Despite its disruptive impacts on economic and social activities, the global coronavirus (COVID-19) pandemic could have a climate-related "silver lining": a reduction in carbon dioxide (CO 2 ) emissions [1, 2] . Several studies attribute COVID-19-related decreases in electricity demand to decreases in power sector CO 2 emissions [1, 2, 3, 4, 5, 6, 7] . Nonetheless, we are not aware of an analysis that reports the statistical significance of CO 2 emissions reductions accounting for typical variability in emissions. We are also not aware of an analysis that assesses the likelihood of sustained reductions in power sector CO 2 emissions.
We attempt to fill such gaps in this paper. Growing public support for power sector decarbonization initiatives and policies underscore the importance of correctly identifying the drivers of reductions in power sector CO 2 emissions [8, 9] .
Demonstrating the causal effects of an event in sociotechnical systems is a difficult endeavor; it requires the comparison of outcomes given the occurrence of a stated cause to counterfactual outcomes reached in the absence of that cause [10] . Confounding factors, those unrelated to the cause being evaluated, hinder our ability to determine to what degree deviations in outcomes are attributable to a causal factor of interest [11] . While causality can be evaluated empirically in many cases with randomized experiments, such methods are not useful in our situation. It is not possible to unequivocally prove the causal effect of COVID-19 on power sector CO 2 emissions without comparing observed emissions to emissions in a fictional world that is identical to ours but in which the pandemic had not occurred. Short of observing that fictional world, we adopt a counterfactual framework to estimate the probability that observed reductions in CO 2 emissions would have occurred in the absence of COVID- 19 .
With respect to the causal effects of COVID-19 on power sector CO 2 emissions, confounding factors include weather, seasonality, socio-demographic changes, and changes in the electricity supply mix. One approach to estimate the causal effects of COVID-19 on power sector emissions would entail modeling each confounding factor in detail. We avoid such an approach because of the complexities associated with the power system, the economy, and the human responses to COVID-19.
Instead, we employ a simple and interpretable probabilistic model that captures historical variability associated with the confounding factors of interest. While the simplicity of our model limits its ability to quantify the causal effects of COVID-19 on power sector emis-sions, it does facilitate statistical hypothesis testing. We use our model to evaluate COVID-19-related CO 2 emissions reductions and the statistical significance of such reductions relative to typical variance in emissions.
We also use a counterfactual framework to determine the relative impacts of changes in electricity generation (E) and carbon intensity of electricity supply (C/E) on CO 2 emissions. We conclude that reductions in gross domestic product (GDP) concurrent with COVID-19 are responsible for most of the total reduction in E. As the U.S. economy recovers, electricity generation is likely to return to levels similar to what we would have expected in the absence of COVID-19.
The reductions in C/E are attributable to changes in the relative supplies of power generation from different fuel sources. We assess the relative electricity supplies of the three principal power generation fossil fuel sources in the U.S.: coal, natural gas, and oil. Reductions in coal-fired electricity generation, relative to what we would expect in the absence of COVID-19, account for the majority of the total reduction in C/E. Economic modeling is employed to evaluate the expected impact of COVID-19 on U.S. coal plant retirements. We analyze the expected profitability through 2021 of the 845 coal-fired power plant units operating in U.S. wholesale electricity and capacity markets. Those 845 coal units represent 74% of coal units and 67% of coal capacity in the contiguous U.S. To estimate the expected profitability of coal-fired power plant units, we use hourly historical electricity market price data, monthly electricity market price forecasts, annual and bi-annual capacity market price data, and data related to the locations, operating capacities, and costs of coal-fired generation units.
We assume that the portion of coal generation capacity that is unprofitable given current expectations of electricity market prices, but that would have been profitable in a counterfactual scenario reflecting an absence of COVID-19, is the portion most likely to retire early as a result of the pandemic.
The paper is structured as follows. In Section 2, we employ a probabilistic model to determine the statistical significance of COVID-19-related reductions on power sector CO 2 emissions. In Section 3, we assess the relative contributions of changes in E and C/E to reductions in CO 2 emissions and discuss the likelihood of sustained reductions in E and C/E. In Section 4, we provide model-informed expectations of the degree to which COVID-19 will affect the rate of U.S coal plant retirements. We conclude in Section 5.
