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Case study on the effectiveness of carbon pricing estimating the impact of carbon tax on natural gas… Gholami, Zahra 2014

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 Case Study on the Effectiveness of Carbon Pricing Estimating the Impact of Carbon Tax on Natural Gas Demandon British Columbia by Zahra Gholami B.A., Alzahra University  THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in The Faculty of Graduate and Postdoctoral Studies (Integrated Studies in Land and Food Systems) The University of British Columbia   August 2014 © Zahra Gholami, 2014    ii  Abstract British Columbia’s carbon tax was implemented in July 2008 at the rate of $10 per tonne of carbon. It increased for four consecutive years and reached $30 per tonne of carbon. The rate of carbon tax is based on the carbon intensity of the fossil fuels. The second biggest source of primary energy in North America, natural gas, is subject to 5.7 cents/cubic metre of carbon tax in the province of British Columbia. In this study, we adopt a difference-in-differences technique to examine whether or not the BC’s carbon tax has impacted natural gas consumption in commercial and residential sectors in BC, where it is primarily used for space heating. We assemble a monthly panel data from Statistics Canada and Environment Canada spanning from Jan 1990-Dec 2013 for six provinces: Quebec, Ontario, Manitoba, Saskatchewan, Alberta, and British Columbia. While the coefficient for carbon tax is insignificant in residential sector, we find the elasticity of carbon tax for natural gas to be -0.35 in commercial sector.    iii  Preface This thesis is an original, unpublished, independent work by author, Zahra Gholami.   iv  Table of Contents     Abstract ................................................................................................................................... ii Preface ................................................................................................................................... iii Table of Contents .................................................................................................................. iv List of Tables ........................................................................................................................ vii List of Figures ...................................................................................................................... viii Acknowledgements ............................................................................................................... ix Chapter 1. Introduction ..................................................................................................... 1 1.1. Background .................................................................................................................. 1 1.2. Problem Statement ....................................................................................................... 2 1.2.1. Objectives ............................................................................................................. 4 1.3. Methodology ................................................................................................................ 4 1.4. Results ......................................................................................................................... 5 1.5. Outline ......................................................................................................................... 6 Chapter 2. Literature Review: Overview of Carbon tax & Natural Gas ........................... 7 2.0. Roadmap ...................................................................................................................... 7 2.1. Carbon Tax .................................................................................................................. 7 2.1.1. Market Based Instruments .................................................................................... 7 2.1.2. Carbon Tax in the World ...................................................................................... 8 2.1.3. BC’s Carbon Tax .................................................................................................. 9 2.1.4. Literature Review of Carbon Tax ....................................................................... 11 2.2. Natural Gas ................................................................................................................ 14 2.2.1. Natural Gas Units of Measurement .................................................................... 14  v  2.2.2. Production and Consumption of Natural Gas in Canada .................................... 14 2.2.3. Literature Review of Natural Gas Demand ........................................................ 17 Chapter 3. Data ............................................................................................................... 21 3.0. Roadmap .................................................................................................................... 21 3.1. Natural Gas Consumption ......................................................................................... 21 3.2. Natural Gas Price ....................................................................................................... 25 3.3. Income and Gross Domestic Product ........................................................................ 27 3.4. Heating Degree Days (HDD) .................................................................................... 29 Chapter 4. Methodology ................................................................................................. 34 4.0. Roadmap .................................................................................................................... 34 4.1. Fixed Effects Estimation ........................................................................................... 34 4.1.1. Randomized Control Trial and Natural Experiments ......................................... 34 4.1.2. Difference-in-Differeces (DD) ........................................................................... 35 4.1.3. Controlling for Unobservables: Fixed Effects or Random Effects? ................... 36 4.2. Single Equation of Natural Gas Demand .................................................................. 37 4.3. Interfuel Substitution ................................................................................................. 38 4.4. Demand Model .......................................................................................................... 39 4.5. Empirical Results ....................................................................................................... 40 4.5.1. Variables unit of measurement ........................................................................... 40 4.5.2. Coefficients and Confidence Intervals ............................................................... 41 4.5.3. Expected Signs ................................................................................................... 44 4.5.4. Log-linear Coefficient Interpretation ................................................................. 44 4.5.5. Elasticities and Coefficient Interpretation .......................................................... 46 4.5.6. Difference in Response Level ............................................................................ 47 4.5.7. Goodness of fit ................................................................................................... 49  vi  Chapter 5. Conclusion ..................................................................................................... 51 5.1. Summary .................................................................................................................... 51 5.2. Limitation of the Study and Further Research .......................................................... 54 Bibliography ......................................................................................................................... 55   vii  List of Tables Table  2-1: Carbon Tax Rates in British Columbia ............................................................... 10 Table  2-2: Natural Gas Conversion Factors ......................................................................... 14 Table  3-1: Monthly Per Capita Real After-Tax Income ....................................................... 28 Table  3-2: Monthly Per Capita Deflated GDP ..................................................................... 29 Table  3-3: Weather Stations and the Cities' Population Weights ......................................... 32 Table  4-1: Variables Units of Measurement ........................................................................ 41 Table  4-2: Residential Regression Results ........................................................................... 42 Table  4-3: Commercial Regression Results ......................................................................... 43 Table  4-4: Coefficient Interpretations .................................................................................. 45 Table  4-5: Natural Gas Elasticities in Commercial and Residential Sector ......................... 46 Table  4-6: Goodness of fit .................................................................................................... 50     viii  List of Figures Figure  1-1: Natural Gas Commercial Price Trend in Canada 2008-2013 .............................. 3 Figure  2-1: Deflated Carbon Tax (2007 dollars) on Natural Gas in BC (¢/m3) ..................... 9 Figure  2-2: Total Energy Consumption in Canada by Type in 2010 (source: eia) .............. 15 Figure  2-3: Canada's Natural Gas Production and Consumption ......................................... 16 Figure  2-4: Canada's Natural Gas Consumption by Sector, 2008 ........................................ 17 Figure  3-1: Per capita Natural Gas Consumption in Residential Sector (cubic metre) ........ 22 Figure  3-2: Averaged Number of Natural Gas Residential Customers (2000-2013) ........... 23 Figure  3-3: Per capita Natural Gas Consumption in Commercial Sector (cubic metre) ...... 23 Figure  3-4: Averaged Number of Commercial Customers (2000-2013) ............................. 24 Figure  3-5: Natural Gas Prices (2007 dollars) in Residential Sector, Deflated by All Item CPI .......................................................................................................................................... 26 Figure  3-6: Natural Gas Prices (2007 dollars) in Commercial Sector, Deflated by GDP CPI................................................................................................................................................. 27 Figure  3-7: Heating Degree Days by Province ..................................................................... 