The impact of EU the emissions trading system on the price of electricity
An econometric analysis of the Nordic electricity market
Andreas Eriksson
Economics, master's level (60 credits) 2018
Luleå University of Technology
Department of Business Administration, Technology and Social Sciences
The impact of EU the emissions trading system on the price of electricity
An econometric analysis of the Nordic electricity market
Andreas Eriksson
SAMMANFATTNING
Målet med denna studie är att undersöka hur priset på EU ETS påverkar priset på den nordiska elmarknaden samt hur framtida förändringar i utsläppsrättspriset kan komma att påverka det nordiska grossist – elmarknadspriset. Fokus är på vad hur elpriset skulle förändras om EU ETS priset ökade till € 30 per ton. I studien ingår de nordiska länderna Sverige, Danmark, Norge och Finland. Syftet besvaras med hjälp av en reducerad ekonometrisk modell där priset på den nordiska elmarknaden utgör den beroende variabeln.
Modellen estimeras med ”ordinary least square” (OLS). Problem med autokorrelation gjorde att kvartalsdata användes istället för månadsdata. Fyra av de oberoende variablerna var statistiskt signifikanta utsläppsrättshandelspriset, vattenmagasinens nivå i relation till maximal nivå, kolpriset och medeltemperaturnivån. En simulering genomfördes beroende på de estimerade värdena för att besvara syftet. Resultatet visade att elmarknadspriset ökar med cirka € 16 per MWh under perioden jämfört med det faktiska elpriset för respektive kvartal.
ABSTRACT
The aim of this study is to examine how the EU ETS price has affected the price of electricity in the Nordic electricity market, and how future changes in the carbon price may affect the wholesale electricity prices. The Nordic countries included are Sweden, Norway, Denmark and Finland. The analysis builds on a reduced econometric model where the Nordic electricity price constitutes the dependent variable. Problem with autocorrelation implied that quarterly data rather than monthly data were used. This model is estimated using ordinary least square (OLS) regression technique. Four variables were found to be statistically significant. These include the EU ETS price, the hydro reservoir level, the coal price and the temperature. The estimated coefficients were used to conduct a simulation on what could happen if the EU ETS price increased to € 30 per ton. The results showed that the electricity price would than increase by about € 16 per MWh from its current level at about € 37 per MWh.
FÖRORD
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TABLE OF CONTENTS
1. INTRODUCTION ... 1
1.1 Background ... 1
1.2 Purpose ... 2
1.3 Delimitations ... 3
1.4 Method ... 3
1.5 Outline ... 3
2. BACKGROUND ... 5
2.1 EU ETS ... 5
2.1.1 The three different phases in EU ETS ... 6
2.2 The Nordic electricity market ... 8
2.2.1 Electricity generators... 9
2.2.2 Wholesale Nordpool electricity market... 10
3. THEORY ... 12
3.1 Emissions trading ... 12
3.1.1 The supply of emission trading ... 12
3.1.2 The demand for emission allowances ... 13
3.1.3 Marginal abatement cost (MAC)... 14
3.2 Electricity Market ... 17
3.2.1 Electricity demand... 17
3.2.2 Electricity supply... 18
3.2.3 Price formation in the electricity market ... 18
3.3 Connection between the markets ... 18
4. LITERATURE REVIEW ... 20
4.1 Search strategy ... 20
4.2 Earlier studies focused on EU ETS ... 20
4.3 Other studies ... 23
4.4 Discussion ... 23
5. MODEL SPECIFICATION AND ESTIMATION ISSUES ... 26
5.1 Model ... 26
5.1.1 Demand side of the reduced regression model ... 26
5.1.2 Supply side of the reduced regression model ... 26
5.1.3 Equilibrium in the market ... 27
5.1.4 Simulation ... 28
5.2 Econometric issues ... 29
5.2.1 Breusch-Godfrey-test ... 30
5.2.2 Alternative methods ... 30
6. DATA ... 32
6.1 Introduction ... 32
6.2 The wholesale electricity price ... 32
6.3 EU ETS price ... 33
6.4 Hydro reservoir level ... 34
6.5 Temperature ... 35
6.6 Coal price ... 36
6.7 GDP ... 37
6.8 Natural Gas price ... 38
6.9 Descriptive analysis ... 39
7. RESULTS... 41
7.1 Regression results ... 41
7.1.1 Regression without natural gas price ... 43
7.1.2 Regression without natural gas price and GDP ... 44
7.2 Autocorrelation results ... 44
7.2.1 Autocorrelation solutions ... 45
7.3 Simulation ... 47
8. DISCUSSION ... 49
9. CONCLUSION ... 51
REFERENCES ... 52
APPENDIX ... 57
Appendix A Data ... 57
Appendix B Quarterly data result ... 62
Appendix C correlation table ... 65
Figures
Figure 1: The EU ETS price (Euro per ton) ... 7
Figure 2 The distribution between different electricity production sources in the Nordic electricity market ... 9
Figure 3: The Nordpool electricity price (Euro per MWh) ... 11
Figure 4: Supply and demand in an emission trading scheme ... 13
Figure 5: The supply and demand for the EU ETS market with financial crisis ... 14
Figure 6: Marginal abatement cost the carbon emissions ... 16
Figure 7: The EU ETS price ... 34
Figure 8: Monthly Hydro reservoir level ... 35
Figure 9: Monthly Temperature ... 36
Figure 10: Monthly coal price ... 37
Figure 11: Monthly GDP averaged over quarterly data... 38
Figure 12: Monthly natural gas price ... 39
Figure 13: Electricity price with different Simulations ... 48
Tables
Table 1 Literature summary ... 22
Table 2: Descriptive statistics (N=125) ... 40
Table 3: Regression with all variables ... 41
Table 4: Breusch-Godfrey test... 45
Table 5: Quarterly data regression results... 46
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1. INTRODUCTION
1.1 Background
The average temperature on earth has increased by 0.74 degrees Celsius since the nineteenth century, and it is only getting worse. The projection from now until the next century is that the average temperature will increase between 1.8 to 4 degrees Celsius. One of the problem that is causing the average temperature to increase is the emission of greenhouse gases and especially CO2 (carbon dioxide) (Energimyndigheten, 2013).
