The majority of our data for the econometric analysis is obtained from the Association of European Transmission System Operators for Electricity (ENTSO-E). Transmission System Operators (TSO) generally correspond to countries, with the exception of Germany and Denmark, which are split into four and two respectively. We obtain hourly data on wholesale electricity prices (EUR/MWh), electricity generation by technology (MWh), and load (MWh). Hourly energy generation is obtained for each available source in each country and includes biomass, coal, lignite, natural gas, dispatchable hydro, nuclear, oil, solar, geothermal, wind, hydro-run-of-river, waste, and other. We focus on those 14 EU countries that utilise hard coal or lignite, in addition to natural gas, in their electricity mix (Supplementary Fig. 9 and 29). This is a requirement for our empirical approach to work as we aim to quantify the substitutability between coal sources and natural gas. This leaves Bulgaria, Croatia, Czechia, Denmark, Spain, Finland, Germany, Greece, Hungary, Ireland, Italy, the Netherlands, Poland, and Romania. The island states of Malta and Cyprus do not have available electricity generation data, while Ireland is left out of the policy analysis (Figs. 4 and 5) due to missing electricity price data.
Price data of natural gas, coal, and carbon are obtained from the Intercontinental Exchange (ICE). The natural gas price data (EUR/MWh) refer to the TTF month-ahead daily futures price (the benchmark gas price of European markets). The coal price data (EUR/tonne) refer to the ARA month-ahead daily futures price. The appropriate conversion to EUR/MWh is used under the assumption of 8.14 tonnes of coal per MWh. Similarly, the carbon price, which refers to the daily futures price for EU allowances in the EU ETS, is in units of EUR/tonne CO2, and converted using an EU-wide average emissions factor of 0.3 gCO2 per kWh, based on the 2018–2021 average emissions intensity of EU countries. In the policy analysis, we use country-specific emission factors given each country’s electricity generation mix.
Our sample comprises a total of 10,224 h spanning the time period of April 2021–May 2022. We focus on data from this time period as it reflects a period in which natural gas prices experienced massive exogenous shocks largely due to the ramping up and eventual conflict in Ukraine and can thus be treated as plausibly exogenous, before any wholesale market distortive mechanisms were put in place (see Supplementary Discussion 1). Hence, this allows us to elucidate electricity generator responses to commodity prices and the environmental impact of the natural gas price crisis. We note that the beginning of our sample period coincides with the late phase of the COVID-19 pandemic, when economic activity and natural gas demand in the EU were still depressed, exerting downward pressure on gas prices. Our analysis therefore spans two distinct crisis episodes with opposing price dynamics: a negative demand shock associated with the late-COVID period and a subsequent positive price shock following the invasion of Ukraine. Given the short time period and the long time it takes to construct new fossil fuel facilities, it is reasonable to assume that the capacity mix is virtually unchanged. While most countries have near complete datasets for this time period, Finland, Croatia, and Ireland have the most missing data, with a total non-missing dataset of 8882, 7981, and 9974 respectively. The remaining countries have fewer than 50 h of missing data (Supplementary Table 28). For the electricity price pass-through regressions, all countries have complete data (Supplementary Table 29).
Econometric model of coal responsiveness
We use the aforementioned exogenous variation in prices to run our main regression specification separately for each country from from 1 April 2021–30 May 2022 as follows:
$$CoalGe{n}_{i,t}= {\beta }_{1}^{i}{\left(\frac{Ga{s}_{p}}{Coa{l}_{p}}\right)}_{i,t}+{\beta }_{2}^{i}{{\left(\frac{Ga{s}_{p}}{Coa{l}_{p}}\right)}_{i,t}}^{2}+{\beta }_{3}^{i}{{\left(\frac{Ga{s}_{p}}{Coa{l}_{p}}\right)}_{i,t}}^{3}\\ +{\beta }_{4}^{i}\,IR{E}_{i,t}+{\beta }_{5}^{i}\,Loa{d}_{i,t}+{\beta }_{6}^{i}\,Loa{d}_{i,t}^{2}\\ +{\zeta }_{m,i}+{\delta }_{h,i}+{\gamma }_{w,i}+{\epsilon }_{i,t}$$
(1)
Our preferred specification utilises hourly electricity generation and load data, and daily commodity price data. CoalGent refers to the log transformed generation of aggregated coal and lignite at any given hour. Our regressor of interest is the price ratio of natural gas to coal, also known as the relative price. The relative price is inclusive of carbon prices and proportional to the amount of CO2 emitted by coal or natural gas (natural gas emits one third as much as coal). In doing so, we implicitly assume that endogeneity between the carbon price and fuel switching is negligible, which is supported by evidence suggesting that fuel-switching behaviour accounts for only a small share of carbon price variation46,47,48,49 and that carbon prices are largely determined by political and institutional factors affecting allowance supply rather than by contemporaneous emissions demand30,31,32. The cubic form of the relative price is used to allow for the flexibility of generator responses to thresholds of these prices that may experience potential nonlinearities. That is, at a certain price point coal generation may exhibit changes in behaviour unexplained by a linear model, due to ramping constraints. This is in line with previous work on coal capacity factor responsiveness to relative prices in the U.S. context12. Alternative specifications including only the quadratic or the linear term are included (Supplementary Table 14), in which the fit is worse than the cubic form through a larger BIC statistic. At the same time, it remains highly plausible that other functional forms (e.g., fourth or fifth power) could also yield qualitatively similar results and we choose this avenue as it is most in line with the extant literature12.
