Wind energy, the price of carbon allowances, and CO2 emissions: Evidence from Ireland

Energy Policy 133 (2019) 110871

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Wind energy, the price of carbon allowances, and CO2 emissions: Evidence from Ireland

T

Kevin F. Forbes∗, Ernest M. Zampelli Department of Economics, The Catholic University of America, Washington, DC, USA

ARTICLE INFO

ABSTRACT

Keywords: Carbon emissions Cap and trade Wind energy Ireland Electricity markets European Union emission trading system

Increased reliance on renewable energy is an important component of the European Union's action plan for reducing carbon emissions. Another key instrument is the European Union Emission Trading System (EU ETS), which caps the overall level of emissions and then permits trade among the emitters. Using data from Ireland, this paper examines the effects of wind energy and the EU ETS on carbon emissions from electricity generation. We estimate a time-series econometric model of CO2 emissions for each half hour over the period 1 January 2015 through 17 April 2018. Results indicate that increases in the carbon allowance price significantly reduce carbon emissions when errors in load assessments and wind energy forecasts are equal to zero. Specifically, emissions over the out-of-sample evaluation period would have been 6% higher in the absence of the EU ETS. Moreover, findings suggest that higher wind energy penetration levels substantially reduce emissions. In particular, out-of-sample analysis suggests that emissions would have been 14.6 percent higher in the absence of wind energy.

1. Introduction Increased reliance on renewable energy is an important component of the European Union's action plan for reducing carbon emissions. The European Union Emission Trading System (EU ETS), which caps the overall level of emissions and then permits trade among emitters, also plays a key role. In contrast to country-specific carbon taxes, a key attribute of the EU ETS is that it facilitates the harmonization of climate policies within the EU. This may be an important consideration given the global nature of the challenge posed by climate change. The EU ETS is not without its critics with some claiming emission trading is immoral while others assert that it is simply ineffective. Theoretically, firms that can reduce emissions relatively more cheaply will sell allowances to firms that find it relatively more expensive to reduce emissions, so that the emissions reduction required to meet the overall cap is achieved at least total cost. But theories are not always supported by facts. Society may be better served by dispensing with cap and trade markets and instead simply impose a carbon tax or require the generation of electricity using clean energy sources such as wind energy. Using data from Ireland, this paper employs time series analysis to assess the reduction in CO2 emissions attributable to the EU ETS and to wind energy penetration levels. We consider each of the two contributions given that an exclusive focus on either wind energy or the EU ETS

∗

would give rise to an excluded variable bias. We do this by estimating an autoregressive conditional heteroskedasticity/autoregressive moving average model with exogenous inputs (ARCH/ARMAX) of CO2 emissions for each half hour over the period 1 January 2015 through 17 April 2018. Explanatory variables include a weighted measure of the carbon allowance price, the megawatt-hour (MWh) equivalent fuel price of coal relative to the of natural gas, the share of load satisfied by wind energy generation, expected versus realized electricity load, wind energy forecast errors, and the ex-post versus ex-ante system marginal electricity price. Results indicate that increases in the carbon allowance price significantly reduce carbon emissions. Findings also suggest that higher wind energy penetration levels reduce emissions substantially, though the marginal effect diminishes as wind energy penetration increases. The remainder of the paper is organized as follows. Section 2 discusses objections to cap and trade. Section 3 outlines the theory underlying allowance trading systems in general and highlights the advantages of the EU ETS relative to a system of country-specific carbon taxes. A review of the literature is presented in section 4. A brief overview of Ireland's power grid is provided in section 5. Section 6 presents our econometric model of CO2 emissions and provides definitions for all model variables. Estimation issues are discussed, and results reported in section 7. Section 8 presents detailed estimates of the incremental effects of wind energy penetration levels and our carbon

Corresponding author. E-mail address: [email protected] (K.F. Forbes).

https://doi.org/10.1016/j.enpol.2019.07.007 Received 29 October 2018; Received in revised form 18 June 2019; Accepted 8 July 2019 0301-4215/ © 2019 Elsevier Ltd. All rights reserved.

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K.F. Forbes and E.M. Zampelli

price metric on CO2 emissions under various operational scenarios. Section 9 summarizes the findings and concludes the paper. 2. The objections to cap and trade The cap and trade approach to pollution reduction has been criticized on several grounds. Some such as Sandel (2005) claim that it is immoral to buy and sell rights to pollute, while Caney and Hepburn (2011) question whether the market outcome is consistent with distributive justice. Others allege that markets for allowances are vulnerable to harmful speculation and hence are ineffective in reducing carbon emissions (Berta et al., 2017). This objection to the use of market forces to curtail emissions is endorsed by Pope Francis in his encyclical on climate change, Laudato Si. In Francis's words,

Fig. 1. The inefficiency of a uniform reduction in CO2.

levels of abatement undertaken by A and B, respectively. The first-order conditions for cost-minimization are L / Q A = L / QB = 0. This requires that dACA/dQ A = dACB / dQB , i.e., marginal abatement costs for firm A (MACA) must equal marginal abatement costs for firm B (MACB). Therefore, unless the marginal abatement cost functions are identical, this condition is not attained when firms are required to reduce emissions by equal amounts (Fig. 1). In theory, the condition for societal cost minimization will be attained if the right to pollute is freely tradable, participants in the market for allowances are “price takers,” and firms are profit-maximizers. To see this, we note that the “profits” from abatement by firm A can be represented as:

“The strategy of buying and selling ‘carbon credits’ can lead to a new form of speculation, which would not help reduce the emission of polluting gases worldwide. This system seems to provide a quick and easy solution under the guise of a certain commitment to the environment, but in no way does it allow for the radical change which present circumstances require. Rather, it may simply become a ploy which permits maintaining the excessive consumption of some countries and sectors.” (Pope Francis, 2015, p. 126, p. 126) Skepticism regarding the use of market forces is understandable given the 2008–2009 financial crisis, the dot-com bubble in the United States in the late 1990s, the United Kingdom's Libor scandal, the South Sea bubble in the 1700s, etc.Another objection to cap and trade has been articulated by the eminent climatologist James Hansen. In his words, “

ΠA = P QA - ACA

where P is the market price of an allowance. The first term is the incremental net revenue from abatement; the second, the cost of increasing abatement from zero to QA. A necessary condition for profitmaximization is