33     ix  Acknowledgements First and foremost I offer my sincerest gratitude to my supervisor, Professor Gulati, who has supported me throughout my thesis with his patience and knowledge. I thank the opportunity he gave me to work with him as his research assistant. I would also like to acknowledge other committee members, Professor Richard Barichello, for his generous time, useful comments, kind smile and encouragements. I thank Professor Carol McAusland for her insightful suggestions and for introducing the Sustainable Prosperity Fund to me which helped me finance my graduate studies to a great extent. I appreciate the Sustainable Prosperity Research Committee for granting us the funding to do this project.  This thesis is dedicated to my parents and my two younger sisters for their love, support, and encouragement.   1  Chapter 1. Introduction  1.1. Background Climate change is known to be one of the most important issues of the century. There is consensus that human activities such as the burning of fossil fuels like coal and oil, deforestation either for agriculture or urbanization to name a few causes have increased the concentration of atmospheric carbon dioxide (CO2) and other heat trapping gases (Stocker et al., 2013). The consequences of climate change, although varying from region to region, are experienced broadly all around the world: from sea-level rises and melting glaciers, to severe droughts, changes in precipitation, and increased extreme weather frequency and intensity. The province of British Columbia has also experienced increased average temperatures which have contributed to the pine beetle epidemic costing the province 17.5 million hectares of lodgepole pine forest (Carroll et al., 2003).   In an action to reduce greenhouse gas emissions, the province of British Columbia (BC) has introduced North America’s most ambitious tax program. According to the program, carbon tax on fossil fuels started at the rate of $10 per tonne of carbon in July 1st 2008, it increased by $5 for four consecutive years, reached $30 per tonne of carbon in July 1st 2012, which rate has been in place ever since. The carbon tax in BC is revenue neutral; meaning the revenue collected will be used to reduce the other taxes in the province. The tax applies to gasoline, diesel, propane, natural gas, and coal. The carbon tax rate is based on the carbon intensity of the fuels, with coal ranking first and natural gas last in the spectrum.  Being the second biggest source of primary energy consumed in North America, natural gas accounts for just under one-third of primary energy consumption in Canada. More than half of natural gas is used to generate heat and power in industry and about one-third in commercial and residential sectors. Natural gas is predominantly used for space heating in residential and commercial sectors. It supplies 54.6 percent of the energy used to heat homes in Canada, with electricity supplying 19.4 percent. Ninety seven percent of Alberta’s households heat their houses with natural gas; sixty percent of households in Manitoba and  2  British Columbia are heated with natural gas. Ontarians also use natural gas as their principal energy source for heating. In 2012, 47 percent of total carbon dioxide emitted by all industries in Canada—an equivalent of 33370 kilo tonnes of CO2—was due to burning natural gas. In 2007, natural gas was responsible for 32 percent of total GHG emissions in the province of British Columbia.  Although natural gas is mainly composed of methane (CH4) --a less carbon intensified fuel compared to coal and oil— it remains subject to carbon tax of $1.4898 per gigajoule or 5.70¢ per cubic metre in British Columbia.  There are some controversies around the effectiveness of carbon tax in BC, for instance there is the belief that the energy demand is inelastic and therefore an increase in the price of energy due to carbon tax will not provoke any changes in consumer behaviour. People also think that many consumers have no alternative to the energy they consume and any increase in the prices is another burden on especially low-income families. In other words, it is not only regressive but also ineffective. While the government of BC has implemented the policy notwithstanding these controversies in the public opinion, there is still need for studies to test for the effectiveness of carbon tax and the extent to which it has succeeded to create a signal in the market.  In our study we utilize a difference-in-difference model to look at the demand for one the most important primary energies in Canada, namely natural gas, and we aim to examine the extent to which the carbon tax has brought change in the natural gas consumption in the residential and commercial sector in the province of British Columbia where the policy has been implemented.  1.2. Problem Statement Once a unique policy like carbon tax in BC is implemented, it immediately calls for evaluation. An important policy question is ―Did BC’s carbon tax work?‖ and if yes ―How effective has it been?‖ These are important policy questions to answer because: 1) the province has taken an ambitious step in introducing the tax with all the controversies surrounding its effectiveness as well as its potentially negative effects for the viability of the economy in the province. 2) the results allow other jurisdictions to do a better job in adopting  3  a similar carbon tax policy knowing the level of response it creates. 3) once we estimate the price and income elasticities we have a better sense of how regressive the tax is, in other words how it affects the poor versus the rich in the society.  Modeling energy demand itself is an interesting topic of research especially as there have been studies since 1930s focusing more on modeling electricity than natural gas (Dagher, 2012). Natural gas price elasticities have diverse ranges based on where in the world the gas is used and what datasets were used in the study. The last attempt to model natural gas demand in British Columbia dates back to Bernadt and Watkins 1977.  The sizeable increase in the production of natural gas in the United States --thanks to shale gas innovation-- has decreased the prices sharply since 2008. The figure below shows the decline in commercial prices in Canada along with its linear trend. The recent declines in the prices of natural gas in Canada and the United States require new studies with updated datasets to investigate the price and income elasticities of natural gas. Figure 1-1 shows the decrease in prices since 2008 in commercial sector in Canada. These are nominal prices in cents per cubic metre.         Figure 1-1: Natural Gas Commercial Price Trend in Canada 2008-2013  4  1.2.1.  Objectives Given that a four step increase from $10 per tonne in 2008 to $30 per tonne of carbon in 2012 was necessary for the implementation of the carbon tax in BC, the researchers had to wait for the policy to complete its increase phase to start estimating the effect of the policy. The main drive of this study is to answer the important policy question: ―the impact of carbon tax on natural gas consumption in residential and commercial sector‖. We aim to measure natural gas price and income elasticities, in plainer terms, ―what is the response of residential and commercial customers to this increase in BC’s carbon tax?‖ Residential and commercial sectors were chosen as they account for one-third of natural gas consumption in Canada, where it is mostly used for space heating.   Commercial sector includes customers engaged in wholesale or retail trade, governments, institutions, office buildings, etc. and residential sector demand constitutes gas sold for domestic purposes—including space heating, water heating, cooking, etc.—to a residential dwelling unit (Statistics Canada, 2014a).The study aims to estimate two separate demand models for commercial and residential sectors by choosing two different income variables as well as controlling for the change in the temperature. We separate these two sectors to see if the response is different in commercial sector where the gains from energy efficiency is relatively higher compared to residential sector.   1.3. Methodology For the research utilized in this thesis, we make use of the monthly natural gas sales and prices provided by Statistics Canada from Jan 1990- Dec 2013 in Quebec (QC), Ontario (ON), Manitoba (MN), Saskatchewan (SK), Alberta (AB), and British Columbia (BC). We use annual after-tax income and GDP for each of the 6 provinces and transform them into monthly data points. All prices, tax, income and GDP are deflated using appropriate consumer price index (CPI). We also make use of quarterly population in each province to create per capita sales, income, and GDP data. As for heating degree days (HDD), which is an index calculated to reflect the demand for energy needed for heating buildings, we make use of monthly data from 22 weather stations in the metropolitan cities of all six provinces  5  and weigh them based on their relative population density. There are 288 observations for each province that give us panel data of 1728 observations over the span of Jan1990-Dec 2013 for all six provinces. Almost all studies so far have used contemporaneous price as their independent variable to estimate price elasticities. It means the literature implies that supply and demand for natural gas are recursive and least squares estimation has no simultaneous equation bias. We use a fixed effect model to control for unobserved factors in our regression as opposed to random effect model which is estimated using Generalized Least Squares (GLS) and requires stronger assumptions than Ordinary Least Squares (OLS) (Angrist and Pischke, 2008). Furthermore, we compare natural gas consumption in BC influenced with carbon tax with the five other provinces unaffected by carbon tax in our panel data. As we won’t include the substitution energy forms in our model, our price coefficient can suffer from omitted variable bias that is there are other variables that may help explain natural gas demand but not included in the model and they may cause a bias for the estimation of natural gas price. However, as carbon tax is determined exogenously and is not influenced by other forms energy as a substitute for natural gas, our study should have no bias in estimating the equilibrium impact of carbon tax on natural gas demand.  1.4. Results As our dependent variable is natural logarithm of per capita natural gas consumption and all independent variables are not logged, one unit increase in our independent variables changes our dependent variable by a constant percentage (Wooldridge, 2013). We estimate that the price elasticities are -0.52 and -0.88 in commercial and residential sectors respectively. One percent increase in HDD increases the consumption by 0.53% in commercial and 0.50% in residential sector. GDP and income elasticities are 2.13 and 4.67 in commercial and residential sectors respectively. Finally, carbon tax elasticity which is only significant in commercial sector is -0.35.   