Identification is based on month-of-year, hour-of-day, and day-of-week fixed effects, included as ζm, δh, and γw, respectively. We thus rely on within-hour and within-month variation across our sample period and natural gas price shocks due to events outside of the energy sector’s domain. We further control for load (flexibly) and intermittent renewable energy generation (solar, wind, and hydro-run-of-river). To address possible heteroskedasticity and serial correlation in commodity prices and coal generation, we cluster standard errors at the level of variation in the treatment variable (natural gas and coal prices), which is daily.We run further robustness checks with different variations of fixed effects, covariates, and functional form, as shown in Supplementary Tables 1–13 for all countries. We further run robustness checks with different time period samples, as shown in Supplementary Tables S16–S19. While most countries show consistent results, few are insignificant when the sample window is shortened before the massive price spikes in 2022, suggesting that a certain relative price threshold was needed to be reached to see the substitution effect.
To validate our choice of standard errors clustering for heteroskedasticity and autocorrelation concerns, the ACF of the regression residuals for each country confirms strong intraday correlation, and the PACF shows dependence of the first few lags, in line with operational fuel-switching dynamics and inertia or ramping of coal generation (Supplementary Tables 22–23). An additional check including a lagged regressor of the relative price of the previous day (24 h before) is included, yielding virtually identical results (Supplementary Table 20), providing no evidence of delayed fuel-switching adjustments, suggesting that generation decisions respond to contemporaneous fuel prices rather than lagged price signals. An additional robustness check is performed by running the pooled regression (Supplementary Table 21) to get an average estimate for all countries, including country fixed effects and thus controlling for any EU-wide shocks. This elasticity estimate (0.21) is significant and similar to the average of the 14 country-specific estimates (0.26).
To ease interpretation, we calculate marginal effects using the delta method and present them as the focal estimate of interest. Through this, we are able to estimate the substitution effect for each country i. Specifically, the marginal effect is calculated as:
$${\mu }_{i}=3*{\beta }_{3}^{i}*\overline{{\left(\frac{Ga{s}_{p}}{Coa{l}_{p}}\right)}_{i}^{2}}+2*{\beta }_{2}^{i}*\overline{{\left(\frac{Ga{s}_{p}}{Coa{l}_{p}}\right)}_{i}}+{\beta }_{1}^{i}$$
(2)
This marginal effect, μi, which represents the responsiveness of the coal generation to the relative price of gas and coal, is then multiplied by the average generation of coal and lignite of each country during the sample period (due to the log-scaling) to obtain a value that reflects the change in coal generation per unit of relative price increase. Utilising the change in relative price for the specified period, we can calculate the change in coal generation in each country at this time (Fig. 2A). Based on the standard emission factors (lignite: 1100 gCO2/kWh; hard coal: 830 gCO2/kWh), we obtain the induced change in CO2 emissions (Fig. 2B). The overall increase across our sample of countries is calculated as the sum of excess emissions for our sample countries during this time period. We further calculate the marginal effect μih at each hour of the day for each country, by including an hourly interaction term (Fig. 3).
Econometric model of pass-through
Pass-through of natural gas prices to wholesale electricity prices in European countries is driven by whether natural gas is the marginal fuel on the merit order system at any given hour. The level of pass-through dictates the change in wholesale electricity price, which in turn influences the studied effects of each policy. Our preferred econometric model of electricity price pass-through is discussed below, based on previous work by quantifying this level of pass-through across European countries during the crisis (50). The model regresses hourly electricity prices on daily natural gas prices, with alternative models used to examine the robustness of our estimates (see Supplementary Tab. 29 for main estimates). Each country is estimated separately to determine the market-wide pass-through of natural gas prices to wholesale electricity prices, as well as for every hour of the day by including an hourly interaction term. Through this, we are also able to calculate the excess electricity price during our sample period, compared to the counterfactual when natural gas prices were at pre-crisis levels (Fig. 2E).
