Estimating the relationship between natural gas prices and renewable energy demand in the industrial sector in the United States

Estimating the relationship between natural gas prices and

renewable energy demand in the industrial sector in the United

States

Author: Quirien Reijtenbagh University of Amsterdam 10549471

Thesis supervisor: Stephan Lagau January 31, 2016

Abstract

In the light of growing global warming concerns, using more renewable energy sources instead of fuel sources can reduce anthropogenic greenhouse gas emissions. Reducing these emissions should be of particular interest to the United States, since the country was the second-most energy consuming country in 2015. In 2015, U.S. total energy consumption equaled 97.7 quadrillion British thermal units (Btu). In the same year, the industrial sector consumed 22% of the U.S. total energy

consumption, which was predominantly used for process heating and cooling of products in the manufacturing process and to power machinery. Natural gas are primarily used as energy source for these activities, though renewable energy sources are also an option. In 2015, 11% of industrial energy consumption originated from renewables, of which 98% originated from biomass. With a future of cheap natural gas being possible in the U.S., it is interesting to know how natural gas prices influence renewable energy demand in the industrial sector. Therefore, the aim of this research to investigate this relationship. To estimate this relationship Ordinary Least Squares (OLS) regression is used in the form of a static log-log model, a dynamic log-log model and a AR(4) dynamic log-log model. Indicators for ‘income’ (real GDP per capita) and ‘the ambition to transfer to renewables’ (CO2 emissions of U.S. total consumption) are used as control variables. For all models time-series data is used. It appears that only for the AR(4) dynamic log-log model all OLS assumptions hold. The results of this model show a significant positive correlation between the natural gas price of the previous month and today’s industrial renewable energy demand . To be precisely, regression results of the model showed that at a 90% confidence level an 1% increase in industrial natural gas prices of one month ago, results in a 0.0250% increase in a current industrial energy demand.

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1. Introduction

1.1 Relevance

The Intergovernmental Panel on Climate Change (IPCC) (2014) is the leading international body for the assessment of climate change. In the report of 2014 the IPCC concluded that “Human influence on the climate system is clear, and recent anthropogenic emissions of greenhouse gases are the highest in history. Recent climate changes have had widespread impacts on human and natural systems” (IPCC, 2014 p. 2). The IPCC names economic growth and population growth as major drivers behind the rise in anthropogenic greenhouse gas emissions. The report is clear about the fact that substantial emissions reductions over the next few decades can reduce climate risks in the 21st century and beyond, increase prospects for effective adaptation, reduce the costs and challenges of mitigation in the longer term and contribute to climate-resilient pathways for sustainable development (IPCC, 2014 p. 17).

In this light, transition to renewable energy sources will be one of the solutions to emission reduction. To consider the cost-effectiveness of these energy policies it is of importance to policy makers and energy economists to gather knowledge about the elasticity’s of substitution of various fossil fuels for renewable energy sources. For example, the more difficult it is to substitute fossil fuels for renewable energy sources, the more expensive climate change mitigation policy will be (Stern, 2011).

Considering the recent shale gas revolution in the United States (2006-2016) that put a downward pressure on natural gas prices (EIA, 2016, 1a) and president Trump being outspoken to explore shale gas operations further (see https://www.donaldjtrump.com/policies/energy), a future of abundant natural gas is likely to occur. This gives a possible prospect of cheap natural gas, which makes the relationship between natural gas prices and renewable energy demand even more

interesting to investigate. Especially in the light of combatting the adverse effects of climate change and the role the transition to renewable energy could play. The urgency to transfer to renewables is particular of relevance for the United States, since the U.S. is the most energy consuming country in the world – after China -. In 2015, U.S. total energy consumption (i.e. the electric power, residential, commercial, industrial and transportation sector) equaled 97.7 quadrillion British thermal units (Btu), equal to 18% of world total primary energy consumption (EIA, 2016, 1b).

In 2015, the U.S. industrial sector was accountable for 22% of total energy consumption, being the third most energy-consuming sector after the U.S. electric power sector (see Table 1.1). As a result, environmental effects of energy consumption of the industrial sector can have a vast impact climate change. However, this could be mitigated by using more renewable energy instead of using fossil fuel sources. Therefore, the aim of this research is to investigate the effect of the natural gas price on renewable energy consumption in the industrial sector in the United States. To answer this question three empirical models are constructed: a static log-log model to investigate whether there is a contemporary relationship between natural gas prices and renewable energy demand in the industrial sector; a dynamic autoregression to see whether this relationship is dynamic; and a dynamic AR(4) regression log-log model to correct for serial correlation and multicollinearity problems.

The structure of this research is as follows; section 1.2 contains a short introduction of the industrial sector and its energy consumption. Subsequently, Chapter 2 offers a literature review. In section 2.1 previous research is covered on interfuel substitution of natural gas by renewable energy in the industrial sector. This information is useful for providing information about the relation of interest. Section 2.2. contains research on drivers behind renewable energy demand to estimate which control variables should be included in the empirical model. Chapter 3 explains all variables used in the empirical models and which data sources are used. Chapter 4 gives an overview of the empirical

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models used in this research and model results. In sector 4.1. the static model and its results are covered and 4.2. contains the dynamic autoregression model. In chapter 5 the conclusion of this research is presented, following results from chapter 4. Section 5.1. displays the conclusion, section 5.2. provides a discussion and section 5.3 further recommendations

1.2. Industrial energy consumption

The primary business of the industrial sector is to produce, assemble or process goods. The industrial sector includes the following types of activities: manufacturing (e.g. paper milling, breweries and manufacturing of pesticides, aircrafts, paint, motor vehicle parts); agriculture, forestry, fishing and hunting (e.g. farming, cattle and aquaculture); mining, including oil and gas extraction (e.g. gold, iron, coal, limestone and metal mining and natural gas extraction); and construction (e.g. highway, oil pipeline and housing constructions). See for more information https://www.naics.com/ NAICS codes 31-33, 11, 21 and 23, respectively. Subsequently, industrial activities are divided into three

manufacturing categories all having particular industry subgroups: energy-intensive manufacturing (i.e. food, pulp and paper, basic chemicals, refining, iron and steel, nonferrous metals, nonmetallic minerals), nonenergy-intensive manufacturing (i.e. other chemicals and other industrials) and nonmanufacturing (i.e. mining, construction, agriculture, forestry and fishing) .

In the industrial sector overall energy consumption is predominantly for process heating and cooling of products in the manufacturing process and the powering of machinery. Furthermore, it is used for boiling to generate hot water or steam, for cogeneration or as basic chemical. To a lesser extent energy is consumed for facility heating, air conditioning, and lighting. Conclusively, in this research, industrial energy consumption is defined as energy consumed for above mentioned

activities, including generators that provide useful thermal output and/or electricity for these activities i.e. industrial electricity-only plants and industrial combined-heat-and-power (CHP) (EIA, 2016, 1c).

In 2015, the U.S. industrial sector was accountable for 22% of total energy consumption. From the 22%, U.S. total industrial energy consumption, 39% originated from prom petroleum, 44% originated from natural gas, 7% from coals and 11% originated from renewables. Renewable energy consists of energy sourced from hydroelectric power, geothermal, solar, wind and biomass (EIA, 2015, 2a). The historical U.S. industrial energy consumption is shown in Figure 1.1. From roughly 2009 i.e. after the financial crisis of 2008 – an increasing trend in use of all energy sources can be seen.

