Figure 1: Natural gas price in Europe
Figure 1 shows the quarterly index of the Title Transfer Facility (TTF) natural gas price in Europe from 2020 Q1 through 2022 Q4, with the index normalized so that 2021 Q1 equals 100. The horizontal axis represents time by quarter, ranging from 2020 Q1 to 2022 Q4, while the vertical axis represents the price index, which ranges from 0 to approximately 750. The line begins near zero in early 2020 and remains low through most of that year. It then increases gradually throughout 2021, reaching around 100 in 2021 Q1, about 250 by 2021 Q3, and about 500 in 2021 Q4. The index rises sharply during 2022, peaking at roughly 750 in the third quarter, before falling quickly to about 400 by the end of 2022. Overall, the figure depicts a period of very low natural gas prices in 2020, followed by steady growth through 2021, a dramatic surge to a peak in mid-2022, and a notable decline toward the end of the period.
Notes: The price index of the Title Transfer Facility (TTF) gas in the Netherlands. Most price setters use this price as the reference price and gas contracts are indexed to this price, the TTF price index is the standard
gas price benchmark for Europe (Rogge, 2024).2 For longer time series, see Figure 16 in Appendix C.
Data source: IMF Data (2024).
Figure 2: Inflation in the Euro Area 2020 - 2022
Figure 2 has two panels. Panel (a) on the left shows energy inflation, and panel (b) on the right shows headline inflation. Each panel presents quarterly data from 2020 Q1 to 2022 Q4, comparing countries with an energy price cap (shown in blue) and countries without a cap (shown in red). The vertical axis in panel (a) ranges from 0 percent to about 75 percent, while in panel (b) it ranges from 0 percent to about 25 percent. In both panels, inflation rates for all countries remain near zero during 2020, then begin to rise gradually through 2021. In the energy inflation panel, both groups’ rates accelerate sharply during 2022, but countries without a cap experience much steeper increases, reaching a weighted average of roughly 55 percent by mid-2022 compared with about 30 percent for countries with a cap. By the end of 2022, both groups show slight declines. In the headline inflation panel, the same overall pattern appears but with smaller magnitudes: headline inflation peaks around 15 percent for countries without a cap and near 10 percent for those with a cap in late 2022. Overall, the figure shows that while inflation rose across all Euro Area countries between 2020 and 2022, the increase was notably more pronounced in countries that did not implement an energy price cap.
Notes: Annualized energy and headline inflation rates in the Euro Area. Source: Eurostat. Countries with an energy price cap in 2022 are Austria, Estonia, France, Germany, Luxembourg, Malta, Portugal, Slovakia, Slovenia, Spain. Countries without are Belgium, Cyprus, Finland, Greece, Ireland, Italy, Latvia, Lithuania, The Netherlands. Bold lines are weighted averages for each group.
Figure 3: Data exercise to calibrate the non-homotheticity parameters
Figure 3 has two panels. The left panel shows gas inflation, and the right panel shows gas consumption, both covering the period from 2020 Q3 through 2022 Q3. In the left panel, gas inflation is plotted for France, representing a country with a price cap (blue dashed line), and for the Netherlands, representing a country without a cap (red dashed line). The vertical axis ranges from -10 percent to 30 percent. Both series remain near zero until mid-2021, after which the inflation rate rises gradually. Inflation in the Netherlands (no cap) increases much more sharply, reaching around 25 percent in early 2022 before declining slightly, while inflation in France (cap) peaks around 10 percent. The right panel plots gas consumption data (dotted lines) and model-implied gas consumption (solid lines) for the same two countries, with the vertical axis ranging from -30 percent to 10 percent. Gas consumption remains close to zero through 2021, then declines markedly in 2022, especially in the Netherlands, where both the data and the model show decreases of about 25 percent. In France, consumption falls more moderately, to roughly -10 percent by late 2022. Overall, the figure illustrates that gas inflation and consumption diverged significantly between capped and uncapped markets, and that the model closely matches observed consumption patterns.
Notes: The left panel shows the gas inflation of France (cap) and the Netherlands (no cap). I feed this data into the model and find the parameters $$\varepsilon_1$$ and $$\varepsilon_2$$ that minimize the Mean Squared Error (MSE) between the gas consumption data (right panel, dotted) and the model-implied gas consumption (solid). Sources for data: Eurostat.
Figure 4: Responses to an adverse energy supply shock $$\vert$$ No caps
Figure 4 displays the responses to an adverse energy supply shock in an economy without price caps, presented in eight panels arranged in two rows of four. All panels share a common horizontal axis measuring time in quarters from 0 to 14. The top row shows: Total energy, Energy inflation, Other inflation, and CPI inflation. The bottom row shows: Output, Energy consumption by households, Total consumption, and Nominal interest rate.
In the "Total energy" panel, the vertical axis ranges from 0% to -15%. The line remains at approximately -15% from quarter 0 through quarter 6, then sharply returns to 0% by quarter 8, where it remains stable.
The "Energy inflation" panel shows values ranging from -200% to 200%. The line begins at approximately 200%, quickly drops to near 0% by quarter 2, maintains this level until quarter 6, then sharply plunges to about -200% at quarter 7 before returning to 0% by quarter 8.
In the "Other inflation" panel, the scale ranges from -20% to 20%. Starting at around -20%, the line rises to reach a peak of approximately 15% by quarter 7, then gradually returns to 0% by quarter 8.
The "CPI inflation" panel shows values from 0% to 10%. The line begins at about 1%, steadily increases to peak at roughly 10% by quarter 6, then gradually declines to 0% by quarter 8. In the "Output" panel, the vertical axis ranges from 0% to -0.15%. The line starts and remains at approximately -0.15% through quarter 6, then rapidly returns to 0% by quarter 8, maintaining this level afterward.
The "Energy consumption by households" panel shows values from 0% to -15%. The pattern mirrors the Total energy panel, with the line remaining at about -15% until quarter 6, then sharply returning to 0% by quarter 8.