Due to the increase in the global average temperature, policy makers introduced the Kyoto protocol in 1997 and it took effect in 2008 and lasted until 2012. The agreement aimed to decrease the world’s emission of greenhouse gases. As a response to the Kyoto protocol, the European Union (EU) introduced the European Union emission trading system (EU ETS) (Ellerman and Buchner, 2007). The number of European Union allowance’s were distributed to fulfill the commitments in the Kyoto protocol. There were a total of 192 parties in the Kyoto protocol agreement. The goal of the system was to reduce the total carbon dioxide emission by five percent for developed countries and economies in transition between 2008 and 2012. To achieve this goal, EU needed to decrease its carbon dioxide emission by eight percent, Japan six percent and USA seven percent compared to the 1990 pollutant level (David, 2004).
EU ETS was therefore introduced to accomplish the Kyoto protocol and the goal of EU ETS was to reduce the greenhouse gas emission. After 2012, the EU has decided to keep EU ETS as a major vehicle for greenhouse gas reduction in EU. The restriction in emission made the emissions scarce, and this leads to a price on emissions. During the first eight years of the EU ETS, the greenhouse gas cap decreased by 1.74 percent annually. A total of four percent of the world’s total greenhouse gas emission is included in the EU ETS (Ellerman et al., 2014).
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The industry sector is heavily affected by the EU ETS price. For example, in Sweden about 35 percent of the Swedish industry energy usage is electricity. If the electricity price goes up due to the introduction and increase in the EU ETS price, industries might substitute to other energy sources, but this might affect the firm’s competitiveness in the world markets.
Therefore, it is important to analyze how the EU ETS price could affect the electricity price and to observe the new electricity price. The EU ETS affects the electricity price primarily because coal and natural gas are two relatively large sources of electricity production and those sources are affected by EU ETS since coal and natural gas releases greenhouse gases in form of CO2 (Energimyndigheten, 2015). The Nordic wholesale electricity market is a well-established and deregulated market thanks to Nordpool which is a day-ahead and future market for producers and distributors trade for Denmark, Sweden, Norway and Finland (Fell, 2010). Today’s EU ETS price is too low according to Brink et al. (2016), and the scheme would benefit from an increase in the price to a price of about € 30 per allowance (ton) in 2020.
In the EU ETS the power generation sector is the largest sector that emits CO2, and it is therefore important to observe how the EU ETS affect the electricity price with a focus on the Nordic wholesale electricity market. Fell (2010) conducted an earlier study to observe how the EU ETS price affects the Nordic wholesale electricity price, and the conclusion was that there is a relationship between EU ETS and the electricity price in the Nordic countries.
The problem is that the study was made during phase one of the EU ETS scheme and phase one was characterized by a highly fluctuating price. Therefore, a new study is motivated. In this paper, we use data from 2005 to 2015, and this includes data from phase one, phase two and phase three instead of just phase one. To get a new perspective an updated study is conducted to analyze the EU ETS effect on the Nordic wholesale electricity market.
However, we also conduct a simulation to analyze how the Nordic wholesale electricity price could be affected if the EU ETS price increases to 30 € per ton.
1.2 Purpose
The purpose of this study is to examine how the EU ETS price has affected the wholesale price of electricity in the Nordic wholesale electricity market and, how future changes in the price of these emission allowances may affect the Nordic wholesale electricity price.
3 1.3 Delimitations
Data from August 2005 to December 2015 are used, and this implies that phase one, phase two and three years of phase three are included in the empirical analysis. The restriction with the data is that EU ETS was introduced in 2005 and earlier data could not be obtained.
Moreover, the temperature variable from World Bank (2018) was only offered until the end of 2015.
This study does not focus on how the environment or the society can benefit from a higher EU ETS price. Also, how to make EU ETS more efficient or how the system is designed are not discussed in this study; it, only discusses how the EU ETS affects the Nordic wholesale electricity market.
1.4 Method
The model used in this study is a reduced regression model following the approach employed by Brännlund et al. (2012), which use the electricity price as the dependent variable. The reduced regression model is derived from the assumption that demand and supply in the electricity market are equal. The supply side of the reduced function includes the following variables: the EU ETS price, the coal price, the natural gas price and hydro reservoir levels, while the demand side includes temperature level and GDP. These independent variables are assumed to be exogenous, and for this reason the model was estimated using ordinary least square (OLS) technique. An AR (12) test conducted with help of a Breusch-Godfrey test to check for autocorrelation in the model. Both monthly and quarterly data are tested.
In a second step, the estimated coefficients are used to simulate how the electricity price would be affected if the EU ETS price increases to € 30. This is done by including the actual values for the variables but, only changing the EU ETS price from the actual price to the new assumed price level.
1.5 Outline
Chapter 2 discusses and explains the background of the Nordic wholesale electricity market and the EU ETS scheme and the connection between these two markets. Chapter 3 is the theory chapter which discusses what variables determine the EU ETS price in the first stage,
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and then how the EU ETS price will affect the wholesale electricity price. Chapter 4 provides literature review which describes earlier literature and how this study contributes to the existing research. Chapter 5 is the methodology chapter. It outlines the different methods and discusses why the variables incorporated in the model have been chosen. Chapter 6 explains the data used to measure the variables, as well as the perks and flaws of the selected the data set. Chapter 7 displays the results from the OLS estimations, autocorrelation test and the simulation. Chapter 8 contains a discussion, which argues this study’s findings in relation to earlier studies. Finally, chapter 9 is the concluding part where the main findings of the study are outlined.
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2. BACKGROUND
This chapter begins with a summary of the EU ETS and the different phases of the emissions trading system. That transition into how the EU ETS affects the electricity market, and concludes in the basics of the electricity market.
2.1 EU ETS
EU ETS is a trading system scheme, and it is the largest in the world. Emission trading is an economic policy and is a combination of tax and emission cap in a sense that the total amount of emission trading allowances represents the cap and the amount paid for an emission trading allowance is the ‘tax’. The goal of the EU ETS is to make an efficient greenhouse gas emission trading scheme and to accomplish the Kyoto protocol that took effect in 2008 and lasted until 2012 (Ellerman and Buchner, 2007).
The system is driven by policy decisions because the policy makers determines the supply for the EU ETS and the EU Member States allocate the emission allowances. One allowance is equivalent to one-ton carbon dioxide emission and is the base for the system. The number of allowances may change depending up on what greenhouse gas that is emitted, for example methane gas is equivalent to 25 allowances. The allowances are at the end of the year counted and compared to the greenhouse gas emission. If a firm does not have enough allowances it has to pay a fine of € 100 per missing allowance from phase two and forward (European commission, 2015).
