Transitioning to Net-Zero: Macroeconomic Implications and Welfare Assessment

JAVIER ANDRÉS

JOSÉ EMILIO BOSCÁ

RAFAEL DOMÉNECH

JAVIER FERRI

Estudios sobre la Economía Española 2024/01

Enero 2024

fedea

Las opiniones recogidas en este documento son las de sus autores y no coinciden necesariamente con las de Fedea.

La urgencia de la transición hacia una economía baja en carbono no puede subestimarse, especialmente a la luz de la creciente evidencia del cambio climático. En línea con los objetivos establecidos en el Acuerdo de París, la Agencia Internacional de la Energía ha delineado un escenario normativo destinado a lograr emisiones netas cero (NZE) para el año 2050, con las economías avanzadas liderando este esfuerzo. Los países de la UE, con sus políticas nacionales y comunes están a la vanguardia de la descarbonización de sus economías.

Los gobiernos nacionales cuentan con una variedad de políticas en sus estrategias para mitigar las emisiones de carbono, cuya implementación debería estar basada en su eficacia para reducir las emisiones, sus efectos macroeconómicos, y su impacto sobre el bienestar. La implementación efectiva de políticas económicas diseñadas para facilitar esta transición influirá de forma significativa en la dinámica macroeconómica de estas economías y, obviamente, no estará exenta de costes en el corto plazo.

En este documento se plantea un modelo que permite estudiar las relaciones entre la evolución de la tecnología, la política fiscal y las repercusiones macroeconómicas y de bienestar asociadas con la transición energética en España.

Hay varias formas en las que el progreso técnico puede contribuir a frenar las emisiones y que se contemplan en el documento, como el progreso técnico que favorece la eficiencia en la generación de energía verde, la reducción de las emisiones por unidad de producción de energía sucia, o la mejora de la eficiencia en el suministro de energía. Sin embargo, otro tipo de progreso técnico que favorece el crecimiento puede ir acompañado de un aumento de las emisiones, como la mejora en la productividad total de los factores. La combinación de estas diferentes fuentes de progreso técnico no será suficiente para garantizar la consecución del objetivo de N ZE en el año 2050.

Como medida complementaria al progreso técnico, los gobiernos deberían establecer estrategias proactivas para mitigar las emisiones de gases de efecto invernadero, tales como ofrecer subsidios para invertir en energía limpia, establecer objetivos para el crecimiento de los precios de los combustibles fósiles (gas, carbón y petróleo), lo que supone de facto una penalización a su demanda, o introducir impuestos a las emisiones.

El modelo se utiliza para simular el esfuerzo necesario para alcanzar el objetivo de NZE bajo diferentes estrategias de mitigación. En todas las estrategias consideradas, el gobierno utiliza algún instrumento de política para lograr la reducción deseada de las emisiones bajo tres escenarios relacionados con el progreso técnico: el escenario base, en el que se supone que las tasas de progreso técnico en sus diferentes modalidades, observadas en la década anterior a la pandemia, se mantienen en el futuro; el pesimista, en el que el progreso técnico reductor de emisiones se ralentiza en un tercio, y el optimista, en el que éste se acelera en un tercio.

Mantener o acelerar el ritmo de crecimiento de distintas modalidades de progreso técnico es fundamental, ya que el escenario base de continuación de la tendencia observada consistente con el modelo implica reducir casi un tercio las emisiones en 2050 con respecto a 2019, dejando a políticas costosas de mitigación una reducción adicional de 38%. Sin embargo, la ralentización de la tasa de crecimiento del progreso técnico en un tercio, con respecto al observado entre 2010 y 2019, trasladaría a las políticas de mitigación un 58% de la reducción de emisiones.

De la comparación entre políticas destinadas a mitigar las emisiones de carbono, y de una misma política a través del tiempo, obtenemos los siguientes resultados. Las políticas muy concentradas al principio del periodo (front-loaded) pueden resultar efectivas para alcanzar el objetivo intermedio del Green Deal 2030, aunque resultan insuficientes para cumplir con el objetivo de NZE para 2050, al menos sin un aumento sustancial en el coste en términos de bienestar. Por otro lado, los subsidios a la inversión verde requieren más tiempo para generar una reducción significativa en las emisiones en comparación con otras políticas. A diferencia de otras políticas de mitigación, subsidiar la inversión verde conlleva un aumento en la intensidad energética por unidad de producción debido al gran desarrollo en la producción de energía verde. De todas las políticas consideradas, el aumento en los precios de los combustibles fósiles para desincentivar su uso conlleva los mayores costes en términos de bienestar tanto en la transición a 2050 como en el largo plazo. Sin embargo, los impuestos a las emisiones emergen como la política más preferible en términos de bienestar durante la transición a 2050 aunque, a diferencia de estos impuestos, los subsidios a la inversión verde generan ganancias sustanciales en el bienestar a muy largo plazo, incluso sin una política de reducción de emisiones coordinada entre economías. Reasignar ingresos de impuestos al carbono hacia subsidios a la inversión verde genera el efecto de bienestar más equilibrado entre el corto y largo plazo.