In the "Total consumption" panel, the scale ranges from 0% to -1%. The line begins at approximately -1%, remains there until quarter 6, then returns to 0% by quarter 8.
The "Nominal interest rate" panel shows values from 0% to 20%. The line begins near 2%, gradually increases to peak at approximately 17% around quarter 6, then declines to around 0% by quarter 8.
Notes: Impulse responses to a 15% decline in energy supply. Preferences are non-homothetic. Output is equal to the output gap. The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 5: Responses to an adverse energy supply shock $$\vert$$ Cap vs. no cap
Figure 5 presents the responses to an adverse energy supply shock, comparing economies with a price cap (blue, solid lines) and without a cap (red, dashed lines). The figure consists of eight panels arranged in two rows of four, with all panels sharing a horizontal axis measuring time in quarters from 0 to 14, with gridlines at 4, 8, and 12 quarters.
The top-left panel shows "Government expenditure on cap" with a vertical scale from 0% to 2%. The blue line is elevated at 2.5% until quarter 6, then returns to 0% by quarter 7. The red line remains at 0% throughout, as there is no cap in this country.
The "Energy inflation" panel has a vertical range from -500% to 500%. The red dashed start at approximately 500%, quickly falling to near 0%. Around quarter 6, the red dashed line (no cap) sharply drops to around -500% before returning to 0% by quarter 8, while the blue line (with cap) shows minimal fluctuation throughout.
The "Other inflation" panel shows values from -20% to 20%. The red dashed line begins near -20%, while the blue line begins near -5%. Both lines rise to positive territory with peaks around quarter 6. The blue line peaks at approximately 5%, while the red line reaches a higher peak of about 15% before both return to near 0% in quarter 8.
The "CPI inflation" panel displays values from -20% to 20%. The red dashed line starts near 20%, whereas the blue solid line at around -5%. The blue line gradually increases and peaks at about 5% around quarter 7, while the red line reaches approximately 10% before dropping sharply to about -15% around quarter 7, then returning to 0%. In the bottom row, the "Output" panel shows values from 0% to -0.2%. The blue line starts and remains around 0% throughout. The red line starts deeper at about -0.25%, maintaining this level until quarter 6 before returning to 0% by quarter 7.
The "Energy consumption by households" panel shows values from 0% to -30%. The blue line remains near 0% throughout, while the red line stays at approximately -30% until quarter 6, then sharply returns to 0%.
For "Total consumption," the scale ranges from -20% to 10%. The blue line starts at around 9%, while the red line begins near -15%. Both lines maintain this level until quarter 6, then return to 0%.
The "Nominal interest rate" panel shows values from 0% to 10%. There is only one line, since there is only one central bank. The line starts around 1% and gradually increases to around 10% in quarter 6, before it turns to 0% in quarter 7.
Notes: Impulse responses to a 15% decline in energy supply. Preferences are non-homothetic. The bigger country, of size $$\Theta$$ imposes a price cap on the energy price (blue, solid) and the smaller country, of size 1−$$\Theta$$ does not (red, dashed). The black solid lines show the union-wide variables. Output is equal to the output gap. Government expenditure on the price cap (Govt. exp. cap) is the cost of the cap as a share of annual total output of the country (GDP). The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 6: Responses to an adverse energy supply shock $$\vert$$ Caps
Figure 6 displays the responses to an adverse energy supply shock in an economy with a price cap, presented in eight panels arranged in two rows of four. All panels share a common horizontal axis measuring time in quarters from 0 to 14. The top row shows: Government expenditure cap, Energy inflation, Other inflation, and CPI inflation. The bottom row shows: Output, Energy consumption by households, Total consumption, and Nominal interest rate.
In the "Govt. expenditure cap" panel, the vertical axis ranges from 200% to 0%. The line remains at approximately 200% from quarter 0 through quarter 6, then sharply returns to 0% by quarter 8, where it remains stable.
The "Energy inflation" panel shows values ranging from -40% to 40%. Since there is a price cap in this economy, the line does not move and remains around 0%.
In the "Other inflation" panel, the scale ranges from 0% to 45%. Starting at around 5%, the line rises to reach a peak of approximately 45% by quarter 7, then gradually returns to 0% by quarter 8.
The "CPI inflation" panel, the scale ranges from 0% to 45%. Starting at around 5%, the line rises to reach a peak of approximately 45% by quarter 7, then gradually returns to 0% by quarter 8. In the "Output" panel, the vertical axis ranges from -0.01% to -0.05%. There are some small deviations but the line stays at around 0%. The "Energy consumption by households" panel shows values from 0% to -15%. The line remains at about -15% until quarter 6, then sharply returning to 0% by quarter 8.
In the "Total consumption" panel, the scale ranges from 0% to -18%. The line begins at approximately -18%, remains there until quarter 6, then returns to 0% by quarter 8.
The "Nominal interest rate" panel shows values from 0% to 70%. The line begins near 10%, gradually increases to peak at approximately 70% around quarter 6, then declines to around 0% by quarter 8.
Notes: Impulse responses to a 15% decline in energy supply and a price cap in both countries. Preferences are non-homothetic. Output is equal to the output gap. The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 7: Responses to an adverse supply shock $$\vert$$ Core inflation targeting
Figure 7 displays the responses to an adverse energy supply shock in a currency union in which the central bank targets core inflation, presented in three panels. All panels share a common horizontal axis measuring time in quarters from 0 to 14. The panels are: nominal interest rate, CPI inflation, other inflation.
In the "Nominal interest rate” panel, the scale ranges from -1% to 1% and the line for the nominal interest rate does not move throughout. In the "CPI inflation” panel, the scale ranges from -25% to 25%. The red dotted line, the line for the "no cap” country, starts at around 25% and returns to 0% immediately. In quarter 6, it declines to -25% and then goes back to 0% to remain. The blue line, the line for the "cap” country does not move substantially during this time.