The allowances are distributed by the 31 member states involved in EU ETS but are regulated under a single EU wide cap. The supply during phase one was constant at around 2.2 billion allowances but in the beginning of phase two, the number of allowances decreased to around two billion in 2010. The allowances began to decrease linearly by 1.74 percent every year which meant that the supply decreased by about 38.26 million allowances each year. In 2012,
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the cap increased by about 210 million allowances because the aviation sector was introduced to the EU ETS (European commission, 2015).
In 2008 the economic crisis leads to less economic activity and therefore a lower production level and the emission decreased. This resulted in an estimated energy demand decrease of about three percent. (Rickels et al., 2010)
2.1.1 The three different phases in EU ETS
EU ETS is divided into three phases and below are the different goals and characteristics described.
The first phase of EU ETS was between 2005 and 2008 and was a pilot period. The goal of the phase was to evaluate how the system work and prepare the system for phase two which is during the Kyoto protocol commitment (European commission, 2015). Phase one was characterized by only covering CO2 and focused only on emission from power generation and other energy intense industry. Almost all allowances were grandfathered and the penalty for not having an allowance for releasing CO2 was a € 40 fine per emission allowance (European Commission, n.d.).
The second phase was between 2008 and 2012 which was the years the Kyoto protocol was in effect. Multiple changes happened during this period, Iceland, Liechtenstein and Norway joined EU ETS, the cap on allowances was decreased by 6.5 percent compared to 2005 level and the penalty for non-compliance was increased to € 100 per allowance. The goal was to auction 10 percent of the allowances, but only four percent of the allowances were auctioned (European commission, 2015). In 2008 the financial crisis began which decreased the total demand which led to a surplus of allowances which affected the allowance price negatively throughout phase two (European Commission, n.d.).
The third phase from 2013 to 2020 is the current period and the goal is for the allowance price to reach € 30 for the system to be efficient (Brink et al., 2016). At this point EU ETS cover about 45 percent of the total greenhouse gas emission within the EU. Some goals for the period are that new gases and sectors are introduced into EU ETS and auctioning is the default method to distribute the allowances, but the industry sector still uses grandfathering
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as the default method instead of auctioning while the power generating sector will subject 100 percent to auctioning. (European commission, 2015)
The EU ETS affects firms with greenhouse gas pollutant and the electricity market is the single largest sector within the EU ETS. The allowance price therefore affects the electricity price which in turn indirectly affect all firms and especially those firms that have a high electricity consumption.
Figure 1: The EU ETS price (Euro per ton)
According to Brink et al. (2016), the low price is a problem for the EU ETS due to the transition from fossil fueled energy to renewable energy goes slower than expected. The incitement to transition from fossil fueled power to renewable energy is low because of the low allowance price. One way to increase the incitement is to increase the allowance price to the expected price level 2020 of € 30 per ton.
According to Brink et al. (2016) there are three reasons why the EU price is too low.
1. Banking of allowances is allowed.
2. Too many allowances are being “grandfathered”.
3. National policies favor renewable energy, which reduce the demand for allowances.
0 5 10 15 20 25 30 35
05 - Aug Dec,2005 Apr,2006 Aug,2006 Dec,2006 Apr,2007 Aug,2007 07- Dec Apr,2008 Aug,2008 08- Dec Apr,2009 Aug,2009 Dec,2009 10 - Apr Aug,2010 Dec,2010 11 - Apr 11 - Aug 11 - Dec 12 - Apr 12 - Aug 12 - Dec 13 - Apr 13 - Aug 13 - Dec 14 - Apr 14 - Aug 14 - Dec 15 - Apr 15 - Aug 15 - Dec
Euros per EUA
TIme
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Important to note is that even when the allowance price is low, the Kyoto protocol is fulfilled.
The low price only affects the economic efficiency within the EU ETS and not the total emission. If the price is too low, it is reasonable to see a price increase on emission in the future. Therefore, it is important to analyze how the electricity price would be affected by this price increase but to be able to analyze the effect we first need to understand the electricity market.
2.2 The Nordic electricity market
The supply in the Nordic countries are built up by wind, Hydro, nuclear, coal, biomass, gas and oil. The base load supply is built up by renewable energy in wind and hydro power, nuclear energy is green energy but not renewable due to the use of uranium. The renewable electricity has lower marginal cost than the fossil fuel electricity such as coal and natural gas.
If the cost for emission would increase the fossil fuel electricity (coal, gas and oil) would increase which lead to an electricity price increase at both day and night. It is because there is not enough renewable electricity to cover for the whole load production. That means that the EU ETS affects both the night and the day price. If the allowance price increases the electricity price would automatically be affected (International Energy Agency, 2018). Oil, coal and natural gas power generation is not only affected by the EU ETS, they also have their own input prices which also affects the electricity price.
Sweden and Norway both have a lot of hydro- and nuclear power which, are greenhouse gas emission free power generation sources. The problem is that Denmark and Finland both have coal and natural gas power generation, and these electricity sources are affected by EU ETS leading to the emission of greenhouse gases (Fell, 2010). Other power sources are also producing electricity such as oil, wind and bioenergy but their contribution to the total energy production is relatively small and is only used during times with a lot of demand due to their high marginal cost (Brännlund et al., 2012).
The hydro reservoir level is an important variable because of the large amount of electricity coming from hydro power and is used as load provision of electricity and has lower marginal cost than conventional electricity production. Lower hydro reservoir levels can lead to more conventional electricity production due to low load provision of electricity. This means for
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countries like Sweden and Norway with a lot of hydro power, the low hydro reservoir levels will lead to that conventional electricity production will be imported. (Rickels et al., 2010).
As shown in figure two the lowest pollutant production choices are wind and hydro followed by nuclear, coal, biomass, natural gas and oil (International energy agency, 2018). The Nordic countries are outliers in the European electricity production. The renewable electricity part is only 20.9 percent in Europe but in the Nordic countries is a lot larger with Sweden and Norway in charge where Sweden have about 50 percent and Norway about 95 percent renewable electricity in form of hydro power (Rickels et al., 2010).
Figure 2 The distribution between different electricity production sources in the Nordic electricity market
Source: International Energy Agency (2018) 2.2.1 Electricity generators
Before we can discuss the wholesale market price the electricity market must be defined. The Nordic wholesale electricity producers are concentrated to a few companies and the four biggest are Vattenfall, Statkraft, Fortum and E. ON which combined have over half the market share in the region. The Swedish state owned Vattenfall is the biggest with a market
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share of 19 percent followed by the Norwegian state owned Statkraft with a market share of 14 percent (Lundin and Tangerås, 2017). The Nordic wholesale electricity market is characterized by a large part hydro power where Norway has almost 100 percent hydro power and Sweden above 50 percent, which other regions do not have. None of the Nordic countries have a large part fossil fuel power base but Denmark and Finland have the largest in the region. It is the fossil fuel power that is affected by EU ETS which in term affect the electricity price. Often are the renewable resources the base load production and the fossil fuel production is used during peak load production. The load production is the energy production that works regardless of the weather or season and good examples are nuclear power and hydro power. The peak production is the production that is used during high demand or low supply and are often electricity produced by coal or natural gas and can be seen in figure two. This is important because electricity cannot be stored (Lundin and Tangerås, 2017).