For each country i, we separately estimate the following regression specification:
$${p}_{i,t}^{Electricity}= {\beta }_{i}^{h}\,{p}_{i,t}^{Gas}+{\gamma }_{1,i}\,IR{E}_{i,t}+{\gamma }_{2,i}\,Loa{d}_{i,t}\\ +{\gamma }_{3,i}\,Loa{d}_{i,t}^{2}+{\delta }_{m,i}+{\eta }_{d,i}+{\zeta }_{h,i}+{\epsilon }_{i,t}$$
(3)
where hourly electricity price \({p}_{t}^{Electricity}\) is regressed on daily natural gas prices \({p}_{t}^{Gas}\), exogenous controls including hourly intermittent renewable energy generation of solar,wind, and hydro-run-of-river IntermittentRenewablest (dispatchable hydro is not included, since it is endogenous), hourly load Loadt and its quadratic \(Loa{d}_{it}^{2}\), month fixed effects δm, hour fixed effects ζh, and day-of-week fixed effects ηd (see Supplementary Discussion for an exception of month fixed effects regarding Greece). This is estimated for the period of April 2021–June 2022, with a robustness check of January 2022–December 2022 and January 2021–December 2022 (see Supplementary Tab. 26–27).
The coefficients of interest, βh, that we obtain for each country i are the changes in hourly h wholesale electricity price (EUR/MWh) per 1 EUR/MWh increase in TTF natural gas prices. Month and hour fixed effects are a key control variable as they control for any systematic, unobservable trends over the time sample that may be correlated with gas and electricity prices (e.g. drought, planned nuclear outages). Day-of-week fixed effects ηdh similarly control for any systematic, unobservable hourly differences in prices on different days of the week (e.g., weekday vs weekend). Thus, within the same month, on the same day of the week, with the same intermittent renewable energy generation and load, we are statistically comparing two otherwise identical hours, but for the difference in daily gas prices.
Relative responsiveness index
To understand the hourly interplay between coal and natural gas usage in each country, we construct an index that relates the hourly coal responsiveness to the hourly natural gas price pass-through coefficients. Specifically, we utilise the Pearson correlation coefficient with the 24 time points for each country, calculated as the covariance of the two estimates, divided by the product of their standard deviations as:
$$\,{{{\rm{Relative\; Responsiveness}}}}\,=-\frac{1}{n}\left(\frac{\sum ({A}_{i}-\overline{A})({B}_{i}-\overline{B})}{\sqrt{\sum {({A}_{i}-\overline{A})}^{2}\sum {({B}_{i}-\overline{B})}^{2}}}\right)$$
(4)
whereby A is the hourly coal responsiveness, and B is the hourly pass-through coefficient (the left and center panels of Fig 3. for a subset of countries and Panels A–C of Supplementary Fig. 20–26 for the rest), and n is the number of observations (24). Intuitively, this is negated to ensure that a more positive score is also a more responsive country to the competition between coal and natural gas. A score of 1, which reflects a perfectly negatively correlation, is interpreted either as that country being very reliant on coal to balance out the fluctuations in gas price and prevent electricity prices from rising, or that coal generation does not increase and thus wholesale prices increase. Conversely, a score of −1 can be interpreted as that country using both coal and natural gas at any given hour and the coal is insufficient in preventing prices from rising. Further, a higher relative responsiveness score can suggest that when coal generation does down (e.g., due to a policy such as the one we suggest) wholesale electricity prices are more likely to go up. On the other hand, a low score suggests that coal is not eliminating this vulnerability to higher price. In presence of a gas cap, when coal generation goes down, the price responsiveness effects are diminished.
Policy analysis
We use our estimates of coal responsiveness, μi, and pass-through, \({\beta }_{i}^{h}\), for each country, to assess the environmental and economic impact of counterfactual policies imposed on natural gas or carbon prices during 2022, as shown in Figure 3. It is important to note that in each of these policy scenarios, we assume that while the cap or tax is imposed all other prices remain the same and are not directly affecting coal or natural gas prices. We subsequently explain the calculation of the responses shown in Fig. 5.