Several studies report a causal link between COVID-19, decreases in electricity demand, and decreases in power sector CO 2 emissions [1, 2, 3, 4, 5, 6, 7] . Nonetheless, an undisputed quantification of the effects of COVID-19 on power sector CO 2 emissions would require a comparison of actual emissions to emissions in a fictional world in which the pandemic had not occurred but is otherwise identical to ours. We employ a simple and interpretable probabilistic model to evaluate the statistical significance of COVID-19-related CO 2 emissions reductions relative to typical variability in emissions. In the section that follows, we elaborate on the data and methods that we employ in that modeling exercise. The results are presented and the implications for decision-makers are discussed.
Our analysis of U.S. power sector CO 2 emissions requires two data types: net generation time series by fuel type and emissions factors for each fuel type. Net generation time series by fuel type is obtained from the U.S. Energy Information Administration (EIA) Form EIA-923 [12] and the EIA API for "Net Generation by Energy Source" [13] . EIA-923 reports monthly generation and fuel consumption at the power plant-level and "Net Generation by Energy Source" reports aggregate hourly net generation by fuel type. We obtain Form EIA-923 data for the period January 2001 through February 2020, and "Net Generation by Energy Source" data for the period October 2018 through July 2020.
Form EIA-923 reports generation quantities for all U.S. power plants and categorizes power plants by fuel type. Monthly plant-level emissions are computed by multiplying fuel consumption for each plant by fuel code-specific emissions factors published by the EIA [14] . Total CO 2 emissions for the contiguous U.S. are evaluated by aggregating plant-level emissions.
Hourly "Net Generation by Energy Source" data is converted to CO 2 emissions in a similar way. We multiply net generation by fuel type for the contiguous U.S. by fuel type-specific emissions factors that we obtain from the Emissions and Generation Resource Integrated Database (eGRID) published by the U.S. Environmental Protection Agency (EPA) [15] .
We combine the CO 2 emissions time series that we derive from Form EIA-923 and the EIA API for "Net Generation by Energy Source." First, hourly generation data from the EIA API is aggregated into monthly data. Then the Form EIA-923 time series is shifted by a constant such that the Form EIA-923 data matches the monthly mean value of the hourly time series in the months in which the two data series overlap. Such a shift ensures that historical data from EIA-923 are consistent with current data series from the EIA API. Concurrent points from the two series are averaged such that we use a single series in our regression model.
Gaussian process (GP) regression is employed to model and forecast CO 2 emissions in the contiguous U.S. GP regressions are attractive because of their interpretability, simplicity and ease of use, ability to fit periodic functions to capture seasonal effects, and ability to characterize uncertainty [16, 17] . GP regressions have been used to forecast electricity demand and prices, wind and solar power generation, CO 2 emissions, battery state-of-charge, and optimal grid management strategies, among other related applications [18, 19, 20, 21, 22, 23, 24, 25, 26] .
We develop a GP regression that represents a counterfactual scenario in which the COVID-19 pandemic had not occurred. The GP regression is fit using historical CO 2 emissions data. It is developed using the Python GPy library [17] . We employ a linear kernel, a bias kernel, and a standard periodic kernel in GP regression to capture both short-term and medium-term trends over the time period that we consider. The linear and bias terms capture average year-over-year trends while the standard periodic kernel, which is constrained to model one-year periods, describes repeating seasonal patterns in the time series. The GP model is fit using a SciPy implementation of the L-BFGS-B algorithm with five random restarts [27] . We attribute uncertainty in the model to variability in factors that include weather, short-term macroeconomic changes, and population and demographic changes.
The GP regression is fit to historical emissions data for the period between January 2016 and February 2020. That historical period is long enough to obtain a reasonable model fit but not so long as to necessitate nonlinear approximations for year-over-year trends. The regression model is used to forecast emissions in March, April, May, June, and July 2020. Such a forecast is a probabilistic representation of what emissions would have been in a counterfactual scenario characterized by the absence of COVID-19. We compare observed data to forecasted data and evaluate deviations between the two. We assess whether those deviations could be related to the COVID-19 pandemic. 
We show in Figure 1 deviations from the GP regression's predictive distribution for power sector CO 2 emissions in the contiguous U.S. CO 2 emissions are reported in million metric tonnes (MMT) of CO 2 on an annualized basis. Figure 1 reflects model results fit to more than four years of historical data through February 2020, the last month before shelter-in-place orders took effect in the U.S. The black and green points show CO 2 emissions that are obtained from Form EIA-923 and the EIA's hourly "Net Generation by Energy Source" data. We show GP regression means, or expected values, as a dark blue line, and the 95% credible interval as the light blue shaded area. Seasonal variation in power sectorrelated CO 2 emissions are observed. Additionally, an overall decreasing trend in emissions is observed.
