The Impact of Government legislation in the Housing Market
An Empirical Study of the Housing Market in Oslo after the implementation of Lending Restrictions
Lars Andreas Mork Myking
Master of Philosophy in Economics Department of Economics UNIVERSITETET I OSLO
November 2017
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© Lars Andreas Mork Myking
2017
The Impact of Government Legislation in the Housing Market
Lars Andreas Mork Myking
http://www.duo.uio.no
Trykk: Reprosentralen, Universitetet i Oslo
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Abstract
This thesis is a study of the housing market in Oslo and Norway, and is a first attempt to look into the potential changes and consequences of government intervention in the Norwegian housing market, in particular the Government legislation applying for the capital city of Oslo.
In the first part of this thesis I describe the history and characteristics of the Norwegian housing market and how government involvement historically has been very strong, how Norwegians relate to housing and how liberalization and deregulations have affected and created the housing market as we see it today. The increase in household debt is discussed and found correlated with the increasing housing prices. Further on I will statistically address the development in housing prices in Oslo controlled for the Norwegian average and changes observed after the implementation of stricter borrowing conditions using a Difference-in- Difference model. I start out with a simple regression model design and later expand the model to better specify and test the findings. I conclude with three main effects, the “policy effect” of an observed increase in price for the Oslo area during the first months of 2017 followed by a decrease in prices from April 2017. I further identify the “spillover effects” to neighbouring areas and other larger Norwegian cities which also experience an increase in housing prices but do not see the same decrease as in Oslo. The last main effect is the “unit effect” which is identified as the difference in responsiveness of two different housing units, residential buildings and apartments. I find that apartments in Oslo are more responsive to the legislation but this effect is not found elsewhere. The thesis will focus on the real estate market as a whole, with specific focus on the dwelling units, in the thesis called “housing units” while the real estate market will be addressed as the “housing market”. The government mortgage regulation, implemented on the 1st of January 2017, will most often be referred to as the “legislation”.
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Preface
I wish to say thank you to everyone who has help me during the process of writing this thesis.
Fist I would like to thank my supervisor Yiaki Wang for patients and guidance. Special thanks to Camilla for proofreading and Morten for contributions with the model. Thanks to Catharina for support and help and to Mats for discussions. Thanks to Eiendom Norge for providing data and to my fellow student and friends and family.
The regression is done in STATA with figures made in Excel. DO files are available on request. Any error or mistakes are my sole responsibility.
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Contents
1 Introduction ... 1
2 The Norwegian Housing Market ... 3
2.1 Norwegian Housing Policies ... 3
2.1.1 Husbanken and the housing coops. ... 4
2.1.2 The Bank Crisis ... 5
3 Theory ... 7
3.1 Household debt and the housing market today ... 7
3.2 The legislation ... 9
3.3 Housing as consumption and investment ... 10
3.3.1 The consumer ... 11
3.3.2 The investor ... 12
3.3.3 Three groups of borrowers ... 13
3.4 Data ... 14
3.5 Adjusting the data ... 14
4 The Difference-in-Difference model ... 16
4.1 Outline ... 16
4.2 Assumptions ... 17
4.2.1 Political assumptions ... 17
4.2.2 Statistical assumptions ... 18
4.2.3 Causation ... 18
4.3 Assumptions to Difference-in-Difference models ... 19
4.3.1 Observation rule (SUTVA) ... 19
4.3.2 Strickt Exogeneity ... 20
4.3.3 Common trend ... 20
4.4 Spillover effect to other areas ... 22
4.5 The Benchmark Model Design ... 24
5 Regression Results ... 26
5.1 Extensions to the Benchmark model ... 32
5.1.1 Extension to residential buildings and apartments. ... 35
5.1.2 Panel Data Fixed Effects and Random Effects Regression ... 36
5.2 Comments and analysis to the Difference-in-Difference results ... 37
6 Critique ... 40
7 Conclusion ... 41
References ... 43
Appendix ... 46
OLS assumptions ... 48
Figures and Tables
Figure 2.1 ... 4
Figure 3.1 ... 9
Figure 3.2, ... 11
Table 3.1: Number of housing and secondary housing units in Oslo ... 13
Figure 4.1 ... 19
Figure: 4.2 ... 22
Table 4.1: Treatment area for neighbouring areas in the DiD regression ... 22
Table 4.2: Treatment area for large cities in the DiD regression ... 23
Table 5.1: The Panel Data Regression Benchmark DiD regression results ... 26
Table 5.2: Panel Data Regression for total housing units, Residential Buildings and Apartments. ... 28
Table 5.3: The Panel Data Regression output for spillover effect to control areas ... 30
Figure 5.1 ... 34
Figure 5.2 ... 34
Table 5.4: The DiD monthly term and the time fixed effects from December 2016 to September 2017. ... 34
Figure 5.3 ... 36
Table 5.5: Regression robust output for the Oslo average, residential buildings and apartments. ... 37
Table 5.6: Sum up of the different regressions: ... 37
Figure A1: Nord-Trøndelag compared to the Norwegian average ... 46
Table A1: Regression from the Panel Data regression with Fixed- and random effects ... 46
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1 Introduction
The housing market or the real estate market, is an important submarket in almost every country as fraction of GDP. It generates jobs to workers, wealth to investors and has the ability to cast national economies into financial crisis (van der Klaauw, 2011). The housing market is of particular importance as it presents shelter, something everyone is in need of from the day of being born, till the day one dies. For most households buying a home is most likely the single biggest investment throughout their lifetime, hence the costs and consequences of disturbances in the housing market can be crucial for people at an individual level. The housing market is difficult to understand due to the share complexity of the marked as the combination of easily obtainable information such as numeric variables, households’ income, GDP growth, interest rates and a number of variables, such as preferences, locations and psychology of prices which are more difficult to measure or predict precisely. Combined, these issues make the housing market challenging to interpret.
Furthermore, the sector is a large employer and an economic engine in the national economy.
An independent Norwegian consulting firm, Prognosesenteret, claims in a report from April 2017 that the construction and building sector together counts for 16 percent of Gross National Product (GDP) (Eriksson, 2017). They further state that this is the highest share of GDP ever recorded to be derived from the construction and building sector in Norway.