Because cap and trade is enforced through the selling and trading of permits, it actually perpetuates the pollution it is supposed to eliminate. If every polluter's emissions fell below the incrementally lowered cap, then the price of pollution credits would collapse and the economic rationale to keep reducing pollution would disappear.” (Hanson, 2009)

d A/ dQA = P

dACA/dQ A = 0

(3)

or equivalently, when P = MACA. Intuitively, the optimal emissions level is achieved when the reduction in cost savings from reducing emissions by one unit equals that from paying the allowance price for that unit of emissions. If the allowance price P is equal across firms, i.e., the market for allowances is competitive, then MACA will equal MACB, satisfying the condition for social cost minimization. It follows from Eq. (3) that the cost minimizing solution will not be attained if firms A and B are located in different countries that have each eschewed the cap and trade policy approach and have instead levied different tax rates on carbon. This point appears to be unrecognized by carbon tax advocates such as Mankiw (2007, 2009), Green et al. (2007), and Parry et al. (2018). In contrast, we believe that the international harmonization is important given that country specific carbon taxes may result in taxes that are too low relative to the global optimum since policymakers in each country may not want to imperil the competitiveness of their exports. There is also the point that countries with low to moderate carbon emissions per capita are more likely to embrace a global cap and trade system over a global carbon tax scheme depending on how the allowances are distributed. Another implication of Eq. (3) is that profit-maximizing firms will respond to higher allowance prices by reducing emissions. This paper tests whether the variation in carbon prices (Fig. 2) and wind energy generation (Fig. 3) have any implications for Ireland's CO2 emissions (Fig. 4).

Hansen's views are inconsistent with the vast economic literature that indicates that the most economically efficient way to reduce greenhouse gas emissions is through the use of a policies that place a price on carbon emissions, whether through direct taxation of emissions or the creation of a market for allowances (Aldy and Stavins, 2012; Aldy, 2015; Edenhofer et al., 2015; Schmalensee and Stavins, 2015). To us, Hansen's statement is indicative of the economics profession's inability to adequately explain the economics of cap and trade to noneconomists and policymakers. In the hope of redressing this inadequacy, the next section offers a simple exposition of the theory underlying the cap and trade approach to CO2 mitigation. 3. The theoretical underpinning of cap and trade Consider two carbon emitting firms, A and B, with total abatement cost functions represented by ACA and ACB, respectively. For each firm, we assume that the private and social costs of abatement are equivalent and that marginal abatement costs rise as more abatement is undertaken. Assume emissions by each firm in the absence of any abatement equals Q0. Suppose also that policymakers want total CO2 emissions reduced by 50%. and that on a per-polluter level this works out to an abatement level of QT. Clearly, this can be accomplished with a regulation that would require each firm to reduce its emissions by 50%. However, unless A and B have identical marginal abatement cost functions, the policy would entail unnecessarily higher abatement costs. To see this, consider the Lagrangain: L = ACA + ACB + λ[ 2*QT – QA – QB]

(2)

4. Literature review Our review of the extant literature on the carbon abatement impacts of EU ETS begins with Ellerman and Buchner (2008). Assuming 2002 emissions as a baseline and using data on emissions, economic activity, and trends in energy and carbon intensity, the authors conduct a counterfactual analysis and estimate that EU ETS reduced carbon

(1)

where λ is the Lagrange multiplier while QA and QB are respective 2

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K.F. Forbes and E.M. Zampelli

Fig. 2. The near-month futures market price of carbon allowances in the EU ETS, 2 January 2015–31 December 2018. Source: https://www.quandl.com/data/CHRIS/ICE_C1-ECX-EUA-FuturesContinuous-Contract.

Fig. 4. CO2 emissions from the Irish power grid, 1 January 2015–30 September 2018. Source: Eirgrid. Note: The gaps in the graph are attributable to missing data.

analysis to examine the carbon abatement by the EU-25 member states over the 2005–2012 period. Of the estimated total abatement in industrial emissions of 294.5 Mt, their results suggest that only somewhere between 33.78 and 40.76 Mt was a consequence of EU ETS, with the remainder due to the economic recession. With difference-in-difference and semiparametric analyses of a panel of German manufacturing firms, Petrick and Wagner (2014) find that between 2007 and 2010 CO2 emissions of ETS participating firms declined by 20% relative to non-participants. A similar result is reported by Wagner et al. (2014) for French manufacturing plants. There is also a nascent literature on the effect of wind energy on CO2 emissions. A review of the literature by Inhaber (2011) notes that while some proponents of wind energy have suggested that one MW of wind energy will offset CO2 emissions from fossil fuel energy sources almost unit for unit, a number of studies have indicated that the reduction in CO2 is less than this because of wind energy's intermittent nature. One reading of this literature suggests that the marginal CO2 reduction from increased wind energy penetration declines at some point because of wind energy induced increases in the cycling of generating stations powered by fossil fuels. Consistent with this view, Wheatley (2013), using data for each thermal connected generating station in Ireland, concludes that wind energy reduced emissions by 0.28 tCO2/MWh on average, relative to an implied average carbon intensity in the absence of wind of about 0.52 tCO2/MWh. Wheatley presents the following rationale for this finding:

Fig. 3. Wind energy generation in Ireland, 1 January 2015–30 September 2018.

emissions moderately, between 50 and 100 million tonnes (Mt) in both 2005 and 2006, relative to the Business as Usual (BAU) scenario. Anderson and Di Maria (2011) employ counterfactual analysis and variables similar to Ellerman and Buchner, supplemented by fuel price and weather data, and estimate net carbon abatement due to EU ETS of 174 Mt over the 2005–2007 period, a modest reduction of about 2.8% relative to their estimate of BAU emissions. In an analysis of the EU electricity sector, Delarue et al. (2010) estimate that positive carbon allowance prices reduced emissions by about 34 Mt and 19 Mt in 2005 and 2006, respectively. Egenhofer et al. (2011) extend Ellerman and Buchner (2008) and find larger emissions reduction from EU ETS of 1.3% in 2008 and 5.4% in 2009. Using a panel of emissions and performance data for over 2000 EU ETS firms, Abrell et al. (2011) estimate a 5.4% emissions reduction between 2007 and 2008. Studies by Declercq et al. (2011) and Bel and Joseph (2015) focused on abatement impacts of EU ETS during the Great Recession of 2008–2009, when the European Union Allowance (EUA) prices collapsed from between 20 and 30 euros per ton to between 10 and 15 euros per ton, reaching lows of less than 10 euros per ton in early 2009. Declercq et al. (2011) used BAU analysis and estimated that the collapse in economic activity reduced emissions by 175 Mt, while the collapse in the carbon price increased emissions by only 30 Mt. Bel and Joseph (2015) use historical data analysis rather than counterfactual