Red points show CO 2 emissions in March, April, May, June, and July 2020. Those emissions are 3.9%, 10.5%, 15.4%, 8.9%, and 0.9% lower than the levels we would expect in the absence of COVID-19, respectively, but are not outside of the 95% credible interval. Thus, those deviations are not statistically significant under hypothesis tests at 5% significance levels. The rightmost column of Table 1 shows those percent deviations in addition to credible interval bounds at each month in units of percent deviation.
An average CO 2 emissions reduction of 5.6% is observed in the five month period relative to the expected values given by the GP regression model. Nonetheless, each of the monthly reductions are within historically typical ranges of variability after adjusting for seasonality and linear trends in emissions reductions. Such variability could result from weather, short-term macroeconomic changes, and population and demographic changes that are unrelated to COVID-19. Such a finding suggests that a causal link between COVID-19 and reductions in CO 2 emissions is not as obvious as it is reported in other analyses [3, 5] . Figure 1 shows that certain historical deviations from the GP regression mean are larger than deviations concurrent with COVID-19 shelter-in-place orders. For example, emissions in January 2018 are outside of the 95% credible interval. In January 2018, the "bomb cyclone" weather event in the Northeast and Mid-Atlantic constrained natural gas pipelines and prompted large increases in oil-fired and dual-fired generation [28] . Another month, January 2020, is also outside of the GP regression model's 95% credible interval. The reasons for such a deviation are not as clear as they are for January 2018. However, January 2020 was among the warmest Januarys on record in the U.S. [29] . Those historical deviations from the GP regression mean suggest that the magnitude of deviations concurrent with COVID-19 are not unprecedented.
It is instructive to consider the magnitude of COVID-19-concurrent U.S. power sector CO 2 emissions reductions relative to state and national decarbonization targets, such as the former national target associated with the Paris Agreement. The U.S. submitted its intended nationally determined contribution (INDC) to stabilizing atmospheric greenhouse gas (GHG) concentrations in March 2015 for the Conference of the Parties-21 (COP21) held in Paris. The U.S. INDC signalled the U.S. Federal Government's intent to achieve a 26 to 28% reduction in economy-wide GHG emissions below 2005 levels by 2025 [30] , consistent with a long-term deep decarbonization pathway to reduce 80% of emissions by 2050 [31] .
Although the U.S. withdrew from the Paris Agreement, several state governments and electric utilities established deep decarbonization targets in the past two years [8] . Those targets in aggregate require a reduction in U.S. CO 2 emissions of about 50% by mid-century. If the 5.6% observed average reduction in CO 2 emissions concurrent with COVID-19 were to persist, such a reduction would constitute rapid progress toward state and utility decarbonization targets and toward the INDC that was formerly pledged by the U.S. Federal Government.
In the sections that follow, we describe the drivers of observed emissions reductions and make modelinformed predictions about whether those emissions reductions are likely to persist.
We extend upon the statistical hypothesis tests that we present in Section 2 to determine the relative impacts of changes in electricity generation (E) and carbon intensity of electricity supply (C/E) on reductions in power sector CO 2 emissions. We describe the data sources and methods that are used to estimate the impacts of changes in E and C/E on COVID-19-related reductions in CO 2 emissions. The results of counterfactual analyses based on GP regression predictive distributions are presented. Further, we discuss the relative contributions of changes in factors that impact E, such as GDP, and the impacts of changes in coal-, natural gas-, and oil-fired electricity generation on C/E.
The steps we perform to obtain CO 2 emissions time series are described in Section 2. We follow analogous steps to derive time series for E and C/E. Additionally, we use the same data sources that are described in Section 2 for data related to CO 2 emissions, electricity generation, electricity generation by fuel type, and CO 2 emissions by fuel type.
We assess counterfactual and observed values of electricity generation (E) and carbon intensity of electricity supply (C/E). The counterfactual scenario assumes the continuation of historical power sector CO 2 emissions. The same probabilistic modeling framework that is described in Section 2 is used to estimate counterfactual values for E and C/E.
As in our counterfactual analysis of CO 2 emissions, we include a linear kernel, a bias kernel, and a standard periodic kernel in the GP regressions to capture both short-term and medium-term trends in E and C/E over a period from January 2016 to February 2020. The GP regression-defined counterfactual data is compared to observed data in March, April, May, June, and July 2020.