Volatility in such a large sector may cause repercussions throughout the economy. The Norwegian housing market have experienced a tremendous price increase since the early 1990s. Due to concerns of a potential price bubble and high household debt levels, the Norwegian government have gradually increased capital requirements for lenders and the latest mortgage regulation put further constraints on lending. Bloomberg stated in an article 5th of July 2017 on the Norwegian housing market that “The housing market, which has been an economic bulwark against a crash in the nation’s oil industry, is cooling after the government tightened lending standards, specifically targeting speculative buying in Oslo”
(Sleire, 2017). The correlation between debt and housing prices, and government regulations and legislations, is the focal point of this thesis.
In the first part of the thesis I will describe the Norwegian housing market from the second world war up to today. I will further discuss Norwegian housing politics and present characteristics of the Norwegian housing market. The close connection between government
politics and the housing market through direct regulation and through the regulation of the finance markets is important background information for the empirical part of the thesis. The correlation between household debt and housing prices will be discussed both through literature from important Norwegian institutions such as Norges Bank and Statistics Norway and through simple economic reasoning. In the second part of the thesis I will, by means of a Difference-in-Difference type model, test whether the Government legislation, introduced on 1st of January 2017, on lending and capital requirements in Oslo has had an effect on housing prices in Oslo controlled Norwegian average. I will also look at spillover effects to two categories of areas, neighbouring areas to Oslo, called “neighbours”, and the other larger cities, called “big cities”. These areas are comparable across characteristics to Oslo and are suspected to attract buyers and investors who finds Oslo too expensive due to the price level or strict lending restrictions. To elaborate the analysis, I will look at the partial effects of price development for residential buildings and apartments. The main three effects found are the “Policy effect”, the “Spillover effect” and the “Unit effect”. The Policy effect is the effect of housing prices in Oslo which show an initial increase in prices in the early months of 2017 up till April, from where a significant decrease in prices are found. The policy effect is the clearest result as the legislation was particularly focused on Oslo. The spillover effect is the housing price effect on other areas not directly affected by the legislation i.e. whether the legislation specific to Oslo affects prices elsewhere. For the two categories of areas, neighbours and big cities, the positive price increase from December 2016 to April 2017 is also observed, but does not show the same significant decrease in prices from April 2017.
This could indicate that buyers and investors relocate from Oslo to areas with more flexibility on lending. The unit effect is the effect observed in different price development for different types of housing unit, residential buildings and apartments. The effect is larger for apartments in both increase and decrease in Oslo although this pattern is not shared for the neighbouring areas of the other big cities. I will in the last part expand the model and further test my findings and compare result across models before some critique and possible extensions to the thesis are presented followed by a conclusion. The question in hand is massive and the market structure complex, however the preconditions seems to be in place to at least make an attempt, although it may be early to fully conclude on any post-legislation effects.
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2 The Norwegian Housing Market
2.1 Norwegian Housing Policies
After World War two, there was a widespread political necessity and ambition to rebuild the country as part of the building mass was destroyed by the war. Especially in the northern parts of Norway, Troms and Finmark, the retreating former occupants left by scorched-earth tactics and leaving almost no intact building mass (Rein, 2014, p. 28). For the post war period under the labour party, government led by then prime minister Einar Gerhardsen, housing the population was a top priority. Historian Jardar Sørvoll (Sørvoll, 2011) claims in his paper
“Norwegian Housing Politics in change 1970 – 2010” that we can divide the history of Norwegian housing politics into four main categories.
Table 2.1: The four categories of Norwegian housing policy from (Sørvoll, 2011).
Name: Approximately time period:
Initial phase 1880 – 1945
Construction phase 1945 – 1975
Management phase 1975 – 1990
Abolishing phase 1990 -
I will continue to use Sørvolls categories of periods throughout my thesis. The term
“construction phase” speaks for its self; a period where the nation focused on “getting back on its feet” and rebuilding what was destroyed during the war years together with an addition post-was baby boom increased the demand for housing. Sørvoll claims we can observe a threshold in the 1970s with the political consensus shifting away from the policies central in the construction phase. This shift in wider politics can be interpreted to be caused by an understanding that the worst housing shortages was eradicated and that during the 1970s the supply of housing was expected to meet the demand. The emerging political shift turned away from general subsidies and aimed towards a more “means-tested” housing policy, which was the start of the liberalization of the Norwegian housing market.
Figure 2.1
(Eitrheim, 2004)
From Figure 2.1, the historical price index from Norges Bank (NB), we observe a sharp increase from and during the 1980s till present day. In addition, the volatility seems to have increased in the liberalized period after 1980 compared to the period of regulated market conditions between the 1940s up to 1980.
2.1.1 Husbanken and the housing coops.
The close linkage between government policies and the housing market is evident through a number of different political “channels” and there are a number of ways housing was, and to a certain extent still is, subsidized. During the “construction phase”, housing cooperation’s like OBOS (Oslo Bolig- og sparelag, translated to “Oslo housing and savings coop”) founded in 1929 and BOB (Bergen og omegn Boligbyggelag, translated to “Bergen and region housing coop”) founded in 1941, played an important role. Another important institution originated from this era is Husbanken (translated “The House Bank”), founded in 1946.
According to their own website Husbanken was an initiative through which the government could offer financing over the national budget to the population in need of new homes (Husbanken, 2010). OBOS, as stated in their official history, claims that “the municipality provided the plots, the House Bank provided the funding and OBOS was doing the building”(OBOS, 2017). The coops task was mainly to provide housing for its members. This task was extended during the acute housing shortage as result of the war, and the coops was
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to become a provider of housing for “everyone” in line with the consensus post war politics.
The saying for OBOS in the 1940s, 50, and early 60s, was “As many as possible, as fast as possible and as cheap as possible” (OBOS, 2017).