“… it is now appreciated that thermal generation responds in a nontrivial way when operated in parallel to stochastic power sources to meet system demand. Not all thermal plants are displaced equally, with flexible and/or high marginal cost generation being displaced the most. Average efficiency is reduced and higher cycling rates occur than would otherwise be the case. These effects tend to reduce the effectiveness of wind power in meeting its primary goal, namely emissions reduction.” (Wheatley, 2013, p 89) Wheatley's findings are consistent with Clack et al.’s (2017) critique of Jacobson et al. (2015) who claim that the goal of 100% renewable energy is feasible using existing technology. There is a dearth of research that examines the effects of both renewable energy penetration and the EU ETS on the emissions from a power grid. One exception to this is Weigt et al. (2013) who estimate that renewable energy policies reduced emissions from the German 3

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electricity sector by about 10%–18%. They also report that the effect of the EU ETS is about 1–3% but that there are synergies between the two effects. This is a potentially an important finding but we believe that more analysis is needed given that the conclusions are based on simulated as opposed to real data. As the authors themselves concede, the analysis assumes that time-series effects are unimportant in the sense that the generation in any given hour does not depend on generation in previous hours. There is also the omission of forecasting errors from their model. In short, there is a gap in the research that needs to be resolved. 5. The All-Island Irish power grid The All-Island Irish power grid has two control areas, one corresponding to the Republic of Ireland, the other to Northern Ireland. System operators are Eirgrid (http://www.eirgridgroup.com/) and SONI (http://www.soni.ltd.uk/), respectively. In 2005, EirGrid and SONI established a joint venture, SEMO (Single Energy Market Operator, http://www.sem-o.com/pages/default.aspx), which oversees the electric power system for the entire island of Ireland. Our analysis uses data for the entire island over the period 1 January 2015 through 30 September 2018 where 30 September 2018 is one day prior to a major change in the trading arrangements. Over the study period, the Single Energy Market (SEM) was a mandatory pool for any generator with an export capacity of more than 10 MW. All electricity was traded through a market clearing mechanism based on the generators bidding their Short Run Marginal Cost (SRMC) and receiving the System Marginal Price (SMP) which is an all-island system-wide price for each half-hour. It equals the shadow price, the cost of the marginal MW required to meet demand, plus uplift costs which equals start-up costs (e.g. the costs of starting up a generating unit from a cold state) plus the costs of running a generating unit when output equals zero MW. In terms of timing, bids by generators are submitted in the morning one day before real-time to the market operator. Following the submissions by the generators, the least-cost security constrained solution is solved. The ex-ante two (EA2) results are subsequently published by the market operator at 13:00. The ex-post two (EP2) results are published four days after the trading day. Given the goal of keeping production costs to a minimum, generators in SEM were selected for dispatch based on their bid price per MW. This favors the dispatch of wind energy because of its low marginal costs. It may also favor generation from coal given the relative price difference between coal and natural gas (Fig. 5). Because the fuel price advantage for coal is just one factor in the overall competition between coal and natural gas, it may partially explain coal's persistence in the generation mix (Fig. 6). The dispatch of generation from Ireland's generating stations fueled by peat was largely exempt from market forces over the sample period. There are three plants in question. Their total dispatchable capacity is about 250 MW (MW) out of a total all-island dispatchable capacity of about 7,600 MW (Eirgrid & SONI, 2016). This policy has been defended on the grounds that electricity generation using peat reduces Ireland's dependence on energy imports. It is also maintained that the peat plants are useful from a system security perspective (Tuohy et al., 2009). The carbon intensity of the generating stations fueled by peat is about 1,098 g of CO2 per kWh in 2016, which was about three times the carbon intensity of the stations fueled by natural gas (SEAI, 2018, p. 24). Because of their high carbon intensity, these three plants accounted for about 20% of Ireland's carbon emissions from electricity generation in 2016 (SEAI, 2018, table 14). The dispatch of electricity from Moneypoint, Ireland ’s largest generating station with a dispatchable capacity of about 855 MW (EirGrid & SONI, 2016), and the only generating station primarly fueled by coal (it can also generate electricity using heavy fuel oil), was also shielded from market forces over the sample period. Specifically, at

Fig. 5. The MWh equivalent price of coal relative to natural gas, 1 January 2015–30 September 2018. Based on natural gas pricing data from National Grid in the UK and coal pricing data from GlobalCoal.

Fig. 6. The 2017 all-island fuel mix in Ireland. Source: SEMO.

least one of the three generating units at the Moneypoint station over the sample period was required to be dispatched at all times to support the transmission system (Eirgrid, 2017, p. 11). Moneypoint's three generating units are also on a list of 15 units, five of which must be run at all times to provide dynamic stability (Eirgrid, 2017, p. 9). The effect of these requirements on carbon emissions may be nontrivial given that the carbon intensity of electricity generation fueled by coal was about 911 g of CO2 per kWh in 2016 (SEAI, 2018, p. 24). Given its “system security” sanctioned protected status and high carbon intensity, Moneypoint accounted for about 34% of Ireland's carbon emissions from electricity generation in 2016 (SEAI, 2018, table 14). Differences between ex-ante and ex-post loads can be nontrivial (Fig. 7). By our calculations, the weighted mean percent absolute error (WMAPE) in the ex-ante load assessment is about 5.9% of the mean expost load. These errors have implications for power grid operations, and 4

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K.F. Forbes and E.M. Zampelli

Fig. 7. The ex-ante vs ex-post system load in Ireland, 1 January 2015–30 September 2018. Source: SEMO.