E and C/E are modeled independently and the joint relationships between those terms are not modeled. As such, the product of the E and C/E values that are computed in a given month is not necessarily equal to C, the CO 2 emissions that are computed in that month. Table 1 shows the deviations in E, C/E, and C, relative to what we would expect in our counterfactual scenario, for March, April, May, June, and July 2020, and the average deviations for the five month period. Fig. 2 and 7.0%, 7.4%, and 1.2%, lower than the levels we would expect in the absence of COVID-19, respectively, and 2.3% higher in July 2020. The values in April and May are statistically significant at 5% significance levels.
E and C/E are -7.4% and -8.7%, respectively, and both occur in May. The deviations in E in April and May are statistically significant at 5% significance levels, while the deviations in C/E are not statistically significant in any month. Additional analysis is performed to show the relative impacts on C/E associated with changes in coal-, natural gas-, and oil-fired electricity generation ( Table 2 ). The GP regressions for each of those fuel sources exhibit large credible intervals. For example, the 95% credible interval for CO 2 emissions from coal-fired electricity generated ranges from +/-36% in April 2020. We attribute such a result to confounding factors such as variability in weather and in merit-order dispatch schedules.
Nonetheless, CO 2 emissions from coal-fired generation decreased much more than CO 2 emissions from natural gas-or oil-fired generation, relative to estimated counterfactual values. The average reduction in CO 2 emissions from coal-fired electricity generation is 14.5% compared to average increases in CO 2 emissions from natural gas-fired and oil-fired generation of 1.0% and 7.9%, respectively.
The possibility of sustained impacts of COVID-19 on E and C/E is discussed. With respect to E, we assess changes in factors that impact E and that are concurrent with COVID-19, such as reductions in GDP and COVID-19-related deaths. We discuss the possibility of a sustained reduction in the energy intensity of the economy due to COVID-19-related increases in teleworking and automation. With respect to C/E, the relative impacts from changes in coal-, natural gas-, and oil-fired electricity generation are discussed.
Reductions in E are observed relative to what we would have expected in the absence of COVID-19, in March, April, May, and June, and an increase in E is observed in July. The reductions in April and May are statistically significant at 5% significance levels. The largest reduction in E is 7.4% in May. Factors that impact the observed changes in E include changes in GDP, population, and in the energy intensity of the economy. We discuss below the relative impacts of such factors on changes in E concurrent with COVID-19, and the likelihood of sustained changes in each factor. Reductions in economic output concurrent with COVID-19 are larger in magnitude than changes in other factors that impact E. The U.S. Bureau of Economic Analysis (BEA) reports reductions in real GDP of 5.0% in Q1 2020 and 32.9% in Q2 2020 [32] . Reductions in population due to COVID-19 are much smaller in percentage terms. As of August 1st 2020, there are 142,024 reported COVID-19-related deaths in the contiguous U.S. [33] . Those deaths represent a 0.04% reduction in population in the contiguous U.S. relative to population forecasts for the same period made in August 2019 [34] .
The energy intensity of the economy represents the amount of electricity generated per dollar of economic output. The impacts of COVID-19 on the energy intensity of the economy are not as clear as the impacts of COVID-19 on GDP or on population. COVID-19-related shelter-in-place measures prompted educational institutions, companies, and public agencies to adopt organization-wide online learning and working procedures ("teleworking"), which could persist in various sectors after governments relax shelter-in-place measures [35, 36, 37] . While teleworking could reduce commuting-related and commercial building energy consumption, estimates of the potential impacts of teleworking on energy use are inconclusive [38] . An-other long-lasting impact to the energy intensity of the economy relates to a possible acceleration of automation in U.S. industries. The loss of jobs in middleskill, routine occupations is concentrated in economic downturns, but much of the new economic output following recessions is not accompanied by a recovery in employment of those same routine occupations [39] . Furthermore, employers impacted by a recession are more likely to permanently replace routine workers with higher-skilled workers and machine technologies [40] . The potential for substituting automation for labor is largest in sectors with high concentrations of routine occupations, such as food services, manufacturing, transportation, and retail trade [41] . The possible impacts of automation on electricity generation are not well understood. For example, studies that focus on the impacts of widespread electric vehicle automation on electricity demand report results that range from large decreases to large increases in energy consumption and GHG emissions [42, 43, 44, 45, 46, 47, 48] . The lasting impacts of COVID-19 on the energy intensity of the economy are uncertain and may be as likely to increase CO 2 emissions as to decrease emissions. Moreover, GDP is expected to recover to levels that we would have expected in the absence of COVID-19. With respect to GDP, the American Staffing Association (ASA) expects GDP to increase by 15.2% in Q3 2020 on an annualized basis, and by 6.8%, 5.8%, and 4.9% in subsequent consecutive quarters. Those forecasts reflect the average expectations of more than 70 Wall Street Journal economists [49] . As a consequence of that economic recovery, electricity generation is likely to increase to levels that we would have expected in the absence of COVID-19.