This model of government funding through Husbanken and the important role of the housing coops to provide sufficient housing lasted through and up to the “management phase”. As a result of the liberalization and deregulation of the housing market Husbanken provided less funding while the municipalities began to sell plots for market price causing the housing coops to face competition from commercial construction firms. The housing coops were no longer in a special position to provide housing. The deregulation in the “management phase”
and the following years saw a great increase in both consumption and borrowing/lending increased massively in this period as Bent Vale wrote in Norges Banks Occasional Papers No. 33. (Moe & Solheim, 2004, p. 3) and is known in Norway as “Jappetiden” or
“Yappie/yuppie era”(Stoltz, 2017). The generations born in the 50s and 60s had less experience with the post war period of shortages as their parental generation and the deregulation and globalization and technological progress opened up for new possibility for money making new businesses, perhaps best known through Gordon Gekko´s famous words from the 1987 film “Wall Street” “Greed is good”. The Norwegian encyclopaedia (SNL) points at two main factors contributing to the boom. Liberalization of the credit market and generous interest deductibility’s leading to massively increased borrowing (Gram, 2017) and as Sandal writes in (Moe & Solheim, 2004, p. 81) combined these factors with macroeconomic unrest.
2.1.2 The Bank Crisis
In the years 1981 – 1988 the conservative government, with prime minister Kåre Willoch, led forward the deregulation of the Norwegian housing marked. Bad bank managing, deregulation and failed government interventions led to the crisis, which started in 1987 and ended with the government nationalizing the three biggest business banks in 1992, as Bent Vale writes in (Moe & Solheim, 2004). Vale argues that the banks where not used to the new competitive environment after the deregulation in 1984 as the credit markets had been under strict regulation since the war, and the last bank collapse prior to this area was in the 1930s.
Vale further points at the inexperience of the banks and the aggressive competition for market shares in combination with the lack of liquidity, as one of the key explanations for the
crisis. Erling Steigum points at several macroeconomic issues that affected the banking crisis in (Moe & Solheim, 2004). Norway had, like many western countries, high inflations rates during the 1970s and at the time, had a fixed exchange rate system to the German Mark (DM). To counter expectations of devaluation of the NOK and to bring down the inflation rate, Norges Bank was delegated to defend the NOK in December 1986 Steigum in (Moe &
Solheim, 2004). “In 1988 and 1989 wage regulation laws were passed to speed up the disinflation process. In 1988, the economy went into a recession and unemployment increased.” (Moe & Solheim, 2004, p. 33). The bank losses started to increase as the economic situation worsened, which led to several bank mergers, some bankruptcies and some banks being nationalized. Norwegian encyclopaedia recons that the bank crisis hit banks which accounted for near 60 percent of loans to non-financial domestic sector (Gram, 2017). The households’ debt levels are again actualized in the housing market today and will be futher discussed in the chapter 3.
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3 Theory
3.1 Household debt and the housing market today
The Norwegian Bank crisis was very much a result of factors as discussed including high debt at non-financial in non-financial sectors (Moe & Solheim, 2004, p. 18). Since the end of the bank crisis a massive increase in housing prices have been observed. Factors such as increased national wealth, globalization and liberalization of the financial sectors could contribute to the understanding of the inflation. However, the main concerns have been raised about the debt levels for Norwegian households. In a report from Norges Bank in 2003, special advisors in Norges Banks financial department, Magdalena Riiser and Bjørn Helge Vatne point out that households with high debt levels was reduced in the period 1993 – 1998 relative to the levels of highly indebted household during the bank crisis, however that has since been reversed from 1998 onwards (Riiser & Vatne, 2006, p. 22). Riise and Vatne also point at the increase in debt levels in higher for younger households (25 – 36 years of age) in the period 1998 – 2003 and that the increase in debt levels is correlated with the increases in housing prices (Riiser & Vatne, 2006, p. 28). The International Monetary Fund (IMF) have also expressed concern about the Norwegian housing market. In a report from September 2015 the IMF estimated the Norwegian housing market to be overvalued to an estimated 25 to 60 percent (International Monetary Fund. European, 2015, p. 15). The report also expressed concern about the household debt levels and the amount of liquid assets held by households. The report also stated: “Household debt is heavily skewed toward housing, with about 85 percent in the form of mortgages from banks and mortgage companies”
(International Monetary Fund. European, 2015, p. 15). Since the IMF report was published, the prices have continued to increase to an all-time high in April 2017. Statistics Norway (SSB) wrote in a report from 5th of December 2011 that housing prices have increased three times that of the income since 1970 (Jansen, 2011). The most recent example of awareness of household debt levels comes from Norges Banks report on Financial Stability, published on 2nd of November 2017 and points out the high household debt as the single biggest threat to the Norwegian financial stability (Norges Bank, Finansiell Stabilitet, 2017, p. 4) in terms that the high debt could lead households to cut back on consumption or on household’s default on their mortgages payment leading to loss for the banks (Norges, 2017, p. 48). Norges Banks´
report further states that: “The increase in household’s debt is higher than the increase in income” (Norges, 2017, p. 10). The same report states on page 56 that the household’s debt is
reflected by higher income and higher collateral values, in practice houses. Norges Banks points at the household debt increase of 23 percent from 2010 to 2015 is mainly caused by the debt increase in younger households in response to the constant increase in housing prices pressure on potential buyers pull towards getting into the housing market. This is again reflected by the high debt ratio among younger house owners (Norges, 2017, p. 50). The relative high share of people owning their own housing in Norway help shed light on the perspective of lending and young people who strive to get in to the housing market. The discussion and concern over the “never ending” price increases have led to the government to intervene. In a mortgage regulation from December 2012 the government put a new capital requirement on issued mortgages with collateral from 10 to 15 percent. Since then, the legislation has been rewritten several times, but the 15 percent capital requirement have remained unchanged. However, in the replacement legislation announced on the 14th of December 2016 and implemented on 1st of January 2017, introduced new regulations on lending. This latest legislation did not change much from previous housing legislations in most of Norway but did limit any mortgage issues by a bank for house purchase in Norway to five times a person’s income. The lending conditions was further tightened for Oslo which saw a demand of a 40 percent capital requirement for secondary housing units bought in Oslo, a part of the legislation intended to target speculation. Minister of finance, Siv Jensen, said in a press release with the announcement of the legislation: “Buyers of secondary housing units may drive up the prices for other buyers. Stricter capital requirements for purchases of secondary housing unit in Oslo could limit speculation and reduce the pressure in bidding rounds…”(Finansdepartementet, 2016).
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Figure 3.1
Source: (Sentralbyrå, 2017j)
From Figure 4.2 we see the development of square meter prices on all housing in the four largest cities in Norway – Oslo, Bergen, Trondheim and Kristiansand between 1980, just before the deregulation, up to 2016, with a trend line in total for all five cities and a trend line for Oslo. The highest square meter prices are found in the capital city of Oslo. We also see from the chart that the financial crisis in 2008 seemingly had little impact on housing prices across the cities included. For Oslo, there is a sharp price increase from late 2015.