Fig. 9. Ex-ante vs. ex-post system prices in Ireland, 1 January 2015–30 September 2018. Source: SEMO.

in turn, CO2 emissions. Based on more recent data for Ireland we have obtained from the ENTSO-E Transparency Platform (https:// transparency.entsoe.eu/), the WMAPE corresponding to Ireland's new load forecasting system is a more moderate 3.7% With respect to wind energy, our calculations indicate that the WMAPE in the short run wind energy forecasts is about 13.5% of the mean level of wind energy generation (Fig. 8) (We note that a portion of this “error” can be attributed to wind energy curtailments by the system operator but that the magnitude of this effect appears to be small). This reported error is higher than the capacity weighted error metrics reported by Eirgrid (http://www.eirgridgroup.com/site-files/library/ EirGrid/Wind-Forecast-Accuracy-Report-March-2018.pdf), but Forbes et al. (2012) have sharply questioned the logic of weighting an error in energy supply by energy capacity given that the crucial balance between short run energy supply and demand is in terms of actual level of electricity as opposed to the capacity of the equipment used to generate the electricity. Consistent with this view, Green and Tashman (2009), conclude that “The Actual [ level of the activity] is the only consistent basis for comparing forecast accuracy against a benchmark or for judging improvement over time.” The errors in the load assessments and the wind energy forecasts have implications for the differences between the ex post and ex ante SMPs (Fig. 9). Other contributing factors to the ex post vs ex ante differences in the SMPs include the uplift costs (measured as the difference

between the SMP and the shadow price) where the WMAPE between ex ante and ex post uplift costs has a WMAPE of approximately 100 percent of the mean level of the ex post level of uplift costs. 6. Modeling carbon emissions One of the pioneers of the methods that we use was the eminent statistician Professor George Box. While perhaps not well known to the readers of this journal, Google Scholar reports that there are over 150,000 citations to his research (https://scholar.google.com/citations? user=qR6KIVQAAAAJ&hl=en). Among his other contributions to the scientific literature, he was the co-developer of the Box–Jenkins method which applies an autoregressive moving average to find the best fit of time series data (Box and Jenkins, 1970). Our modeling approach accepts his well-known aphorism that “All models are wrong; some models are useful” (Box et al., 2005, p. 440). They are all “wrong” in the sense that all are simplifications of a complex reality but can be useful if they capture salient or major aspects of that reality. This is a humbling state of affairs. It is also realistic in light of the potentially long list of picayune objections to any empirical analysis of the CO2/carbon price or CO2/ wind energy penetration relationships. For instance, it may be claimed that the modeling results reported here are tainted because of multicollinearity, even though two of the leading solutions to this “problem” are 1) do nothing because the least squares estimates remain unbiased in the presence of multicollinearity, and 2) increase the sample size (Kennedy, 2008, p. 196). It may also be claimed that we have overlooked the seasonality of CO2 emissions even though the influence of seasonality is reflected in our explanatory variables. In short, there is potentially a long list of ways in which our model may deemed to be “wrong.” Following Box, we cheerfully concede this shortcoming but also note his point that the true test of a model is whether it is useful. In our view, there are two important metrics of a time-series model's usefulness. The first is the finding of model adequacy measured by whether the residuals have the property of white noise. This view of model adequacy is endorsed by Becketti (2013, p. 256) who notes, “… the measure of a well-specified and accurately fitted time-series model is evidence that the residuals … are white noise.” This standard of model adequacy is consistent with Kennedy (2008, p. 315) and Granger and Newbold (1974, p. 119). A second, perhaps more important, metric of a time-series model's usefulness is its out-of-sample predictive accuracy. Modeling results devoid of an out-of-sample assessment are inherently vulnerable to skepticism. Accordingly, our modeling approach proceeds by estimating the model using three years and approximately five months of half-hour data and then performing an

Fig. 8. Forecasted vs Actual Wind Energy Generation in Ireland, 1 January 2015–30 September 2018. 5

Energy Policy 133 (2019) 110871

K.F. Forbes and E.M. Zampelli

approximately two-month out-of-sample analysis with 3,227 observations. Our model assumes that carbon emissions are a function of the price of a carbon allowance relative to the day-ahead price of electricity, the level of system load, the share of load accounted for by wind energy, the MWh equivalent price of coal relative to natural gas, and various metrics of operational uncertainty. These metrics include the errors in the SMP assessments, the errors in the system load assessments, and the errors in the wind energy forecasts. A key variable in our model is the ratio of the carbon price to the day-ahead electricity price. We do not make use of the carbon price independently from other variables for the following two reasons:

otherwise. LoadRatioLT1 equals EP2 system load relative to EA2 reported level of system load when the ratio is less than one. It equals zero otherwise. Please note that both LoadRatioLT1 and LoadRatioGT1 are equal to zero if LoadEA2 equals LoadEP2 WindRatioGT1 is the ratio of actual wind energy generation relative to forecasted when the ratio is greater than or equal to one. It equals zero otherwise. WindRatioLT1 is the ratio of actual wind energy generation relative to forecasted when the ratio is less than one. It equals zero otherwise. Please note that both WindRatioLT1 and WindRatioGT1 are equal to zero if forecasted actual energy generation equals forecasted. CoalGasPratio is the price of coal in Euros per MWh relative to the price of natural gas in Euros per MWh; Hi is a binary variable representing the hour of the day

● An augmented Dickey-Fuller test indicates that the null hypothesis that the carbon price has a unit root cannot be rejected, an outcome that does not occur when the relative prices are employed. Accordingly, including the carbon price in isolation as a regressor would yield spurious results. ● From demand theory, the effect of the price change is best understood in terms of relative prices. For example, in a world where there are two factors of production, labor and capital, the demand for labor is dependent on the wage relative to the price of capital. In the case before us, the effect of a 10 Euro increase in the price of a carbon allowance is apt to be quite different when the day-ahead electricity price in the absence of a carbon cap mandate is 15 Euros per MWh as opposed to 50 Euros per MWh.

Most data for Eq. (4) were downloaded from SEMO (http://www. sem-o.com/Pages/default.aspx) or EirGrid (http://www.eirgridgroup. com/how-the-grid-works/system-information/) websites. Exceptions are the data used to construct the variable CoalGasPratio, which was calculated based on the MWh equivalent price of coal reported by GlobalCoal (https://www.globalcoal.com/) and the MWh equivalent price of natural gas reported by National Grid in the UK (http://mipprod-web.azurewebsites.net/DataItemExplorer/Index). These prices were converted to their Euro equivalents using exchange rate data from SEMO and the U. S. Federal Reserve. The variable CoalGasPratio was calculated under the assumption that the price signal it represents was available to market participants one day before the submissions of the day-ahead bids by electricity market participants to the system operator. The calculation takes into account the gap in information flows associated with weekends and holidays by making use of the most recent market information. For example, for an operating day that occurs on a Monday, the variable would be calculated using the spot prices for coal and natural gas reported on Friday. Our calculation of the variable CO2Pratio follows this same method. Specifically, the numerator of the variable, i.e. the carbon price, is the market price of an allowance one day prior to the submissions of the day-ahead bids by electricity market participants to the system operator. As with the variable CoalGasPratio, the calculation takes into account the gap in the information flows associated with weekends and holidays by making use of the most recent market information. In this way, the variable CO2Pratio reflects the effects of the carbon price on the day-ahead market price. Observations were deleted from the sample if there were missing values, reported wind energy generation was negative or if EA2 SMP was negative. We also dropped observations if the reported load or CO2 levels in time period t is more than 40% higher or lower than in period t-1, i.e. the period 30 min earlier. The total number of deleted observations was 3,007. Questionable or missing CO2 data were the leading causes of the deletions. The final sample consisted of 54,709 observations. Summary statistics for the primary variables are reported in Table 1.