2.2.2 Wholesale Nordpool electricity market
The electricity producers offer their electricity on the wholesale market for electricity which is the Nordpool market where distributers buy electricity. The price is given by day-ahead price where the buyers plan what volume they need the next day and buy the volume a day- ahead, hour by hour. The seller does the same thing but with their production. The wholesale electricity price is the price that the producer’s offers to the market which is the price distributors pay. The data is taken from Nordpool which is an electricity power exchange.
The electricity price is divided into different regions e.g. Sweden is divided in four regions and Norway five regions. The regions have their own supply and demand which may make the regions have their own price, but if that occur the lower price region well sell power to the higher price region. This will equalize the price between the regions, but small regional changes may still exist and increases the society’s welfare. Instead the system price is used in this study because the system price is calculated on sales and purchase orders and does not include the available transmission capacity between different regions, but also is the reference price for trading and most of the available financials contracts. All regions in Nordpool are included in the system price and that includes Estonia, Lithuania and Latvia but, they are not included in the study. The system price is called the wholesale price in the rest of the study. (Nordpool, 2017)
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The last part is the retail market and the retail market price are the price given to the consumers. The prices differ between wholesale price and what the consumers pay since consumer price includes taxes and extra cost from distributers.
(Energimarknadsinspektionen, 2017)
This study looks at the wholesale electricity price and therefore the retail price is not taken into consideration when conducting the study.
On a day to day basis the day and night cycle is a big factor for the price changes, the demand changes since more electricity is used during the day than during the night. It is realistic because most of the population is awake and have access to electricity while they sleep during the night and not using electricity.
Over monthly periods the wholesale electricity price fluctuate a lot which can be seen in figure three. The large fluctuations in the first part of the time period is because of heavy fluctuations in the EU ETS price and the latter part is related to the financial crisis in 2008 and 2010 which affected the price. The price in figure three show the price to buy one MWh electricity.
Figure 3: The Nordpool electricity price (Euro per MWh)
0 100 200 300 400 500 600 700 800
05 - Aug Dec,2005 06 -Apr 06 - Aug 06 - Dec 07 - Apr 07 - Aug 07 -Dec 08 -Apr 08 - Aug 08 - Dec Apr,2009 09 - Aug Dec,2009 10 -Apr 10 - Aug 10 -Dec 11 - Apr 11 - Aug 11 - Dec 12 - Apr 12 - Aug 12 - Dec 13 - Apr 13 - Aug 13 - Dec 14 - Apr 14 - Aug 14 - Dec 15 - Apr 15 - Aug 15 - Dec
Price in EURO per MWh
Time
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3. THEORY
This chapter is discussing the function of emission trading systems and electricity markets in conceptual terms: what characterizes the markets as well as how they are connected?
3.1 Emissions trading
EU ETS is a system that uses cap and trade which means that the system has a cap on how much emissions that are released. One allowance is equal to one-ton carbon dioxide and can be traded between parties.
The EU ETS cap and trade system has the perks of having a certainty of quantity and cost- effectiveness. The first perk, certainty of quantity, arises only because a certain amount of trading emissions is on the market which becomes the cap. The system is cost-effective because the flexibility the emissions trading has; this means that all firms face the same carbon price and make sure that the firms cut emission where it is the cheapest.
3.1.1 The supply of emission trading
If we introduce the EU ETS supply and demand to the market, we theoretically have figure four. The supply is vertical because it is the cap, no more allowances can be introduced to the market and all allowances are used during each period which creates a scarcity in the supply. If the supply is too large an excess of allowances would arise, and the price would drop to zero (Rickels et al., 2010). If we assume we are in period one the equilibrium price is where supply period one (S1) and demand period one (D1) intersect and we get the price equilibrium in period one (P1).
If we assume that the policy makers agree on that the price is too low, and therefore agree to solve the problem by allocating fewer allowances in period two. When the supply decreases, we get a new supply at S2. We assume the demand has not changed and there are no
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differences other than the supply decrease between period one and two. This means that the new equilibrium in period two is where S2 and D2 intercross and concludes on a new equilibrium price at P2, which indicates a price increase from period one.
Figure 4: Supply and demand in an emission trading scheme
3.1.2 The demand for emission allowances
The demand for emission trading allowances is for example if the price for an allowance has a lower cost than the cost to do the intended action of the economic control measure, for EU ETS the case is to reduce greenhouse gas emission. For example, if the goal of the emission trading system is to reduce greenhouse gas, a firm will buy allowances if the price to abate greenhouse gas is more expensive than the emission trading allowance price. The firm will abate if the price to abate is cheaper than the price of the emission trading allowance.
The demand side of the EU ETS are driven by the variables economic activity and fuel price.
In 2008 the financial crisis occurred which resulted in a decreased economic activity and a decreased energy demand by three percent. Fuel prices such as coal and natural gas also plays a role for energy demand. A higher fuel price results in a higher cost and the firms will therefore increase their prices which result in less quantity of goods being produced and therefore less pollutant leading to fewer allowances being utilized. (Laing et al., 2013)
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If we assume two periods for EU ETS and the demand for allowances decreases due to a financial crisis it will decrease the economic activity in period two. The equilibrium price in period one is where the supply and demand intersect which is where D1 is equal to S1. In period two the supply decreases due to yearly decrease in the number of allowances to S2.
The demand decreases because of the financial crisis which lead to less economic activity and lower production and the demand is therefore in D2. This means that we have a new equilibrium where S2 intersect with D2 and the result is in this case that the price of allowances does not change.
Figure 5: The supply and demand for the EU ETS market with financial crisis
3.1.3 Marginal abatement cost (MAC)
The basic underlying theory of the EU ETS is the MAC, the MAC theory illustrates the relationship between abatement cost and the total pollutant. The MAC model is a popular model and illustrate the situation on markets. Different MAC between different firms and sectors generates incentives for firms to trade. This means that the carbon market is created to enable trade between firms and to find the lowest abatement cost. In general, cost minimizing with higher abatement cost than the allowance price will buy allowances instead
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of reducing its emissions in new abatement technology or reduce output. Vice versa, cost minimizing firms with lower marginal abatement cost than the allowance price would like to invest in new abatement technology to save allowances and to be able to sell the allowances.