Figure 1.3 shows the historical trend of industrial total renewable energy consumption. As shown, almost all renewable energy consumed over the years originated from biomass. From 11% renewable energy consumption by the industrial sector in 2015, 98, 6 % of industrial renewable energy consumption originated from biomass. From total biomass consumption 56.8% originated from wood; 8.52% from waste; 0.66% from fuel ethanol (excluding denaturant) and 34.03% from biomass losses and co-products from the production of fuel ethanol and biodiesel in the Industrial Sector. Wood contains wood and wood-derived fuels. Waste included municipal solid waste from biogenic sources, landfill gas, sludge waste, agricultural byproducts, and other biomass (EIA, 2017, 3a, p. 153).

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Table 1.1: Total Energy Consumption in the United States, in 2015

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This included conventional hydroelectric power, geothermal, solar/photovoltaic, wind and biomass

Source: EIA, 2015, 2a

Figure 1.1: Industrial total energy consumption (Quadrillion Btu), by major source, 1949-2015

Source: EIA, 2017, 3a, p.34

Figure 1.2: Total industrial renewable energy consumption (Trillion Btu), by source, 2001-2016

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2. Literature review

From the introduction follows that almost all renewable energy consumed in the industrial sector is originated from biomass. As a result, the literature review of this research gives some

background literature on the substitutability of natural gas for biomass in the industrial sector. This is found in section 2.1. Since the aim of this research is to investigate the relationship between natural gas and renewable energy in the industrial sector, it is also interesting to know which academic literature is available on the drivers behind renewable energy demand.

Information about these drivers is of relevance of gathering knowledge about which control variables to add in the empirical models used in this research. This information is found in section 2.2.

2.1. The substitutability of natural gas for biomass

Natural gas is used for different purposes i.e. feedstock, fuel for boilers, fuel for combined heat and power (CHP) plants and other power generation plants and for process heating. Most natural gas is used for process heating (for example, heating accounted for 42% of total natural gas use, in 2010). Process heating is the production of heat from electricity to heat raw material inputs during manufacturing. Industrial boilers are also used for heat and steam generation. Combined heat and power (CHP) plants are used to cogenerate power and heat more efficiently. Natural gas is still the most common used energy source for boilers, process heating and CHP and other power plants (C2ES, 2012).

Biomass is used for the same purposes of natural gas. For example, the forestry and paper and pulp industry use wood waste to generate steam and electricity for their manufacturing plants (EIA, 2011, 4a). The usage of industrial residual biomass for heating purposes is widely spread in industrial sector, because of its cost-effectiveness. Often biomass is co-fired with steam coal. Also, biomass is used for petrochemical feedstock (Taibi et al. 2012). Conclusively, it can be assumed that there is competition between using biomass or natural gas for generation activities for heat and power. But then there must also be a real switching possibility i.e. dispatchability between the usage of natural gas to biomass as energy source for these activities.

Unfortunately, there is not much research available on this topic. Though, still there are a lot of factors that influence the possibility of switching from one energy resource to another. For example, the dispatchability of biomass-fired power plants matters for heat and power generation. According to research of Dincer & Acar (2015) biomass plants are fully dispatchable, meaning that they can be loaded from zero to full capacity without significant delay. This would mean that switching between biomass and natural gas as energy source is possible. Indeed, Jones (2014) examined the interfuel substitutability of biomass and other fuels in the U.S. industrial sector and found a 0.064 short-run and 0.348 long-run substitutability between biomass demand and natural gas prices. The results imply a positive relationship between natural gas prices and biomass demand. In conclusion, above information gives evidence that natural gas and renewable energy resources (i.e. 97% biomass in the industrial sector) are to a certain extent substitutes of each other. Therefore, in this research natural gas and renewable energy are assumed to be substitutes. 2.2. Drivers of renewable energy demand

There is scarce academic literature available on the drivers of renewable energy demand. Apergis et al. (2010) conducted a research on the relationship between economic growth and renewable energy consumption. He concludes by running a panel cointegration and error correction model of twenty OECD countries over the period 1985–2005 that economic growth, real gross fixed capital formation, and labor force have a positive and statistically significant impact on renewable energy consumption.

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They concluded that both short-and long-run estimates show an at 1% significant bidirectional causality between renewable energy consumption and economic growth. Also, Sadorksy (2009) concluded that per capita real GDP has a significant positive impact. The rationale behind this is that and increase in real GDP results in an increase in energy demand and create an opportunity to increase the usage of renewable energy. Sadorsky (2009) estimated that a 1% increase in per capita real GDP increases the per capita renewable energy consumption in emerging economies by approximately 3.5%.

In a more recent research, Sadorsky (2011) concluded that in the long-run per capita CO2 emissions have significant positive impacts on per capita renewable energy consumption. Moreover, Omri et al. (2014) analyzed drivers behind renewable electricity demand of a global panel consisting of 64 countries over the period 1990-2011 by using a dynamic system-GMM panel model. Their findings on the panel of high-income countries indicate that economic growth and CO2 emissions have a positive and statistically significant effect on renewable energy consumption at significance levels of 1% and 5%, respectively. Furthermore, they find that 1% increase in the per capita CO2 emissions raises the per capita renewable energy consumption by 0.42% and per capita GDP raises the per capita renewable energy consumption by 0.2%, indicating renewable energy consumption being less elastic to economic growth than to CO2 emissions. Both researches use per capita CO2 emissions as an indicator for awareness about global warning. The rationale behind this is that in most developed countries global warming is considered as a real issue, which have put the amount of CO2 emissions emitted into spotlight of energy policies of (local) governments and/or companies. Consequently, when CO2 emissions are increasing this would foster the ambition of these entities to reduce their CO2 emissions, resulting in an increase in renewable energy demand. On the contrary, a decrease in CO2 emissions will lead to weaker ambition to do something about reduction of emissions and would result in a decline in renewable energy demand (Omir et al., 2014; Sadorsky., 2011).

3. Data sources and variables

From the existing literature mentioned in the previous chapter follow two variables, which are of influence of renewable energy demand i.e. income and the ambition to switch to renewables. Since these variables affect renewable energy demand in general, they will also affect industrial renewable energy demand. Therefore, these two variables are therefore used as control variables in the empirical models to minimize omitted variable bias. All empirical models used for this research are using the same data-sets. In each section of this chapter, each variable is explained on what it is indicating and where data is retrieved from. Methodology and results of the empirical models can be found in the following chapter.

3.1.

Industrial natural gas price

Natural gas is considered a substitute for renewable energy in the U.S. industrial sector, according to the research of Jones (2011). Natural gas prices are in Dollars per Thousand Cubic Feet and differ across sectors. Data on natural gas prices is retrieved from

https://www.eia.gov/dnav/ng/ng_pri_sum_dcu_nus_m.htm. In particular, U.S. Natural Gas Industrial Price is collected from source key N3035US3 and measure in Dollars per Cubic Feet from the only available period of January 2001- April 2016.

3.2.