Un aumento lineal en los impuestos por tonelada de carbono emitido, desde 0€ en 2019 hasta 227€ en 2050, y su posterior estabilización a este precio desde 2050, lograría la reducción de emisiones necesaria para cumplir el objetivo de NZE. La pérdida promedio de bienestar resultante de esta política durante el periodo de transición es relativamente reducida, de -0.44% en términos de consumo equivalente desde 2019 hasta 2050; sin embargo, aumenta a -19% en el muy largo plazo que cubre el período desde 2019 hasta 2200. Como sería esperable debido a la tendencia creciente en los impuestos a las emisiones, los efectos en el bienestar muestran un declive significativo y persistente que se extiende mucho más allá del año 2050. Para ese año, el escenario de referencia registraría una pérdida de bienestar que superaría los 1.5 puntos porcentuales (pp) en consumo equivalente. El análisis de robustez demuestra, sin embargo, que el coste en términos de bienestar asociado con la transición hacia las NZE sigue siendo manejable en una amplia gama de configuraciones de las simulaciones.

En ausencia de una estrategia coordinada de mitigación de las emisiones a nivel internacional, donde las emisiones de carbono globales se mantendrían constantes al nivel de 2019, se proyecta que la temperatura media del planeta aumentara en 1.8 grados Celsius por encima de los niveles preindustriales para el año 2050 y en más de 3.5 grados Celsius para el año 2200. Sin embargo, en un escenario coordinado donde la economía mundial redujera las emisiones en la misma proporción que la economía española en su transición hasta el objetivo de NZE, la temperatura se mantendría por debajo de 1.5 grados Celsius para el año 2050 y volvería a niveles casi preindustriales para el año 2200. El impacto positivo en el bienestar de una política coordinada a nivel mundial es muy evidente, aunque tarda varios decenios en materializarse. A largo plazo, el bienestar promedio podría aumentar en más del 50% en términos de consumo equivalente entre 2019 y 2200, a medida que la economía mundial evita los daños del cambio climático.

J. Andrés^a, J.E. Boscá^a,b, R. Doménech^a,c and J. Ferri^a,b

a University of Valencia, Spain b Fedea, Spain c BBVA Research, Spain

January, 2024.

Abstract

We assess the macroeconomic and welfare implications of carbon mitigation strategies using an environmental Dynamic General Equilibrium model. The economy uses energy from both green renewable technologies and fossil fuels. We set an emission reduction target in line with the Paris Agreement and analyze the welfare and macroeconomic impacts of various strategies, including (1) raising the domestic price of fossil fuels, (2) implementing a subsidy on green investment funded through lump-sum taxes, (3) imposing taxes on emissions with rebates to households, and (4) utilizing emission taxes to support green investment. Our model provides a framework for evaluating the welfare consequences of various carbon mitigation strategies, emphasizing the need to balance the short and long-term effects of incentives for investment and innovation in green technologies, as well as taxes and other policies designed to reduce carbon emissions.

Keywords: carbon emissions, green energy, brown energy, energy transition, welfare JEL Classification: Q43, Q58.

This paper has been financed by Agencia Estatal de Investigación (AEI) grant PID2020-116242RB-I00, Ministerio de Ciencia e Innovación grant TED2021-132629B-I00 and Generalitat Valenciana grant GVPROMETEO2020-083. José E. Boscá and Javier Ferri acknowledge the financial support of Fundación Rafael del Pino, BBVA Research and Fedea. We extend our gratitude to Clive Belfield, Hess T. Chung, Julen Esteban-Pretel, Cristina Fuentes-Albero, Francesc Ortega, Matthias O. Paustian, Nikolai Stahler and Ángel de la Fuente for their valuable comments. We have also benefited from discussions with participants at seminars hosted by BBVA Research in Madrid (January and November 2023), QC-CUNY in New York (May 2023), the Federal Reserve Board in Washington DC (June 2023), the 30th Encuentro de Economía Pública in Badajoz, the VI Workshop of the Spanish Macroeconomic Network in Seville, and the 48th Conference of the Spanish Economic Association in Salamanca.