(Haisan, 2011)
The MAC model has some problems according to Kesicki and Ekins, (2012) which should be taken into consideration when observing a MAC model. Some of the problems the model has is that it does not capture transaction costs, limited treatment of uncertainty in the underlying assumptions and problem analyzing market failure.
Figure six shows the theoretical marginal abatement cost for carbon emission but we can assume that EU ETS have a similar MAC curve. The MAC for the new technology is rated from the lowest on the left side of the figure and the MAC increases the more right in the figure. In reality there are one stack for each technology and the width of a stack illustrate the amount of carbon emission that can be reduced from that source, a wide stack means a lot of carbon emission can be reduced with that technology while the reverse is for a slim stack. Technologies below the zero reduces the energy consumption as well as the carbon emission. (Kesicki, 2010)
The first part of the MAC curve shows a negative MAC curve which is the potential abatement once market barriers are overcome and are command and control options. That include end user sectors such as industry, building and transport sectors. The second part of the figure is the middle part which focus on mid-cost alternatives and is the most interesting part of the curve due to this part containing policies focused on markets which results in different abatement level and carbon prices. The right most part of the figure indicates innovation, research and development policies. (Kesicki, 2010)
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Figure 6: Marginal abatement cost the carbon emissions
That marginal abatement cost is the price the EU ETS should be reflected in and the abatement can be archived by investing in cleaner technologies, reducing production level or fuel switching. The first, investing in cleaner technology, is a long or medium run solution to reduce pollutant while the other two solutions are short run solutions. Reducing the production level is self-explanatory and is just reduced produced quantity. (Rickels et al., 2010)
In the short run one of the most important ways to reduce the emission is the switching cost.
The medium and peak load production for electricity is mainly determined by coal and natural gas. The electricity and heat sector producers are the largest emitters with about 75 percent of the total emissions but are only allocated 65 percent of the total allowances.
Changing the dispatch order, for example changing from coal to natural gas allows the producer to reduce its emission with about 40- to 60 percent. The problem is that it changes from country to country because of different dispatch order and country specific composition of the electricity production sector. (Rickels et al., 2010)
When the EU ETS was introduced in 2005 there were some problems with the marginal abatement cost efficiency, Hintermann (2010) found during the first 16 months of phase one of the EU ETS (2005 – 2007) the assumption about the lowest cost pollution being abated
-0,5 0 0,5 1
marginal abatement cost
abatement potential
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first did not hold. This was due to the heavily fluctuated price during the first period of the EU ETS, the price fluctuated between € 0 and € 30. In the second part of phase one the allowance price reached zero euro due to banked allowances not being transferrable to phase two of EU ETS resulted in that the banked allowances were worthless when phase one ended.
The conclusion is that the marginal abatement cost affects the EU ETS demand. If the EU ETS price would increase, more technologies would be profitable which in turn decreases the demand if new profitable technology is used, but that is only in the long or medium run a new technology is introduced and all else is the same. As earlier stated the supply is decreasing each period but, other macroeconomic event or changes toward the EU ETS may also affect the demand in a negative or positive way. This means that new technologies are not used as soon as they are profitable. (Bloomberg, 2010)
3.2 Electricity Market 3.2.1 Electricity demand
There are multiple factors that determine the demand for electricity, temperature and GDP plays an important role. The higher GDP the more goods are produced and therefore more electricity is used but from 1980 the GDP has increased in a faster pace than the electricity price. If GDP were to increase the electricity price would also increase, ceteris paribus.
(Brännlund et al., 2012)
Temperature is an important variable and is heavily affecting the electricity price. During times with extreme temperature, both warm and cold, the electricity demand increase. During colder periods demand for heat increases which increase the electricity demand and during warmer periods there is a higher demand for cooling which in terms increases the electricity demand. The relationship is therefore non-linear due to the relation between temperature and energy demand is shaped as an U. (Rickels et al., 2010)
According to Morss and Small, (1989) is the price elasticity in the electricity market inelastic.
In the long run is the price elasticity -0.38 and in the short run is the price elasticity -0.23.
This means that if the price is increasing by one percent the quantity will decrease by 0.38 percent in the long run. In the short run the quantity will decrease by 0.23 if the price increases by one percent. This is due to problem with substitution because there are a few other goods that can substitute for electricity. The difference between the long and short run is that the
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consumers can change their behavior patterns in response to a higher price in the long run but not in the short run.
3.2.2 Electricity supply
The electricity supply is the stock of electricity which is being produced. Figure two shows the composition for the Nordic countries, but the composition differs from region to region due to geographical differences. For example, France has a lot of nuclear power while Poland has a lot of coal power. (Agora Energiewende and Sandbag, 2018)
A problem with electricity production is that it is hard for electricity producers to change production from one sort of electricity production to another. If for an example input prices increased drastically over a short duration of time the producers cannot change electricity production type, but rather stick to the electricity production and hope for an input price decrease. The enter barrier is high and it is expensive to enter a new electricity production site and it does also take a lot of time to establish which is a great risk. (Rickels et al., 2010) The supply is more elastic than the demand. The base production for the Nordic wholesale electricity market is built up by nuclear and hydro power and are supplied at a lower price.
When the price increases due to an increase in demand the thermal production will be used (Lundin and Tangerås, 2017).
3.2.3 Price formation in the electricity market
The inelasticity confirms what Morss and Small, (1989) concluded in their study which was that the demand for electricity were inelastic and especially in the short run which Lundin and Tangerås (2017) confirms. If more demand is needed suddenly the price will increase rapidly for a small amount of supply because it is hard for the producers to change their production quantity in the short run.
3.3 Connection between the markets
To be able to conduct the study there must be a connection between the emission trading system market and electricity market. Theoretically would an increase in the emission trading price for example the EU ETS price result in a decrease in electricity supply, sell volume.
The input price for fossil fueled electricity would be more expensive which would increase the price in the Nordic wholesale electricity market. The non-fossil fueled electricity would not be affected by the EU ETS price increase.
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The reverse would happen if the emission trading price would decrease. The electricity production would increase due to lower production costs for fossil fueled electricity production which would result in a higher electricity supply and therefore a lower electricity price.