Income

As an indicator for income, Gross Domestic Product (GDP) per real capita is used, in accordance to the literature of Omri et al. (2014) and Sadorsky (2011). Quarterly data is collected on U.S. real gross domestic product (GDP) per capita from the Federal Reserve Economic Data from the Federal

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Reserve Bank of St. Louis (https://fred.stlouisfed.org/series/A939RX0Q048SBEA). Quarterly data of GDP per capita is measured (2009 $US) with a seasonally adjusted annual R and interpolated into monthly data using cubic spline from SRS1 software (see:

http://www.srs1software.com/SRS1CubicSplineForExcel.aspx).

3.3.

Ambition to switch to renewables

CO2 emissions are also included as an explanatory variable for renewable energy demand as an indicator of the ambition to switch to renewables. In this research, it is assumed that there at least some subsectors and/or companies (or sector initiatives) included in the industrial sector that do have global warming concerns. As a result, the relationship between CO2 emissions and renewable energy demand following from the literature of Omri et al. (2014) and Sadorsky (2011) is also likely to occur in this research. In U.S. total energy CO2 emissions of U.S. total energy consumption (i.e. of all sectors: U.S. commercial, residential, industrial and electric power and transportation sector together) are used as an explanatory variable, since only yearly data until 2013 was available on per capita CO2 emissions. So, in this research, it is assumed that increasing CO2 emissions of U.S. total energy consumption increase the ambition of the industrial sector to reduce CO2 emissions. Consequently, this will result in increase in renewable energy demand. CO2 emissions of total energy consumption are measured in million metric tons of carbon dioxide and are stemming from the burning of coal, natural gas, petroleum and derivative products of petroleum .Total Energy CO2 emissions data is retrieved from Table 12.1 Carbon Dioxide Emissions From Energy Consumption by Source, reported in the December 2016 Monthly Energy Review of the EIA. The dataset is publicly available on (http://www.eia.gov/totalenergy/data/monthly/#renewable).

3.4

Industrial renewable energy demand

Industrial renewable energy demand consists of a total of all renewable energy sources consumed in by the U.S. industrial sector. This includes net renewable energy consumption in Trillion Btu from the renewable resources hydropower, wind energy, solar energy and geothermal energy (together

accountable for approximately 3% of total U.S. industrial renewable energy consumption) and biomass (accountable for approximately 97% of total U.S. industrial renewable energy consumption). Data is retrieved from Table 10.2b Renewable Energy Consumption: Industrial Sector from

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4. The empirical models

To estimate whether and how natural gas prices affect renewable energy consumption in the industrial sector, three empirical models are used to investigate this. All empirical models are Ordinary Least Squares (OLS) regressions. To estimate whether regression are reliable for every model the OLS assumptions must hold. Therefore, at every regression all assumptions are investigated, except for the assumption 2 and 3. OLS assumption 2 is “All independent variables and the dependent variable are independently and identically distributed (i.d.d.) draws from their joint distribution”. Since the model deals with only time series data this assumption is likely to be violated. Often in time-series data what happens at t tends to be correlated with what happens at t+1, making the data non stationary. As a result, estimators can be biased and inefficient or conventional OLS-based statistical inferences can be misleading (Stock & Watson, p. 588). To keep things simple, in this research it is assumed that the time-series are jointly stationary. Additionally, it is assumed that there is sufficient randomness in the data for the central limit theorem and the law of large numbers to hold. As a result, it can be assumed that assumption 2 holds. OLS assumption 3 is “Large outliers are unlikely” i.e. that all variables have nonzero finite fourth moments. Since for all variable included in the empirical models included natural logarithms are used for all variables, so it is assumed that this assumption holds.

This chapter is structured as follows. First, a simple static log-log model is used, which is described in section 4.1. Second, as a result of the static model not meeting the OLS assumptions, a dynamic log-log model is used to estimate whether the relationship is more dynamic. This model is described in section 4.2. Lastly, an AR(4) log-log model is used, since the dynamic log-log model does not meet OLS assumptions.

4.1. The static log-log model

To proper examine the relationship between natural gas prices and renewable energy demand, the first step of this research is to establish whether there exists a contemporaneous relationship between natural gas prices and renewable energy demand. To estimate this, the static log-log model in

Equation 4.1 is used. For this model multiple regressors are included and only time-series data is used. A static model with time-series data represent a model in which all variables exclusively react to current events i.e. only interact at time- period t.

Equation 4.1

(4.1) RECIt = β1 NGPIt + β2GDPt + β3CO2t + ut In which t =Jan, Feb, March etc., denotes a monthly time-period

RECIt: the natural logarithm of total renewable energy consumption by the U.S. industrial sector at point t

NGPI t: the natural logarithm of the natural gas price for the U.S. industrial sector at point t GDP t: the natural logarithm of per capita GDP at point t

CO2 t: the natural logarithm of total carbon dioxide emissions of U.S. total energy consumption 1

at point t

1

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For OLS regression using time-series data with multiple regressors the following assumptions hold: 1. εt ~ N(0,σ2) :

a. The error termis homoscedastic b. The error termis normally distributed c. The error term has a conditional mean of zero d. E(εt,εt-1) has no autocorrelation (or serial correlation)

2. All independent variables and the dependent variable are independently and identically distributed (i.d.d.) draws from their joint distribution

3. Large outliers are unlikely 4. No perfect multicollinearity

First is tested whether CO2 t and GDP t individually and together add significant improvement to the goodness of fit of the model. The regression output can be found in Table 4.1. All regressions in Table 4.1 are evaluated on the presence of homoscedasticity in the error term to estimate whether robust errors should be used in the regression. To test for homoscedasticity the Breusch-Pagan-test is used. The results are shown in Table 4.2. The null hypothesis is that the error term has a constant variance i.e. presence of homoscedasticity in the error term. As a threshold is used that if Prob > χ2 is smaller than 0.05, the null hypothesis of constant variances is rejected and standard robust errors are used in the regression. Under this conditions, the results in Table 4.1 show that at regressions (1) and (3) the null hypothesis of constant variance is rejected. As a result, only at regression (1) and (3) robust errors are used.

Table 4.1 Results of running regression for model set-up Dependent variable RECIt Independent variables (1) (2) (3) (4.1) NGPIt -0.0942*** -0.103*** -0.0375 -0.112*** (0.0234) (0.0151) (0.0297) (0.0183) GDPt 2.333*** 2.374*** (0.124) (0.133) CO2t -0.429*** 0.0657 (0.111) (0.0763) constant 5.288*** -19.84*** 7.826*** -20.68*** (0.0447) (1.335) (0.642) (1.653) n 184 184 184 184 R-square 0.068 0.685 0.131 0.686 F-value 16.16 196.6 23.89 155.1 Prob > F 0.0001 0.0000 0.0000 0.0000

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Table 4.2 Results Breush-Pagan/ Cook-Weisberg test for homoscedasticity for regressions shown in Table 4.3

Breusch-Pagan / Cook-Weisberg test for heteroscedasticity

Ho: Constant variance

Regression Prob > χ2 (1) χ2 (1) = 16.18 0.0001 (2) χ2 (2) = 0.31 0.8550 (3) χ2 (2) = 21.69 0.0000 (4) χ2 (3) = 2.32 0.5092 Discussing results in Table 4.1.