6   1.5. Outline The rest of the study is organized as follows: Chapter 2 reviews the literature of carbon tax policy evaluation and natural gas demand, the two most important components of this study. Chapter 3, which introduces the dataset, defines the dependent and independent variables used in this study. Dedicated to the methodology, chapter 4 describes empirical strategies as well as empirical results of our study. Finally, chapter 5 summarizes the paper and gives recommendation for further research.      7  Chapter 2. Literature Review: Overview of Carbon tax & Natural Gas  2.0. Roadmap This chapter has two arteries: section 2.1 overviews carbon tax as a market based instrument; reviews the policy in BC, and carbon tax’s literature review; section 2.2 is devoted to natural gas in Canada: its consumption, production, export as well as the review of natural gas demand .  2.1. Carbon Tax 2.1.1. Market Based Instruments Economists view climate change as a market failure. The forces of the market fail to impose the costs and consequences of an economic activity such as burning fuels on the agents responsible. The third condition of a market to be complete-which is for all the costs of the economic activity to be borne by those in the trade-is not satisfied. The firms and individuals do pay for the cost of the fuel which includes cost of extraction, refining and delivery but fail to pay for the cost of carbon dioxide emissions that are borne by the other agents in the market-- simply because there is no price to pay (Keohane and Olmstead, 2007). Market-based instruments like carbon tax, highly favored by environmental economists for their ability to tackle market failures such as climate change, are regulations that aim to change the agents’ behavior through market signals.  In this sense, market-based instruments are in contrast with more directive methods such as ―command and control.‖ While the latter demands forcefully that firms employ certain technology standards or reduce pollution to a desired level regardless of its costs, th0e more flexible market-based instruments--such as tradable permits or carbon tax—encourage firms to shoulder pollution controls by taking  8  actions that are to their interest and the policy maker’s ultimate goal (Stavins, 2003). Carbon tax uses the existing structure and administration system of government to enforce a new tax, therefore it is cheaper to implement by a government and more difficult to avoid by consumers (Stavins, 2003). 2.1.2. Carbon Tax in the World There are a few countries and regions around the world that have a carbon tax in effect. Finland was the first to implement a carbon tax in 1990, others include: Denmark, Netherlands, Sweden, Norway, Italy, New Zealand, Switzerland, Colorado in the United States (Lin and Li, 2011), and Australia which introduced  a national carbon tax in 2012 and repealed it after two years. There are some tax exemptions for industry in the five northern European countries. BC’s tax exemptions, which we will mention later in this chapter, seem small relative to the tax exemptions in Europe. Finland has exempted heavy fuel oil and liquefied petroleum gas from carbon tax. However, it doesn’t offer tax exemptions or relief to industry which remains subject to the tax just like private users (Ekins and Speck, 1999). Denmark has implemented carbon tax for both domestic and business sectors; however the businesses are exempted from 50% of the standard rate. Based on the energy intensity of the fuels, further exemptions are applied, for instance: if the carbon tax bill is more than 1% of the business’s sales revenue, the tax will be decreased to 25% of the original fee (Wier et al., 2005). Eventually, a high-energy consuming business ends up paying no carbon tax at all. The Dutch tax affects small energy consumption levels, namely households which use energy for non-transport purposes. Once again, energy-intensive industries are exempted for the large portion of their fossil fuel consumption (Lin and Li, 2011). Sweden’s carbon tax is based on the carbon and heat capacity of the fuels. Sweden has also given a relief equal to 75% of carbon tax to manufacturing industry, and commercial greenhouse horticulture. Norway’s pulp and paper industry pays half of the carbon tax, the coal and coke used in producing cement and leca are fully exempted from carbon tax (Lin and Li, 2011).  9  2.1.3. BC’s Carbon Tax Carbon Tax on fossil fuels in BC started at the rate of $10 per tonne of carbon in 2008 and increased by $5 for four consecutive years to reach $30 per tonne of carbon in 2012, the tax has been in place ever since. The carbon tax in based on the carbon intensity of the fossil fuels putting coal on the first and natural gas the last in carbon tax rates, table 2-1 below shows the carbon tax rate for some of the fuels. Figure 2-1 shows the deflated carbon tax on natural gas from July 2008 -Dec 2013, the tax is the same for both commercial and residential sectors.             Figure 2-1: Deflated Carbon Tax (2007 dollars) on Natural Gas in BC (¢/m3)  10  Table  2-1: Carbon Tax Rates in British Columbia   Exemptions from carbon tax in BC include:  Fuel that is to be exported for use outside the province of BC.  Fuel purchased by a registered air or marine service.  Fuel consumed in an inter-jurisdictional cruise ship  Sealed, pre-packaged fuel of four litres or less  Coloured fuel purchased by a farmer that is delivered to their farmland (also exempt from Motor Fuel tax) (Ministry of Finance, 2014)  Carbon tax is known to be a Pigouvian tax which is levied on the activities that impose negative externality on others. In other words, the tax is a way of internalizing the marginal social cost of pollution (Helm, 2005). Although carbon tax is a Pigouvian tax it can still be regressive.  A regressive tax is the one that affects the low-income families more than high-income families. Intuitively, a higher percentage of the income in a low-income family is spent on fossil fuel than in a high-income family. Furthermore, it is easier for a high-income family to switch to more efficient devices or cars as the price of fuel increases in comparison to a low-income family who is sunk with the devices they have-- which tend to be older or less efficient.   11  Taxes are often treated by suspicion from the public that any tax is a way for government to bridge the gap in budget deficits. Therefore, to make the carbon tax more acceptable by general public, the carbon tax in British Columbia was introduced as revenue neutral. It means all the revenue collected from carbon tax is used to reduce personal and corporate taxes. The tax reductions for individuals and families for the years 2009/10 to 2012/13 fiscal years consist of:  The first two personal income tax bracket rates which were reduced by 5 per cent effective January 1, 2008;  Low Income Climate Action tax credit which is paid quarterly along with the federal GST credit and BC HST Credit;  A Northern and Rural Homeowner benefit of up to $200 as of the 2011 taxation year. All carbon tax revenue is returned to taxpayers through tax reductions Revenue neutrality also aims to protect the competitiveness of the businesses in British Columbia. In fact, the revised report of the carbon tax revenue in 2013/14 shows the tax has been revenue negative as the government has returned $20 million more than the total carbon tax revenue gathered of $1,212 million  (P. A. Ministry of Finance, 2014).  2.1.4. Literature Review of Carbon Tax Cansier and Krumm (1997) review the tax on air pollutants like sulphur dioxide, nitrogen dioxide, and carbon dioxide in the Scandinavian countries, as well as in the Netherlands, France, and Japan. They look at the structure of the tax and review the exemptions and reliefs offered by each country to help the competitiveness of their industries. Whalley and Wigle (1991), and Nordhaus (1990) estimated the effect of carbon tax on carbon dioxide emissions globally and find the tax had significant impact in reducing CO2 emissions. Whalley and Wigle (1991) emphasize in their second observation on the rule for distributing tax or quota revenues between regions, and particularly between the developing and developed regions.   12  Wissema and Dellink (2007) in an analysis of the impact of carbon tax on Irish economy employ a general equilibrium model and estimate that a carbon tax equivalent of €10 to €15 per tonne of carbon dioxide will reduce CO2 emissions by 25.8%. They estimate significant changes in production and consumption of high carbon-intensity fuels and a shift towards lower carbon-intensity fuels. Bjørner and Jensen (2002) investigate the impact of Danish carbon tax on industrial energy demand in Denmark using a large micro-panel data. Their study shows that the carbon tax revolution during 1990s resulted in a 10% decrease in energy consumption. Bohlin (1998), in a study of Swedish carbon tax on CO2 mitigation, finds that the impact of the tax differ across different sectors. The study shows while the impact of carbon tax is significant in the transportation system, it does not impact consumption in the industrial sector largely due to the fact that industry receives much greater exemptions than other sectors in Sweden. Lin and Li ( 2011) adopt a difference-in-difference method to estimate the impact of carbon tax in five European countries, namely: Denmark, Finland, Sweden, the Netherlands and Norway. They find that in Finland carbon tax has a negative significant effect on CO2 emissions. The impact for Denmark, Sweden and Netherlands is negative but statistically insignificant. They also blame tax exemptions for weakening the impact of carbon tax on the consumption of energy intensive industries. ―BC’s Carbon Tax Shift After Five Years: (An Environmental and Economic Success Story)‖ is the title of a research report that compares the fossil consumption of British Columbia with the rest of Canada with the base year of 2007 without controlling for any other variables in the demand models or any specifications about the type of fuels consumed (Elgie, 2013). In a study called ―Carbon Tax Salience and Gasoline Demand‖, Brandon and Rivers look at the impact of carbon tax on short-term gasoline consumption and show the impact of tax to be greater than an equivalent increase in the market price of gasoline. Their findings suggest that carbon tax is more salient than the same price change,  13  meaning that consumers don’t react the same way to the tax as they do to a shock to the supply market (Rivers and Schaufele, 2012).  Elgie ( 2013) uses a difference-in-difference technique to evaluate the impact of carbon tax in BC on all fossil fuels subject to carbon tax including natural gas in the first five years of the policy. The study reports the fossil fuel consumption has reduced by 16.1% in BC when elsewhere in Canada it has risen by 3%. The study claims to have captured the impact of 2008 recession in their technique by comparing BC with other provinces including Ontario that is known to be most impacted by the 2008 recession. Our study is the first one to look specifically at the impact of carbon tax on natural gas consumption in commercial and residential sectors by controlling for income and the change in temperature in the Canadian province of British Columbia.    