3.2 The legislation
The legislation in question for the thesis was the new mortgage regulation announced on the 14th of December 2016 and implemented on the 1st of January 2017, replacing a previous mortgage regulation which expired on the 31st of December 2016 (Finansdepartementet, 2017a). The old legislation set a 15 percent capital requirement constraint on issued mortgages with a flexibility to bypass this constraint in 10 percent of issued loans. Said differently, up to 85 percent of the purchase value of the housing unit could be financed through the mortgage and the remaining 15 percent had to be covered by bank reserves, cash, or a collateral least equal to 15 percent of the purchasing value of the unit. The new legislation continued the capital requirements with the flexibility from the old legislation for the whole of Norway except for a borrowing constraint set to five times a person’s income.
The new borrowing constraint allowed the banks a 10 percent flexibility to bypass the five times income constraints. For Oslo the legislation was extended to include a 40 percent capital requirement constraint on secondary housing units and limited the amount possible to borrow to five times a person’s income with a decreased flexibility to bypass the borrowing constraints to 8 percent of issued mortgages (Finansdepartementet, 2017a). The specific Oslo rule of 40 percent capital requirement on secondary housing and the decreased flexibility of the banks for mortgages in Oslo is the focal point of the empirical analysis of this thesis. One important assumption of the statistical analysis is the exogeneity of the legislation. If the new regulations in the legislation was anticipated by the buyers and investors, the statistical assumptions fail.
3.3 Housing as consumption and investment
After the financial crisis in 2008 the western world has been characterized by low, and for some countries even, negative interest rates1. The low interest rate is beneficial towards those with debt, as holding debt becomes cheaper ceteris paribus and households can afford to hold more debt for a given income. When there is a massive housing price increase, like in Norway, the collateral increases in absolute value, and relative to the mortgage the value of the mortgaged house becomes larger. This larger collateral gives the household a possibility to borrow even more form the banks without higher income or increased wealth. The Mortgage regulation presented by the ministry of finance apply to mortgages with collateral in a housing unit. Statistics from OECD indicates that debt increases as a fraction of income and is plotted on the Figure 3.2, which show the household debt to income ratio on the left Y- axis and with income growth on the right Y-axis from the period 1995 to 2016. We can observe the doubling of the debt to income ratio with the blue plotted line from a little over 120 percent in 1995 to over 220 percent in 2016. Note also that in this period the income has also risen year by year represented by the dark blue line in Figure 3.2 for the whole period except for the period 2005 – 2007 and 2016 and is on average above 2,5 percent inflation target of Norges Bank, indicating an increase in real income and not just nominal income.
This increase in real income expands purchasing power for the households and allows the household to hold more debt.
1 The Swedish national bank set their main interest rate to – 0,10 % in effect form 18th of
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Figure 3.2,
Source: (OECD, 2017; Sentralbyrå, 2017k)
3.3.1 The consumer
Housing is both an investment good for investors and consumption good for homeowners.
This makes the housing market special in the sense that it is both a consumption good and an investment good or asset. There are two ways to consume housing. One is to buy (invest) in a house to live in, and the other is to rent from someone else, an investor. In Norway, there is a rather large share of homeowner compared to comparable countries like Denmark or Sweden.2 The utility from housing differs for the investor and the homeowner. The investor gets a utility form the financial performance of the housing units whereas the consumer gets utility from consuming. A standard economic assumption is that consumers want their consumption to consist of a basket of goods and services which includes more than just housing and the total utility of an individual is the sum of the entire basket consumed. For a given budget constraint, the consumption of all other goods but housing, depends on mainly two factors, prices and income. For the consumer and investor, the interest rate and size of mortgage affects the budget, hence partly determining how much an individual can afford to consume in addition to housing. When the interest rate is low the budget expands in which more consumption is possible, but that makes it riskier to potentially higher interest rates to
2 According to an article in Norwegian newspaper Aftenposten, claims that 84 percent of Norwegians are homeowners compared to 69 percent in Sweden and 63 percent in Denmark with data from Eurostat (Langberg, 2016).
cut back on consumption as the budget decreases. For a tenant, the price of housing is determined by the level of the rent thus the rent affects how much of the budget is left for consuming other goods.
3.3.2 The investor
The special regulations to Oslo in the legislation was designed with particular stricter demands for secondary housing, assumed to be owned by investors. Imagine an institutional investor who has three investment possibilities. 1) The stock market, 2) the bank or 3) the housing market. The stock market has experienced uncertainty and volatility after the financial crisis in 2008-09 hence the stock market may not be tempting for a risk averse investor. The historically low interest rates observed in the Western World in the wake of the financial crisis leave a low expected return for placing money in the bank. In Norway, a tax on wealth was introduced in 1999 and although wealth of housing is included in the calculations of wealth tax, it is discounted up to 30 percent of the value of the unit and all housing debt can be deducted (KPMG, 2017) i.e. debt free housing units are valued more in the calculation of individual wealth tax than debt financed units. In such conditions holding debt may be more profitable than not holding debt in the aspect of wealth tax. A property tax was introduced locally in Oslo after the local election in 2015 with effect from 2016. This property tax base is calculated as 80 percent of the valuation of the property above four million NOK in 2017(Kommune, 2017). The valuation of primary- and secondary housing is different.3 This property tax could shift preferences to cheaper units and decrease the demand for units above the tax base threshold both for investors and buyers. The benefits of investing in housing include a low cost of financing due to the low interest rates and with the possibility of tax deduction. Based on the two assumptions stated, volatility stock market and wealth tax, it may be argued that these are factors that may have shifted investors preferences towards housing and that property tax shifted investors preferences towards smaller housing units like apartments. Another type of investor is the non-institutional investor, typically a household with savings. If the non-institutional investor owns a housing unit the household can potentially have the collateral to get a mortgage to buy a second or third housing unit.
3 The valuation of the property is done by square meter prices calculated from SSB multiplied by the square meter area of the unit. The tax base is then 25 percent of the valuation of the unit for primary housing units and 90 percent form 2017 for secondary
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The type of housing unit the non-institutional investor I assume are smaller units as the budget is typically smaller than for an institutional investor.
