figure 5.3

*Source: SCB, 2017b; Own calculations *

Next, we look to the capital of Sweden, Stockholm. We did this for Norway as well to see if there were any deviations between the situation in the entire country and in the capital. In Norway, this happened to be the case. Looking at figure 5.4 the same trends are seen in Stockholm as in Sweden in general.

0 50 100 150 200 250 300

1975 1980 1985 1990 1995 2000 2005 2010 2015

### Real house prices with trend lines, Sweden (1975-2016)

Real House Prices HP - 6.25 HP - 400

Interestingly enough, it looks like the Financial Crisis did not have as great of an effect in Stockholm as it did for Sweden in general. If we look at the current market situation, the housing market in Stockholm seems to be even more overpriced and further away from the trend lines than in Sweden in general. This is also in line with recently published articles which state that Stockholm currently is experiencing record high prices per square meter of 94.000 SEK (SvD Naringsliv, 2017).

Figure 5.4

*Source: SCB, 2017b; Own calculations *

*Denmark *

Unfortunately, the only data we have been able to retrieve for Danish housing prices goes back to 1992.

Therefore, the Danish time series is both shorter than the Norwegian and the Swedish time series.

However, as we argued for the Swedish times series our main interest is recent developments, hence, there is no need to go as far back as the Norwegian time series. What is interesting to investigate is how the Danish housing market is doing compared to the Financial Crisis period, where the Danish housing market was hit particularly hard, compared to the other Scandinavian countries. The Danish housing market slumped around 30% through 2009 and only recently got back to the same housing prices level (Bloomberg, 2016).

0 50 100 150 200 250 300 350 400

1975 1980 1985 1990 1995 2000 2005 2010 2015

### Real house prices with trend lines, Stockholm (1975-2016)

Real House Prices HP - 6.25 HP - 400

Many chief economists and analysts in Danish banks have raised concerns about the current Danish
housing market, mostly because of the fact that Denmark is currently the country which has experienced
negative key rates the longest. Chief analyst Tore Stamer at Nykredit in Copenhagen said, *“To be *
*concrete, there is a danger that Danes will go blind to the risk of rates ever rising again” (Bloomberg, *
2016). From this it will be interesting to see how the current situation is for the housing market in
Denmark in general and Copenhagen.

When looking at figure 5.5 the Financial Crisis is very easy to spot. The housing market clearly experienced an overpricing compared to the long-term trend, and was eventually corrected. The housing market slumped so much that between 2010-2015 the housing market could have been considered underpriced. It is only in the past year the real house prices have yet again, only barely, moved above the long-term average for Denmark in general. This implies that Denmark in general is barely overpriced, using both smoothing constants.

Figure 5.5

*Source: Boligøkonomisk Videncenter, 2017; Own calculations *

Now, if we look at figure 5.6 we can see the development for Copenhagen alone. The development of the figure is similar to Denmark in general. What is interesting to notice is the current deviation between the real house prices and both trend lines are larger than for Denmark in general. Therefore, the HP filter

0 50 100 150 200 250 300

### Real house prices with trend lines, Denmark (1992-2016)

Real House Prices HP - 6.25 HP - 400

implies that there is an overpricing in the Copenhagen housing market, arguably showing bubble
tendencies. This is also in line with what the director for the national bank of Denmark, Lars Rohde, said
in mid-2016, *“We have seen a moderation of price developments this year compared to last year. *

*However, it is still very strong for apartments. This is particularly true for Copenhagen’s housing *
*market, which should be closely followed” (DR Nyheter, 2016). *

Figure 5.6

*Source: Boligøkonomisk Videncenter, 2017; Own calculations*

By looking at Sweden and Denmark in general as well as their respective capitals we are able to investigate and compare whether Norway is experiencing an abnormal housing market or not. As the mentioned Scandinavian countries are relatively similar there are good premises to compare them to each other.