14   2.2. Natural Gas  2.2.1. Natural Gas Units of Measurement Natural gas is either measured based on energy content in Gigajoules (GJ), or measured in volume in metric units. The other common measures is Million British Thermal Units (MMBtu). One GJ is almost 0.948 MMBtus which has the same energy level of 27 litres of fuel oil, or 39 litres of propane, 26 litres of gasoline or 277 kilowatt hours of electricity. Canada’s volume of supply and demand of natural gas is measured in Trillion Cubic Feet (Tcf), where 1 Tcf equals 1,000,000,000,000 cubic feet (cf). The standard consumer billing in Canada uses cubic metres, and 1000 cubic metres as the volumetric measure. A cubic metre is approximately 0.038 GJs. The table below shows the common conversion factors for natural gas (Statistics Canada, 2014a). Table  2-2: Natural Gas Conversion Factors British Thermal Units (BTU) Cubic Feet (CF) Gigajoules (GJ) 1000 Cubic Metres (103m3) 1 Million (1MMBtu) 1000 (1Mcf) 1.055 0.028 0.948 Million 0.948 1 0.027 35.3 Million 35.315 37.3 1  2.2.2. Production and Consumption of Natural Gas in Canada Natural gas—a fossil fuel mainly composed of methane (CH4) – is the second biggest energy source consumed in North America. Natural gas is used extensively in commercial and residential sectors for purposes such as: space heating, water heating, cooking and  15  clothes drying. In 2010, natural gas was about 22% of total energy consumption in Canada (EIA, 2012).            Figure 2-3 above pictures total energy consumption in Canada, with natural gas providing 22% of it. Canada is amongst the first three largest natural gas producers in the world after the US and Saudi Arabia. Canada’s production is transferred across provinces and borders mainly through pipelines. Alberta, British Columbia, and Saskatchewan are of the biggest producers of natural gas with 67%, 27% and 3% share of natural gas production in Canada in Dec 2013. Canada is a net exporter of natural gas to the United States. Figure 4 above taken from the   Figure 2-2: Total Energy Consumption in Canada by Type in 2010 (source: eia)  16   U.S Energy Information Administration Website shows the trend of production and consumption of natural gas in Canada from 2000-2011. The change in consumption and production patterns has led to a fall in the gas export to the United States (EIA, 2012).  Statistic Canada defines commercial sector as customers whose businesses involves wholesale or retail trade, as well as government institutions, office buildings, etc. The definition for residential sector is the sale of gas for domestic purposes including: space heating, water heating, cooking, etc. Berndt and Watkins (1977) give a very similar definition residential gas requires the gas used in space heating and appliance consumption such as water heaters; commercial gas consumption include the gas consumed by hotels, restaurants, stores, offices, and apartment blocks. For both sectors, space heating is the primary usage of natural gas. The pie chart below (figure 2-4) shows the natural gas consumption by different sectors in Canada. About half of natural gas in Canada is used in industry and the other third to heat Figure 2-3: Canada's Natural Gas Production and Consumption  17  buildings in residential and commercial sectors, other usages are: generating electricity and road transport (Bramley, 2011).              2.2.3. Literature Review of Natural Gas Demand Modeling energy demand has always been of great interest to economists. An overview of the number of studies done on estimating natural gas demand by Dagher (2012) counts 182 studies on natural gas demand compared to 405 studies on electricity until 2007. The majority of the studies were done during 1970s and 80s following the oil shocks. The demand estimation is usually separated between residential and commercial, and industrial sectors. While it is harder to separate the demand of residential and commercial Figure 2-4: Canada's Natural Gas Consumption by Sector, 2008  18  sectors from each other, the industrial demand is normally estimated separately as the industry uses the gas to produce heat and power which require a different econometric method compared to residential and commercial. One of the first studies to look at natural gas demand in this manner in Canada is Fuss et al (1977) . Their data is annual during 1960-71 in four regions of Canada; the method of estimation is: Zellner efficient producer. The study reports commercial and residential price elasticities to be -0.72 and -0.96 respectively.  Followed by Balestra and Nerlove (1966) in a study of commercial and residential sectors using panel data of 36 American states during 1957-62 which resulted in the estimate of -0.63 for price elasticity and 0.62 for income elasticity using log-linear specification--Berndt and Watkins (1977) use the annual data spanning from 1959-74 in Ontario and British Columbia to estimate  two separate equations for free demand in residential and commercial sectors. They find the price and income elasticities to be -0.686 and 0.133 respectively.  Danielson (1977) also uses a log-linear model to estimate the price and income elasticities using monthly data spanning from 1949-74 from the United States. The findings suggest price elasticity of -4.6 and income elasticity of 6.40. However, it should be noted that this study is estimating the demand at the national level. The results from more than a hundred studies since 1940 on natural gas demand give the researchers a divergent range of elasticities. Some of the studies claim income is the most important determinant of the demand, others emphasize on the importance of price in natural gas demand, interfuel substitution is known to be important by some studies and not others. Dagher (2012) concludes that using different estimation methods, and not reporting the associated standard errors of the coefficients make it difficult for researchers and end-users to use the results in the literature, rely on the estimates, and compare them across different studies. The first survey of natural gas price and income elasticities along with other forms of energy were done by Taylor (1977). He surveyed 18 studies and found natural gas price  19  elasticity to range between -0.15 to -1 and generally thought to be inelastic. Al-Sahlawi (1989) attempts to update Taylor’s results, this survey classifies natural gas demand studies by demand type (residential, commercial, and industrial), and reports their estimation technique, their data type, and the regions or countries where the data comes from. This survey also blames different estimated periods, data sources, and demand types for the variation of price and income elasticities from a study to another. He finds the price elasticities vary between -0.05 to -0.88 in the short run and between -0.39 to -4.6 in the long run, the income elasticites vary from -0.33 to 0.95 in the short run, and between -2.19 to 6.4 in the long run. The wide range of income and elasticities are heavily due to using different regions and time-series for the estimations. The national studies tend to differ from those with a more disaggregated data at the state or province level. The results found in the literature imply that the level of study influences the results greatly (Bohi and Zimmerman, 1984). A number of factors such as: change in the efficiency of appliances, innovation in the area of Shale gas which led to a drop in natural gas prices and the increase in natural gas access in general-- call for using more updated data in estimating the natural gas demand. The literature strongly recommends using data at a more disaggregated level to increase the accuracy of the price and income elasticities. Therefore in our study we use monthly data from Jan 1990-Dec 2013 at the provincial level to estimate natural gas demand for BC by comparing it to Quebec, Ontario, Manitoba, Saskatchewan, and Alberta using a log-linear model widely used in the literature. As natural gas is mainly used for space heating, inclusion of Heating Degree Days is essential in modeling natural gas demand (Berndt and Watkins, 1977). The change in temperature is responsible for the large portion of demand.  If the base temperature is assumed to be 18 degrees Celsius, the cumulative number of days in which the temperature is below the base will represent HDD, which reflects how much energy will be needed due to the change in temperature.   20  We describe all our variables specification: definition, collection and cleaning in chapter 3.     21  Chapter 3. Data  3.0. Roadmap In this chapter we review the data used in our analysis: the data sources, their collection and modification. Section 3.1 looks at natural gas consumption in residential and commercial sectors; section 3.2 examines natural gas prices; in section 3.3 we review income and GDP; finally, section 3.4 introduces HDD.  3.1. Natural Gas Consumption Statistic Canada (2014) in table 129-0003 (Sales of natural gas, monthly) provides monthly data on natural gas sales and prices at the provincial level. The sales data and prices are divided into three sectors: industrial, commercial, and residential. The units of measurement for the natural gas sales are cubic metres ×1000, the prices are in cents per cubic metre.  For our analysis, we need per capita gas consumption. Using table 051-0005 (estimates of population, Canada, provinces and territories) we create per capita consumption in commercial and residential sectors. We expand the quarterly population data into monthly data, and divide the total sales in each sector by the population in the corresponding month which yields per capita natural gas sales in that sector.                where Ys,t, in cubic metres, is per capita natural gas consumption in province s, at time t. For instance: Quebec in Jan-2008. TYs,t is the total natural gas consumption in province s at time t. Hs,t is the population of province s at time t. Figure 6 below shows the trend in per capita natural gas sales (in cubic metres) in residential sector in the six provinces of our study for the period of 2004-2013.  22  The bar chart that follows compares the average number of customer in residential sectors during 2000-2013 (number of customers averaged over 14 years).                   