The carbon intensity of electricity supply (C/E) is impacted by changes to the relative supplies of power generation fuels. We observe deviations in C/E of -1.4%, -6.1%, -8.7%, -4.7%, and 1.2% in March, April, May, June, and July 2020, respectively, relative to the counterfactual estimates.
The reduction in coal-fired electricity generation drives much of the overall reduction in C/E. Table 2 shows that the reduction in CO 2 emissions from coalfired electricity generation is much larger than increases in natural gas-and oil-fired electricity generation in absolute terms. Average monthly emissions from coalfired generation between March and July 2020 were 116.9 MMT lower than our counterfactual estimates, on an annualized basis. Meanwhile, average monthly emissions from natural gas-and oil-fired generation were 5.8 and 1.6 MMT higher than counterfactual estimates, on an annualized basis. CO 2 emissions may decline permanently to the extent that decreases in electricity demand accelerate coal power plant retirements in the U.S. In the next section, the economic impact of COVID-19 on coal-fired power plant retirements is analyzed. We compare the expected profitability of U.S. coal-fired power plants under two scenarios: a counterfactual scenario in which we employ an electricity market price forecast published in January 2020, and a scenario that reflects current expectations. Current expectations reflect a scenario in which we employ actual electricity market prices between March and July 2020 and an electricity market price forecast published in July 2020.
Coal generation capacity and utilization in the U.S. decreased every year after a peak in 2008 [50] . Such decreases persisted in recent years despite policy interventions by the Trump administration intended to support the coal industry [51] . Decreases in coal generation were driven by reductions in natural gas prices, flat or negative growth in electricity demand, and increasing state-level support for renewable generation technologies [52, 53, 54] . Additionally, some financial institutions are reluctant to support new coal power plants and refurbishments [55, 56] .
In this section, we assess expectations for whether COVID-19 will accelerate coal plant retirements in the contiguous U.S. To evaluate potential retirements, we estimate the expected profitability through 2021 of each of the 845 coal-fired power plant units in the seven unbundled power market regions in the U.S. Those coalfired power plant units comprise 74% of coal units and 67% of coal capacity in the contiguous U.S.
Profitability is estimated in two scenarios: a counterfactual scenario in which we employ an electricity market price forecast developed prior to COVID-19-related shelter-in-place orders; and a scenario that reflects current expectations in which we use observed electricity market prices from March to July 2020 and an electricity market price forecast developed after shelter-inplace orders took effect. Both energy and capacity market revenues are taken into account. We identify coal plants that were expected to be profitable prior to COVID-19-related shelter-in-place orders but are no longer expected to be profitable due to expected reductions in electricity demand and prices. Those plants are considered to be at risk of retirement due to COVID-19.
Estimates of coal-fired power plant profitability rely on data related to electricity market prices and capacity auction clearing prices. We also rely on data related to the locations, installed generating capacities, variable costs, and fixed costs of coal-fired electricity generation units.
Historical hourly zonal electricity market prices are obtained from S&P Global Market Intelligence (S&P) [57] . We obtain hourly historical price data for 57 electricity market zones for the period between January 1, 2018 and July 31, 2020. 1 Forecasts of monthly average regional electricity market prices are obtained from the EIA [58, 59] . The EIA publishes monthly average wholesale electricity market prices in a single zone in each electricity market region. 2 Two market price forecasts published by the EIA are obtained: a forecast published in January 2020 prior to COVID-19-related shelter-in-place orders, and another forecast published in July 2020, after shelter-inplace orders took effect.
Two electricity market price scenarios are constructed. A counterfactual price scenario reflects electricity market price forecasts from March 2020 through December 2021; this scenario was published by the EIA in January 2020. The other scenario reflects our current expectations of electricity market prices. The current expectations scenario reflects actual historical market prices from March through July 2020 and electricity market price forecasts from August 2020 through December 2021. These forecasts were published by the EIA in July 2020. Fig. 4 shows the capacity-weighted monthly average electricity prices in our counterfactual and current expectations scenarios.