In the "Other inflation” panel, the scale ranges from around -5% to 5%. The blue line starts around 5% returns to 0% for a few quarters and dips at quarter 7 at around 5%, before returning to 0% in quarter 8. The red dashed line exhibits exactly a mirrored behavior.
Notes: Impulse responses to a 15% decline in energy supply under core inflation targeting. Preferences are non-homothetic. The bigger country, of size $$\Theta$$ imposes a price cap on the energy price (blue, solid) and the smaller country, of size 1 − $$\Theta$$ does not (red, dashed). The black solid lines show the union-wide variables. The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 8: Responses to an adverse gas supply shock $$\vert$$ Energy production
Figure 8 presents the responses to an adverse gas supply shock, comparing economies with a price cap (blue, solid lines) and without a cap (red, dashed lines). This economy includes a domestic energy sector. The figure consists of eight panels arranged in two rows of four, with all panels sharing a horizontal axis measuring time in quarters from 0 to 14, with gridlines at 4, 8, and 12 quarters.
The top-left panel shows "Energy inflation" with a vertical scale from -100% to 100%. The red dashed line, of the uncapped country, starts off at around 75% and comes down immediately for a few quarters, before it dips to -75% in quarter 7 and returns to 0% in quarter 8 to remain.
The "Energy production" panel has a vertical range from 0% to 4%. The red dashed line starts at approximately 4% and remains there until quarter 7. Around quarter 7, the red dashed line (no cap) drops to 0% to remain. The blue line (with cap) shows minimal fluctuation throughout.
The "Energy consumption households" panel shows values from -10% to 1%. The red dashed line begins near -8%, while the blue line begins near 1%. Both lines remain there until quarter 7 when they converge to 0%.
The "CPI inflation" panel displays values from -5% to 5%. The red dashed line starts near 5%, whereas the blue solid line at around -2%. The blue line gradually increases and peaks at about 2% around quarter 7, while the red line reaches approximately 1% before dropping sharply to about 5% around quarter 7, then returning to 0%.
In the bottom row, the "Other inflation" panel shows values from -5% to 5%. The blue line starts at around -1% and the red-dashed line at around 4%. Both lines gradually increase before they peak at quarter 7, at 4% for the red dashed line and 1% for the blue line, before they go back to 0% at quarter 8.
The "Other production" panel shows values from -0.1% to -0%. The blue line starts at around -0.06% and the red dashed line at around -0.1%. They remain there until quarter 7 in which they return to 0% to remain.
For "Total consumption," the scale ranges from -4% to 2%. The blue line starts at around 2%, while the red line begins near -4%. Both lines maintain this level until quarter 6, then return to 0%.
The "Nominal interest rate" panel shows values from 0% to 1%. There is only one line, since there is only one central bank. The line starts around 0.1% and gradually increases to around 1% in quarter 6, before it turns to 0% in quarter 7.
Notes: Impulse responses to a 15% decline in gas supply, in a model with energy production. Preferences are non-homothetic. The bigger country, of size $$\Theta$$ imposes a price cap on the energy price (blue, solid) and the smaller country, of size 1 − $$\Theta$$ does not (red, dashed). The black solid lines show the union-wide variables. The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 9: Historical shock decomposition $$\vert$$ Contributions from the energy price cap
Figure 9 presents a historical shock decomposition showing contributions from the energy price cap, arranged in four panels. The top row displays energy inflation with and without a price cap, while the bottom row shows CPI inflation with and without a cap. All panels cover the same time period from 2020 Q3 to 2022 Q4, with quarterly observations on the horizontal axis.
The upper-left panel shows "Energy inflation: Cap" with a vertical scale ranging from -10% to 20%. The stacked bars represent contributions from "Other shocks" (blue) and "Cap" (red). The total effect, represented by a black line overlay, begins negative at around -10% in 2020 Q3, gradually rises to become positive in 2021 Q1, and reaches peaks of approximately 12-14% during 2022 before declining to near 0% by 2022 Q4. The red "Cap" component appears as negative contributions from 2021Q4 that partially offset the blue "Other shocks" component, particularly in 2022.
The upper-right panel shows "Energy inflation: No cap" with the same vertical scale. Here, the total energy inflation starts similarly negative in 2020 but rises more dramatically, peaking at nearly 25% in 2022 Q1. The red "Cap" component in this panel represents additional positive contributions to inflation, about a third of the total, particularly in 2022 Q1-Q3, pushing the total inflation higher than in the capped scenario. In 2022 Q4, the line is around 10% and is solely accounted for by the red "Cap” component.
The lower-left panel displays "CPI inflation: Cap" with a vertical scale from -2% to 4%. The pattern resembles that of energy inflation but with smaller magnitudes. Inflation starts negative around -1.5% in 2020, becomes positive in 2021 Q2, and gradually increases to peak at approximately 3% by 2022 Q2 before slightly declining. The red component shows modest negative contributions from the cap.
The lower-right panel shows "CPI inflation: No cap" with the same vertical scale. Again following a similar pattern to energy inflation, CPI inflation starts negative but rises more steeply than in the capped scenario, reaching approximately 4% in 2022. The red component adds positive contributions to inflation, particularly in 2022, and is about a fifth of the contribution throughout.
Notes: Historical shock decomposition of the annual inflation rates in deviations from the sample mean. "Other shocks” consist of total factor productivity (TFP) shocks for other goods and energy sector, demand shocks, cost-push shocks in the other goods sector, shocks to gas supply, monetary policy shock, and measurement errors for energy consumption and energy inflation. Those shocks and measurement errors are separate for the two countries in the union, except for the monetary policy shock. Mean energy inflation is 2.15% and 2.72% for capped and no-cap countries respectively. Mean CPI inflation is 1.42% and 1.46% for capped and no-cap countries respectively. The red bars indicate the contributions from the energy price cap, whereas the blue bars aggregate all other shocks. More details are in Appendix B.
Figure 10: Consumption response decomposition $$\vert$$ Cap and no cap
Figure 10 presents the consumption response decomposition comparing scenarios with and without energy price caps, displayed across three panels. The horizontal axis in all panels represents time in quarters, ranging from 0 to approximately 14 quarters.