Table 3.1: Number of housing and secondary housing units in Oslo
Year No. of housing units No. of secondary housing units
Secondary housing as share of building mass
2013 324 247 51 573 15,91
2014 327 078 51 369 15,71
2015 330 032 51 166 15,50
2016 331 492 51 817 15,63
Jan. 2017 331 560 51 867 15,64
Feb. 2017 331 688 51 959 15,67
Source: NEF (Pihl, 2017)
Table 3.1 contains the information about the share of secondary housing units in Oslo. In the first two month of 2017, about 15,6 percent of all housing units in Oslo where secondary housing units. Assuming all these are owned by an investor whose main interest is the financial performance of the unit, including income from rents and possible resale with a profit. The Oslo legislation specifically stated that the new capital requirements for secondary housing where increased from the standard 15 percent to 40 percent in Oslo (ref.
Boliglånsforskriften 1/1 2017, § 5), specifically to prevent potential investors to take on too much debt.
3.3.3 Three groups of borrowers
Having established in simple terms the tax deductibility, I will now categorize three different groups of people who in different ways take on debt. The first are the young households who want to establish themselves in the housing market. They experience a highly priced market and have to take on a lot of debt in order to be able to buy a housing unit. In Husbankens annual report for 2016 (Husbanken, 2016, p. 4) (Husbanken, 2016, p. 4) , reported that 51 percent of issued loans and financial support are to families with children, potentially younger households. The second group are the households who already are within the market and who’s housing units price increase give them the possibility to realize a premium of the price increase by taking on more debt and buy a larger housing unit. This is typical for the consumer whose premium of owning a unit is realized through the acquisition of a larger unit to consume. The third group of people are the investors. I assume most of the investors already own at least one housing unit of their own and have the potential higher collateral as
a source of finance another housing unit. The institutionalized investor are less risky to the banks with the assumption that they are aware of the risk and better understand the potential downside whereas the non-institutionalized investor may be a hazard to the banks if there are many such investors and the financial security to the mortgages are housing units.
3.4 Data
A balanced panel data set is used in the Difference-in-Difference (DiD) model. Panel Data consists of repeated observations over time for the variables included and is balanced as it contains repeated observations with the same time interval for the whole sample. The DiD model is solely based on the data set published monthly by Eiendom Norge (EN). Eiendom Norges price index is a computed and published as a cooperation between Eiendom Norge, Eiendomsverdi AS and Finn.no. The index accounts for 96 percent of housing transactions in the Norwegian housing market for private property and is also used by Norges Bank. The index is published monthly starting in January 2003 where all prices for all area observations are normalized to 100 (𝑃𝑟𝑖𝑐𝑒&'()*(+, .//0 = 100). This means that any price difference prior to January 2003 is equalized. The index work well when the variable of interest is the change in prices, but does not say anything of the actual prices in numeric terms. Any reference to housing prices before 2003 are based on Norges Banks (NB) historical statistics and housing prices in numeric terms are based on data from Statistics Norway (SSB). Some data is collected from other sources, and these will be specifically stated when they appear. The main sources of information are Statistics Norway (SSB), Norges Bank (NB) and Eiendom Norge.
3.5 Adjusting the data
The price index from Eiendom Norge which the DiD model is based on, is very thorough in geographical segregation and housing categories in the data which again makes it easy to pick and choose control variables to include in the regression. The original dataset includes 94 different categories of price areas which I have reduced to 43 by omitting any area that will cause a double count in the dataset. As an example, Hordaland county is omitted, but the biggest city in Hordaland, Bergen, and Hordaland minus Bergen is included so the whole county is represented in the data set. Included terms in the regression like lags, first
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differences and interaction terms are calculated in STATA. The further outline of the data description if the model follows in the next chapter.
4 The Difference-in-Difference model
4.1 Outline
The first known Difference-in-Difference (DiD) study if from Snow (Snow, 1855), who studied a cholera outbreak in Soho, London, in 1854 to find out whether cholera bacteria infected through water or air. He used two neighbouring groups of people exposed to the same air quality and the same water supply and observed how a switch in the water supply for one of the groups affected the death rates after the switch, to the death rates prior the switch. He then had the difference in time, old water supply and new water supply, and the difference in the treatment and control groups. The DiD model setup is well known in economics, but is perhaps more easily explained in fields such as medicine. As an example, a new drug can be tested by randomly assigned volunteers to either a treatment group who receives the drug or control group who receives a placebo drug. Then both groups are observed, and the effect of the drug is evaluated through the averages of the observations and the difference in time across different individuals. To control for individual peculiarities the averages of groups are measured against each other. In economics, it is often more difficult to randomly expose someone to a treatment or placebo. Often a natural experiment is needed or a difference in politics to comparable areas such as Card & Krueger did in a famous study on the effect of a change in the minimum wage on employment for fast food restaurants in the neighbouring states of New Jersey and Pennsylvania (Card & Krueger, 1994). The general idea of such a regression design rests on some important assumptions. It is impossible to observe the same area both treated and untreated as an individual volunteer in a medical experiment cannot be recipient of both the placebo drug and the actual medicine for any reasonable result to emerge. We have to rely on the assumption that potential outcomes or a
“counterfactual” (Lee, 2016, p. 135), is represented through the development of the controls.
In medical research, one can rely on averages of large groups on potential outcomes whereas a natural- or quasi experiment relies on the common trend assumption. The common trend assumption states that the two groups follow the same trend and that without the treatment or change in status quo, the two groups or areas would see the same development on average.
This is a strong assumption and is discussed more thoroughly later.