Regression 1 shows that NGPIt seems to be highly significant but the model has a very low R2 of 0.069 meaning that not much of a change in RECIt would be caused by a change in NGPIt. Also, the standard error of NGPIt is relatively high. Nevertheless, from literature review follows that natural gas prices do affect renewable energy demand, so the low R2 will probably be due to omitted variable bias.

Regression 2 shows a highly significant GDPt and also a highly significant NGPIt with improved i.e. smaller standard errors. Furthermore, it increased the R2 up to 0.685, which is a significant improvement in comparison with the R2 of regression (1).

Regression 3 shows a highly significant CO2t but an insignificant NGPIt, also the goodness of fit is relatively low with R2 being 0.131.

Regression 4.1 shows the regression of Equation 4.1 In this regression CO2t is added to regression 2. CO2t increase the standard errors GDPt and NGPIt, but these variables remain significant. Thereby, regression 4.1 offers a slightly improvement of 0.001 in the R2 compared to regression 2.

In conclusion, adding CO2 emissions seems not to be of much relevance for improvement of the model according to the regression outputs in Table 4.1. But since academic researchers Omir et al. (2014) and Sadorsky (2011) concluded that CO2 emissions do affect renewable energy demand, regression 4.1. is chosen as the model to elaborate on in this chapter. So, the reason for CO2

emissions adding not much significance can also be due to misspecification of the modeling approach of regression 4.1. To conclude whether this is the case, the OLS assumptions of regression 4.1 should be investigated.

Meeting assumptions of model 4.1

εt ~ N(0,σ2)

1a. Homoscedasticity of the error term

As previously discussed this assumption is not met, but this is solved by using standard robust errors when running regression.

1b. Normal distribution of the error term

Figure 4.1. shows Kernel density estimate of the residuals, which is an estimate of the distribution of the error term. Following the shape of the Kernel density estimate and comparing it to the normal distribution line, leads to the conclusion that the distribution of the error term substantially deviates from normal distribution.

11 1c. The error term has a conditional mean of zero

In Figure 4.2 residuals are plotted against fitted values RECIt of Equation 4.1. A lowess line is added to the residual plot, which shows the residuals cycle. From Figure 4.2 follows that the error term does not have a conditional mean of zero.

Figure 4.1 Kernel density estimate residuals, model 4.1 Figure 4.2 Residual plot with lowess line, model 4.1

.

1d. E(ε

t

,ε

t-1

) has no autocorrelation (or serial correlation)

If autocorrelation of the error term indeed is present, this means that the errors of the different observations are not independently distributed. If so, the probability of an error observation point above the line in the residual series will dependent on its residual history. Serial correlation results in the problem that the OLS estimator is not the best linear unbiased estimator (BLUE) because it is not the most efficient estimator. For example, if serial correlation of the error term is found positive the goodness of fit, R2, is exaggerated and estimated standard errors being underestimated and biased variances. This resulting in t-statistics being overestimates, causing regression coefficients to appear significant, whereas they are actually not. F-tests and t-test are no longer valid (Ramanathan, 2002). The lowess line in In Figure 4.4 showing indeed a strong residuals cycle, which strongly suggest that the error term is serial correlated. To estimate whether there is indeed serial correlation a

nonparametric test is conducted O’Halloran (2005). The z- value of -4.278 is found significant, so the null hypothesis of the errors being generated randomly is rejected. So, there seem to be presence of serial correlation in the error term.

4. No perfect multicollinearity

Multicollinearity occurs in a multiple regression analysis when one of the independent variables is a linear combination of the other variables. This makes estimation of the individual regression

parameters not reliable anymore. To estimate whether there is multicollinearity between the regressors included in the model the variance inflation factor (VIF) of all regressors are estimated. In Appendix 1 in Figure 1.a. the VIF values are presented for the model 4.1. The rule of thumb for multicollinearity is that VIF estimates exceeding 10 are signaling multicollinearity between variables (O’brien, 2007). None of the variables appear to have VIF values greater than 10, meaning that perfect

multicollinearity is not present in the model.

-. 2 -. 1 0 .1 .2 4.9 5 5.1 5.2 5.3 Fitted values

Residuals lowess r plncind

0 2 4 6 D e n si ty -.2 -.1 0 .1 .2 Residuals Kernel density estimate Normal density kernel = epanechnikov, bandwidth = 0.0207

12 4.2. The dynamic log-log model

As the results of the static model show, it is not very likely that there is a significant static relationship between natural gas prices and renewable energy demand, since OLS assumptions are not met. A dynamic time-series model can account for seasonality (DeFusco et al. 2015, p.499) and decision-making processes by including lagged values (Keele & Kelly, 2005). Using lagged dependent

variables to incorporate these processes makes sense from the theoretical point of view, since there is theoretical foundation for including lagged dependent variables. Therefore, this section start with theoretical foundations on how many lags of each variable should be included in the model. Consequently, the optimal model is chosen and showed in Equation 4.2. Subsequently, the OLS assumptions of model 4.2 are investigated and conclusions are drawn.

RECI

According to EIA (2013, 5a) “seasonal changes can affect industrial activity in the refining industry. For example, different seasonal slates of petroleum products as well as different seasonal processes may affect electricity needs”. Since renewable energy consumption is dependent on industrial activity taken place, it will also be affected by seasonal processes of the industry. To estimate whether this seasonality is indeed seen in the data, a graph of RECIis made for only a three year period of Dec 2013 until Dec 2016. By looking at the renewable energy consumption pattern from the periods of Dec 2013 until Dec 2014 and Dec 2015 until Dec 2016 the patterns of the two years were quite similar, which indicate a certain pattern. By looking at one year, the same upward and downward sloping trends occurred between Dec and Feb downward sloping; between Feb and March upward sloping; between March and September generally upward sloping; between July and September downward sloping; and between September and December upward sloping. Accordingly, a first, a third and a fourth lagged variable of are included in the model; RECIt-1, RECIt-3 and RECIt-4 , respectively.

GDP

From the quote from the EIA follows that renewable energy demand depend on the activity of the industry. Since the industrial output contributes Gross Domestic Product (GDP), a change of GDP is likely to cause a change in renewable energy demand. Since GDP per capita is growing more or less exponential, it is reasonable to assume that GDP at point t-1 is a good predictor of GDP at time t. Consequently, it seems reasonable to assume that industrial activity of t-1 affects renewable energy demand. So, for GDP only the first lagged variable is included; GDPt-1.

CO2

The total carbon dioxide emissions of all sectors together follow a strong seasonal pattern. From Jan to April a downward sloping trend; from April till July/August an upward sloping trend; from July/August till October and downward sloping trend; and from October till January an upward sloping trend (see Figure Appendix 1). Therefore, the first and fourth lagged variables of CO2 are included in the model; CO2t-1 and CO2t-4, respectively.