The left panel, titled "Cap: Constrained," shows the consumption response for constrained households in an economy with a price cap. The vertical axis ranges from approximately -0.2% to 0.4%. The total effect (black line) begins slightly negative around -0.15%, remains relatively flat through quarter 5, then rises to peak at about 0.15% around quarter 6-7 before returning to 0% for the remainder of the period. The stacked bars show contributions from energy consumption (green), real wage (purple), and tax effects (pink). The energy consumption component dominates.
The middle panel, "Cap: Unconstrained," displays the consumption response for unconstrained households with the same vertical scale as the first panel. Here, the total effect starts substantially positive at around 0.35-0.4% and remains elevated through quarter 7, driven primarily by positive energy consumption effects (green bars) and consumption smoothing (yellow bars). Around quarter 7, the total effect drops sharply to near zero.
The right panel, "No cap," uses a different vertical scale ranging from approximately -1.5% to 0.5%. This panel shows consistently negative consumption effects throughout most of the period, with the total reaching about -1.5% in the early quarters. There is a brief partial recovery around quarter 7 where consumption approaches 0.5% before declining to 0%. The panel distinguishes between contributions from constrained households (blue) and unconstrained households (red), with unconstrained households accounting for most of the negative consumption effect.
Notes: Impulse responses to a 15% decline in energy supply (black lines) and the decomposition of the responses (colored bars). Preferences are non-homothetic. The bigger country, of size $$\Theta$$ imposes a price cap on the energy price (left two panels) and the smaller country, of size 1 − $$\Theta$$ does not (rightmost panel). The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 11: Consumption response decomposition $$\vert$$ Transfers and no transfers
Figure 11 presents the consumption response decomposition comparing scenarios with and without targeted transfers, displayed across three panels. The horizontal axis in all panels represents time in quarters, ranging from 0 to approximately 14 quarters.
The left panel, titled "Transfers Constrained," shows the consumption response for constrained households in an economy with targeted transfers. The vertical axis ranges from approximately -0.2% to 0.1%. The total effect (black line) begins around 0.7%, remains relatively flat through quarter 6, then returns to around 0% around quarter 6-7. The stacked bars show contributions from energy consumption (green), real wage (purple), and transfer effects (pink). The energy consumption and the transfers both have increasing effects of around the same magnitude.
The middle panel, "Transfers: Unconstrained," displays the consumption response for unconstrained households with the same vertical scale as the first panel. Here, the total effect starts at around -1.5% and there through quarter 7, driven primarily by negative energy consumption effects (green bars). The consumption smoothing (yellow bars) effects are positive, but too small to offset the first effect. Around quarter 7, the total effect comes back to zero.
The right panel, "No transfers," uses a different vertical scale ranging from approximately -1.5% to 0.5%. This panel shows consistently negative consumption effects throughout most of the period, with the total reaching about -0.2% until quarter 6, before it returns to 0% in quarter 7. The panel distinguishes between contributions from constrained households (blue) and unconstrained households (red), with unconstrained households accounting for most of the negative consumption effect. There is an extra line in this graph, labeled "Cap baseline” which shows the total effect of the third panel in Figure 10, to compare the spillovers from cap and the transfers.
Notes: Impulse responses to a 15% decline in energy supply (black lines) and the decomposition of the responses (colored bars). Preferences are non-homothetic. The bigger country, of size $$\Theta$$ conducts targeted transfers to the constrained households (left two panels) and the smaller country, of size 1 − $$\Theta$$ does not (rightmost panel). The dashed line indicates the baseline scenario with the energy price cap. The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 12: Responses to an adverse energy shock $$\vert$$ Transfers vs. no transfers
Figure 12 presents the responses to an adverse gas supply shock, comparing economies with targeted transfers (blue, solid lines) and without (red, dashed lines). This economy includes a domestic energy sector. The figure consists of six panels arranged in two rows of four, with all panels sharing a horizontal axis measuring time in quarters from 0 to 14, with gridlines at 4, 8, and 12 quarters.
The top-left panel shows "Energy inflation" with a vertical scale from -20% to 20%. The red and blue line move together. They start at around 17% and come down immediately for a few quarters. The lines dip at around -17% in quarter 7 before returning to 0% in quarter 8.
The "Other inflation" panel has a vertical range from 0% to 0.3%. The lines move together again, starting off at around 0.25% and gradually decreasing to 0% in quarter 8.
The "CPI inflation” panel shows values from -1% to 1%. Again, the lines move together, starting off at around 1%, decreasing to -1% in quarter and coming back to 0% at quarter 8.
The "Total output" panel displays values from 0% to 0.1%. The red dashed line starts very slightly above 0.1%, whereas the blue line starts at around 0.1%. They both remain there until quarter 6, before coming back down to 0% in quarter 7.
The "Total consumption, constrained" panel shows values from -0.05% to 0.1%. The blue line starts at around 0.75% and the red-dashed line at around -0.05%. Both lines remain there until quarter 6, before converging to 0% in quarter 7.
The "Total consumption, unconstrained" panel shows values from -0.15% to 0%. The lines move together starting from -0.15% and remaining there until quarter 6. They return to 0% at around quarter 7.
Notes: Impulse responses to a 15% decline in energy supply. Preferences are non-homothetic. The bigger country, of size $$\Theta$$ conducts targeted transfers to the constrained (c) households (blue, solid) and the smaller country, of size 1−$$\Theta$$ does not (red, dashed). u stands for the unconstrained households. Output is equal to the output gap. The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 13: Data used for estimation of parameters
Figure 13 displays the data used for parameter estimation, presented in six panels across two rows. All panels share a common horizontal axis representing time from 2008 to 2019.