In my Difference-in-Difference model on housing prices, I will look at regulations that are area specific to Oslo as Card & Krueger looked at regulations specific for New Jersey. The
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main instrument in this model is the Oslo legislation of 1st of January 2017. This legislation was announced on the 14th of December 2016, and came into effect on 1st of January. The announcement of the legislation could affect the behaviour of investors and buyers thus the first treatment will be from the month of the announcement date, December 2016. The second treatment is four months after the legislation went into effect, namely from the 1st of April. This is because a confirmation of financing from a bank normally has a duration of three months in Norway. In practice, this means that those who were granted a confirmation of financing from the bank in late December 2016 could use them up to April 2017. If the Oslo legislation would impact the possibility for these potential buyers to obtain a confirmation of financing this may influence the decisions made by potential buyers. If for example the potential buyer would not be able to renew their bank confirmation with the new regulations, this could give the potential buyers a strong incentive to push forward a purchase this period, December 2017 – April 2017. If enough people were affected by the new constraints or the psychology that follows it, this could affect the local prices in Oslo and even create spillover effects to other areas. Since the legislation has region specific regulations to Oslo a control can be made for areas with a common trend where this legislation does not apply. The area specific legislation opens up for a “natural experiment”
which have some of the same properties as if randomization in an “standard” statistical experiment (Stock & Watson, 2014, p. 131).
4.2 Assumptions
4.2.1 Political assumptions
The Oslo legislation is a politically regulation, however not in the extent as during the
“management phase” as the government does not supply buyers with loaning opportunities in the large extent as during the “management phase”. The political effort of regulating the housing market in the Oslo area will not have an effect unless the commercial banks follow up on the legislation. I questioned both the ministry of finance and Norway’s biggest commercial banks DNB on the issue. The ministry of finance answered through email and confirmed that the rules does apply to anyone who issues mortgages with collateral in a housing unit in Norway including foreign banks (Finansdepartementet, 2017b, Personal Communication, 3rd of November). The head of mortgages and property in DNB, Øyvind Bøe, also answered through email that all banks issuing mortgages in Norway are committed
to follow any legislation issued by the ministry of finance. He also stated that
“Finanstilsynet” (the Norwegian equivalent to the SEC in the USA or FAC in the UK) is the institution responsible to follow up any legislation and regulation from the Ministry of Finance and any sanctions for bank who does not follow up on the legislations. (Bøe, 2017,Personal communication, 30th of October ). Øyvind Bøe did add that the banks can show flexibility with regards to the legislation as long as the exceptions to the legislation does not exceed 10 percent of the total mortgaged issued a month. With these assurances, I will simplify and assume that all mortgages issued by banks in the post-legislation period from the 1st of January 2017 are within the legislation issued by the ministry of finance for the model. I will also assume that the same rules apply for all, domestic and foreign buyers and investors.
4.2.2 Statistical assumptions
The Difference-in-Difference model rests on the standard OLS assumptions, and can be found in the Appendix under “OLS assumptions”. The main assumptions are the Gauss- Markov assumptions and exogeneity assumption.
4.2.3 Causation
When dealing with regression models, the question of causation is highly relevant. Causation is merely how different variables affect each other. The problem with causation is that we only observe correlation but cannot directly observe causation. Bårdsen and Nymoen point at spurious and nonsense correlation where spurious correlation is correlation between two variable caused by a third variable and nonsense correlation as correlation between two independent variables (Bårdsen & Nymoen, 2011, p. 25). In both cases of spurious and nonsense correlation the assumption that correlation is the same as causation, is wrong. We can observe that a change in X is correlated with a change in Y, but whether X Causes Y or Y Causes X is not observed and cannot be tested. To make a good assumption about causation we must make use of economic theory. A good example on causality is Verbeek’s study on marriage and wages. It has been observed that married workers earn more than unmarried workers. “…but it is not very likely that being married causes people to have higher wages”
(Verbeek, 2012, p. 60). I will not comment to much on causality, but assume that debt and housing prices show signs of a two-way causality with the argument in section three.
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4.3 Assumptions to Difference-in-Difference models
In addition to the standard OLS assumptions, the Difference-in-Difference model rest on a few key assumptions.
4.3.1 Observation rule (SUTVA)
SUTVA (Stable Unit Treatment Value Assumption) is an important assumption in DiD design models. “The first assumption implies that one, and only one, of the potential outcomes is indeed observable for every member of the population” (Lechner, 2011, p. 176).
Lechner further gives an example of violations of the SUTVA. If a job training program is large enough, it might affect the labour market and thus affect non-participants of the job training program. Thus, this violates the two potential outcomes. The assumption basically states that only one observable outcome is possible for each cohort in the model i.e. for a participant in a medical experiment only the drug or the placebo drug is given. The patient cannot get both the actual drug and the placebo drug, and we can only observe one state of the patient. The patient’s reaction given the other option, is only a potential outcome, not an observed outcome.
Figure 4.1
Figure 4.1 shows a potential outcome as the red line from the pre-treatment point of group A E[yi| s=A, t=0] to the post-treatment point E[yi| s=A, t=1] – β. The observable post-treatment point, is the E[yi| s=A, t=1], but corrected for the estimated treatment effect, we get the potential outcome effect which is the expected development in the absence of treatment. In the same way the treatment effect, β, is calculated by controlling the observable post- treatment point E[yi| s=A, t=1], for the observable development of group B from point E[yi|
s=B, t=0] to the E[yi| s=B, t=1]. If not controlling for the group B post-treatment, the treatment effect would be overrated, only estimating the change in E[yi| s=A, t=1] - E[yi|
s=A, t=0] > β.
4.3.2 Strickt Exogeneity
(Stock & Watson, 2014) describes strict exogeneity as an extension of exogeneity assumption as the independence of 𝑢5 for future, past and present values of 𝑋5 (Stock & Watson, 2014, p.
642). Mathematically written:
𝐸 𝑢5 𝑥5 = 0 → 𝐸 𝑢5 … , 𝑥5<., 𝑥5<=, 𝑥5, 𝑥5>=, 𝑥5>., … = 0
(Lechner, 2011), describes exogeneity [EXOG] in a Difference-in-Difference model as 𝑋= = 𝑋/ = 𝑋, ∀ 𝑥𝜖 𝜒
“χ denotes the subspace of X that is of interest to the researcher” (Lechner, 2011, p. 177).
Said in words; if future treatments or anticipation for an upcoming treatment changes the behaviour of the sample prior to the treatment this is a violation of the exogeneity assumption.
In my thesis, the treatment was announced on the 14th of December 2016 and implemented on the 1st of January 2017 so the exogeneity assumption fails for any changing behaviour in that period. However, in the regression, the first treatment variable is implemented in December 2016 as one period and thus internalizing any violation of the exogeneity assumption in the analysis. Since the announcement date and the implementation date comes within two weeks of each other I assume any change in the legislations was not expected, the exogeneity assumption holds for the housing prices.