Figure 3-1: Per capita Natural Gas Consumption in Residential Sector (cubic metre) 01002003000100200300Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Jan, 2004Jan, 2005Jan, 2006Jan, 2007Jan, 2008Jan, 2009Jan, 2010Jan, 2011Jan, 2012Jan, 2013Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Quebec Ontario ManitobaSaskatchewan Alberta British ColumbiaPer capita natural gas sales to residential sector (cubic metre)Time: monthly frequencies Jan2004-Dec2013 23                    050100150050100150Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Quebec Ontario ManitobaSaskatchewan Alberta British ColumbiaPer capita natural gas sales in commercial sector (cubic metre)Time: monthly frequencies Jan 2004-Dec 2013Figure 3-2: Averaged Number of Natural Gas Residential Customers (2000-2013) Figure 3-3: Per capita Natural Gas Consumption in Commercial Sector (cubic metre)  24          As we can see from the graphs, Alberta has the greatest per capita natural gas consumption in the commercial sector, followed by Saskatchewan and Ontario. Quebec has the smallest per capita natural gas consumption in the residential sector. As for the number of customers: Ontario has the largest number of gas residential customers followed by Alberta and British Columbia; Quebec has the smallest number of customers between the six provinces. Note that about 97% of Alberta’s homes are heated with natural gas, 60% of households in Manitoba and British Columbia use natural gas. Ontarians also use natural gas as their principal energy source for heating.  The trend seen in the consumption needs to be modeled using price, income and HDD that explains the differences in the level of consumptions in the six provinces. The figure below shows the per capita natural gas consumption (in cubic metre) in the commercial sector. The bar chart in figure 3-4 compares the average number of customers (averaged over 2000-2013) in the commercial sector in the six provinces. Figure 3-4: Averaged Number of Commercial Customers (2000-2013)  25  The largest per capita consumption in the commercial sector belongs to Saskatchewan, closely followed by Alberta and Manitoba. Once again Quebec has the smallest per capita consumption. The largest number of customers belongs to Ontario and the smallest number is in Manitoba’s possession.   3.2. Natural Gas Price Along with the natural gas sales, Statistics Canada reports monthly natural gas prices in cents per cubic metre in table 129-0001. To calculate real prices, we deflate the prices in residential sector by all item monthly Consumer Price Index (CPI) which is provided in table 326-0020 (Consumer Price Index (CPI), 2011 basket, monthly (2002=100)) of Statistics Canada (2014b), and for commercial prices we use table 380-0066 (Price indexes, gross domestic product quarterly (2007=100)) (Statistics Canada, 2014c).  For our analysis, we choose to have the year 2007 as the base year (2007=100). We give an example here on how to make the new CPI*. Suppose        is the CPI with base year of 2002 in province s at time t for example British Columbia in March 1998(           ) to calculate              we divide             by              .                                        ×100 We repeat the same practice for all CPI data points to get CPI* (2007=100). Using the formula below we deflate the prices:                          ⁄ where Ps,t is the price of natural gas in province s at time t.         is all item CPI  for province s at time t (2007=100) .  26  The graphs below show the trend in residential and commercial real prices in the provinces for the period of 2004-2013 in 2007 dollars (2007=100).                   Figure 3-5: Natural Gas Prices (2007 dollars) in Residential Sector, Deflated by All Item CPI 2040608020406080Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Quebec Ontario ManitobaSaskatchewan Alberta British ColumbiaDeflated Natural Gas Price in Residential Sector (cents/cubic metre)Time (monthly frequencies) 27             As it can be seen in the price graphs in both residential and commercial sectors, Alberta has the lowest price ranges; Quebec has the biggest average gas prices. Generally, the prices tend to be lower in the colder seasons and higher in the warmer seasons with some exceptions. This trend is more often observed in the residential prices, as it can be seen in the graphs: residential prices tend to fluctuate more accordingly than commercial prices.   3.3. Income and Gross Domestic Product The next variable in modeling energy demand is income. We choose the households after tax income to be the income variable in the residential sector, and the gross domestic product (GDP) to be the income representative in the commercial sector.  Figure 3-6: Natural Gas Prices (2007 dollars) in Commercial Sector, Deflated by GDP CPI 020406080020406080Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Jan 2004Jan 2005Jan 2006Jan 2007Jan 2008Jan 2009Jan 2010Jan 2011Jan 2012Jan 2013Quebec Ontario ManitobaSaskatchewan Alberta British ColumbiaDeflated Natural Gas Price in Commercial Sector (cents/cubic metre)Time (monthly frequencies) 28  We obtain the household disposable income from Statistics Canada (2014) table 384-0040 (Current accounts - Households, provincial and territorial). The data in this table is annual household income in million dollars. For our analysis, we divide the data by 12 to obtain monthly data—we are aware that obtaining data with this method does not give us as much variation as we would have obtained from data that is collected monthly, however, we are restricted to the annual data offered by Statistics Canada. To obtain per capita income we also divide the income by monthly population in each province. Finally, we gain real income by deflating the income using the all item CPI. The table below shows the mean and median in the six provinces for Jan2000-Dec 2013.          To obtain gross domestic product, we use table 384-0038 (Gross domestic product, expenditure-based) provided by Statistic Canada (Statistics Canada, 2014e). This data is provided across provinces annually, therefore we divide it by 12 to obtain monthly GDP. To obtain per capita GDP we divide it by the monthly population. Lastly, we deflate per capita GDP by its CPI provided in 380-0066 (Price indexes, gross domestic product quarterly (2007=100)). Table 3-1: Monthly Per Capita Real After-Tax Income M nthly per capita defalated after-tax income (2007 dollars)Statistics for Jan 2000-Dec 2013Province mean median min maxAlberta $2,626 $2,699 $2,205 $3,049Ontario $2,163 $2,179 $2,020 $2,315British Columbia $2,146 $2,215 $1,825 $2,382Saskatchewan $2,006 $1,993 $1,651 $2,397Manitoba $1,908 $1,925 $1,696 $2,096Quebec $1,892 $1,924 $1,686 $2,028 29            3.4. Heating Degree Days (HDD) Natural gas is mainly used for space heating in residential and commercial sectors. The first study to include HDD as a variable in natural gas demand was Berndt & Watkins (1977). We also include HDDs to control for the change in temperature that directly influences the demand. Heating degree days (HDD) is an index that calculates the difference between the temperature of a building with a base temperature of 18  in a month .This index helps estimate how much energy will be demanded to heat buildings based on the change in temperature. Basically, it says how much and for how long the outside temperature is below 18 degrees Celsius. We explain more thoroughly with a simplified example: suppose we are to calculate the heating degree days for the month of May. On May 1st the outside temperature is 16 degrees (2 degrees below 18) Celsius the entire day (although that is rarely the case, it makes it easier to demonstrate how HDD is calculated)  Table 3-2: Monthly Per Capita Deflated GDP Monthly per capita real GDP (2007 dollars)Statistics from Jan 2000-Dec 2013Province mean median min maxAlberta $5,699 $5,832 $4,647 $6,729Saskatchewan $4,376 $4,172 $3,289 $5,644Ontario $3,863 $3,860 $3,682 $4,058British Columbia $3,596 $3,665 $3,261 $3,889Manitoba $3,325 $3,379 $2,983 $3,668Quebec $3,286 $3,292 $3,090 $3,436 30  The HDD on May 1st is:  2(degrees) × 1(day)=2 heating degree days;  On May 2nd the outside temperature is 15 degrees Celsius for 18 hours of the day (3/4 of the day) and 14 degrees Celsius for the other 6 hours of the day (1/4 of the day). The heating degree day on May 2nd is:  [3(degrees) × 0.75(day) ]+ [4(degrees) × 0.25(day)] =3.25 heating degree days On May 3rd the outside temperature is 18 degrees Celsius for the entire day which means there is no need to use energy to heat the building, therefore the heating degree days is zero and so on.  We can accumulate the heating degree days of each day in a month to reach the heating degree days in that month (HDDMay1+HDDMay2+…+HDDMay31= HDDMay ). The higher the number, the more energy is needed to heat buildings. Note that there are no negative heating degree days, meaning that if the temperature is above 18 degrees in a day the heating degree days is zero on that day.  HDDs are calculated by hundreds of weather stations across Canada. Environment Canada (2011) reports monthly HDDs collected from these weather stations scattered around Canada. In order to calculate one data point for each province, we make use of HDDs reported by major weather stations in metropolitan cities of that province. We use the relative population of each city to weight the city’s HDD and obtain the provincial HDD by summing up the weighted HDD of each individual city.        ∑                 31  where HDDs,t is the HDD in province s at time t; HDDi,t is the HDD in city i at time t; n is the number of metropolitan cities in that province, and   is the relative population of that city,                            ∑             For our analysis we pick 22 weather stations in the six provinces. We use the data from census 1996, 2001, 2006 and 2011 to calculate the relative population in each city. In the table below the city population density belongs to the census in 1996. We have mostly used the weather stations at the airports as they are known to provide more reliable weather reports. We download 288 excel files—one for each month of the data—from Environment Canada’s website, select the weather stations, extract their data and give them their corresponding weight, and  finally create one data point for each province in each month: a total of 1728 HDD observations across Canada from Jan 1990-Dec 2013. If a weather station throughout this time has been removed from the list of Environment Canada, we replace it with another weather station in the same area.    32   Figure 3-7 below shows the HDD for different provinces from 2004 to 2013.  The higher the HDD is for a month, the colder that month is, which means more energy is needed to heat buildings. Manitoba is the coldest province in our data followed by Saskatchewan; British Columbia has the mildest winters between the six provinces. We use the same HDD for residential and commercial sectors.   