The top-left panel shows "Energy/gas inflation" with values ranging from -0.04 to 0.04. Two series are plotted: gas inflation (dashed line) and energy inflation (solid line). Both series exhibit considerable volatility, with notable peaks around 2010-2011 and 2016, and troughs in 2009 and 2014-2015. The gas inflation series shows slightly more extreme fluctuations than energy inflation, particularly in 2010 when it reaches approximately 0.03.
The top-middle panel presents "Gas consumption" with values ranging from -0.1 to 0.1. This single solid line shows significant fluctuations throughout the period, with major peaks in 2010 and 2015 reaching nearly 0.1, and sharp declines in 2009, 2013, and 2017, falling to approximately -0.08.
The top-right panel displays the "Nominal interest rate" with values ranging from -0.004 to 0.004. The curve begins negative around 2008, rises to a peak of approximately 0.0025 in 2010, gradually declines with minor fluctuations through 2014, then stabilizes slightly below zero for the remainder of the period.
The bottom-left panel shows "CPI inflation" with values ranging from -0.004 to 0.004. Two series are plotted: countries with energy price caps (blue line) and without caps (red line). Both series generally track together, showing peaks around 2010-2011 and 2017, with troughs in 2009 and 2014-2015.
The bottom-middle panel presents "Energy consumption" with values ranging from -0.02 to 0.02. Two series compare countries with caps (blue) and without caps (red). The two series show distinct patterns, with the capped countries experiencing fewer extreme fluctuations generally ranging from -0.005 to 0.01, while uncapped countries show sharper changes ranging from -0.02 to nearly 0.02.
The bottom-right panel shows "Total output" with values ranging from -0.02 to 0.02. The blue line represents countries with price caps and the red line countries without caps. Countries with caps appear to experience higher output growth during 2010-2012 (reaching approximately 0.02), while both groups show similar declining trends from 2015 onward, ending at about -0.015 by 2019.
Notes: Plot of the Euro Area data used in the Bayesian estimation of the parameters. For the lower panels I separate the Euro Area countries into "Cap” and "No cap” countries, according to whether countries imposed an energy cap in 2022 or not. See Figure 2 for details.
Figure 14: Data used for historical shock decomposition
Figure 14 presents the data used for historical shock decomposition across seven panels arranged in two rows. All panels share a common horizontal axis representing time from 2008 to 2022, with a prominent vertical gray bar marking a significant event around 2020. Each panel compares countries with energy price caps (blue line) and without caps (red line), except for the nominal interest rate panel which shows a single black line.
The top-left panel shows "Energy inflation" with values ranging from -0.05 to 0.05. Both series track closely until around 2020, after which countries without caps (red) experience higher inflation, reaching approximately 0.05 by 2022 compared to about 0.03 for countries with caps (blue).
The top-middle panel displays "Gas inflation" with a scale from -0.05 to 0.1. The pattern is similar to energy inflation but with greater magnitude, with uncapped countries reaching about 0.08 by 2022 versus 0.05 for capped countries. The top-right panel presents "CPI inflation" ranging from -0.005 to 0.01. Both series follow similar trajectories until 2020, after which uncapped countries experience higher inflation, peaking at approximately 0.01 compared to 0.008 for capped countries.
The top-far-right panel shows the "Nominal interest rate" from -0.002 to 0.004. Unlike other panels, this shows a single black line representing interest rates, which begin slightly negative around 2009, stabilize near zero from 2012-2020, and then rise sharply after 2020 to approximately 0.003.
The bottom-left panel displays "Energy consumption" with values from -0.04 to 0.02. Countries maintain relatively stable consumption even after 2020.
The bottom-middle panel shows "Gas consumption" with a wider range from -0.2 to 0.2. Both series exhibit considerable volatility throughout the period. After 2020, the uncapped countries (red) show a marked decline reaching nearly -0.2, while capped countries (blue) experience a less severe drop.
The bottom-right panel presents "Total output" ranging from -0.1 to 0.05. Both series track closely until 2020, after which both experience a sharp decline followed by recovery.
Notes: Plot of the data used in the historical shock decomposition. I separate the Euro Area countries into "Cap” and "No cap” countries, according to whether countries imposed an energy cap in 2022 or not. See Figure 2 for details. Grey-shaded area are 2020Q1 and Q2, the quarters most affected by the COVID-19 pandemic.
Figure 15: Prior and posterior distributions
Figure 15 displays prior and posterior distributions for three different parameters across three panels. All panels show probability density on the vertical axis with parameter values on the horizontal axis, featuring gray curves (prior distributions) and black curves (posterior distributions). Each panel also contains a vertical blue line marking a specific parameter value.
The left panel shows distributions for parameter epsilon 1, with horizontal axis ranging from 0 to 1 and vertical axis from 0 to 6. The prior distribution (gray) is centered around 0.7-0.8, while the posterior distribution (black) is narrower and centered around 0.3-0.4, with the blue vertical line positioned at approximately 0.3.
The middle panel presents distributions for parameter zeta, with horizontal axis ranging from 0 to 30 and vertical axis from 0 to 0.4. The prior distribution (gray) is concentrated near 2, while the posterior distribution (black) is centered around 15-20, with the blue vertical line at approximately 15.
The right panel shows distributions for parameter zeta star, with horizontal axis ranging from 0 to 65 and vertical axis from 0 to 0.5. The prior distribution (gray) is again concentrated near 2, while the posterior distribution (black) is centered around 25-35, with the blue vertical line positioned at approximately 30.
Notes: Plot of the prior distribution (gray) and the posterior distribution (black). The vertical blue line indicates the posterior mode. The y-axis displays the density of the distributions.
Figure 16: Natural gas price in Europe
Figure 16 displays the natural gas price in Europe from 2002 Q1 to 2022 Q2, presented as an index where 2021 Q1 equals 100. The horizontal axis shows time in quarters from 2002 to 2022, while the vertical axis represents the price index ranging from 0 to approximately 900. The line graph begins with relatively low values around 50 in the early 2000s, remaining below 100 until around 2007. It then increases gradually, reaching its first significant peak of about 250 in 2009 Q1. After declining to approximately 100, the index fluctuates between 100 and 200 throughout the 2010-2020 period, with minor peaks and valleys. During this middle period, gas prices show relative stability compared to later developments. After 2020, the index begins a dramatic ascent, rising rapidly to around 500 by late 2021, then briefly declining before surging to its highest point of approximately 900 in early 2022. The final reading shows a partial retreat to around 450.