First, each policy creates a so-called substitution effect of an emissions change from the change in coal generation in response to the relative price of natural gas to coal (Supplementary Fig 4). The effect is determined through the responsiveness of coal generation to the relative price based on our estimates for μi (Supplementary Tab. 28) and the coal generation of each country. For instance, a cap on the price of natural gas makes coal relatively more expensive and thus disincentivizes its usage in lieu of the alternative. A certain level of a carbon price can have the same effect, since coal is more emissions intensive and thus a 1 EUR increase in the carbon price makes coal relatively more expensive in relation to natural gas. We determine that equivalent additional carbon tax to be 12.18 EUR/tonnes, through an iterative approach.That is, the additional carbon price that would have been needed in 2022 to cause the exact same coal-to-gas switch as the natural gas price would. Specifically, the added price of carbon is found for which the relative price (inclusive of carbon price) during the year of 2022 is equivalent to the average relative price under the hypothetical natural gas cap in this period, as shown in SI Equation (1). The underlying assumptions are the assumed average emission factors of natural gas, in comparison to coal. The iterative approach entails a grid-approach of 10000 points calculating the new relative price with incremental carbon prices (from 0.1 EUR/tonne to 20.0 EUR/tonne) until it equated the relative price under the natural gas price cap in 2022.
Second, each policy induces a change in the wholesale electricity price (Fig. 5C). This is determined through the change in natural gas price multiplied by the level of pass-through of natural gas to electricity prices,\({\beta }_{i}^{h}\), (Supplementary Tab. 29). The pass-through of the change in price from carbon is assessed through its impact on the price of natural gas, in which we assume 0.37 EUR/ton CO2 is passed through for every 1 EUR/MWh of natural gas, given its relative lower emitting nature than coal. Taking Germany (DE) as a numerical example, the natural gas cap reduces the average wholesale price of electricity for 2022 by 13.2 EUR/MWh, while the equivalent carbon tax increases it by 3.2 EUR/MWh, using the pass-through coefficient of the natural gas to electricity price of 1.61 multiplied by the change in natural gas during this period (8.2 EUR/MWh), or the change in carbon tax adjusted via the country-specific emissions factor (2.0 EUR/MWh for Germany after the conversions), respectively.
Third, through the impact on the wholesale electricity price each policy induces demand effects for electricity and thus change in emissions—the so-called output effect (Fig. 5B). Intuitively, an increase in the wholesale electricity price yields a certain reduction in emissions given that a higher price disincentives the consumption of electricity. By assuming an average short-run elasticity of demand of electricity price coherent with the extant literature of −0.06, we are able to calculate this effect for each policy, given each country’s average emissions factor (the average emissions from an additional kWh generated in each country’s grid). Though previous studies for this estimate vary considerably51,52,53,54,55,56,57,58, we use a conservative estimate, with different assumptions yielding qualitatively similar results (Supplementary Fig. 6). Continuing the example of Germany, we arrive at an output effect increase of 712 MWh and −172 MWh respectively for the natural gas cap and the equivalent carbon tax, by multiplying the change in electricity wholesale price (−13.2 or 3.2 EUR/MWh from above) by the elasticity (0.06) and average load (54.96 MWh) and dividing by the average electricity price (236.1 EUR/MWh). This is then converted to emissions from generation using the country specific emissions factor (tCO2/MWh). The sum of the output and the substitution effect (7580 ktonnes CO2/year) reflecting the total emissions change for each policy is depicted in Fig. 5A, specifically a reduction of 6867 ktonnes CO2/year for the natural gas price cap and a reduction of 7752 ktonnes CO2/year for the carbon levy.
Fourth, each policy can induce a relief and burden on consumers (Fig. 5D). This impact is assessed through the change in wholesale electricity price adjusted via each country’s average load and country-specific average emissions factor, to obtain units of EUR and allow for appropriate comparisons. That is, a given additional carbon levy increases the amount of revenue equivalent to the carbon levy (in units of EUR/MWh by adjusting for the average country-specific emissions factor) multiplied by average load (MWh), while similarly burden the country by an additional amount corresponding to the increase in wholesale electricity price multiplied by average load. Continuing the case of Germany, the revenue is equivalent to 12.18 times the average load (54.96 MWh) divided by the emissions factor (0.441 tCO2/MWh) times 1000 for unit conversions for a total of 1518,000 EUR. The relief is similarly calculated as the average load times the price change under the gas cap times 1000 to convert units, yielding 130,000 EUR for Germany. The burden is calculated as the average load times the price change under the carbon levy times 1000 to convert units, yielding 176,000 EUR for Germany. As shown, approximately 12% of the revenue is needed to offset the burden from the increase in electricity price for Germany. On average across countries, this value is just 8%, while the relief generated from the natural gas cap is a 32% of the value of the revenue.
Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.