NGPI

Since the natural gas price is merely determined by supply and demand, there is no clear pattern is seen in the data on natural gas prices for the industrial sector. Still, it is more likely that renewable at

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time t is dependent on the natural gas price of t-k . For example, today’s value of the natural gas price is not likely to impact today’s renewable energy demand, because the choice to use renewable energy is probably already made for today. It is more plausible that there is a certain lag in the decision-making process on which energy source to consume at time period t. How many lags should be included to capture this decision-making process, is somewhat arbitrary to suggest. Therefore, BIC and AIC estimates are used to estimate which number of lags should be used. For each of the eight candidate models the BIC and AIC values are estimated. BIC refers to Bayes information criterion and AIC to Akaike Information Criterion. In the statistical academic field, both information criterions are used to estimate the optimal lag length for candidate models. The protocol of the BIC and AIC criterions to estimate what the optimal lag length is, to run regressions on different lag lengths of the variable of interest and then determine the lowest value of the BIC and AIC. All candidate models must be estimated over the same sample. The candidate model with the lowest BIC/AIC value is the preferred model. However, the optimal lag length can differ when using BIC or AIC as information criterion.

Before running regressions of the candidate models, the Breush Pagan / Cook-Weisberg test for heteroscedasticity is used. Again, as a threshold is used that if Prob > χ2 is smaller than 0.05, the null hypothesis of constant variances is rejected and standard robust errors are used in the regression. As can be seen from Table 4.3 for all candidate models the null hypothesis is rejected and standard robust errors are used.

Table 4.3. Results Breush-Pagan/ Cook-Weisberg test for homoscedasticity for regressions in Appendix 1.

Breusch-Pagan / Cook-Weisberg test for heteroscedasticity Ho: Constant variance

Regression Prob > χ2 (1) χ2 (6)= 14.65 0.0232 (2) χ2 (7)= 16.67 0.0197 (3) χ2 (8)= 19.82 0.0111 (4) χ2 (9)= 18.12 0.0338 (5) χ2 (10)= 25.45 0.0045 (6) χ2 (11)= 26.67 0.0052 (7) χ2 (12)= 25.26 0.0136

Appendix 2 shows that candidate model 4 has the lowest AIC value (-653.5), whereas model 3 has the lowest BIC value (-624.0). The outcome values of regression 7 and 8 are not valid candidate models because for drawing conclusions on AIC and BIC, only BIC and AIC values of regression run over the same sample can be compared. Because AIC’s property is overestimating adding additional lags in large samples with nonzero probability (Stock & Watson, p.595), BIC is regarded as a more reliable information criterion. Consequently, adding the first and second lag of natural gas prices are regarded as most reliable option; NGPIt-1 and NGPIt-1, respectively.

Conclusively, all above theoretical arguments and the estimation of the optimal lag length of NGPIt-k

result in the model of Equation 4.2. Equation 4.2

(4.2)

RECI

t

= β

1

RECI

t-1

+ β

2

RECI

t-3

+ β

3

RECI

t-4

+ δ

1

NGPI

t-1

+ δ

2

NGPI

t-2

+ δ

3

14

To estimate whether the dynamic model performs better than the static model, the model of Equation 4.2. is examined on whether the OLS assumptions of time series data for lagged models hold. Presumed is that the model in Equation 4.2 performs better, since in model 4.2. takes into account decision-making processes, seasonality and other patterns.

For OLS regression using time-series data with multiple lags the following assumptions hold: 1. εt

~ N(0,σ2) :

a. The error termis homoscedastic b. The error termis normally distributed

c. The error term has a conditional mean of zero

d. E(εt,εt-1) has no autocorrelation (or serial correlation)

2. (a) The random variables (i.e. X1t,..., Xkt and Yt) have a stationary distribution and (b)The random variables and lagged variables become independent as Xkt-j and Ykt-j becomes larger.

3. Large outliers are unlikely: random variables have nonzero, finite fourth moments; and 4. There is no perfect multicollinearity

The regression results of model 4.2. are found in Appendix 4. For the variables of interest NGPIt-1 and NGPIt-2, significant short-run elasticities of 0.0919 (p < .05) and -0.0699 (p < .01), respectively. So, a 1% increase in last month’s industrial natural gas price will lead to a 0.0919% increase in today’s industrial renewable energy demand. And a 1% increase in industrial natural gas price of two months ago will lead to a -0.0699% decrease in today’s renewable energy demand. This is a

somewhat contradictory result and does not stroke with the results Jones (2014) found. Again, it is investigated whether model 4.2 meets all OLS assumptions.

Meeting assumptions of model 4.2

εt

~ N(0,σ2)

1a. Homoscedasticity of the error term

The Breusch-Pagan / Cook-Weisberg test for heteroscedasticity is used to test if standard robust errors should be used in regression χ2_{(8) = 19.82, Prob > χ}2

= 0.0111. Since this probability values is smaller than Prob > χ2 = 0.05, the null hypothesis of constant variance is rejected. As a result robust errors are used, so the violation of 1a is not regarded as a problem anymore.

1b. Normal distribution of the error term

Figure 4.3. contains the distribution of the error term shown by the Kernel density estimate. From Figure 4.3 it can be concluded that assumption 1.b. is met, because the distribution of residuals, compared to normal distribution line, appear to follow a nearly normal distributional pattern.

1c. The error term has a conditional mean of zero

In Figure 4.4 residuals are plotted against fitted values RECIt of Equation 4.2. A lowess line is added to the residual plot, showing the residuals cycle. From Figure 4.4 becomes clear that the residuals do not have a conditional mean of zero

15

Figure 4.3 Kernel density estimate residuals, model 4.2 Figure 4.4 Residual plot with lowess line, model 4.2

.

1d. E(ε

t

,ε

t-1

) has no autocorrelation (or serial correlation)

When lagged dependent variables are included among the regressors, the past values of the error term are correlated with those lagged variables at time t, implying that they are not strictly exogenous regressors. The lowess line in Figure 4.4 suggests the error term still is autocorrelated. To test whether the residuals are autocorrelated the alternative Durbin-Watson test is used. This Durbin-Watson test is used when exogenous variables are included in the model. This is the case in model 4.2, since the model includes lags. The test is performed for each order separately. In Table 4.6 the Durbin-Watson d-statistics are found. The null hypothesis of no serial correlation is at all four lags rejected, meaning that there still is serial correlation in the residuals and assumption 1.d. is still not met.

Table 4.6 Durbin's alternative test for autocorrelation, regression 4.2 Durbin's alternative test for autocorrelation

lags(p) χ2-value df Prob > χ2-value

1 17.329 1 0.0000

2 17.970 2 0.0001

3 20.328 3 0.0001

4 21.714 4 0.0002

4. No perfect multicollinearity

Since the regression includes lagged variables of time-series data, it seems logical that there will be multicollinearity problems. In time-series data there is always a certain degree of multicollinearity present. This is not regarded as problem as long as there exists no collinearity between the variable of interest and the control variables. Said otherwise, if only control variables show collinearity this is not regarded as a problem. However, this only applies if the other OLS assumptions are met.

In Appendix 1 in Figure 1b VIF values are examined of all the explanatory variables. Both NGPIt-1 and NGPIt-2 appear to have high VIF values, 12.14 and11.15 respectively. Both VIF values are higher than 10, signaling multicollinearity problems. The multicollinearity produce the

coefficients of NGPIt-1 and NGPIt-2 being imprecisely estimated i.e. have a large sampling variance (Stock & Watson, p.251).