Table 3-3: Weather Stations and the Cities' Population Weights 1 Victoria BC VICTORIA INT'L AIRPORT 0.132 Abbotsford-Mission BC ABBOTSFORD AIRPORT 0.063 Vancouver BC VANCOUVER INT'L AIRPORT 0.764 Kelowna BC KELOWNA AIRPORT 0.065 Edmonton AB EDMONTON INT'L AIRPORT 0.516 Calgary AB CALGARY INT'L AIRPORT 0.497 Regina SK REGINA AIRPORT 0.478 Saskatoon SK SASKATOON AIRPORT 0.539 Winnipeg MAN WINNIPEG INT'L AIRPORT 1.0010 Ottawa QC OTTAWA CDA 0.0611 Ottawa ON OTTAWA MACDONALD-CARTIER INT'L AIRPORT 0.1012 St. Catharines - Niagara ON ST CATHARINES AIRPORT 0.0513 Windsor ON WINDSOR AIRPORT 0.0414 London ON LONDON AIRPORT 0.0615 Kitchener-Cambridge-Waterloo ON WATERLOO WELLINGTON AIRPORT 0.0516 Hamilton ON HAMILTON AIRPORT 0.0817 Oshawa ON OSHAWA WPCP 0.0418 Toronto ON TORONTO LESTER B. PEARSON INT'L AIRPORT 0.5820 Quebec QC QUEBEC/JEAN LESAGE INTL AIRPORT 0.1521 Montreal QC MONTREAL/PIERRE E TRUDEAU INTL AIRPORT 0.7622 Sherbrooke QC SHERBROOKE AIRPORT 0.03City' Population WeightWeather StationProvinceCityNum 33     Figure 3-7: Heating Degree Days by Province  34  Chapter 4. Methodology   4.0. Roadmap In the first section we describe fixed effects estimations and why it was chosen over random effects estimation; section 4.2 explains why choosing a single equation for estimating the natural gas demand  is justified. Section 4.3 tells the reader why we choose to have only own-price elasticity of demand; finally section 4.4 gives us the demand equation for the regression.   4.1. Fixed Effects Estimation In this section we describe why we choose a difference-in-differences (DD) method of estimation which is one kind of fixed effects method of estimations for analysis. We begin by comparing natural experiments and randomized control trails; proceed with requirements for DD, and we compare fixed effects models with random effects model. 4.1.1. Randomized Control Trial and Natural Experiments Randomized control trails are also called the gold standard for the ability they give to a researcher to identify causal effect relationship by randomly assigning treatment to the treatment group and comparing them to the control group. These types of experiments, more common in development economics, are known to be extremely expensive and are often times considered to be unethical.  Economists often evaluate a policy or estimate the impact of an event by the help of the existing data which is created by the policy or event itself. These types of experiments are called natural experiments.  Natural experiments, also known as quasi-experiments, are created when an event such as a change in government policy creates two groups (individuals, firms, cities, provinces, etc.) where one is affected by the policy and the other is not. Unlike randomized control trials the treatment in a natural experiment is not randomly assigned to the treatment and control  35  groups. However, by controlling for differences that exist between the control and treatment group through a difference-in-differences (DD) method, a researcher can evaluate the impact of the policy.  4.1.2. Difference-in-Differeces (DD) Utilizing DD techniques to estimate average treatment effect requires having at least two data points for both the control and treatment group in the study, one before and one after the policy change. This type of data is known as panel or longitudinal data: repeated cross sections over time or time-series for each cross-sectional unit (individuals, firms, cities or provinces. For example: natural gas consumption, prices, temperature and income of six provinces over a period of fourteen-year period. When we have the same time period (T) for each cross-sectional units (S), we say our data is a balanced panel data with T×S number of data points.  DD was first utilized by John Snow in 1855 who suspected dirty Thames water was responsible for epidemic of cholera in Soho. The data, John Snow believed, showed that fewer people had died in districts whose water supplier changed their source of water from dirty Thames to a cleaner water source which was free of sewage. Both groups of people breathed the same air but used different water sources, which lead him to conclude that bad water , not bad air, was responsible for the epidemic (Angrist and Pischke, 2008). We proceed with a simplified version of our DD regression based on Wooldridge (2013). Suppose we aim to evaluate the impact of carbon tax policy in BC on natural gas consumption. BC is our treatment group, we choose Ontario (ON) to be our control group which didn’t have a policy in place. Let     be a dummy variable equal to 1 for BC and 0 for ON. Let     be a time dummy variable equal to 1 for after policy (2009) and zero before the policy (2007) (we had the carbon tax policy in 2008).                                             36   ̅      ̂   ̅      ̂   ̂   ̅      ̂   ̂   ̅      ̂   ̂   ̂   ̂   ̂1= ( 09,BC  ̅09,ON    ̅07,BC  ̅07,ON   ̂  is the DD estimator in absence of other factors in the regression such as price, income, etc. It is also called average treatment effect as it evaluates the impact of the policy on the average y which is noted by  ̅.  ̅     is the average outcome for BC before the policy in 2007. 4.1.3. Controlling for Unobservables: Fixed Effects or Random Effects? DD is one kind of fixed effects estimation with the identifying assumption that the trend in consumption would be the same for both provinces in the absence of the carbon tax (Angrist and Pischke, 2008). We know that British Columbia differs from Ontario but these differences will be captured by province fixed effects. A simple regression equation will suffer from the omitted variable bias if we don’t control for unobserved factors that affect the dependent variable. We categorize the unobserved groups into two groups: those that change over time and those that are fixed over time. Let us assume we only have one explanatory variable x.                                      where the subscript s denotes provinces and subscript t denotes time, 2007 pre- and 2009 post-policy time. The dummy variable      is one at t=2009 and is zero at t=2007. This would allow the intercept to change with time. The variable    captures the time-invariant factors that impact    . In the literature    is known as a fixed effect as it is fixed over time, it  37  controls for unobserved province heterogeneity. With larger number of time periods compared to cross-sections we get a better estimate of   , which is usually not the case (Wooldridge, 2013) , however in this study we have 288 time periods for each cross-sections. An alternative to fixed effects models are random effects models. Random effects strategies are estimated using Generalized Least Squares (GLS) which requires stronger assumptions than Ordinary Least Squares (OLS). Fixed effects estimations are used when the fixed effect  is thought to be correlated with the regressors. Allowing this correlation makes fixed effects model a better tool compared to random effects in ceteris paribus evaluation. Fixed effects models require the key explanatory variables to vary over time; if there are variables like gender or demographics that hardly change with time, random effects estimation is a better choice than fixed effects (Wooldridge, 2012).  Based on the requirements needed for using a DD method and characteristics of our data and the nature of the policy, we conclude that using a fixed effect model for our analysis is a better choice in controlling for unobserved factors across provinces than a random effects model. We think that our annual fixed effect captures unobserved factors such as price of electricity that is revised annually. Controlling for the price of electricity as a substitute for natural gas is important to make sure that our estimates won’t suffer from omitted variable bias.  4.2. Single Equation of Natural Gas Demand Almost all studies so far have used contemporaneous price as their independent variable to estimate price elasticities. It means the literature knows that supply and demand for natural gas are recursive and least squares estimation has no simultaneous equation bias. Berndt and Watkins (1977) have justified the use of independent estimation of the single demand equation to estimate natural gas demand. They say in case of natural gas, prices are determined recursively, in other words the parameter estimation doesn’t suffer from simultaneity and potential identification problem. They mention that the price that the  38  distributor charges is inflexible in relation to the quantity the buyers demand in the short term.  As Canada is a net exporter of natural gas to the United States, a formal test to check whether natural gas prices are exogenous or not, is to compare Canada’s market with a bigger market in the United States using a co-integration test. Comparing the two markets with a formal test is beyond the scope of this study. For our analysis we assume the natural gas prices are exogenous, we are aware that if this assumption is not fully met it will bias the coefficient for price. As we don’t prove that the prices for natural gas are determined exogenously, the price for natural gas can suffer from simultaneous bias. We will later compare our results with those reported in the literature, but warn our readers that our results can be biased to some extent.  4.3. Interfuel Substitution Since we don’t have access to monthly prices of electricity for commercial and residential across provinces we won’t be able to check the interfuel substitution between electricity and natural gas. It is worth mentioning that there might be substitution from other fuel sources like coal and oil to natural gas as natural gas has a lower carbon tax rate but we won’t be able to capture that in our model. We try to capture the impact of the unobserved variables across provinces by introducing annual province fixed effects which we think will capture the unobserved electricity prices across provinces that are revised annually however this is not the same as having the price for electricity for each month of our data. While fixed effects in our model will reduce the omitted variable bias in natural gas estimation it could still be the case that natural gas price coefficient is suffering from omitted variable bias and as we discussed earlier from simultaneous equation bias.  The simultaneous equation bias or omitted variable bias will affect the price variable as the price might be determined endogenously or influenced by the price of substitutes that are not  39  presented in the model, however, carbon tax that is determined exogenously based on the carbon intensity of fossil fuel won’t suffer from either simultaneous equation bias or omitted variable bias as neither are impacting carbon tax. Thus, our results for estimating the equilibrium impact of carbon tax on natural gas consumption are not biased.  