Notes: The price index of the Title Transfer Facility (TTF) gas in the Netherlands. Data source: IMF Data (2024).
Figure 17: Decomposition of the variance of headline inflation
Figure 17 presents a decomposition of the variance of headline inflation from 2002 Q1 through 2022 Q1. The vertical axis measures variance in percent squared, ranging from 0 to approximately 30, while the horizontal axis tracks time by quarter across two decades. The figure uses a stacked area chart with three color-coded components: Var(energy) in red/pink, Var(other) in green, and Cov(energy & other) in yellow.
Throughout most of the period from 2002 to 2020, the total variance of headline inflation remains notably low and stable, generally below 2 percent squared. A minor elevation appears around 2010 Q1, where the variance briefly approaches 3 percent squared, with small increases in all three components. The pattern of relative stability continues until late 2021.
The most striking feature of the figure is the dramatic spike occurring in 2022 Q1, where the total variance surges to approximately 30 percent squared before quickly declining toward the end of the period. During this spike, all three components increase substantially, with the yellow Cov(energy & other) component showing the largest contribution at the peak, followed by the red Var(energy) component, and a smaller but still significant increase in the green Var(other) component.
Notes: The headline inflation in country $$i$$ in quarter $$t$$ is $$\Pi_{it} = (1 − \alpha^E_{it})\Pi^O_{it}+ \alpha^E_{it} \Pi^E_{it}$$ where is $$\alpha^{ENG}$$ the share of energy in the consumption basket, $$\Pi^E_{it}$$ and $$\Pi^O_{it}$$ energy and other goods inflation. The variance decomposition is across countries for each quarter, so $$V_{ art}(\Pi_{it}) = V_{art}\left[(1 − \alpha^E_{it})\Pi^O_{it}+ \alpha^E_{it} \Pi^E_{it}\right]$$. Data source: Eurostat.
Figure 18: Responses to an adverse energy supply shock $$\vert$$ Cap vs. no cap under core-inflation targeting
Figure 18 presents the responses to an adverse energy supply shock, comparing economies with a price cap (blue, solid lines) and without a cap (red, dashed lines), in an economy in which the central bank targets core inflation. The figure consists of eight panels arranged in two rows of four, with all panels sharing a horizontal axis measuring time in quarters from 0 to 14, with gridlines at 4, 8, and 12 quarters.
The top-left panel shows "Government expenditure on cap" with a vertical scale from 0% to 2%. The blue line is elevated at 2.5% until quarter 6, then returns to 0% by quarter 7. The red line remains at 0% throughout, as there is no cap in this country.
The "Energy inflation" panel has a vertical range from -500% to 500%. The red dashed start at approximately 500%, quickly falling to near 0%. Around quarter 6, the red dashed line (no cap) sharply drops to around -500% before returning to 0% by quarter 8, while the blue line (with cap) shows minimal fluctuation throughout.
The "Other inflation" panel shows values from -5% to 5%. The red dashed line begins near -5%, while the blue line begins near 4%. Both lines converge back to 0% for the next few quarters, before diverging again in quarter 7, when the red dashed line peaks to near 5% and the blue line drops near -4%. In quarter 8, they converge back again to 0%.
The "CPI inflation" panel displays values from -25% to 25%. The red dashed line starts near 25%, whereas the blue solid line at around 5%. They converge to 0% in the next few quarters, but in quarter 7 the red dashed line drops to -25% and the blue line to -5%. In quarter 8 they converge back again to 0%.
In the bottom row, the "Output" panel shows values from 0% to -0.25%. The blue line starts and remains around 0% throughout. The red line starts deeper at about -0.25%, maintaining this level until quarter 6 before returning to 0% by quarter 7.
The "Energy consumption by households" panel shows values from 0% to -30%. The blue line remains near 0% throughout, while the red line stays at approximately -30% until quarter 6, then sharply returns to 0%.
For "Total consumption," the scale ranges from -20% to 10%. The blue line starts at around 9%, while the red line begins near -20%. Both lines maintain this level until quarter 6, then return to 0%.
The "Nominal interest rate" panel shows values from -1% to 1%. This line does not move throughout.
Notes: Impulse responses to a 15% decline in energy supply, in a model in which the central bank targets other inflation (core inflation). Preferences are non-homothetic. The bigger country, of size $$\Theta$$ imposes a price cap on the energy price (blue, solid) and the smaller country, of size 1 − $$\Theta$$ does not (red, dashed). The black solid lines show the union-wide variables. The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 19: Responses to an adverse energy supply shock $$\vert$$ Cap vs. no cap with TANK
Figure 19 presents the responses to an adverse gas supply shock, comparing economies with a price cap (blue, solid lines) and without a cap (red, dashed lines). This economy includes a domestic energy sector and has two types of households. The figure consists of eight panels arranged in two rows of four, with all panels sharing a horizontal axis measuring time in quarters from 0 to 14, with gridlines at 4, 8, and 12 quarters.
The top-left panel shows "Energy inflation" with a vertical scale from -50% to 50%. The red dashed line, of the uncapped country, starts off at around 45% and comes down immediately for a few quarters, before it dips to -45% in quarter 7 and returns to 0% in quarter 8 to remain.
The "Energy production" panel has a vertical range from 0% to 2.5%. The red dashed line starts at approximately 2.5% and remains there until quarter 7. Around quarter 7, the red dashed line (no cap) drops to 0% to remain. The blue line (with cap) shows minimal fluctuation throughout.
The "Energy consumption households" panel shows values from -10% to 0%. The red dashed line begins near -8% and remains there until quarter 7 when it returns to 0%. The blue line shows minimal fluctuations throughout.