-. 1 -. 0 5 0 .0 5 .1 4.9 5 5.1 5.2 5.3 Fitted values

Residuals lowess r plncind

0 2 4 6 8 10 D e n si ty -.2 -.1 0 .1 Residuals Kernel density estimate Normal density kernel = epanechnikov, bandwidth = 0.0113

16 4.3. The AR(4) dynamic log-log model

The regression results of model 4.2 are not much reliable, because there appear to be two crucial violations of the OLS assumptions. Firstly, there appears to be serial correlation in the error term, meaning that the OLS assumption of εt

~ N(0,σ2) is violated. Secondly, there is indication of

multicollinearity in the variables of interest i.e. NGPIt-1 and NGPIt-2 which cause a problem of precision of the coefficients of NGPIt-1 and NGPIt-2 . To see whether an autoregression (4) model performs better, a dynamic AR(4) log-log model is developed. The lags of RECIt-2, CO2t-2, CO2t-3 are added to model 4.2 to solve the problem of autocorrelation. It must be added that these lags are only added to overcome the problem of serial correlation and do not have proper theoretical foundation. The only reason that no lags greater than t-4 (i.e. t-5, t-6 etc.) are added is because these are assumed not to be suitable, since the data of RECIt and CO2t are containing more or less seasonality.

In Equation 4.3. the AR(4) log-log model is developed. The same OLS assumptions hold for Equation 4.3. as mentioned for Equation 4.2. To estimate how many lagged values should be included for

NGPI

t in the AR(4) dynamic log-log model BIC/AIC estimates are used, in the same way as for

Equation 4.2, Again, the BIC values give conclusion about how many lags should be included. In Appendix 3 results of regressions are showed and it appears that the BIC value is lowest (-633.1) at including one lags, resulting in Equation 4.3.

(4.3)

RECI

_t

= β

₁

RECI

_t-1

+ β

₂

RECI

_t-2

+ β

₃

RECI

_t-3

+ β

₄

RECI

_t-4

+

δ

₁

NGPI

_t-1

+ δ

₂

GDP

_t-1

+

δ

3

CO2

t-1 +

δ

4

CO2

t-2

+ δ

5

CO2

t-3

+

δ

6

CO2

t-4

+ u

t Meeting assumptions of model 4.2

εt

~ N(0,σ2)

1a. Homoscedasticity of the error term

The Breusch-Pagan / Cook-Weisberg test for heteroscedasticity is used to test if option robust should be used in regression χ2

(10) = 34.77, Prob > χ2 = 0.0003, meaning a rejection of the null hypothesis of constant variance, indicating the presence of heteroscedasticity. As a result, robust errors are used for regression of model 4.3. So, the violation of assumption 1a. is not considered as a problem anymore.

1b. Normal distribution of the error term

Figure 4.5 shows that the Kernel density estimate of the residual plot is close the normality line. So, normality of the error term is assumed.

1c. The error term has a conditional mean of zero

Figure 4.6 shows that most of the time the residuals of model 4.3. indeed have a conditional mean of zero.

1d. E(ε

t

,ε

t-1

) has no autocorrelation (or serial correlation)

In Figure 4.6 the residuals are plotted against the fitted values of RECIt in Equation 4.2. Again a lowess line is added to the residual plot, showing the residuals cycle. To test whether the residuals are autocorrelated the alternative Durbin-Watson test is used In Table 4.6 the Durbin-Watson d-statistics are found. The null hypothesis of no serial correlation is at all four lags not rejected, meaning that there is no serial correlation in the residuals and assumption 1.d. is met

17

Figure 4.5 Kernel density estimate, regression 4.3 Figure 4.6 Residual plot with lowess line, model 4.3

Table 4.6 Durbin's alternative test for autocorrelation, regression 4.3 Durbin's alternative test for autocorrelation

lags(p) χ2-value df Prob > χ2-value

1 1.578 1 0.2090

2 4.051 2 0.1319

3 4.859 3 0.1824

4 6.093 4 0.1923

4. No perfect multicollinearity

In Appendix 1 in Figure 1c VIF values are examined of all the explanatory variables. RECIt-1,

RECI

t-2,

RECI

t-3,

RECI

t-4 appear to have high VIF values, 13.66, 16.67, 17.96 and 12.44 respectively.

So the coefficients of these variables are imprecisely estimated i.e. have a large sampling variance (Stock & Watson, p.251). Since multicollinearity in time series data, is not regarded as problem as long as there exists no collinearity between the variable of interest and the control variables i.e. if control variables only show multicollinearity, multicollinearity in this model is not regarded as a problem. Since the variable of interest NPGIt-1 appears to have a very low VIF value of 2.46 and since the other OLS assumptions for time series data are met, multicollinearity is not regarded as a problem in the regression.

Conclusively, form the OLS assumption analysis of model 4.3. follows that is seems reasonable to assume that all OLS assumptions hold (in combination with assuming that the assumptions 3 and 4 do hold). From output results of the regression of model 4.3 in Appendix 4 follows that NGPIt-1 has a coefficient estimate of 0.250, which is insignificant at p < .05. Nevertheless, the p-value of NGPIt-1 is 0.077, which is significant at p < .10. As a result, it can be concluded with a 90% confidence level that an 1% increase in industrial natural gas prices of one month ago (t-1) results in a 0.0250% increase in a today’s industrial energy demand (t).

18

5. Conclusion and discussion

5.1

Conclusion

From the regression analyses described in Chapter 4 follow several conclusions. From the results on the static log-log model of Equation 4.1 follows that it is not likely that there is a contemporary statistical relationship between natural gas prices and renewable energy demand, since different OLS assumptions are violated. The regression results of the dynamic log-log model of Equation 4.2. suggest that it is more likely that renewable energy demand responds to longer-term changes in natural gas prices i.e. respond to natural gas prices of previous month(s). Also, by allowing for lags to be included in this model, decision-making processes and seasonality are captured.

However, the model of Equation 4.2 contains an error term that suffers from serial correlation and show high multicollinearity present in the variables of interest i.e. NGPIt-1 and NGPIt-1 . So,

these results are not much reliable either.

The AR(4) dynamic lagged model of Equation 4.3. was estimated to solve the serial correlation and multicollinearity problems, which it indeed did. The model of Equation 4.3. showed no presence of serial correlation in the error term and has no multicollinearity present in the variable of interest: NGPIt-1. Consequently, the results of the model of Equation 4.3 are regarded as most reliable compared to the previous models, from the statistical point of view. The regression results of the model of Equation 4.3. show a significant positive correlation between natural gas price of previous month and today’s industrial renewable energy demand. To be precisely, regression results of showed that at a 90% confidence level an 1% increase in industrial natural gas prices of one month ago (at time-period t-1) results in a 0.0250% increase in a current industrial energy demand (at time-period t). Comparing this value to the research of Jones (2014), results in the conclusion that in both researches significant positive relationships are found between natural gas prices and renewable energy in the U.S. industrial sector. Jones’s short-run estimation is a1% increase in natural gas prices lead to a 0.064% increase in industrial biomass consumption. Here must be noted that the estimate found in this research is obviously not perfectly comparable of estimate of Jones (2014), because he used different models for his investigation and only used biomass consumption (though this might not be regarded as a

problem for comparison, because roughly all U.S. renewable energy demand consists of biomass).