In retrospect, we concluded that the HP filter implied that the Norwegian housing market in general was not overpriced, and hence does not show bubble tendencies. However, both Denmark and Sweden in general showed signs of overpricing, although Denmark showed very little. To sum this, Norway in general is, relative to the HP filter, closer to its long-term average compared to its counterparts. With that said, all capitals; Oslo, Stockholm and Copenhagen are showing signs of overpricing and hence,

0 50 100 150 200 250 300 350 400 450

### Real house prices with trend lines, Copenhagen (1992-2016)

Real House Prices HP - 6.25 HP - 400

bubble tendencies. The fundamental factors for why this could be happening in Norway will be covered in a later section.

### 5.2. Price-to-Rent Ratio

The alternative to owning a dwelling is strictly speaking renting from another dwelling owner. The development between housing prices and rent prices is a relationship that has gotten more and more attention from economists in recent years. By looking at this relationship, one can try to identify a potential mispricing of dwellings relative to a long-run horizon and investigate whether there are bubble tendencies in the housing market. The Price-to-Rent ratio (P/R ratio) stems from the more known Price- to-Earnings ratio (P/E ratio) which is used to price stocks. The well-known P/E ratio was first developed by Gordon and Shapiro in 1956 (Gordon & Shapiro, 1956) and was further developed by Miller and Modigliani in 1961 (Miller & Modigliani, 1961). Both the real and the fundamental P/E ratio are presented in the equations below;

Equation 5.3

𝑅𝑒𝑎𝑙 𝑃

𝐸= 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 (𝐸𝑃𝑆)

Equation 5.4

𝐹𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙 𝑃

𝐸= 𝑃_{𝑡}

∑ 𝐸𝑡(1 − 𝑏) (1 + 𝑟)

∞𝑡=0

The real P/E ratio calculates the value of a stock by dividing the current stock price (market price) by the earnings per share, as shown in equation 5.3 above.

The fundamental P/E ratio, which is found in equation 5.4, equals the sum of all discounted future
dividends and the expected earnings in period t (𝐸_{𝑡}), deducted with the company’s retained earnings (𝑏),
discounted with the rate of return (𝑟). The fundamental P/E ratio shows how much a stakeholder must
pay for each unit of dividend he or she will receive in the future. One can identify a mispricing in the

market by comparing the real and the fundamental P/E ratio. If there is a deviation between the two, where the real P/E ratio is over the fundamental P/E ratio, one can argue for bubble tendencies.

The P/R ratio, which was developed by Poterba in 1984, is similar to the P/E ratio in the sense that it considers a dwelling price to be equal to the discounted value of all future profits tied to owning a dwelling (Poterba, 1984). By profit it is meant to be the value of the cost of owning and/or rental income, or alternatively the rent costs for similar housing. Poterba referred to the cost of owning a dwelling as;

Equation 5.5

𝐶𝑜𝑠𝑡 𝑜𝑓 𝑜𝑤𝑛𝑖𝑛𝑔 𝑎 𝑑𝑤𝑒𝑙𝑙𝑖𝑛𝑔 = 𝑃(𝑖^{𝑞}+ 𝜏 + 𝑓 − 𝜋)

Where:

𝑃 = Housing price index

𝑖^{𝑞} = Nominal interest rate after tax

𝜏 = Property tax

𝑓 = Other costs of owning (maintenance, risk premium, etc.) 𝜋 = Expected capital gain

Equation 5.5 can be explained such as, the cost of owning is the sum of interest expenses given by owning a dwelling (this includes interest expenses that follows when owning a dwelling, but also interest income one gives up by locking up equity in housing), other costs of owning, minus the expected capital gain of owning a dwelling.

A rational dwelling owner will undertake a cost-benefit analysis of the dwelling he or she owns, where the benefit is the rent income one forgoes by living in the dwelling alone, and the cost is the cost of owning the dwelling (Poterba, 1984). In other words, in a long-run horizon the costs of owning a dwelling will be equal to the rent costs for a similar housing. This relationship is show in equation 5.6.

below.