Allowing for asymmetries in the load and SMP ratios (e.g. SMPEP2 > SMPEA2 vs SMPEP2 < SMPEA2) and interactions between some of the key variables, (e.g., the share of wind energy and the price of coal relative to natural gas) the linear version of the model can be represented as follows:

CO2 = Constant + 1 CO2 Pratio + 2CO2 Pratio*WindShr + 3 SMPratioGT1 + 4 SMPratioLT1 + 5LoadEP2 + 6CO2 Pratio*LoadEP2 + 7LoadRatioGT1 + 8LoadRatioLT1 + 9 (CO2 Pratio*LoadRatioGT1) + > 10 (CO2 Pratio*LoadRatioLT1) + 11WindRatioGT1 + 12WindRatioLT1 + 13 (CO2 Pratio*WindRatioGT1) + 14 (CO2 Pratio*LoadRatioLT1) + 15WindShr + 16CoalGasPratio + 17CoalGasPratio*WindShr + 18CO2 Pratio*CoalGasPratio + 19WindRatioGT1*CoalGasPratio 24 H + WindRatioLT1* CoalGasPratio + 20

i

i

(4)

where CO2 is the level of CO2 emissions for the entire island of Ireland in metric tons per hour; CO2Pratio equals the price of an EU ETS carbon allowance relative to the EA2 system marginal price; WindShr equals wind energy generation for the entire island of Ireland relative to the EA2 reported level of system load; SMPratioGT1 equals the ratio of EP2 SMP relative to the EA2 SMP when the ratio is greater than or equal to one. It equals zero otherwise. SMPratioLT1 equals the ratio of EP2 SMP relative to the EA2 SMP when the ratio is less than one. It equals zero otherwise. Please note that both SMPratioLT1 and SMPratioGT1 are equal to zero if SMPEA2 equals SMPEP2 LoadEP2 is the EP2 system load for the entire island of Ireland; LoadRatioGT1 equals EP2 system load relative to EA2 reported level of system load when the ratio is greater than one. It equals zero

7. Estimation and results The model was estimated over the period 1 January 2015 through 17 April 2018. The model was subsequentially evaluated over the period 25 July through 30 September 2018. The gap between these two time periods is attributable to missing CO2 values. The evaluation period terminates on 30 September 2018 because new trading arrangements went into effect on 1 October 2018. The empirical analysis was conducted in two phases. In the first phase, we provide evidence that rejects the model's linear form given by Eq. (4) and subsequently, identifies a non-linear functional form that is a more statistically reliable descriptor of the complex relationships 6

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Table 1 Summary statistics of the primary variables.

CO2 LoadEP2 LoadRatio CO2Pratio SMPratio WindRatio WindShr CoalGasPratio

TCO2 =

Sample Mean

Sample Standard Deviation

Sample Minimum

Sample Maximum

1909.794 3912.003 0.950 0.161 1.067 1.029 0.248 0.507

395.562 830.100 0.049 0.064 0.371 0.284 0.187 0.130

676.500 2010.070 0.679 0.004 0.000 0.000 0.000 0.067

3588.000 6359.320 1.293 7.365 12.958 4.635 0.859 1.017

(CO2 + 2 ) 1 ln(CO2 +

1)/

1

2 );

1

; 1 =0

0 (5)

where 1 is a parameter estimated from the Box-Cox procedure and 2 is a value that ensures the left-hand side of Eq. (4) is positive. In this case, 2 was taken to be equal to zero. The null hypothesis of linearity in the dependent variable is supported if 1 = 0 . Inspection of Eqs. (4) and (5) reveals that the directions of the relationships between the dependent variable and the explanatory variables are preserved under the transformation. Under the assumption of linearity in the explanatory variables, the estimated value of 1 is 0.4913309. With a p-value less than 0.001, linearity in the dependent variable is not supported. To address the issue of linearity in the explanatory variables, we relied on the multivariable fractional polynomial (MFP) methodology, a useful technique when one suspects that some or all relationships between the dependent variable and explanatory variables are non-linear (Royston and Sauerbrei, 2008). The MFP is initiated by estimating a model that is strictly linear in the explanatory variables. Subsequent estimations cycle through a battery of nonlinear transformations of the explanatory variables (e.g., cube roots, square roots, squares, etc.) until the model that best predicts the dependent variable is found. In the present case, the MFP results provided support for specifying some of the explanatory variables with powers other than unity. Moreover, the MFP analysis suggested that the WindShr variable should be represented as a second-degree polynomial. One possible reason for this is that the CO2 benefits of wind energy may be subject to diminishing marginal returns because of the operational challenges of integrating an energy source that is not fully dispatchable and whose forecasted generation levels have a WMAPE of 13.5% relative to the mean level of wind energy generation. In short, the conclusions of Inhaber (2011) and Wheatley (2013) may be the driver of the MFP suggested specification. Inconsistency between the Box-Cox parameter estimate and the MFP recommended exponents cannot be ruled out. Fortunately, there is a straightforward solution—iterate between the two methods until the Box-Cox transformation of the dependent variable is consistent with the MFP transformations of the explanatory variables. This iterative process yielded a revised estimate of 0.4019797 for 1 along with recommended exponents different from one for 13 of the explanatory variables. The transformed structural equation is given by:

between carbon emissions and the model's explanatory variables. Given Wheatley's (2013) findings, any serious attempt to define these relationships must also assess the relationship between the share of load accounted for by wind energy and CO2 emissions. Our rationale for the proposed second step is to recognize that the level of CO2 emissions in period t is highly correlated with the levels in previous periods. The autocorrelations in the CO2 emission levels do not monotonically decline over time, but instead have a significant diurnal pattern over the 48 half-hour market periods for each day (Fig. 10). For example, the emissions level in market period t is highly correlated with that in market period t-48 (48 half-hours previously), relative to its correlations with the emission outcomes in other market periods from the day before. Additionally, emissions in period t are highly correlated with those in periods t-96, t-144, t-192, t- 240, t-288, t-336, t-384 etc. In our opinion, the estimation needs to accommodate these characteristics of the emission levels, as well as the results of the Engle Lagrange multiplier (LM) test for autoregressive conditional heteroskedasticity. Our estimation approach acknowledges that the Box-Jenkins philosophy of being parsimonious in the application of ARCH/ARMA terms may conflict with the goal of within-sample model adequacy, i.e., white noise in the residuals, when modeling half-hour CO2 emission data; the goal of model adequacy should be the higher priority. Thus, while researchers who analyze daily, monthly, or quarterly data may make use of ARMA(1,1), ARMA(2,2), or ARCH(1) specifications, our approach will go substantially beyond this, given the autocorrelation evidenced in Fig. 10 and the results of the Engle LM test. Specifically, we will estimate an ARMA(31, 73) model with an ARCH(17) process for the conditional variance. The first step of our estimation begins by testing whether it is appropriate to transform the dependent variable. Following Box-Cox (1964, p. 214), the dependent variable in Eq. (4) is transformed as follows:

TCO2 = Constant +

1

CO2 Pratio

+

3/4 1 (CO2 Pratio*WindShr)

+

1/4 3 SMPratioGT1 3 SMPratioLT1 4 1/4 5 LoadEP2

+ + + + + + + + +

6 CO2 Pratio*LoadEP2 7 LoadRatioGT1 1/4 8 LoadRatioLT1 9 (CO2 Pratio*LoadRatioGT1) 10 (CO2 Pratio*

4/3

LoadRatioLT1)

11 WindRatioGT1 12 WindRatioLT1 2/3

+

13(CO2 Pratio*WindRatioGT1)

+

14 (CO2 Pratio*WindRatioLT1) 5/4 + 3 15 WindShr 15 WindShr 3/4 17 CoalGasPratio 3 (CoalGasPratio*WindShr) 18 3/4 (CO Pratio*CoalGasPratio) 2 19

+ + + + +

20 WindRatioGT1*CoalGasPratio

+ 21(WindRatioLT1*CoalGasPratio)3 + Fig. 10. Autocorrelations in the CO2 emissions.

24

iH

(6)

Estimating Eq. (6) by least-squares yields an R2 value of about 0.74. 7

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Unfortunately, the least-squares parameter estimates are highly suspect given that a Portmanteau (Q) test indicates that the least squares residuals do not even remotely possess the property of “white noise.” Specifically, the p-values for the portmanteau test for the first 100 lags are all less than 0.0001, indicating that the null hypothesis of white noise is rejected. Visual inspection of the autocorrelations in the residuals easily confirms this result (Fig. 11). Furthermore, the error distribution has greater kurtosis, i.e., a higher incidence of outcomes in the tails, than a Gaussian distribution. Not surprisingly, the null hypothesis of normality is rejected by the Shapiro-Wilk Normality Test (Shapiro and Wilk, 1965). The null hypothesis of no autoregressive conditional heteroskedasticity was rejected with p-value less than 0.0001 using Engle's Lagrange multiplier test (1982). As discussed above, the time-series issues in the least-squares residuals are addressed in the second step of the estimation procedure using ARCH/ARMA methods. Specifically, step two of the estimation is accomplished by first making use of an ARCH model. This modeling approach splits the residual error term into a stochastic element and a time-dependent standard deviation. This is a useful method in modeling times series data that exhibit time-varying volatility, i.e., periods of turbulence followed at some point by periods of relative calm. The second step in the modeling also makes use of an autoregressivemoving-average with exogenous inputs model specification (ARMAX), with the transformed explanatory variables from the first step (e.g., WindShr) included as the exogenous inputs, and where the disturbance terms are presumed to follow an autoregressive moving-average (ARMA) specification. With respect to our modeling of the ARCH process, we note that there are several variants of the basic ARCH specification. The specification employed here is the TARCH version which is one way to model the ARCH process when it responds asymmetrically to positive and negative innovations. The modeled lag lengths in the ARCH process were chosen based on the observed diurnal pattern in the CO2 autocorrelations reported in Fig. 10, as well as inspection of the leastsquares residuals (Fig. 11). The specific lags modeled are 1 through 8, 46, 48, 95, 96, 97, 477, 481, 482, and 485. In addition, the conditional variance is modeled as a function of the following variables:

SMPEA2 , ,

SMPEP 2 ,

ForecastedWind ,

LoadEA2 ,

terms. For the MA(q) process, the modeled lag lengths are q = 1 through 48, 55, 72, 143, 144, 192, 197, 288, 335, 336, 383, 384, 388, 432, 470, 477, 478, 480, 481, 482, 485, 573, 576, 624, 671 and 672. We estimated Eq. (6) under the assumption that the error distribution corresponds to a Student's t distribution, which allows for greater kurtosis than the Gaussian distribution. Specifically, the kurtosis accommodated by this distribution in excess of the Gaussian level of three equals 6/(v - 4), for v > 4, where v is the distribution's “shape” parameter (Harvey, 2013, p. 20). The estimation yielded an estimate of v of approximately 6. Thus, the kurtosis in excess of the Gaussian level of three accommodated by the distribution equals 6/(6-4) or three. The advantage of using this distribution is the resulting asymptotic normality of the maximum likelihood estimators, which ensures that tests of statistical significance will be meaningful. As a further precaution, standard errors are based on the full Huber/White/sandwich formulation and thus, from Bollerslev and Wooldridge (1992), variance estimates are robust to symmetric non-Gaussian disturbances. Estimation results for the structural parameters exclusive of the binary variables for the hour of the day are presented in Table 2. Regarding the time-series terms, 22 of 31 AR terms, 56 of 73 MA terms, 6 of 17 ARCH terms and 26 of 39 conditional variance terms are statistically significant. These estimates are unreported but available upon request from the corresponding author. An Augmented Dickey-Fuller test rejected the null hypothesis of a unit root in the residual error term at 1%. Inspection of the coefficient and p-value corresponding to CO2Pratio in Table 2 indicates that increases in CO2Pratio in the absence of other considerations has a negative and statistically significant effect on carbon emissions. However, the positive and significant coefficients corresponding to (CO2Pratio* LoadRatioGT1)4/3 and CO2Pratio* LoadRatioGT1 indicates that the errors in load assessments impairs the carbon reducing effects of the CO2 price. Moreover, the positive and statistically significant coefficients corresponding (CO2Pratio* WindRatioGT1)2/3 and CO2Pratio* WindRatioLT1 indicates that the errors in the wind energy forecasts also adversely affects the performance of the carbon market. With respect to wind energy's effects on emissions, we further note that the coefficients corresponding to WindShr5/4, WindShr3, (WindRatioGT1*CoalGasPratio)½, (WindRatioLT1*CoalGasPratio)3, and (CoalGasPratio*WindShr)3 are all statistically significant with some of the coefficients being negative (e.g. WindShr5/4) while others are positive (e.g. WindShr3). In short, the effect of wind energy on CO2 has a mixed effect on emissions. While some may be tempted to reject this finding out of hand, the results are consistent with Wheatley (2013) and the literature reviewed by Inhaber (2011). With respect to the issue of within-sample model adequacy, the residuals, taken as a whole, do not exhibit the white noise property. This occurs largely because of the model's shortcomings associated with lags 1, 2, 3, 4, 8, and 573. Nevertheless, the vast proportion of the residuals are within the band corresponding to the null hypothesis of white noise (Fig. 12). To assess the model's predictive accuracy, we performed an out-ofsample analysis using half-hour data over the period 25 July through 30 September 2018. Over this period, the average carbon price was about 19.7 Euros per ton while the average level of wind energy penetration was approximately 28.5%. Over this period, the level of actual CO2 emissions was highly volatile (Fig. 13). Despite this, the model's out-ofsample predictive R2 equals 0.611 when based exclusively on the model's structural parameters but increases dramatically to 0.963 when the ARCH/ARMA terms are included. In short, the model's overall outof-sample predictive accuracy is quite respectable (See Fig. 14). Thus, though the model fails to achieve the within-sample goal of “white noise” in the residuals, the out-of-sample performance of the model strongly suggests that the model is indeed “useful.” To put these results in perspective, the linear specification with the interaction terms, i.e. equation (4), was estimated using the same ARCH/ARMA terms as in the nonlinear model reported in Table 2. The