The "CPI inflation" panel displays values from -2% to 2%. The red dashed line starts near 2%, whereas the blue solid line at around -0.2%. The blue line gradually increases and peaks at about 0.5% around quarter 7, while the red line reaches approximately 0.5% before dropping sharply to about -2% around quarter 7, then returning to 0%.
In the bottom row, the "Other inflation" panel shows values from -1% to 1%. The blue line starts at around -0.3% and the red-dashed line at around -1%. Both lines gradually increase before they peak around quarter 7, at 1% for the red dashed line and 0.7% for the blue line, before they go back to 0% at quarter 8.
The "Other production" panel shows values from -0.5% to 1%. The blue line starts at around -0.05% and the red dashed line at around 0.5%. They remain there until quarter 7 in which they return to 0% to remain.
For "Total consumption," the scale ranges from -1.5% to 0.5%. The blue line starts at around 0.5%, while the red line begins near -1%. Both lines maintain this level until quarter 6, then return to 0%.
The "Nominal interest rate" panel shows values from -0.5% to 1%. There is only one line, since there is only one central bank. The line starts around 0.5% and peaks at 1% in quarter 6. Before returning to 0% in quarter 8, it slightly dips in quarter 7 to -0.5%.
Notes: Impulse responses to a 15% decline in energy supply, in the two-agent version of the model. Preferences are non-homothetic. The bigger country, of size $$\Theta$$ imposes a price cap on the energy price (blue, solid) and the smaller country, of size 1 − $$\Theta$$ does not (red, dashed). The black solid lines show the unionwide variables. The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 20: Responses to an adverse energy supply shock $$\vert$$ Cap vs. no cap with elastic labor supply
Figure 20 presents the responses to an adverse energy supply shock, comparing economies with a price cap (blue, solid lines) and without a cap (red, dashed lines), in an economy with elastic labor supply. The figure consists of eight panels arranged in two rows of four, with all panels sharing a horizontal axis measuring time in quarters from 0 to 14, with gridlines at 4, 8, and 12 quarters.
The top-left panel shows "Government expenditure on cap" with a vertical scale from 0% to 2%. The blue line is elevated at 2.5% until quarter 6, then returns to 0% by quarter 7. The red line remains at 0% throughout, as there is no cap in this country.
The "Energy inflation" panel has a vertical range from -500% to 500%. The red dashed start at approximately 500%, quickly falling to near 0%. Around quarter 6, the red dashed line (no cap) sharply drops to around -500% before returning to 0% by quarter 8, while the blue line (with cap) shows minimal fluctuation throughout.
The "Other inflation" panel shows values from -20% to 20%. The red dashed line begins near -20%, while the blue line begins near -5%. Both lines rise to positive territory with peaks around quarter 6. The blue line peaks at approximately 5%, while the red line reaches a higher peak of about 15% before both return to near 0% in quarter 8.
The "CPI inflation" panel displays values from -20% to 20%. The red dashed line starts near 20%, whereas the blue solid line at around -5%. The blue line gradually increases and peaks at about 5% around quarter 7, while the red line reaches approximately 10% before dropping sharply to about -15% around quarter 7, then returning to 0%.
In the bottom row, the "Output" panel shows values from -5% to 10%. The red dashed line has a delayed start, but fluctuates around 5% until quarter 7, before returning to 0% in quarter 8. The blue line drops on impact to about -4% and recovers, peaking at quarter 7 at around 4% before returning to 0% in quarter 8.
The "Energy consumption by households" panel shows values from 0% to -30%. The blue line remains near 0% throughout, while the red line stays at approximately -30% until quarter 6, then sharply returns to 0%.
For "Total consumption," the scale ranges from -20% to 10%. The blue line starts at around 9%, while the red line begins near -20%. Both lines remain around this level until quarter 6, then return to 0%.
The "Nominal interest rate" panel shows values from 0% to 10%. There is only one line, since there is only one central bank. The line starts around 0% and gradually increases to around 10% in quarter 6, before it turns to 0% in quarter 7.
Notes: Impulse responses to a 15% decline in energy supply, in a model with elastic labor supply. Preferences are non-homothetic. The bigger country, of size $$\Theta$$ imposes a price cap on the energy price (blue, solid) and the smaller country, of size 1 − $$\Theta$$ does not (red, dashed). The black solid lines show the union-wide variables. Output is equal to the output gap. Government expenditure on the price cap (Govt. exp. cap) is the cost of the cap as a share of annual total output of the country (GDP). The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 21: Responses to an adverse energy supply shock $$\vert$$ No price caps with flexible prices
Figure 21 displays the responses to an adverse energy supply shock in an economy without price caps, presented in eight panels arranged in two rows of four. All panels share a common horizontal axis measuring time in quarters from 0 to 14. The top row shows: Total energy, Energy inflation, Other inflation, and CPI inflation. The bottom row shows: Output, Energy consumption by households, Total consumption, and Nominal interest rate.
This Figure displays the same impulse responses as Figure 4, but adds a second, thinner line for each panel from the simulation of the model without homothetic preferences.
In the "Total energy” panel, the thinner line is not distinguishable, meaning that the responses of the two cases (homothetic and non-homothetic) are identical.
In the "Energy inflation” panel, the thinner line shows a similar pattern to the thicker line, but is much more subdued: the peak is around 50% and the drop around -50%.
In the "Other inflation” panel, again, the thinner line is similar to the thicker one, but with more subdued values: -5% at the lowest and gradually increasing to 5% in quarter 7.
In the "CPI inflation” panel, it is the same story. The thinner line starts off close to 0% and peaks at around 2.5% in quarter 7.
For the "Output”, "Energy consumption households”, and "Total consumption” panel, we cannot distinguish between the thin and the thick line.
In the "Nominal interest rate” panel, the thinner line starts off close to 0% and peaks at around 2.5% in quarter 7, more subdued than the thicker line.
Notes: See Figure 20. Impulse responses to a 15% decline in energy supply, in a model with flexible prices.