4.3.3 Common trend
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The common trend assumption is a key DiD assumption and focuses on the development of the variables included before and after the treatment. The common trend assumption focuses on the hypothetical question regarding the absence of any treatment for the treated or a “what if” outcome (Angrist & Krueger, 1999, p. 1228). “It implies that if the treated had not been subjected to the treatment, both subpopulations defined by D = 1 and D = 0 would have experienced the same time trends conditional on X” (Lechner, 2011, p. 179). The common trend assumption is vital and generally states that without the treatment, the treatment and control areas would follow their intended trend. The illustration in Figure 4.1 can be used to describe the common trend assumption as we assume the development in the absence of treatment is the red line from point E[yi| s=A, t=0] to point E[yi| s=A, t=1]. If the control and treatment areas are dependent on different variables the comparison between the areas becomes less meaningful and ultimately not valid. This is also the reason for omitting Stavanger and Sandnes from the comparable treatment group of the analysis. Stavanger is the oil capital of Norway with a high dependence of oil related jobs and again a heavily oil dependent housing market whereas neighbouring Sandnes is highly integrated with Stavanger and share much the same characteristics. Since the oil price drop in 2014, the Stavanger housing market saw a steady decline in housing prices, which is not observed for the other three large cities in Norway. From Figure 4.2, we see the housing price development for Stavanger compared with Oslo, Bergen and Trondheim. We clearly see a higher price increase in Stavanger, leading up to August 2013 during the years of higher oil prices. The development since 2014 is quite negative compared to the other cities. The different price development of Stavanger indicates that the common trend assumption is suspected to be violated, hence Stavanger is omitted as a from the comparable treatment group “Big Cities”
in the analysis. From Figure 4.2 the average price index increase has been plotted for the four biggest cities in Norway, Oslo, Bergen, Stavanger and Trondheim from December 2009 to September 2017 with the oil prices for 2013 - 2016. As observed in the figure, the price development for Stavanger differs from the three other cities in line with the drop in the oil price. However, this is not a statistical analysis, mere an assumption that housing prices in Stavanger is correlated with the oil price and thus omitted as a treatment area. We also observe that the prices for Oslo compared to Bergen and Stavanger follow each other’s trend seemingly close up to December 2015 where Oslo experience an increase in price.
Figure: 4.2
Source: (Administration, 2017; Eiendom Norge AS, 2017)
4.4 Spillover effect to other areas
In the Difference-in-Difference model, I have included two categories of areas all who are used to estimate any treatment effect compared to Oslo controlled for the Norwegian average.
These treatment areas will be represented in the regression with an area specific dummy variable to easier be able to interpret the potential spillover effects of the legislation and how they may manifest itself in the different areas. The first category is the neighbouring areas and is summed up in table 4.1. All areas included are within one hour of driving time to Oslo and can be categorized as “urban areas” consisting of both cities and regions. The regions are Follo, Asker, Bærum and Nedre Romerike i.e. cities, towns and settlements which all can be categorized as having a relative high population density and in relative closeness to Oslo. The cities Drammen and Moss are included as the characteristics of cities easier compare to Oslo and is in such a distance as commuting is frequent. Whole counties are omitted as the population density and geographical size cannot typically be characterized as similar to Oslo and would not be directly comparable for potential buyers or investors in the analysis.
Table 4.1: Treatment area for neighbouring areas in the DiD regression
City Population Source Driving time from Olso
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Drammen 68 523 (Sentralbyrå, 2017f) 50 min
Asker 61 105 (Sentralbyrå, 2017b) 35 min
Bærum 124 798 (Sentralbyrå, 2017e) 21 min
Follo 139 701 (Fylkeskommune, 2017b) 30 min
Nedre Romerike 177 007 (Fylkeskommune, 2017a) 25 min
Moss 32 541 (Sentralbyrå, 2017a) 50 min
Dummy variable
name Neighbours = 1 𝑖𝑓 𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑖𝑛𝑔 𝑎𝑟𝑒𝑎
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
The second category includes the other larger cities in Norway not in a “neighbouring area”
to Oslo, and are listed in table 4.2. These are the largest cities outside of the eastern region of Norway with the exception of Stavanger. These cities could be comparable investments opportunities for investors who no longer finds Oslo attractive due to the new legislations.
Table 4.2: Treatment area for large cities in the DiD regression
City Population Source
Bergen 279 035 (Sentralbyrå, 2017c)
Trondheim 191 152 (Sentralbyrå, 2017h)
Kristiansand 89 760 (Sentralbyrå, 2017g)
Ålesund 47 336 (Sentralbyrå, 2017i)
Bodø 51 110 (Sentralbyrå, 2017d)
Tromsø 75 128 (Sentralbyrå, 2017a)
Dummy variable name Big Cities = 1 𝑖𝑓 𝐵𝑖𝑔 𝑐𝑖𝑡𝑦
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
It is tempting to think that a reaction to the new legislation could change the behaviour of both investors and potential buyers. Investors, faced with a 40 percent capital requirement on housing units in Oslo, but only 15 percent in the rest of the country, may shift their preferences towards to investing outside of Oslo with weaker constraints on borrowing. If we differentiate between local and foreign investors we could suspect to see that local investors in Oslo rather invest in neighbouring areas such as Asker and Bærum in Akershus, Drammen in Buskerud or in areas and cities in Østfold close to Oslo. All these areas are in commuting distance from Oslo and have a relative high population density and could be a real alternative for those who find Oslo too expensive or face difficulties to get mortgage to under the new
constraints. Foreign investors could move investments to other areas, and be more flexible in where to invest as personal preferences are secondary to business decisions which could lead to moving their investment to other larger cities such as Bergen, Trondheim or Stavanger if beneficial from a business perspective. The price effect is expected to be somewhat larger in the neighbouring areas as mobility and relative closeness is expected to be amplified of any spillover effect from the Oslo legislation.
4.5 The Benchmark Model Design
The regression design of the model is standard linear regression with Ordinary Least Squares (OLS). The OLS method minimizes the average distance between data points to get the best fit of the regression line is well proven as a statistical and econometric tool. The standard design of the Difference-in-Difference model is like the model below.