This fit for both load and peak production due to coal is being used during load production and during peak production more fossil fueled production being used which is all affected by the emission trading system price which can be seen in figure two. Therefore, it is possible that coal and natural gas is affected by emission trading (Fell, 2010). Earlier studies such as Fell (2010) and Freitas and da Silva (2015) found a connection between EU ETS and the electricity market in Nordic countries and in Spain respectively.
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4. LITERATURE REVIEW
This chapter is discussing previous studies about EU ETS, electricity market and theory affecting the EU ETS. The chapter begins with an introduction about previous studies affecting EU ETS and a discussion about MAC and continues into studies affecting the electricity and pollution in general and ends with a discussion about the topics and about the current knowledge gap.
4.1 Search strategy
The EBSCO host database, Science direct and Google scholar was used during the search process. The EBSCO host database and Google scholar were used during the search process while Science direct was used to see which articles was cited such as Fell (2010), later on Science direct was used as the main database. In the beginning EU ETS was the most searched keyword due to information was needed to build up the knowledge basis, later on specific searches like Kyoto protocol and marginal abatement cost was the most common searched keywords.
4.2 Earlier studies focused on EU ETS
Fell (2010) study estimate the dynamic relationship between the wholesale Nordic wholesale electricity price and the allowance price where the cointegrated vector autoregressive model (CVAR) was used to show the short- and long run dynamic relationship between the variables. Fell (2010) observed that the fossil-fuel generated electricity where at the margin, to be more specific the coal-fueled electricity was at the margin. The conclusion was that the short-term wholesale electricity prices were heavily affected by the short-term changes in the EU ETS prices, this may not come as a surprise due to the coal-fueled electricity is at the margin and therefore affected by changes and price of the allowances. Another conclusion was that the electricity market in the Nordic countries was a competitive market. The allowance price change did not affect the wholesale electricity price in the long run. Hourly
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wholesale electricity data was used to detect small price changes but the rest of the data being weekly. Data from phase one of EU ETS (2005 to 2007) was used for the model.
A later study about the allowance price effect on the electricity market was made in Spain by Freitas and da Silva (2015). Data from 2008 to 2013 were used which means phase two and first year of phase three were covered in the data set. Cointegrated variation method (CEVM) was used to capture the relation between the allowance price and the wholesale electricity price. It is a variation of a vector autocorrelation model (VAR) which is described in the method chapter. In short CEVM deals with the stationarity problem VAR have. The data used was allowance price, coal price, natural gas price, electric price and exogenous variables such as temperature and rainfall. The result showed that the long run in phase two, when the allowance allocation was free, the elasticity was 0.24, if the allowance price increases by one percent the electricity price increases by 0.24 percent.
Honkatukia et al. (2006) focused on how the Finish wholesale electricity market is affected by the allowance price. The authors used hourly, weekly and monthly data from February 2005 to May 2006 and estimated the CO2 pass through rate. The authors used three different methods, vector error correlation model (CVEM), autoregressive integrated moving average (ARIMA) model and autoregression-generalized autoregressive conditional heteroscedasticity (AR-GARCH). The findings from the models were that during the period, on average about 75 percent to 95 percent of the allowance price passes through to the wholesale electricity price in Finland. Another finding was that the power system characterizes by domestic electricity generation as well as other factors as hydro reservoir level, sensitivity to the different input spot price level, including the allowance cost.
Honkatukia et al. (2006) also simulated how an allowance price increase would affect the wholesale price at 15 percent, 25 percent and 50 percent price increases with a base EU ETS price at € 21.3 per allowance. The simulation was made during three different production loads, low, medium and high load. The conclusion was that at low load non-fossil fueled power can compete with fossil fueled power.
22 Table 1 Literature summary
Study Purpose Method Result
Fell (2010) The purpose of the study is to examine how the Nordic wholesale electricity market is affected by the allowance price.
Fell (2010) uses a cointegrated vector autoregressive model (CVAR).
The short-term wholesale electricity prices were heavily affected by the short-term changes in the EU ETS prices while the long run wholesale electricity price not was affected.
Another conclusion was that the electricity market in the Nordic countries is a competitive market.
Freitas and da Silva (2015)
The allowance price effect on the electricity market in Spain.
Data from 2008 to 2013 was used in the cointegrated variation method (CEVM).
The result showed that the long run elasticity in phase two was 0,24 during a period when the allowances were grandfathered.
Honkatukia et al.
(2006)
How the Finnish wholesale electricity price is affected by the allowance price.
The authors used three different methods. CVEM, ARIMA and AR-GARCH.
A simulation was also made with three different
allowance price increases, at 15-, 25- and 50 percent increase.
The findings from the models were that on average 75 percent to 95 percent of the allowance price passes through to the wholesale electricity price in Finland. Another finding was that the power system characterizes by domestic electricity generation as well as other factors as hydro reservoir level, sensitivity to the different input spot price level, including the allowance cost.
Brännlund et al.
(2012)
The purpose of the study is to estimate how the Swedish electricity price would be affected if the nuclear power were phased out.
The authors used a reduced regression model.
The result showed that a capacity shortage would increase the Swedish electricity price by ten Swedish öre per kWh.
23 4.3 Other studies
There are studies that come with interesting conclusions, different angle and knowledge that do not focus on EU ETS but on other areas. Brännlund et al. (2012) used the reduced regression model to estimate what would happen if the nuclear power where phased out over time in the Swedish electricity market. The result showed that the firms remaining on the market got increased profits due to less supply which lead to higher prices. The problem was that this would lead to a total welfare loss due to the consumer’s welfare loss were bigger than the producer’s welfare gain. Data were collected from 1970 to 2010 and used temperature, rainfall, coal price, nuclear power, GDP and tax. The result showed that a capacity shortage would increase the electricity price by ten Swedish öre per kWh.
Crago and Stranlund, (2015) investigated what would be the optimal taxation for carbon dioxide (CO2) and sulfur dioxide (SO2) in the USA. The study uses the model, regulation of heterogeneous firms under asymmetric information about their abatement cost. The study explains the problems with the greenhouse gases and why a regulation is necessary which include different sorts of pollutions such as stock and uniformly mixed pollutant. The authors conclude that the welfare gain is larger if CO2 and SO2 is regulated. The system does not work efficient if one of the pollutants are over taxed to adjust for an inefficient taxation on the other greenhouse gas.