Figure 22: Responses to an adverse energy supply shock $$\vert$$ Price caps with flexible prices
Figure 22 displays the responses to an adverse energy supply shock in an economy with a price cap, presented in eight panels arranged in two rows of four. All results are qualitatively and quantitatively indistinguishable from Figure 6 which has price rigidities.
Notes: See Figure 20. Impulse responses to a 15% decline in energy supply, in a model with flexible prices.
Figure 23: Responses to an adverse energy supply shock $$\vert$$ Cap vs. no cap with flexible prices
Figure 23 presents the responses to an adverse energy supply shock, comparing economies with a price cap (blue, solid lines) and without a cap (red, dashed lines). It presents the case of a flexible price economy. The results are qualitatively and quantitatively similar to Figure 5, with minor differences in the point estimates.
Notes: See Figure 20. Impulse responses to a 15% decline in energy supply, in a model with flexible prices.
Figure 24: Responses to an adverse energy supply shock $$\vert$$ Cap vs. no cap in world with flexible nominal exchange rates
Figure 24 presents the responses to an adverse energy supply shock, comparing economies with a price cap (blue, solid lines) and without a cap (red, dashed lines). It presents the case of flexible exchange rates. The results are qualitatively and quantitatively similar to Figure 5, with the exception of the nominal interest rate graph. Instead of there being only one line for the union, there is a line for each country. Both lines start out at 0% and remain there until quarter 5. In quarter 6, the blue line increases to about 10%, whereas the red dashed line decreases to -15%. In quarter 7, they converge back at 0% again.
Notes: See Figure 20. Impulse responses to a 15% decline in energy supply, in a model with flexible nominal exchange rates.
Figure 25: Responses to an adverse energy supply shock $$\vert$$ No caps with CES preferences
Figure 25 displays the responses to an adverse energy supply shock in an economy without price caps, presented in eight panels arranged in two rows of four. All panels share a common horizontal axis measuring time in quarters from 0 to 14. The top row shows: Total energy, Energy inflation, Other inflation, and CPI inflation. The bottom row shows: Output, Energy consumption by households, Total consumption, and Nominal interest rate.
This Figure displays the same impulse responses as Figure 21, but adds an extra dashed line, for constant-elasticity of substitution (CES) preferences.
In the "Total energy” and "Total consumption” panel, the dashed line is not distinguishable, meaning that the responses of the three cases (Cobb-Douglas, non-homothetic, and CES) are identical.
In the "Energy inflation” panel, the dashed line follows the non-homothetic preferences more closely, and with the peaks and drops slightly bigger than the non-homothetic preferences case. In the "Other inflation” panel and "Output”, the dashed line follows the non-homothetic case closely again, with slightly more fluctuations as well.
In the "CPI inflation” panel and the "Nominal interest rate” panel, the dashed line is identical to the Cobb-Douglas line, as explained in Figure 21.
In the "Energy consumption households” panel, the three lines are all very close to each other around -15%, with the dashed line slightly above and the thin line slightly below the thick, baseline case.
Notes: Impulse responses to a 15% decline in energy supply. The graph compares three types of preferences: Cobb-Douglas (solid, thin), Constant Elasticity of Substitution (CES) (dashed), and non-homothetic preferences (solid, bold). Output is equal to the output gap. The y-axis is in terms of percentage deviations from steady state. The x-axis is in quarters. Inflation and interest rates are annualized.
Figure 26: Responses to an adverse energy supply shock $$\vert$$ Cap vs. no cap with CES preferences
Figure 26 presents the responses to an adverse energy supply shock, comparing economies with a price cap and without a cap. The figure consists of eight panels arranged in two rows of four, with all panels sharing a horizontal axis measuring time in quarters from 0 to 14, with gridlines at 4, 8, and 12 quarters. Essentially, this Figure adds a case of CES preferences to Figure 5, doubling the number of lines in each panel. The lines and scales for the non-homothetic preferences are identical to the one in Figure 5, so the differences with those preferences are explained here.
The top-left panel shows "Government expenditure on cap". In the CES case, the government expenditure on the cap is around 0.5% for the blue line, whereas the red line remains at 0%. The "Energy inflation" panel shows that the energy inflation does not peak as high as the non-homothetic case, but is still around 450% and dropping around -450%.
For the "Other inflation”, "CPI inflation”, "Output”, "Energy consumption”, "Total consumption”, and "Nominal interest rate” panels, the case for CES preferences is slightly more subdued than the case of non-homothetic preferences, but qualitatively similar. The "Other inflation" panel shows values from -20% to 20%. The red dashed line begins near -20%, while the blue line begins near -5%. Both lines rise to positive territory with peaks around quarter 6. The blue line peaks at approximately 5%, while the red line reaches a higher peak of about 15% before both return to near 0% in quarter 8.
The "CPI inflation" panel displays values from -20% to 20%. The red dashed line starts near 20%, whereas the blue solid line at around -5%. The blue line gradually increases and peaks at about 5% around quarter 7, while the red line reaches approximately 10% before dropping sharply to about -15% around quarter 7, then returning to 0%.
In the bottom row, the "Output" panel shows values from 0% to -0.2%. The blue line starts and remains around 0% throughout. The red line starts deeper at about -0.25%, maintaining this level until quarter 6 before returning to 0% by quarter 7.
The "Energy consumption by households" panel shows values from 0% to -30%. The blue line remains near 0% throughout, while the red line stays at approximately -30% until quarter 6, then sharply returns to 0%.
For "Total consumption," the scale ranges from -20% to 10%. The blue line starts at around 9%, while the red line begins near -15%. Both lines maintain this level until quarter 6, then return to 0%.
The "Nominal interest rate" panel shows values from 0% to 10%. There is only one line, since there is only one central bank. The line starts around 1% and gradually increases to around 10% in quarter 6, before it turns to 0% in quarter 7.
Notes: See Figure 20. Impulse responses to a 15% decline in energy supply, in a model with CES preferences.