4.4. Demand Model We use a log-linear regression principle to estimate natural gas demand and the impact of carbon tax on the gas consumption. A constant elasticity model could be obtained by using a log-log functional form, however, due to the presence of zeros in some of our explanatory variables we stick to log-linear model. Our independent variable is natural logarithm of per capita natural gas sales in residential and commercial sectors, other explanatory variables expect the dummies will be in their linear forms. In this manner, we will be able to interpret the change in explanatory variables with percentage change in the dependent variable. The equation below shows the demand equation:  Natural gas demand for residential sector:                                                 ∑∑                        where i represents provinces 1 to 6 and t is time that runs from Jan 1990 to Dec 2013 (288 months) we will have               dummy variables  log(y) is the natural logarithm of per capita natural gas consumption,   pric is the price of natural gas in cents per cubic metre (2007 dollars)  inc is per capita after-tax income in 100× Canadian dollars (2007 dollars)  hdd is 10×heating degree days  40   cotax is carbon tax in cents per cubic metre (2007 dollars)  Fixed effects: s is the province dummy; yr is the annual dummy 143 dummies ((24 years*6 provinces )-1).  Natural gas demand for commercial sector:                                                ∑∑                       where i represents provinces 1 to 6 and t is time that runs from Jan 1990 to Dec 2013 (288 months)  log(y) is the natural logarithm per capita of natural gas consumption  pric is the price of natural gas in cents per cubic metre (2007 dollars)  gdp  is per GDP in 100 × Canadian dollars (2007 dollars)  hdd is 10×heating degree days  cotax is carbon tax in cents per cubic metre (2007 dollars)  Fixed effects: s is the province dummy; yr is the annual dummy 143 dummies (24 years*6 provinces -1).  4.5. Empirical Results 4.5.1. Variables unit of measurement  41  Table 4-2 shows the units of measurement for the variables used in the regressions. It should be noted that our dependent variable is natural logarithm of per capita natural gas sales therefore one unit increase in our independent variable changes the dependent variable by a certain percentage equal to its corresponding coefficient. For instance, GDP per capita is measured in 100 dollars. Once we interpret its coefficient we know $100 increase in GDP per capita will increase the consumption by 0.18 %.  4.5.2. Coefficients and Confidence Intervals In table 4-3 we demonstrate all the coefficients with their corresponding standard errors, p-values, 95% confidence interval, and whether or not the coefficient is significant at the 5 and 10 percent alpha level. If the p-value for a coefficient is smaller than                , we reject the null hypothesis that the coefficient is equal to zero that is the coefficients are significant. Table 4-1: Variables Units of Measurement Vari bl Unit of measurement Variable Unit of measurementPrice cents/cubic metre Price cents/cubic metreGDP per capita 10×dollars Income per capita 10×dollarshdd 10×heating degree days hdd 10×heating degree dayscarbon tax cents/cubic metre carbon tax cents/cubic metreCommercial Residential 42  As we can see in table 4-2 below the p-value for carbon tax is greater that alpha therefore for both levels of alpha we can’t reject the null hypothesis. The coefficient for carbon tax in the residential sector is statistically insignificant.   Residential Regression Results: price, income and carbon tax deflated by all item CPI (2007=100)[95% Conf.  Interval]5% 10%Residentialprice -0.027 0.001 -22.58 0.000 -0.029 -0.024 yes yeshdd 0.020 0.000 71.36 0.000 0.019 0.020 yes yesincome 0.023 0.004 6.23 0.000 0.015 0.030 yes yescarbon tax -0.060 0.051 -1.18 0.239 -0.161 0.040 no no** Fixed effects in both regressions are year*province fixed effects, 143 dummy variables ((24 years*6 provinces)-1).Variables Coef. Std. Err. t P>tsignificanceTable 4-2: Residential Regression Results  43   Table 4-3 shows the regression results for commercial sector. We use different deflator for each set of the results. Section I of the table 4-3 demonstrates the regression results when the quarterly GDP deflator was used. This deflator was obtained from Statistics Canada table 380-0066 (Price indexes, gross domestic product, quarterly (2007=100)), which gives the GDP deflator at the national level. For Section II we show the results when an annual GDP   Table 4-3: Commercial Regression Results  44  deflator at the provincial level was used to deflate price, GDP per capita and carbon tax. This deflator is offered in table 384-0039 (Implicit price indexes, gross domestic product, provincial and territorial, annual (2007=100)) (Statistics Canada, 2014f). Section III in table 4-3 gives us the result when we use the same deflator we used for the residential sector, which is all item Consumer Price Index.  As we can see from table 4-3 the results are almost identical in section II and III, but the coefficient for carbon tax is slightly higher in section I. For commercial sector, GDP deflator is a better choice than all item CPI because GDP deflator includes different subsections of the commercial sector into the calculation of the deflator. As our data is monthly, a quarterly deflator is a better choice than an annual one. Thus, we use the results from section I that is the data which was deflated using quarterly GDP deflator at the national level, as the basis of our interpretation in the rest of the study. 4.5.3. Expected Signs  We can see in table 4-3 and 4-4  that all the coefficients in commercial and residential sectors have the expected signs suggested by theory. Negative sign for price and carbon tax coefficient indicates that any increase in prices is associated with a decrease in the consumption. We expect to see a positive coefficient for per capita income, and per capita GDP. The signs for the coefficients for these two variables in both sectors meet our expectations. HDD, which increases as the temperature goes below 18 , should have a positive coefficient, that is as HDD increases (the weather gets colder) the per capita natural gas sales should increase, specifically because natural gas is primarily used for space heating. 4.5.4. Log-linear Coefficient Interpretation  As mentioned in the previous sections, the dependent variable is natural logarithm of per capita natural gas consumption, therefore the coefficients of our independent variables represent a percentage change on the dependent variable (Wooldridge, 2013).  45                  where y is per capita natural gas consumption and xi is any of our dependent variables. As we multiply    by 100, we get the percentage change in per capita natural gas consumption by one unit change in variable xi.          As it can be seen in table 4-5, the coefficient of price shows that one cent increase in price decreases the consumption by 1.5% and 2.7% in commercial and residential sectors respectively. A ten-degree-day increase in HDD increases the consumption by 2.2% in commercial and 2% in residential sector. A ten-dollar increase in GDP or income leads to 0.6% and 2% increase in natural gas use in commercial and residential sectors respectively. Finally, one-cent/cubic-metre increase in carbon tax decreases consumption by 10.4% in the commercial sector. It should be noted that the carbon tax variable is the tax imposed on natural gas which is currently 5.7 cents/cubic metre when the carbon tax is 30 dollars per tonne of carbon, therefore a one-cent/cubic-metre increase on natural gas-specific carbon tax is equivalent of 5.26 dollars per tonne of carbon increase in carbon tax.  independent variable increase dependent variablecommercialprice 1 cent 1.5% decreasehdd 10 heating degree days 2.2% increaseGDP $10 0.6% increasecarbon tax 1 cent 10.4% decreaseresidentialprice 1 cent 2.7% decreasehdd 10 heating degree days 2.0% increaseincome $10 2.3% increasecarbon tax insignificantTable 4-4: Coefficient Interpretations  46  4.5.5. Elasticities and Coefficient Interpretation  In order to be able to compare our results with the literature, and to eliminate the units of measurement in interpreting the coefficients we estimate the elasticities of our independent variables. We calculate the elasticites by using the mean of independent variables. For price, income, and HDD we compare one-cent, ten-dollar, and ten-degree-day increase with the mean of price, income/GDP, and HDD respectively from Jan 1990-Dec 2013 in British Columbia. For carbon tax we use the mean of carbon tax from Jan 2008-Dec 2013. The results are reported in table 4-5.           In both commercial and residential sectors the results for price and income/GDP elasticities are within the range that was previously calculated in the literature that we reported in the literature review for natural gas (Al-Sahlawi, 1989). Price elastitcities are -0.52 and -0.88 in commercial and residential sector respectively. It should be noted that the results in the literature vary largely from one study to another based on the method of estimation and the Table 4-5: Natural Gas Elasticities in Commercial and Residential Sector Commercial Sector Independent Variable Elasticityprice -0.52per capita GDP 2.13hdd 0.53carbon tax -0.35Residential Sectorprice -0.88per capita after-tax income 4.67hdd 0.50carbon tax NE 47  nature of the data used which makes it hard for researchers to compare their finding with the literature.   The absolute value of price elasticities in both sectors are between zero and one which suggest that natural gas demand is inelastic, moreover commercial sector demand is more inelastic than residential demand. This finding is also aligned with the fact that energy is a necessity. One percent increase in price of natural gas is associated with 0.52 and 0.88 percent decrease in consumption of natural gas in commercial and residential sector respectively.  The sign of income and GDP variable are positive which means natural gas is a normal good, an increase in either income or GDP is associated with an increase in the consumption of natural gas. Intuitively, an increase in income means an increase in purchasing power which can result in more consumption (bigger houses, more appliances, etc.) and an increase in GDP will cause more economic activity which eventually results in bigger consumption level. 4.5.6. Difference in Response Level  The elasticity of carbon tax is -0.35 in commercial sector. As we saw in table 4-5 a one-cent increase in price is associated with 1.5% decrease in consumption whereas one-cent increase in carbon tax is associated with 10.4% decrease in natural gas consumption in commercial sector that is 6.9 times larger response.  