1. Introduction

The urgency of transitioning to a low-carbon economy cannot be understated, particularly in light of mounting evidence of climate change (IPCC, 2023). Aligned with the goals set forth in the Paris Agreement (UNFCCC, 2015), the International Energy Agency (IEA, 2020) has outlined a normative scenario aimed at achieving Net Zero Emissions (NZE) by 2050. Advanced countries, particularly EU countries, with their national and common policies and coordinated national energy and climate plans (NECPs), should be at the forefront of decarbonization. The effective implementation of economic policies designed to facilitate the energy transition will significantly shape the dynamics of these economies. As highlighted by Batten (2018), it is essential to analyze the economic consequences of carbon emission reduction policies, not in isolation but as part of a broader policy framework aimed at fostering economic growth.

This paper contributes to the existing literature exploring the relationships among technology, fiscal policy, and the macroeconomic and welfare consequences associated with the energy transition. To this end, we assess the transition towards a low-emissions economy using an environmental Dynamic General Equilibrium (eDGE) model. These models are specifically designed to capture the relationship between climate change and economic growth, drawing inspiration from earlier works such as Nordhaus (1991) (see Annicchiarico et al., 2021, and Annicchiarico et al., 2022, for two recent surveys).

Our model provides a framework for assessing the macroeconomic and welfare implications of different carbon mitigation strategies, highlighting the importance of balancing the short and long-term effects of incentives for investment and innovation in green technologies, taxes, and other policies aimed at reducing carbon emissions. In our model, the production of goods and services utilizes energy from either environmentally friendly renewable ("green") technologies or fossil fuels that generate CO2 emissions, commonly known as "dirty" or "brown" technologies. Energy producers employ specific capital to generate this input, resulting in CO2 emissions with different intensities depending on the use of these technologies.

By considering the more realistic case of emissions being dependent on a particular type of energy production, we enrich the relationship between carbon generation and aggregate output, allowing emissions reductions to be achieved not only by reducing output but also by changing the combination of inputs. In addition, the model takes into account the transformative potential of technological advances to reduce the prevalence of brown energy and improve the overall efficiency of the energy mix. This aspect of our research aligns with the works of Fried (2018) and Nakicenovic and Swart (2000). Furthermore, we acknowledge the pivotal role that investment in green energy capital plays as a key driver of this transition (see Jackson and Jackson, 2021).

As a numerical illustration and an example of our model’s application, we calibrate it with data from the Spanish economy, which ranks among the four largest countries in the EU. Specifically, we set an emission reduction target consistent with the Paris Agreement and analyze the welfare and macroeconomic effects of different strategies, such as increasing the domestic price of fossil fuels, implementing a subsidy on green investment financed by lump-sum taxes, levying taxes on emissions rebated to households, and using emissions taxes to finance green investment. These policies are strategically designed to mitigate emissions and incentivize the widespread adoption of green technologies. In this context, our study aligns with recent literature, including Marron and Toder (2014), the International Monetary Fund (2019), Semmler et al. (2021), and Delgado-Téllez et al. (2022).

Our main findings can be summarized as follows. Front-loaded environmental policies intended to mitigate carbon emissions may prove effective in achieving the intermediate 2030 Green Deal target, although they are insufficient to meet the 2050 Net Zero Emissions (NZE) target without a substantial increase in welfare costs. Alternatively, green investment subsidies require more time to deliver a significant reduction in emissions compared to other policies. Contrary to other mitigation policies, subsidizing green investment leads to an increase in energy intensity per unit of output due to the upsurge in green energy production. A one-time, front-loaded increase of nearly 60% in fossil fuel prices to discourage their use achieves over 80% of the NZE target, although increasing fossil fuel prices incurs the highest welfare costs in both the transition to 2050 and in the long run. Emission taxes emerge as the most preferable policy in terms of welfare during the transition to 2050, although green investment subsidies yield substantial welfare gains in the very long run, even without a globally coordinated emission reduction policy. Reallocating revenues from carbon taxes toward green investment subsidies yields the most balanced welfare effect between the short and long run. To achieve the NZE target by 2050, we need a linear increase in emissions taxes to reach a level of 227 e per ton of carbon by 2050 and stabilize afterwards. The average welfare loss resulting from this policy stands at a manageable -0.44% in terms of equivalent consumption from 2019 to 2050, however, it rises to -19.11% in the very long run, covering the period from 2019 to 2200.