Capacity auction clearing prices are obtained from S&P for the four electricity market regions that run forward capacity auctions: MISO, New England, New York, and PJM [60] . In these four regions, generators submit offers to electricity system operators to provide generation capacity in a future "capacity commitment period," in exchange for payment from electricity system operators. MISO, New England, and PJM run annual capacity auctions for forward capacity commitment periods beginning June 1 and ending May 31. New York runs biannual capacity auctions that correspond to a winter capacity commitment period between November 1 and April 30, and a summer capacity commitment period between May 1 and October 31. Capacity auction clearing prices are established on a zonal basis.
We obtain actual zonal capacity auction clearing prices through May 31, 2022 for New England and PJM. For MISO, price data are available through May 31, 2021. We assume that prices for the subsequent annual commitment period, ending May 31, 2020, are the same as prices for the period ending May 31, 2021. For New York, price data is available through October 31, 2020. We assume that prices for two subsequent winter commitment periods, ending April 30, 2021 and April 30, 2022, are the same as prices for the winter period ending April 30, 2020. We assume that prices for the subsequent summer commitment period, ending October 31, 2021, are the same as prices for the summer period ending October 31, 2020.
The locations, installed generation capacities, and variable costs of each coal-fired electricity generation unit in the seven U.S. electricity market regions are obtained from S&P [61] . Such data is obtained for 2019, the latest year in which data is available. That data reports the regional and zonal locations of each generation unit, the month and year that each unit entered into service, the operating capacity of each unit, and the variable and fixed costs of each unit. Coal-fired cogeneration facilities that produce both electricity and heat are excluded. Such facilities typically supply electricity directly to industrial and commercial facilities. It is difficult to estimate the profitability of such units because they do not earn electricity market revenues for the electricity they supply directly to those facilities.
Finally, an estimate of the weighted average cost of capital (WACC) of coal-fired electricity generation units is obtained from the National Renewable Energy Laboratory Annual Technology Baseline 2019 (NREL ATB) [62] . We adopt an annual WACC of 4.61%.
The profitability of coal-fired power plant units is estimated. The profitability (P) for a given month (m) and generation unit (u) is calculated as that unit's electricity and capacity market revenues (E m,u and C m,u , respectively) net of variable operating costs and fixed operating and maintenance (O&M) costs (V m,u and F m,u respectively):
We describe below the methods we use to estimate expected zonal hourly electricity market prices, monthly electricity market revenues and variable costs, monthly capacity market revenues, and overall profitability for the period between March 1, 2020 and December 31, 2021.
Profitability is estimated across two sets of electricity market prices: one set based on an electricity market price forecast published by the EIA in January 2020, prior to COVID-19-related shelter-in-place orders, and another set based on actual historical prices between March and July 2020 and an electricity market price forecast published by the EIA in July 2020.
Each of the seven electricity market regions has multiple electricity market zones. The EIA publishes average monthly market price forecasts for each of the seven electricity market regions. Those monthly regional market price forecasts are converted to hourly zonal market price forecasts. Such a step is necessary to accurately model expected electricity market revenues, variable costs, and capacity market revenues, which are allocated on a zonal basis. The following procedure is performed to determine the forecasted hourly prices in a given month and electricity market zone: 1. For a given month and electricity market zone and region (e.g., June, AEP zone, PJM region), average prices in that month (e.g., June) are determined for each of the two years prior to 2020 for which we obtain historical data, 2018 and 2019.
2. We compute the differences of those historical average prices with the corresponding monthly price forecast in the appropriate electricity market region (e.g., June 2020, PJM region) published by the EIA.
3. The hourly prices from the historical month associated with the smallest difference that we compute in Step 2 are adopted as our hourly zonal forecast price profile.
4. We shift the hourly zonal forecast price profile up or down by a constant value such that the average monthly zonal price (e.g., June 2020, AEP zone) is equal to the average monthly regional price (e.g., June 2020, PJM region) published by the EIA.
That series of steps is applied to each forecast month and each zone in each electricity market region. Two sets of hourly price forecasts are developed for each zone: one set based on monthly price forecasts published by the EIA in January 2020, prior to COVID-19related shelter-in-place orders, and another set based on actual historical prices between March and July 2020, and monthly price forecasts published by the EIA in July 2020.
Costs The electricity market revenue and variable operating costs for a given generation unit are estimated by determining the number of hours in a month in which that unit is online. We assume a generation unit is online for the hours in which the electricity market price is greater than or equal to the unit's variable cost of operation. For each month, we generate a price duration curve (PDC) in which we order hourly electricity prices from highest to lowest. The PDC is used to estimate total variable operating costs and electricity market revenues.