5.2

Discussion

Nevertheless, there are some flaws in the models used in this research, which need to be mentioned. First of all, interpretation of the results of the empirical models used in this research must be taken with care, because the two OLS assumptions 3 and 4 are assumed to hold and not investigated on whether they indeed hold. If these assumptions do not appear to hold, regression results are not much reliable. Secondly, there is high multicollinearity in some variables of the models of Equation 4.2 and 4.3 and these are not further investigated and dealt with in this research. Therefore, both models may be misspecified. Furthermore, there are still some issues that are not covered or investigated in the regression analyses, for example omitted variable bias. If these problems appear to be there, which is possible, this will have led to biased estimators and coefficients .

What’s more, in this research it is not investigated whether there exists a bidirectional causality between industrial renewable energy demand and CO2 emissions of U.S. total energy consumption. This is likely to be there, since CO2 emissions of U.S. total energy consumption also include CO2 emissions of the industrial sector. Though knowing this, the variable was still

19

used in this research because of the relevance of including an indicator for the ambition to switch to renewables. This relevance was pointed out by academic literature of Sadorsky (2011) and Omir et al. (2014). The same problem holds for the relationship between GDP and renewable energy demand. In this research, these variables were not tested for bidirectional causality, though Apergis et al. (2010) found a bidirectional causality GDP and renewable energy demand in his research. Unfortunately, testing for bidirectional causality of variables was beyond the scope of this research.

Finally, it must be kept in mind that all regression results are still correlations and not causality. It seems easy to hypothesize the relationship between natural gas prices and renewable energy demand i.e. if natural gas prices increase, renewable energy demand will increase. This follows the economic rational that if the price of a substitute is low, this will be the preferable option to buy. But in reality, there will certainly be factors who limit this hypothesis. For example, certain circumstances can influence the preference for one energy source above another. For example, policy incentives and comparative advantages in efficiency of one particular energy resource are likely to result in preferences for a particular energy source. For these circumstances is not controlled in this research.

5.2

Further recommendations

Besides the conclusions that follow from discussion, it is may be interesting for further research to distinguish between subsectors in the industrial sectors. It is possible that in some sectors the change in renewable energy demand, as a result of a change in natural gas prices, is proportionally bigger than in other subsectors. This can be relevant information for energy policy makers for creating future renewable energy policy into a more targeted and efficient policy by making renewable energy policy specific for subsectors.

20

References

Apergis, N., & Payne, J. E. (2010). Renewable energy consumption and economic growth: evidence from a panel of OECD countries. Energy policy, 38(1), 656-660.

Dincer, I., & Acar, C. (2015). A review on clean energy solutions for better sustainability. International Journal of Energy Research, 39(5), 585-606.

Center for Climate and Energy Solutions (C2ES). (2012, May). Natural gas in the industrial sector. Retrieved from https://www.c2es.org/docUploads/natural-gas-industrial-sector.pdf

1a. Energy Information Administration (EIA). (2016). Natural gas explained, Factors Affecting Natural Gas Prices. Retrieved from

https://www.eia.gov/energyexplained/index.cfm?page=natural_gas_factors_affecting_prices 2a. Energy Information Administration (EIA). (2015). U.S. primary energy consumption by source and sector, 2015. Retrieved from

https://www.eia.gov/totalenergy/data/monthly/pdf/flow/css_2015_energy.pdf

1b. Energy Information Administration (EIA). (2016, November 1). U.S. energy production, consumption has changed significantly since 1908. Retrieved from

https://www.eia.gov/todayinenergy/detail.php?id=28592

1c. Energy Information Administration (EIA). (2016). Glossary. Retrieved from http://www.eia.gov/tools/glossary/index.cfm?id=I

3a. Energy Information Administration (EIA). (2017, January 1). Monthly Energy Review. Table 10.2b Renewable Energy Consumption: Industrial and Transportation Sectors. Retrieved from https://www.eia.gov/totalenergy/data/monthly/pdf/mer.pdf

4a. Energy Information Administration (EIA). (2011, November 10). Renewable energy is used in all sectors of the U.S. economy. Retrieved from https://www.eia.gov/todayinenergy/detail.php?id=3870 5a. Energy Information Administration (EIA). (2013, March 4). Homes show greatest seasonal variation in electricity use. Retrieved from http://www.eia.gov/todayinenergy/detail.php?id=10211 Intergovernmental Panel on Climate Change (IPCC). (2014). Climate Change 2014 Synthesis Report Summary for Policymakers. Retrieved from

https://www.ipcc.ch/pdf/assessment-report/ar5/syr/AR5_SYR_FINAL_SPM.pdf

Jones, C. T. (2014). The role of biomass in US industrial interfuel substitution. Energy Policy, 69, 122-126.

Keele, Luke, and Kelly, N. J. (2005). Dynamic models for dynamic theories: The ins and outs of lagged dependent variables. Political analysis 14.2, 186-205.

O’brien, R. M. (2007). A caution regarding rules of thumb for variance inflation factors. Quality & Quantity, 41(5), 673-690.

O’Halloran, S. (2005). Lecture 8: Serial Correlation, Sustainable Development U9611 Econometrics II [7-15]. Retrieved from http://www.columbia.edu/~so33/SusDev/Lecture_8.pdf

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Omri, A., & Nguyen, D. K. (2014). On the determinants of renewable energy consumption: International evidence. Energy, 72, 554-560.

Ramanathan, R., 2002, Introductory Econometrics with Applications, 5th ed., Harcourt College Publishers. Chapter 9.

Sadorsky, P. (2009). Renewable energy consumption, CO2 emissions and oil prices in the G7 countries. Energy Economics, 31(3), 456-462.

Sadorsky, P. (2009). Renewable energy consumption and income in emerging economies. Energy policy, 37(10), 4021-4028.

Stock, J. H., & Watson, M. W. (2003). Introduction to econometrics (3rd edition). Essex: Pearson Education Limited.

Taibi, E., Gielen, D., & Bazilian, M. (2012). The potential for renewable energy in industrial applications. Renewable and Sustainable Energy Reviews, 16(1), 735-744.

DeFusco R.A., McLeavey D.W., Pinto, Runkle D.E., Anson M.J.P. (2015). Quantitative Investment Analysis. Hoboken: Jon Wiley and Sons Inc.