𝐻𝑜𝑢𝑠𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒&5
O
= 𝛽/
OO
+ 𝛽=𝑇&
OOO
+ 𝛽.𝑂𝑠𝑙𝑜
OU
+ 𝛽0𝐷𝑖𝐷&
U
In the model, Yi = Housing Pricei, is the outcome and is generated by what terms are included in the regression.
I) Y is the average housing price for Oslo when all the terms above are included.
II) 𝛽0 is the intercept. This term shows the average housing prices for Norway in the first period pre-treatment (period t=0) for the whole sample when no lag of price is included.
III) In this term, 𝑇& is the treatment or time variable, [𝑇& = 1 if and after the treatment period, zero otherwise]. This term will calculate the average difference in housing prices (positive or negative) from the constant term from the implementation of the treatment and for the whole period [t=1, post- treatment] for the whole sample. From Figure 3.1, the post-treatment period in the housing price regression is expected to be higher than the constant term 𝛽0
due to the increase in housing prices since the housing price index stats in 2003.
IV) The dummy, Oslo, equals one if the city is Oslo. This term will catch the average price of Oslo compared to the control group for the whole period, both pre- and post-treatment. This term is expected to be higher if the
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expected average housing price index is expected to be higher for Oslo than for the control areas.
V) This term is the main Difference-in-Difference result. The “DiD” term is an interaction term equal to: DiD=[Treatment*Dummy=Oslo]. This term captures the treatment effect for Oslo after treatment, or the verage Treatment effect of the Treated. The t-value of this term will determine whether the difference-in-difference effect comes out significant or not.
I will extend the model to run with two treatments and to include lags of the price variable to correct for any difference in pre-treatment trends between Oslo and any control areas and potential autocorrelation for the dependent variable. The first treatment starts on December 2016 and is active till the end of the period. Since the legislation was announced on 14th of December 2016 the first treatment is arranged to catch any change in behaviour from the announcement till the implementation date on the 1st of January and throughout the period.
𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡= = 1 𝑖𝑓 ≥ 145[𝑜𝑓 𝐽𝑎𝑛𝑢𝑎𝑟𝑦 2017
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 = 1 𝑖𝑓 ≥ 𝐷𝑒𝑐𝑒𝑚𝑏𝑒𝑟 2016 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
The second treatment is active from April 2017 till the end of the period. This treatment is intended to catch the lagged effect of the legislation and any market adjustments that may take some time to be implemented. It is expected that the anticipated effect of the legislation will not be clearly visible in the data till after approximately three months after the implementation date. This is due to the duration of a confirmation of financing from the bank is normally three months.
𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡. = 1 𝑖𝑓 ≥ 1`5𝑜𝑓 𝐴𝑝𝑟𝑖𝑙 2017
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 = 1 𝑖𝑓 ≥ 𝐴𝑝𝑟𝑖𝑙 2017 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
The regression will be run with two area specific dummies for the two categories of control areas and with the two instruments 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡= and 𝑇𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡, denoted 𝑇= and 𝑇. on the Norwegian average. The basic design presented in this paragraph will be used as a benchmark for the discussion that follows with further extensions to the model to follow.
𝑦&5 = 𝐻𝑜𝑢𝑠𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒&5 =
𝛽/+ 𝛽=𝑂𝑠𝑙𝑜 + 𝛽.𝑁𝑒𝑖𝑔ℎ𝑏𝑜𝑢𝑟𝑠 + 𝛽0𝐿𝑎𝑟𝑔𝑒𝐶𝑖𝑡𝑖𝑒𝑠 + 𝛽f𝑇=+ 𝛽g𝐷𝑖𝑑=+ 𝛽i𝑇.+ 𝛽j𝐷𝑖𝐷.+ 𝐿𝑃𝑟𝑖𝑐𝑒&
5 Regression Results
Table 5.1: The Panel Data Regression Benchmark DiD regression results Benchmark
Model Benchmark Model with two
lags Benchmark Model with six lags
(1) (2) (3) (4) (5) (6)
Dummy Oslo -3.152 -3.152 9.163 9.163*** 8.502 8.502***
(15.24) (3.105) (11.69) (2.183) (12.07) (2.164) Dummy
Neighbours -6.655 -6.655* 2.661 2.661 1.903 1.903
(6.698) (3.578) (5.142) (3.826) (5.312) (3.308)
Dummy Big Cities 9.831 9.831** 3.342 3.342 2.571 2.571
(6.698) (4.134) (5.141) (4.573) (5.314) (4.311)
Treatment1 77.64*** 77.64*** 1.109 1.109 0.280 0.280
(3.188) (2.601) (0.818) (2.751) (0.751) (2.481) DiD1 49.77** 49.77*** 30.83*** 30.83*** 33.90*** 33.90***
(20.91) (2.601) (5.162) (2.656) (4.740) (2.933)
Treatment2 3.215 3.215*** 0.201 0.201 0.125 0.125
(4.067) (0.441) (1.004) (0.455) (0.921) (0.438)
DiD2 -9.572 -9.572*** -9.416 -9.416*** -9.702 -9.702***
(26.67) (0.441) (6.585) (0.462) (6.040) (0.605)
L1price 0.552*** 0.552*** 0.431*** 0.431***
(0.0103) (0.110) (0.0114) (0.147)
L2price 0.426*** 0.426*** 0.176*** 0.176
(0.0103) (0.110) (0.0122) (0.129)
L3price 0.322*** 0.322***
(0.0123) (0.111)
L4price -0.138*** -0.138*
(0.0123) (0.0766)
L5price 0.187*** 0.187**
(0.0122) (0.0829)
L6price 0.0102 0.0102
(0.0114) (0.0680)
_cons 170.1*** 170.1*** 2.769 2.769 1.311 1.311
(2.737) (3.105) (2.155) (3.708) (2.215) (2.864)
N 7611 7611 7609 7609 7605 7605
Standard errors in parentheses
* p < 0.1, ** p < 0.05, *** p < 0.01
Table 5.1 contain the regression output for the benchmark Difference-in-Difference regression model. Column (1) and (2) are the result for the standard DiD model design presented in section 4.5, with column (2), (4) and (6) having heteroskedastic robust standard errors. Column (3) and (4) include the two first lagged price variables as a control variable and column (5) and (6) include the first- to sixth lagged price to correct for any difference in