The use of PDCs is illustrated in Fig. 5 . In Fig. 5 , we show two PDCs that correspond to hourly electricity prices in June 2020 in the AEP zone in the PJM region. The prices in Fig. 5 (a) reflect an electricity price forecast published by the EIA in January 2020, prior to shelter-in-place orders, and the prices in Fig. 5 (b) reflect actual prices in June 2020. The horizontal dashed lines reflect the variable operating cost ($/MWh) of a coal unit in the AEP zone, "Rockport ST1." Monthly electricity market profits are shown in blue and monthly total variable operating costs ($) in yellow. The vertical grey lines indicate the numbers of hours in which it is profitable for Rockport ST1 to operate in each of the two scenarios.
Electricity market profits and variable operating costs are calculated for each of the 845 coal-fired generation units in the seven electricity market regions in the U.S. We calculate those profits and costs using the price forecast published by the EIA prior to shelter-in-place orders and a combination of actual electricity market prices, from March to July 2020, and a price forecast published by the EIA in July 2020.
Four of the seven electricity market regions, MISO, New England, New York, and PJM, run annual or biannual generation capacity auctions in which those regional operators solicit bids from generation units to be available to provide capacity in a future capacity commitment period [60] .
We assume that a generation unit bids into a capacity auction such that the unit can expect to be profitable if its bid clears in a given capacity commitment period. For a generation unit (u) that does not otherwise expect to be profitable in a given capacity commitment period (cp), that unit submits a capacity bid such that the present value of cash flows associated with its bid (B cp,u ) would cover the present value of the sum of its variable costs and fixed O&M costs (V cp,u and F cp,u respectively) net of the present value of electricity market revenues (E cp,u ). For a generation unit that does expect to be profitable in a given capacity commitment period, that unit bids zero dollars into the capacity auction for that period. Eq. 2 shows the bidding behavior for generation units that do not expect to be profitable in electricity markets alone, in a given capacity commitment period.
Capacity auction clearing prices are obtained or estimated for each capacity commitment period through 2021 for each of the four regions that run forward capacity auctions. Those clearing prices are established on a zonal basis. A generation unit that submits a bid that is equal to or lower than the auction clearing price receives capacity market revenues. A generation unit (u) that clears in a given commitment period (cp) in a given zone (z) receives capacity market revenue (C) in a given month (m) equal to the zonal auction clearing price (G cp,z ), in units of $/MW-day, multiplied by the operating capacity of the unit (O u ) and the number of days in the month (n):
Capacity market revenues are calculated for every coal-fired electricity generation unit in New England, New York, MISO, and PJM, and for every month in the period from March 1, 2020 to December 31, 2021.
March 1, 2020 and December 31, 2021 The overall profitability of each coal-fired generation unit is estimated for the period between March 1, 2020 and December 31, 2021. The overall profitability (P) for each unit (u) is estimated as the sum of discounted cash flows in each month, where m ranges from 1 to 22, the number of months in the period. L m is the monthly nominal net cash flow, and r is the weighted average cost of capital (WACC) (Eq. 4). We apply a monthly WACC of 0.38% that we derive from an annual WACC of 4.61%, consistent with the NREL ATB.
The monthly nominal net cash flow (L m ) is the sum of monthly nominal electricity and capacity market revenues net of the sum of monthly nominal variable costs and fixed O&M costs. The profitability of every coal generation unit is calculated in two scenarios: a counterfactual scenario that relies on an electricity market price forecast published by the EIA in January 2020 prior to shelter-in-place orders, and a scenario that reflects our current expectations and is based on actual prices in March through July, and a price forecast published by the EIA in July 2020. We assume that the differences in prices in our two scenarios are negligible after 2021.
We analyze the expected profitability from March 2020 to December 2021 of the 845 coal-fired electricity generation units operating in the seven unbundled power market regions in the U.S. Only 76 of the 845 coal-fired generation units, representing 2.0 GW or 1.3% of coal generation capacity in the seven power market regions, were expected to be profitable prior to COVID-19 but are no longer expected to be profitable due to COVID-19-related reductions in electricity prices. We consider those 76 units to be at risk of early retirement due to COVID-19. The mean age and operating capacity of those 76 units are 58.0 years and 25.9 MW, respectively. The newest units were operational in November 2012 and the oldest unit was operational in July 1954. A single at-risk unit resides in SPP, while the remaining units reside in MISO: 66 units in MISO Zone 6 and nine units in MISO Zone 4.