22

Appendix 1: VIF estimates for model 4.1, 4.2 and 4.3

Figure 1.a. VIF estimates of Equation 4.1

Variable

VIF 1/VIF

CO2

t

1.60 0.625548

NGPI

t

1.46 0.682657

GDP

t

1.15 0.867260

Mean VIF 1.41

Figure 1.b. VIF estimates of Equation 4.2

Variable

VIF

1/VIF

NGPI

t-1

12.14 0.082360

NGPI

t-2

11.15 0.089678

RECI

t-3

9.24

0.108171

RECI

t-4

9.03

0.110763

RECI

t-1

8.05

0.124163

GDP

t-1

3.64

0.274402

CO2

t-4

2.40

0.415921

CO2

t-1

1.97

0.507275

Mean VIF 7.20

Figure 1.c. VIF estimates of 4.3

Variable

VIF

1/VIF

RECI

t-3

17.96 0.055692

RECI

t-2

16.67 0.059992

RECI

t-1

13.66 0.073220

RECI

t-4

12.44 0.080411

CO2

t-2

5.70

0.175529

CO2

t-3

5.55

0.180308

CO2

t-4

4.18

0.239408

GDP

t-1

3.67

0.272125

CO2

t-1

3.46

0.289323

NGPI

t-1

2.46

0.406145

Mean VIF 8.57

23

Appendix 2: Results of regressions to estimate how many lags should be included for

NGPIt in model 4.2

Dependent variable

RECI

t Independent Variables (1) (2) (3) (4) (5) (6) (7)

RECI

t-1 0.473*** 0.486*** 0.478*** 0.478*** 0.478*** 0.478*** 0.477*** (0.0736) (0.0735) (0.0719) (0.0725) (0.0728) (0.0734) (0.0730)

RECI

t-3 0.225** 0.207** 0.206** 0.211** 0.216** 0.208** 0.227** (0.0685) (0.0701) (0.0663) (0.0654) (0.0664) (0.0714) (0.0745)

RECI

t-4 0.0391 0.0605 0.0567 0.0408 0.0421 0.0535 0.0440 (0.0842) (0.0844) (0.0848) (0.0848) (0.0846) (0.0856) (0.0867)

GDP

t-1 0.400** 0.289* 0.324* 0.346* 0.340* 0.319* 0.295* (0.136) (0.139) (0.134) (0.139) (0.140) (0.143) (0.144)

CO2

t-1 -0.279*** -0.336*** -0.348*** -0.365*** -0.358*** -0.358*** -0.366*** (0.0493) (0.0555) (0.0556) (0.0593) (0.0586) (0.0588) (0.0595)

CO2

t-4 -0.0606 -0.115* -0.105* -0.0908 -0.0893 -0.0866 -0.0720 (0.0457) (0.0508) (0.0492) (0.0494) (0.0503) (0.0531) (0.0604)

NGPI

t-1 0.0271 0.0919** 0.0848** 0.0836* 0.0842* 0.0843* (0.0150) (0.0317) (0.0325) (0.0326) (0.0331) (0.0333)

NGPI

t-2 -0.0699* -0.0145 -0.0111 -0.0135 -0.00777 (0.0303) (0.0427) (0.0437) (0.0444) (0.0444)

NGPI

t-3 -0.0520 -0.0720 -0.0731 -0.0797 (0.0307) (0.0459) (0.0465) (0.0474)

NGPI

t-4 0.0184 0.0188 0.0206 (0.0313) (0.0505) (0.0499)

NGPI

t-5 0.00376 -0.0252 (0.0342) (0.0436)

NGPI

t-6 0.0307 (0.0337) constant -0.881 0.882 0.587 0.431 0.415 0.599 0.768 (1.298) (1.435) (1.397) (1.419) (1.431) (1.443) (1.453) n 180 180 180 180 180 179 178 R-square 0.887 0.889 0.893 0.894 0.894 0.893 0.892 AIC -647.4 -649.3 -652.8 -653.5 -651.9 -646.4 -641.5 BIC -625.1 -623.7 -624.0 -621.6 -616.8 -608.2 -600.2 F-value 212.3 188.0 176.1 161.1 146.5 132.7 120.2 Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001

24

Appendix 3: Results of regressions to estimate how many lags should be included for

NGPIt in model 4.3

Dependent variable

RECI

t Independent Variables (1) (2) (3) (4) (5) (6)

RECI

t-1 0.281** 0.288** 0.285** 0.287** 0.295** 0.289** (0.100) (0.0998) (0.0979) (0.100) (0.102) (0.100)

RECI

t-2 0.266* 0.269* 0.265** 0.266** 0.264* 0.275** (0.107) (0.104) (0.101) (0.101) (0.102) (0.101)

RECI

t-3 0.325** 0.305** 0.324** 0.324** 0.317** 0.322** (0.101) (0.0977) (0.0970) (0.0974) (0.0983) (0.100)

RECI

t-4 -0.0791 -0.0758 -0.0994 -0.0998 -0.0935 -0.0984 (0.0963) (0.0956) (0.0948) (0.0949) (0.0953) (0.0957)

GDP

t-1 0.227 0.251 0.277* 0.273* 0.252 0.230 (0.133) (0.131) (0.134) (0.135) (0.139) (0.140)

CO2

t-1 -0.232** -0.245** -0.266** -0.263** -0.267** -0.268** (0.0850) (0.0853) (0.0861) (0.0846) (0.0855) (0.0850)

CO2

t-2 -0.0689 -0.0687 -0.0638 -0.0608 -0.0511 -0.0613 (0.0978) (0.0962) (0.0941) (0.0972) (0.101) (0.101)

CO2

t-3 -0.169* -0.147 -0.162* -0.160* -0.167* -0.155 (0.0819) (0.0822) (0.0804) (0.0804) (0.0805) (0.0812)

CO2

t-4 0.0687 0.0622 0.0868 0.0870 0.0919 0.0941 (0.0725) (0.0713) (0.0705) (0.0708) (0.0720) (0.0751)

NGPI

t-1 0.0250 0.0692* 0.0598* 0.0593* 0.0587 0.0584 (0.0141) (0.0290) (0.0298) (0.0299) (0.0304) (0.0307)

NGPI

t-2 -0.0481 0.0186 0.0200 0.0186 0.0221 (0.0288) (0.0397) (0.0404) (0.0414) (0.0416)

NGPI

t-3 -0.0615* -0.0728 -0.0767 -0.0812 (0.0274) (0.0468) (0.0470) (0.0478)

NGPI

t-4 0.0106 0.0237 0.0228 (0.0332) (0.0498) (0.0495)

NGPI

t-5 -0.00660 -0.0169 (0.0354) (0.0455)

NGPI

t-6 0.0145 (0.0321) constant 1.040 0.804 0.635 0.613 0.797 0.978 (1.397) (1.363) (1.385) (1.393) (1.399) (1.408) n 180 180 180 180 179 178 R-square 0.904 0.905 0.907 0.907 0.906 0.906 AIC -668.2 -669.0 -671.4 -669.5 -664.4 -659.1 BIC -633.1 -630.7 -629.9 -624.8 -616.6 -608.2 F-value 168.67 155.03 147.14 140.57 132.88 123.36 Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001,

25

Appendix 4: Output results of regressions model 4.2 and 4.3

Dependent variable RECIt Independent Variables (4.2) (4.3)

NGPI

t-1 0.0919** 0.0250 (0.0317) (0.0141)

NGPI

t-2 -0.0699* (0.0303)

RECI

t-1 0.478*** 0.281** (0.0719) (0.100)

RECI

t-3 0.206** 0.325** (0.0663) (0.101)

RECI

t-4 0.0567 -0.0791 (0.0848) (0.0963)

GDP

t-1 0.324* 0.227 (0.134) (0.133)

CO2

t-1 -0.348*** -0.232** (0.0556) (0.0850)

CO2

t-4 -0.105* 0.0687 (0.0492) (0.0725)

RECI

t-2 0.266* (0.107)

CO2

t-2 -0.0689 (0.0978)

CO2

t-3 -0.169* (0.0819) constant 0.587 1.040 (1.397) (1.397) n 180 180 R-square 0.893 0.945 AIC -652.8 -668.2 BIC -624.0 -633.1 F-value 176.1 155.0