Morss and Small, (1989) discusses how the electricity price differs between short- and long run demand. The difference between the short- and long run are that the consumers can change consumer behavior in the long run but not in the short run. The behavior change can for example be a different way to heat up a house from electricity to another non- electricity product. The authors show this with elasticities due to the simplicity to interpret. The conclusion was that the long run elasticity was -0.38 and the short run -0.23, this means if the electricity price increases by one percent the demand will decrease by 0.38 percent in the long run and 0.23 percent in the short run. A deeper discussion was made in the theory chapter.
4.4 Discussion
Fell (2010), Freitas and da Silva (2015) and Honkatukia et al. (2006) focus on the effect EU ETS have on the wholesale electricity market. The studies focus on different parts of the
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system were Fell (2010) focus on the Nordic market, Freitas and da Silva (2015) on the Spanish market and Honkatukia et al. (2006) on the Finnish market. Fell (2010) and Honkatukia et al. (2006) uses data from the first phase of the EU ETS but Fell (2010) during the whole phase and Honkatukia et al. (2006) from February 2005 to May 2006. Freitas and da Silva (2015) used data from phase two and first year of phase 3. Fell (2010), Freitas and da Silva (2015) and Honkatukia et al. (2006) showed that there is a connection between EU ETS and the electricity price which strengthens the theory about the allowance price effect on the wholesale electricity price.
The problem with Fell (2010) was the problem regarding the EU ETS prices and marginal abatement costs during phase 1. The main finding of Hintermann (2010) was that the market where inefficient because the MAC theory did not hold. The reason why the MAC theory did not hold was due to the assumption about the cheapest emission being abated first. This occurred due to heavy fluctuations in the allowance price of the first 16 months of phase 1.
The price fluctuated between 0€ and 30€ which made it hard for the firms to accurately buy or sell allowances. Kesicki and Ekins, (2012) discusses the different problem with the MAC.
MAC for example treat uncertainty in a bad way and lack transparency concerning the assumptions. Also, additional shortcoming in the individual assessment of the MAC such as non-consideration of interactions and non-financial costs, a possible inconsistent baseline, double counting and a limited perspective of behavior.
The articles affecting the method chapter are Fell (2010) and Freitas and da Silva (2015). The articles use a sort of VAR model but uses a dynamic contingent model to solve the non- stationary problem in the VAR model (Fell, 2010 and Freitas and da Silva, 2015). The model looks at both short- and long-run perspectives. Brännlund et al. (2012) model is a reduced regression model which will be used in this study. The reduced regression model is a model where, in this case, the supply- and demand variables are used to approximate an equation which will later be used in the study to observe the changes to the electricity price when the allowance price changes. The VAR model fits better but due to complexity is the reduced regression model more fitting. A deeper discussion is found in the method chapter.
This study is a more up to date analysis about the EU ETS influence of the Nordic (wholesale) electricity market. Last study was made by Fell, (2010) and used data from phase one (2005
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to 2007) which had a lot of volatility which the later periods do not have (Ellerman and Buchner ,2007). A newer analysis on the Nordic wholesale electricity market is therefore adequate.
Freitas and da Silva (2015) did a study for phase two and first year of phase three (2008- 2013) which is during a time of lower volatility, but the study was made in Spain while this study will focus on the Nordic countries with different conditions such as weather and economic base.
The knowledge this study will provide is how the electricity price in the Nordic market is affected by EU ETS and during a time with lower volatility but with a price that is too low for economic efficiency and how the Nordic wholesale electricity market will react if the allowance price reaches it expected 2020 price at 30€ per allowance.
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5. MODEL SPECIFICATION AND ESTIMATION ISSUES
This chapter will include a discussion about the different models that can be used and arguments for choosing the reduced regression model instead of the more commonly used vector autoregression model. The Breusch-Godfrey test will be used to check for autocorrelation in the model.
5.1 Model
The basic assumption in the reduced regression model is that the supply (QS) and demand (QD) in the electricity market is set equal (QS=QD). To be able to estimate the electricity price as a function of exogenous supply and demand factors, we need to define the supply and demand. When that is done we can complete the reduced regression model by having one function with electricity price as the dependent variable.
5.1.1 Demand side of the reduced regression model
The demand for electricity according to Brännlund et al. (2012) is a function of electricity price (Pel), temperature (TEMP) and GDP. This study will use GDP instead of tax and income to explain the demand due to an increase in GDP means a higher consumption of electricity.
To formulate the variables a simpler demand function can therefore be set up in equation 1.
𝑄𝐷 = 𝑓(𝑃𝑒𝑙, 𝑇𝐸𝑀𝑃, 𝐺𝐷𝑃) (1)
5.1.2 Supply side of the reduced regression model
Brännlund et al. (2012) found that the electricity supply is dependent on nuclear power and inputs such as coal and rainfall and therefore were nuclear power, coal price and rainfall explanatory variables for the supply for electricity. Brännlund et al. (2012) study focus on the nuclear power while this study focuses on the EU ETS.
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This means that the variables used to express the supply function is: electric price (Pel), coal price (PC), and hydro reservoir level (HRL). HRL will be used instead of rainfall since HRL is the input for producing electricity and low HRL can lead to more fossil fuel electricity generation because hydro power is load provision of electricity (Rickels et al., 2010). EU ETS will also be a variable because we want to observe its effect on the electricity price and therefore the quantity. Fell, (2010) uses the price of EU ETS (PEUA) as an explanatory variable which also will be used in this study. Price on natural gas (PGAS) will be used as a sensitivity test variable which is seen in the parenthesis. Equation two to express the supply will therefore be:
𝑄𝑆 = 𝑔(𝑃𝑒𝑙, 𝑃𝑐, 𝑃𝐸𝑈𝐴, 𝐻𝑅𝐿, 𝑃𝐺𝐴𝑆) (2)
5.1.3 Equilibrium in the market
The next step in the model is to combine demand and supply, therefore QD put equal to QS
which can be seen in function 3. This is done because we want to observe the equilibrium and therefore observe the equilibrium quantity and price which is where the demand and supply intersect.
f(Pel, TEMP, GDP) = 𝑔(𝑃𝑒𝑙, 𝑃𝑐, 𝑃𝐸𝑈𝐴, 𝐻𝑅𝐿, 𝑃𝐺𝐴𝑆) (3) The functions are used to make an expression of the electricity price which can be seen in equation 4. The function shows an expression where electricity price is affected by coal price, EU ETS price, temperature, HLR, GDP and price of natural gas.