Estimates of the impacts of COVID-19 on the monthly profitability of coal-fired electricity generation units in aggregate are illustrated in Fig. 6. Fig. 6 (a) shows estimates in the counterfactual scenario, and Fig.  6 (b) shows estimates in the current expectations scenario. Squares represent monthly revenues, diamonds represent monthly costs, and the shaded areas represent monthly profits or losses. Coal generation units in total are $3.9 billion less profitable in the current expectations scenario relative to the counterfactual scenario over the entire period, in present value terms. Of that amount, coal generation units earn $3.2 billion less profit in the current expectations scenario in March through December 2020.
We show in Fig. 4 that actual average electricity market prices in March to July 2020 are lower than what prices would have been in a counterfactual scenario in which COVID-19 had not existed. Those lower prices reduced the amount of time during which it would have been profitable for coal plants to operate and contributed to a reduction in profitability relative to the counterfactual scenario. Those coal-fired generation units that operated less frequently earned the same capacity auction revenues but earned less electricity market revenues than they would have in the counterfactual scenario.
Nonetheless, we show in Fig. 4 that electricity market prices are expected to increase to prices similar to those we would have expected in the absence of COVID-19 by Q4 2020. Additionally, we show in Fig. 6 that coal unit profitability in aggregate is expected to increase to levels of profitability that we would have anticipated in the absence of COVID-19.
For the total period between March 1, 2020 and December 31, 2021, coal generation units in aggregate make $10.9 billion in profit, compared to $14.8 billion in the counterfactual case, in present value terms. Despite such a potential aggregate loss, only 76 units representing 1.3% of total capacity are at risk of early retirement due to COVID-19. That is, those 76 units would have been profitable in the counterfactual scenario but are not profitable in the current expectations scenario. The results suggest that the impact of COVID-19 on coal power plant retirements is limited to about 1.3% of existing coal generation capacity.
Our findings comport with some independent assessments and conflict with others. The results of a survey of representatives of 11 companies that own coal generation facilities suggests none of those companies altered their coal retirement plans due to COVID-19 [63] . The EIA expects coal-fired electricity generation in 2020 will be 22% lower than it anticipated in a forecast published prior to shelter-in-place orders, but that coal-fired electricity generation in 2021 will be only 1% lower than it anticipated previously [58, 59] . In contrast, Moody's concludes that the reductions in coalfired electricity generation in 2020 are unlikely to recover in 2021 or beyond [64] .
A counterfactual framework is employed to analyze the statistical significance of CO 2 emissions reductions in the U.S power sector from March 1 to July 31, 2020. We report the contributions to CO 2 emissions reductions of electricity generation, E, and the carbon intensity of electricity supply, C/E, and present model-informed expectations of the likelihood of sustained reductions in CO 2 emissions.
In Section 2, we show that CO 2 emissions are lower than levels expected in the absence of COVID-19 in each month from March through July 2020 but that those reductions are not statistically significant considering hypothesis tests at 5% significance levels. In Section 3, the relative impacts on CO 2 emissions reductions of E and C/E are reported. Similar average changes in E and C/E are observed in the months concurrent with COVID-19. A reduction in GDP is responsible in large part for the overall reduction in E. As the U.S. economy recovers, electricity generation is likely to return to levels that we would have expected in the absence of COVID-19.
A reduction in the share of coal-fired electricity generation accounts for the majority of the overall reduction in C/E. In Section 4, we analyze the expected profitabil-ity through 2021 of the 845 coal-fired power plant units that are operating in the seven unbundled power market regions in the U.S. Only 76 of those units, representing 1.3% of total coal generation capacity, were expected to be profitable prior to COVID-19 but are no longer expected to be profitable due to COVID-19-related reductions in electricity prices.
Our results suggest that COVID-19 led to reductions in power sector CO 2 emissions in the contiguous U.S.; however, they also suggest that the magnitudes of those reductions are not as obvious as several studies suggest. Reductions in CO 2 emissions concurrent with COVID-19 are within historical ranges of variance. Further, the impact of COVID-19 on U.S. coal plant retirements is limited to about 1.3% of U.S. coal capacity. We conclude that there is no COVID-19 climate "silver lining" in the U.S. power sector. Within a couple of years, CO 2 emissions are likely to increase to levels we would have expected prior to the pandemic.