LoadEP 2 ActualWind

CoalGasPratio

For the AR(p) process, the modeled lag lengths are p = 1 through 12, 47, 48, 49, 96, 144, 192, 240, 287, 288, 336, 383, 384, 432, 480, 485, 528, 576, 624 and 672. The second portion of the ARMA component represents the moving-average (MA) nature of the disturbance

Fig. 11. Autocorrelations in the least squares residuals. 8

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K.F. Forbes and E.M. Zampelli

Table 2 Estimation Results for Equation 6 Variable

Estimated Coefficient

Robust Standard Error

T Statistic

P-Value

Constant CO2Pratio (CO2Pratio*WindShr)3/4 SMPratioLT13 SMPratioGT11/4 LoadEP21/4 CO2Pratio*LoadEP2 LoadRatioGT1 LoadRatioLT1 1/4 (CO2Pratio* LoadRatioGT1)4/3 CO2Pratio* LoadRatioLT1 WindShr5/4 WindShr3 WindRatioGT15/4 WindRatioLT1 (CO2Pratio* WindRatioGT1)2/3 CO2Pratio* WindRatioLT1 CoalGasPratio1/4 (CoalGasPratio*WindShr)3 CO2Pratio*CoalGasPratio (WindRatioGT1 *CoalGasPratio)1/2 (WindRatioLT1* CoalGasPratio)3 R- Squared: based on all the estimated parameters including the ARCH/ARMA terms R-Squared: based on the structural parameters exclusively Number of Observations

31.4818 -1.9338 0.5396 0.0269 0.0382 2.9200 -0.0006 -0.4100 -0.5602 4.4750 3.5612 -17.7630 7.4733 0.0710 -0.0468 0.4213 0.6326 -2.5409 4.9425 -0.5187 -0.3683 -0.3781 0.984 0.642 54,709

1.3137 0.2220 0.3406 0.0089 0.0073 0.1073 0.0001 0.4079 0.4104 0.4678 0.3133 0.3212 0.5228 0.0639 0.0392 0.1629 0.2313 1.2350 1.5142 0.4554 0.0984 0.1281

23.96 -8.71 1.58 3.01 5.24 27.22 -8.60 -1.01 -1.37 9.57 11.37 -55.30 14.29 1.11 -1.19 2.59 2.74 -2.06 3.26 -1.14 -3.74 -2.95

< 0.001 < 0.001 0.113 0.003 < 0.001 < 0.001 < 0.001 0.315 0.172 < 0.001 < 0.001 < 0.001 < 0.001 0.267 0.232 0.010 0.006 0.040 0.001 0.255 < 0.001 0.003

estimation results for this model are reported in Table A1 in the appendix. The linear model's out-of-sample predictive R2 equals 0.598 when based exclusively on the model's structural parameters but increases dramatically to 0.959 when the ARCH/ARMA terms are included. Both of these measures are inferior to the nonlinear model. While some would assert that these differences in accuracy are minor, inspection of the appendix indicates that the linear model would have energy analysts and policymakers believe that a higher carbon price/ electricity price ratio would increase emissions (the coefficient corresponding to CO2Pratio is positive and statistically significant) while the nonlinear model indicates that emissions would decline depending on the magnitude of the errors in the wind energy forecasts and load assessments. 8. An analysis of the incremental effects An analysis of the effect of the carbon price on emissions over the out-of-sample period was performed using the model's structural estimates. Specifically, the predicted level of CO2 emissions was first

Fig. 13. CO2 emissions from the All-Island Power Grid in Ireland, 25 July – 30 September 2018.

Fig. 12. Autocorrelations in the standardized ARCH/ARMA residuals.

calculated using the actual values of all the structural variables and then again under the assumption that the carbon allowance price was equal to zero. The predicted level of emissions was calculated yet again under the assumption that the errors in the wind forecasts and load assessments were equal to zero. The results indicate that the carbon price had only a 0.46% effect on emissions, given the actual errors in the wind forecasts and load assessments, but had an approximately 6.1% reduction when these errors were assumed equal to zero. We suspect that the effect of the EU ETS on emissions would be significantly higher in the absence of the system security status of Moneypoint's generating units and the special status of the generating units in Ireland that produce electricity using peat. The predicted effect of wind energy on emissions over the out-ofsample period was also calculated. The predicted level of CO2 emissions was first calculated using the actual values of all the structural variables and then again under the assumption that all the wind energy related variables were equal to zero. The results indicate that emissions would have been 14.6% higher in the absence of wind energy. Though this is 9

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K.F. Forbes and E.M. Zampelli

calculated. They were calculated again with WindShr equal to 0.51. Based on these results, the change in emissions and the change in wind energy generation were calculated. The ratio of these two values yields the incremental effect of wind energy generation on CO2 emissions. Inspection of Table 3 indicates that the incremental effect initially increases with WindShr but then declines. For example, when all of the other explanatory variables are held at the hour 17 median values, the out-of-sample reduction in emission from a one-point increase in WindShr is calculated to be 10.04 tons per hour when WindShr equals 5%; at 75%, the calculated reduction is 5.13 tons per hour. Table 4 presents the out-of-sample calculated incremental effects for CO2Pratio (the within sample results are available upon request). During this period, the value of CO2Pratio ranged from about 0.15 to slightly more than 0.40. The reported values indicate that the incremental effect of change in CO2Pratio during hour 17 are quite modest when all the other explanatory variables are held constant. For example, an increase in the price ratio from 0.35 to 0.40 only reduces hour 17 emissions by 4.30 tons per hour when all the other explanatory variables are held equal to their hour 17 median values. Interestingly, the calculated reduction is a more robust 18.92 tons per hour when the interaction between CO2Pratio and the error in the load assessments is assumed to be equal to zero.