In the absence of an internationally coordinated strategy, the temperature is projected to increase by 1.8 degrees Celsius above pre-industrial levels by 2050 and by over 3.5 degrees Celsius by 2200. In a coordinated scenario the temperature remains below 1.5 degrees Celsius by 2050 and reverts to almost pre-industrial levels by 2200. The positive impact on welfare of a coordinated policy becomes evident, although it takes several decades to materialize. In the very long run, average welfare may increase by over 50% in terms of consumption between 2019 and 2200, as the world economy avoids the damages of climate change.

This paper is structured as follows: In Section 2, we provide a comprehensive overview of the model, emphasizing the role played by green and brown sources of energy at various stages of demand and production. Section 3 delves into our approach to selecting model parameters, with particular attention given to those governing utility, the damage function, emissions function, and abatement costs function. Section 4 presents the simulation exercises. We start by building our base scenario consistent with some recent trends and with the model equations, from which we derive both optimistic and pessimistic scenarios. Subsequently, we perform a numerical assessment of the effects of different mitigation strategies on emissions, macroeconomic performance, and welfare. This section also includes a sensitivity analysis encompassing scenarios without technological progress or with globally coordinated policies. Finally, Section 5 presents the main conclusions.

2. The Model

The economy operates by producing goods and services through the utilization of labor, capital, and energy. The production process is organized across distinct levels. At the bottom level, energy producers employ specific capital to generate energy, resulting in varying CO2 emissions, contingent on the use of green or brown technologies. Brown energy producers also engage in the importation of fossil fuel commodities at international market prices, which can fluctuate or be influenced by tariffs or subsidies. Companies have the option to invest in emission reduction, which incurs additional costs, and emissions can be subjected to taxation. Technological advancements in fossil fuel utilization aid in the economy’s decarbonization efforts.

The subsequent level comprises energy suppliers, which procure both green and brown energy from producers, amalgamating them into a bundle sold to intermediate goods producers. The pricing of this energy bundle is contingent on the composition of energy sources. Progress in technology favoring green energy production plays a pivotal role in reducing carbon emissions.

At the intermediate non-energy production level, firms engage labor, capital, and energy from the energy bundle to manufacture a diverse range of goods under monopolistic competition. Each product variation faces a demand curve that slopes downward, while firms encounter costs related to price adjustments, resulting in price stickiness. Finally, at the topmost tier, firms aggregate various intermediate goods and market a standardized product for consumption, investment, and public spending. Technological advancements also influence overall productivity in final goods production.

Households contribute labor services, using their income to acquire consumption goods and invest in diverse capital goods. The government can enact mitigation strategies, such as subsidizing green investments, imposing tariffs on fossil fuel imports, or implementing emissions taxes. Government revenues can be redistributed to households through lump-sum transfers. Conversely, subsidies can be financed through lump-sum taxes levied on households.

Next, we provide an overview of our model and highlight the key decision problems faced by agents at each level of production. For a detailed account of the model equations, see Appendix A.

2..1 Households

The representative household in the model maximizes lifetime utility, which is determined by its consumption and working hours . Households earn labor and capital income; the latter comes from renting out different types of capital to firms at rental rates representing the rental rates for green, brow and intermediate production capital), holding government bonds . As the owners of all firms in the economy, they also receive profits , and respectively). After consuming and paying taxes (or receiving subsidies), households save their remaining income in government debt and invest in three types of productive capital: capital for producing intermediate goods , capital for producing green energy , and capital for producing brown energy , subject to quadratic capital adjustments costs. The government has the option of subsidizing households’ investment in green capital and collects a lump-sum tax (or pays a subsidy) every period to balance its budget ).