Rivers and Schaufele (2012) in their study of saliency of carbon tax in the gasoline market find that carbon tax creates a response that is 7.1 times larger than an equivalent gasoline price increase. They make use of the theory in behavioral economics to rationalize the 7.1 times larger response to carbon tax increase versus an equivalent price increase. The logic works as follows: the consumers care about the the impact their behavior or other people’s behavior has on the environment. Carbon tax enters their utility function through prices and a  48  direct argument. Suppose a consumer divides her income between good a and b where good a is clean and untaxed, good b is a fossil fuel that has carbon tax c. The consumer has wealth W and her utility function is             the price of b is f=p+c, p is the price of fossil fuel and c is carbon tax. If a consumer is utility maximizer, she chooses                     where                  and the consumer exhausts all its wealth consuming a and b at the optimum level:         . If we take second derivative with respect to c from           the result is                       we see the impact of carbon tax through direct impact and indirect impact. If the direct impact that is          then there is only a price impact and the prediction is that              . However, the empirical findings are often in contrast with this prediction. Chetty et al (2009) using experimental data find that consumer are more responsive to a visible tax (for instance shown on their bill separately from price-induced cost) than an increase to prices for some other reason.  In short, the saliency of carbon tax suggests as consumers care about the environment and the impact their behavior on the environment, they will not react to carbon tax the same way they do to a similar price increase. Carbon tax creates a response that is larger than equivalent price change as consumers are signaled that consuming fossil fuel is harming the environment. A concerned, rational consumer, who earns utility from the keeping the environment clean, would feel guilty to consume more once she is signaled by a carbon tax. The other reason for justifying the difference between the response to price change versus carbon tax is the short run versus long run impact. As we reviewed in the data sections, natural gas prices are volatile; consumers are familiar with the trend and expect the prices to fall after each increase. The increase in prices doesn’t resemble a permanent change to consumers, whereas an increase in carbon tax based on the carbon intensity of the fuel which does not decrease in the short run works as a credible threat to the consumers. No matter how  49  cheap the fuel gets carbon tax will not decrease therefore the change in carbon tax has a long term impact on consumer’s decision making, choice of new appliance, and investing on efficiency. 4.5.7. Goodness of fit  R-squared and adjusted R-squares are measures to evaluate the goodness of fit. Adjusted R-square penalizes the addition of any independent variable to the regression. Given that R-square will never decrease by addition of any more explanatory variable, adjusted R-square is a better tool of measuring the goodness of fit.  In table 4-6, we report the number of observation, the critical value for the F-test (which tests the significance of the whole regression), p-value, adjusted R-square, and root MSE. The F-test checks for the overall significance of the regression, H0: β1= β2= β3= … = βi=0 and H1: at least one of βi is different from zero. The null hypothesis states that knowing the value of our independent variables doesn’t help explain the expected value of the dependent variable. With the p-values equal to zero to three places after the decimal point we strongly reject the null hypothesis. We conclude that the independent variables explain some variation in per capita natural gas consumption in residential and commercial sectors.     50           Table 4-6: Goodness of fit Number of obs 1728 Number of obs 1728F(147,  1580) 148.75 F(147,  1580) 296.72Prob > F 0.000 Prob > F 0.000R-squared 0.932 R-squared 0.965Adj R-squared 0.926 Adj R-squared 0.962Root MSE 0.2204 Root MSE 0.2273Commercial Residential 51  Chapter 5. Conclusion  5.1. Summary Climate Change with its more than ever visible consequences: melting ice glaciers, increased sea levels, extreme weather events across the world and etc. is one of the most important global issues which is due to an increase of the greenhouse gas emission including carbon dioxide (CO2) in the atmosphere (Oreskes, 2004). The province of British Columbia has also experienced increased average temperatures which have contributed to the pine beetle epidemic costing the province 17.5 million hectares of lodgepole pine forest (Carroll et al., 2003). Economists view climate change as a market failure. The forces of the market fail to impose the costs and consequences of an economic activity such as burning fuels on the agents responsible. The third condition of a market to be complete-which is for all the costs of the economic activity to be borne by those in the trade-is not satisfied (Keohane and Olmstead, 2007). Market-based instruments like carbon tax and tradable permits are the economists’ favourite tools for battling market failures like climate change (Stavins, 2003). British Columbia, in its attempt to utilize a policy instrument to decrease GHG emissions, introduced its unique, comprehensive carbon tax program. Carbon tax on fossil fuels started at the rate of $10 per tonne of carbon in July 1st 2008, increased by $5 for four consecutive years, reached $30 per tonne of carbon in July 1st 2012. The carbon tax in BC is revenue neutral, that is, the revenue collected will be used to reduce the other taxes in the province. Gasoline, diesel, propane, natural gas, and coal are the fuels subject to carbon tax. Natural gas is one the most important primary energy sources in the whole of North America. It accounts for one-third of energy consumption in Canada. Moreover, Canada is the third largest producer of natural gas in the world, following the United States and Saudi  52  Arabia. Over one-third of natural gas consumption in Canada is used to heat homes and buildings. Like other fossil fuels, natural gas is subject to carbon tax based on its carbon intensity, natural gas consumers pay a uniform 5.7 ¢/m3.  The question of our study is: to what extent BC’s carbon tax affects domestic and commercial natural gas consumption in the province. This is an important policy question for the province because it addresses the controversies around the policy, and evaluates its impact. The results are also important for other jurisdictions in Canada and more generally in North America that are after adopting the same policy. We also estimate own-price and income elasticities of natural gas in both sectors, which need to be updated in the literature. We estimate two models for commercial and residential sectors that differ in their inclusion of per capita gross domestic product (GDP) in the commercial sector and per capita after-tax income in the residential.  The main contribution of this study is assembling new data set for estimating the impact of carbon tax on natural gas consumption in BC. For one thing, BC’s carbon tax is a relatively new policy with only one attempt to estimate its impacts (on gasoline consumption), and for another, natural gas energy modeling has always been of great interest to economists and an updated study is always in demand.  For the present study, we create a panel dataset of the monthly natural gas sales and prices from Jan 1990- Dec 2013 for six provinces of Quebec (QC), Ontario (ON), Manitoba (MN), Saskatchewan (SK), Alberta (AB), and British Columbia (BC); 1728 observations: 288 data points for each province. We expand annual after-tax income and GDP into monthly data points for six provinces. We deflate all prices, incomes, and taxes to 2007 dollars. As for heating degree days (HDD), we select monthly data reported from 22 weather stations in the metropolitan cities of all six provinces and weigh them based on their relative population.   53  Commercial sector includes wholesalers or retailers, governmental institutions, office buildings, etc. and residential sector consists in domestic users of natural gas for purposes like space heating, water heating, cooking, etc. (Statistics Canada, 2014a). To use independent estimation of natural gas demand, we need to ensure that the equations don’t suffer from simultaneous equation bias. In other words, we ensure that the prices are determined independently. Berndt and Watkins argue why in case of natural gas single independent demand estimation using Ordinary Least Squares (OLS) is justified: in the short time the prices, offered by the distributors to the commercial and residential buyers, are inflexible to the quantity demanded (Berndt & Watkins, 1977). Finally, we utilize a difference-in-differences method, one kind of fixed effects estimation, to estimate the impact of carbon tax as well as own-price and income elasticities. The coefficient of price shows that one cent increase in price decreases the consumption by 1.5% and 2.7% in commercial and residential sectors respectively. A ten-degree-day increase in HDD increases the consumption by 2.2% in commercial and 2% in residential sector. A ten-dollar increase in GDP or income leads to 0.6% and 2% increase in natural gas use in commercial and residential sectors respectively. Finally, one-cent/cubic-metre increase in carbon tax decreases consumption by 10.4% in the commercial sector. In both commercial and residential sectors the results for price and income/GDP elasticities are within the range that was previously calculated in the literature. Price elastitcities are -0.52 and -0.88 in commercial and residential sector respectively.  Income elasticity is 2.13 and GDP elasticity is 4.67. We conclude that carbon tax does have an impact on reducing natural gas consumption in commercial sector: a one-cent/cubic-metre increase in carbon tax on natural gas, which is equivalent to $5.26 increase in carbon tax per tonne of carbon, will decrease the consumption by 10.4% in commercial sector. The elasticity of carbon tax is equal to -0.35.  54   5.2. Limitation of the Study and Further Research We can’t check for the co-integration of Canada and the States natural gas market. We haven’t proved that the natural gas prices in Canada are influenced by the prices in the US and therefore our price coefficient can suffer from simultaneous bias.  Since we don’t have access to monthly prices of electricity for commercial and residential across provinces we won’t be able to check the interfuel substitution between electricity and natural gas. It is worth mentioning that there might be substitution from other fuel sources like coal and oil to natural gas as natural gas has a lower carbon tax rate but we won’t be able to capture that in our model. We try to capture the impact of the unobserved variables across provinces by introducing annual province fixed effects which we think will capture the unobserved electricity prices across provinces that are revised annually however this is not the same as having the price for electricity for each month of our data. While fixed effects in our model will reduce the omitted variable bias in natural gas estimation it could still be the case that natural gas price coefficient is suffering from omitted variable bias and as we discussed earlier from simultaneous equation bias. Further research is needed to model natural gas consumption in industry where the natural gas bills are much higher and the gains from efficiency are larger. 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