Fig. 14. Predicted vs. actual CO2 emissions, 25 July through 30 September 2018.

an impressive reduction, the fact that it required an average wind energy penetration level of 28.5% raises questions. Table 3 presents calculated incremental effects for wind energy that may provide insights into this result. The within and out-of-sample effects were calculated using the estimated parameters, the assumed values of WindShr, and the assumed values of the other explanatory variables (e.g. the median values for the other explanatory variables for hour 17). For example, with WindShr equal to 0.5, the value of the CO2 emissions was

9. Summary and conclusion Using data from Ireland, this paper has examined the effects of wind energy and the price of carbon on CO2 emissions. The results are consistent with the hypothesis that an increase the price of a carbon allowance relative to the day-ahead price of electricity has the effect of

Table 3 Selected Incremental Effects for Wind Energy for Hour 17 WindShr (%)

Within-Sample calculated incremental effect of a one percent point increase in WindShr (Tons per Hour)

Within-Sample calculated incremental effect of a one percent point increase in WindShr (tCO2/MWh)

Out-of- Sample Calculated incremental effect of a one percent point increase in WindShr (Tons per Hour)

Out-of- Sample Calculated incremental effect of a one percent point increase in WindShr (tCO2/MWh)

Assumed hour 17 percentiles of the other explanatory variables

5 10 25 50 75 5 10 25 50 75

10.30 11.81 12.87 10.29 5.23 10.34 11.85 12.85 10.02 4.54

0.222 0.254 0.277 0.221 0.112 0.202 0.232 0.252 0.196 0.089

10.04 11.56 12.64 10.11 5.13 10.09 11.62 12.70 10.08 4.94

0.221 0.254 0.278 0.223 0.113 0.216 0.249 0.272 0.216 0.106

50th 50th 50th 50th 50th 75th 75th 75th 75th 75th

Table 4 The Out-of-Sample Incremental Effect of CO2Pratio on CO2 Emissions during Hour 17 Assumed Value of CO2Pratio

Out-of-Sample Incremental Effect of a 5-point increase in CO2Pratio in the presence of the adverse interaction between CO2Price and the Load error ratios (Tons of CO2 per Hour)

Out-of-Sample Incremental Effect of a 5-point increase in CO2Pratio in the absence of the adverse interaction between CO2Price and the Load error ratios (Tons of CO2 per Hour)

Assumed hour 17 percentiles for the other explanatory variables

.15 .2 .25 .3 .35

3.85 4.00 4.11 4.20 4.30

18.98 19.01 19.01 18.97 18.92

50th 50th 50th 50th 50th

.15 .2 .25 .3 .35

3.10 3.28 3.41 3.51 3.59

17.15 17.22 17.23 17.22 17.19

75th 75th 75th 75th 75th

10

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K.F. Forbes and E.M. Zampelli

reducing carbon emissions depending on the accuracy of the load assessments and the wind forecasts. The results for wind energy indicate that the CO2 benefits of wind energy penetration given current operational methods are subject to diminishing marginal returns. We suspect that the operational uncertainty associated with the existing wind energy forecasts is the central driver of this result. While a goal of perfect

accuracy is unrealistic, the findings of Forbes and Zampelli (2014, 2017) indicate that significant improvements in forecasting both load and wind energy are possible. The results presented here indicate that improvements in forecast accuracy will significantly enhance the feasibility of attaining a cleaner electric power system.

Appendix Table A1 reports the estimation results when equation (4), the linear version of the model with the interaction terms, was estimated using the same ARCH/ARMA terms as in the nonlinear model reported in Table 2. Table A1

Estimation Results for Equation (4). Variable

Estimated Coefficient Robust Standard Error T Statistic

P-Value

Constant CO2Pratio CO2Pratio*WindShr SMPratioGT1 SMPratioLT1 LoadEP2 CO2Pratio*LoadEP2 LoadRatioGT1 LoadRatioLT1 CO2Pratio* LoadRatioGT1 CO2Pratio* LoadRatioLT1 WindRatioGT1 WindRatioLT1 CO2Pratio* WindRatioGT1 CO2Pratio* WindRatioLT1 WindShr CoalGasPratio CoalGasPratio*WindShr CO2Pratio*CoalGasPratio WindRatioGT1 * CoalGasPratio WindRatioLT1* CoalGasPratio R- Squared: based on all the estimated parameters including the ARCH/ARMA terms R-Squared: based on the structural parameters exclusively Number of Observations Out-of-Sample Predictive R-Squared: based on all the estimated parameters including the ARCH/ARMA terms Out-of-Sample Predictive R-Squared: based on the structural parameters exclusively

1567.543 141.820 81.689 2.261 0.805 0.143 −0.062 109.205 108.776 32.428 53.130 0.770 −3.671 60.632 65.359 −1195.094 −138.315 241.277 −214.582 −28.451 −21.263 0.984 0.651 54,709 0.959

< 0.001 < 0.001 < 0.001 < 0.001 0.233 < 0.001 < 0.001 < 0.001 < 0.001 0.126 0.002 0.923 0.678 0.002 0.005 < 0.001 0.024 0.011 < 0.001 0.046 0.171

40.388 11.151 20.925 0.479 0.675 0.005 0.007 21.854 21.812 21.184 16.817 7.953 8.828 19.792 23.387 50.977 61.446 95.242 18.643 14.286 15.529

38.81 12.72 3.9 4.72 1.19 27.96 −9.57 5 4.99 1.53 3.16 0.1 −0.42 3.06 2.79 −23.44 −2.25 2.53 −11.51 −1.99 −1.37

0.598

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