𝑃𝑒𝑙 = ℎ(𝑃𝑐, 𝑃𝐸𝑈𝐴, 𝑇𝐸𝑀𝑃, 𝐻𝐿𝑅, 𝐺𝐷𝑃, 𝑃𝐺𝐴𝑆) (4)
A reduced regression model expresses an endogenous variable only in terms of the stochastic distribution and the predetermined variables. Stochastic variable means that a variable comes from a random outcome while, predetermined variable is closely related to exogeneity in the sense the variables is uncorrelated with the current and lagged values but may correlate with the future values. The electricity price is a function of the exogenous variables that affect supply and demand of electricity. In the reduced regression model, the stochastic distribution and the predetermined variables are on the right side of the equation, which is coal price, EU ETS price, HRL, TEMP, natural gas and GDP and can be seen in equation 5. Assumption
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about non-correlation between the disturbance term and the other variables is made. This means that OLS method can be used to estimate the coefficients (Gujarati, 2003).
𝑃𝑒𝑙 = 𝛼 + 𝛽𝑃𝐸𝑇𝑆+ 𝛽𝑃𝐶+ 𝛽𝑇𝐸𝑀𝑃 + 𝛽𝐻𝑅𝐿 + 𝛽𝐺𝐷𝑃 + 𝛽𝑃𝐺𝑎𝑠 + 𝑢 (5) Three different regressions were made which concluded that natural gas price and GDP were not significant and was therefore removed from the model. The first regression included all variables but showed that natural gas price and GDP were not significant. The second regression was conducted without natural gas and still showed that GDP was not significant.
The third regression using OLS without natural gas price as well as GDP yielded in a highly significant result for the rest of the variables. A more detailed analysis of the regression is in chapter seven, results.
The α is the intercept or in other words what price the electricity price start at when the other variables are zero. The β is how much the variable varies and if the variable is positive or negative. The last term u is the disturbance term which represents the variables not included in the model that affects the electricity price. Due to restrictions about how many variables that can be included and knowledge about which variables affecting the electricity price it is impossible to use the right variables. The consequences can both be increased or reduced values of variables and the R2 value is therefore lacking. The R2 value explains how good the data fits the model. The higher the R2 the better fit the model. The disturbance term also helps explaining randomness in the dataset (Gujarati, 2003).
5.1.4 Simulation
To be able to observe how the Nordic wholesale electricity price would be affected if the EU ETS price increased to € 30 per allowance, equation 5 is used without GDP and natural gas as variables because they were not significant to estimate the function for the Nordic wholesale electricity price. The simulation uses the actual observed values for the variables coal price, TEMP, and HRL as explanatory variables and the Nordic wholesale electricity price as the dependent variable. Additionally, the EU ETS price is used as an explanatory variable but instead of using the observed values it is changed to € 30. The estimated values are given from the regression model, this means that we can observe what the new electricity price will be with actual realistic values.
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The problem with the simulation is that an analysis on the observed values would change with a drastic increase on the EU ETS price. More firms might change to renewable energy due to the EU ETS price increases which can lead to the coal price might have a smaller impact than with the current lower EU ETS price. But, this is a speculation and an analysis about the changes in the observed values and estimated values will not be included in this study.
5.2 Econometric issues
The OLS will be used to estimate the alpha and beta values in equation 5. To make a good OLS regression the variables need to have exogeneity, non-biasness, non-autocorrelation and homoscedasticity. Now when we have the equilibrium equation in equation four we can now transform the equation where we can use an OLS model to estimate the values. To be able to use the OLS model we assume that all variables are exogenous. That means that the variables are not determined within the model. Temperature and HRL are both weather variables and are because of that not determined in the model. The price variables EU ETS price, coal price and Natural gas price are determined on the world market and not in the Nordic wholesale electricity market which makes the variables exogenous. Electricity is part of the GDP but is a small part and drastic changes in electricity production do not determine the GDP and therefore can GDP be exogenous. This means that the exogenous criteria in the OLS model is confirmed (Gujarati, 2003)
For the model to be unbiased the Gauss-Markov theorem is applied which states that the best linear unbiased estimator is given by OLS but only if error term has an expected value of zero, uncorrelated and have equal variances. (Gujarati, 2003)
Autocorrelation means that there is correlation between different time series and lagged version of itself over multiple time intervals. The goal is to have non-autocorrelation, which means that the previous observations do not affect the current observation or the future observation. Autocorrelation is not to confuse with correlation because two variables can correlate but not have autocorrelation. (Gujarati, 2003)
Autocorrelation ranges from 1 to – 1, autocorrelation at one means that it is perfect positive autocorrelation. If a variable has an autocorrelation at one, an increase in one-time series lead to a proportionate increase in the other time series. Autocorrelation at -1 is the reverse and if
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a one-time series increases the later time series will proportionally decrease. Autocorrelation is a problem due to the assumption about the observations being independent from each other in a time-series. (Gujarati, 2003)
5.2.1 Breusch-Godfrey-test
The Breusch-Godfrey test checks for autocorrelation in a model. The perks of the Breusch- Godfrey test are that the it can test for autocorrelation non-stochastic regressors, in other words lagged values of the regressand. Another perk is that the test can check for higher- order autoregressive such as AR (1), AR (2) etc. Durbin-Watson is the most commonly used test when testing for autocorrelation but can only test for AR (1) which only check for autocorrelation for one period and it is a problem in this case. Due to variables such as hydro reservoir level and temperature being cyclical over a year or twelve months the test need to be able to check AR (12) for autocorrelation. (Gujarati, 2003)
To do the Breusch-Godfrey test a few steps is taken:
1. Estimate the equation with help of OLS and save the residuals (ut)
2. Use the residuals as the dependent variable and the other variables in your model as independent variables but also the lagged residuals ((ut-1)+ (ut-2) etc.) as independent variables. In this case twelve lagged variables are used ((ut-1)+…+(ut-12)). Take the R2 from the regression.
3. If the sample size is big, theoretically infinite, the test show that(𝒏 − 𝒑)𝑹𝟐 ∼ 𝝌𝒑𝟐. 4. If the (𝒏 − 𝒑)𝑹𝟐 exceeds the critical value of chi-square the null-hypothesis can be
rejected and at least one rho is not autocorrelated. (Gujarati, 2003)
If the model has autocorrelation the OLS method assumptions do not hold and the method may therefore not provide the minimum variance and an unbiased mean. This means that the results may be misleading. (Gujarati, 2003)
5.2.2 Alternative methods
Fell (2010) used the cointegrated vector autoregressive model while da Silva (2015) used contingent variation model which is both a different form of the VAR model. The different VAR model solves the problem with stationarity in different ways which is why the different VAR variation is used. A VAR model’s variable is expressed as a linear function of past or