The representative household solves the following problem:

\[\max _ {\{c _ {t}, h _ {t}, i _ {t} ^ {y}, i _ {t} ^ {g}, i _ {t} ^ {b}, k _ {t} ^ {y}, k _ {t} ^ {g}, k _ {t} ^ {b}, b _ {t} \} _ {t = 0} ^ {\infty}} \mathbb {E} _ {0} \sum_ {t = 0} ^ {\infty} \beta^ {t} \left(\frac {c _ {t} ^ {1 - \sigma}}{1 - \sigma} - \kappa_ {L} \frac {h _ {t} ^ {1 + \varphi}}{1 + \varphi}\right)\tag{s.t}\]

(1)

\[\begin{array}{r} P _ {t} c _ {t} + P _ {t} i _ {t} ^ {y} + P _ {t} (1 - \tau_ {t} ^ {i g}) i _ {t} ^ {g} + P _ {t} i _ {t} ^ {b} + b _ {t} = \\ r _ {t} ^ {y} P _ {t} k _ {t - 1} ^ {y} + r _ {t} ^ {g} P _ {t} k _ {t - 1} ^ {g} + r _ {t} ^ {b} P _ {t} k _ {t - 1} ^ {b} \\ + r _ {t - 1} b _ {t - 1} + P _ {t} w _ {t} h _ {t} - P _ {t} \tau_ {t} ^ {h} \\ + P _ {t} \Gamma_ {t} ^ {y} + P _ {t} \Gamma_ {t} ^ {v g} + P _ {t} \Gamma_ {t} ^ {v b} \end{array}\tag{2}\]

\[k _ {t} ^ {y} = (1 - \delta_ {y}) k _ {t - 1} ^ {y} + \left[ 1 - \frac {\kappa_ {I} ^ {y}}{2} \left(\frac {i _ {t} ^ {y}}{i _ {t - 1} ^ {y}} - 1\right) ^ {2} \right] i _ {t} ^ {y}\tag{3}\]

\[k _ {t} ^ {g} = (1 - \delta_ {g}) k _ {t - 1} ^ {g} + \left[ 1 - \frac {\kappa_ {I} ^ {g}}{2} \left(\frac {i _ {t} ^ {g}}{i _ {t - 1} ^ {g}} - 1\right) ^ {2} \right] i _ {t} ^ {g}\tag{4}\]

\[k _ {t} ^ {b} = (1 - \delta_ {b}) k _ {t - 1} ^ {b} + \left[ 1 - \frac {\kappa_ {I} ^ {b}}{2} \left(\frac {i _ {t} ^ {b}}{i _ {t - 1} ^ {b}} - 1\right) ^ {2} \right] i _ {t} ^ {b}\tag{5}\]

where (the numeraire) represents the price of the final good, so all relative prices are referred to this numeraire, and is a parameter that controls for the intensity of the capital adjustment costs.

2..2 Energy producers

Green and brown energies are produced by firms in competitive markets with specific capital using the following technology:

\[v _ {t} ^ {g} = \varsigma_ {t} ^ {g} \left(k _ {t - 1} ^ {g}\right) ^ {\alpha^ {g}}\tag{6}\]

\[v _ {t} ^ {b} = \left(k _ {t - 1} ^ {b}\right) ^ {\alpha^ {b}} \left(m _ {t} ^ {b}\right) ^ {(1 - \alpha^ {b})}\tag{7}\]

where refers to an energy commodity produced abroad , oil or gas) that is combined with capital and represents the efficiency of green energy production, with higher efficiency indicating that less capital is required to produce one unit of energy. This variable can change exogenously over time, and an increase in can be interpreted as a green-biased technological change (i.e. we normalize to one the efficiency in the production of brown energy). More specifically, we assume that evolves exogenously over time according to the equation:

s.t

\[\varsigma_ {t} ^ {g} = \varsigma_ {0} ^ {g} (1 + g _ {\varsigma^ {g}}) ^ {t}\tag{8}\]

Here, represents the initial calibrated value of the green energy production efficiency, and denotes its annual growth rate, reflecting exogenous technological progress biased towards green energy production.

We assume that period carbon emissions are an increasing function of the amount of brown energy produced,

\[e _ {t} ^ {b} = \left(1 - \mu_ {t} ^ {b}\right) \gamma_ {1 t} ^ {b} \left(v _ {t} ^ {b}\right) ^ {1 - \gamma_ {2} ^ {b}}\tag{9}\]

where and control for the curvature and the marginal effect on emissions to brown energy production, respectively. A lower value of can be interpreted as an improvement in the efficiency of emissions by brown energy producers, which contributes to the decarbonization of the economy. We assume the presence of an exogenous rate of technological progress, denoted as , which influences the dynamics of emission efficiency. This relationship is described by the following equation:

\[\gamma_ {1 t} ^ {b} = \gamma_ {1 0} ^ {b} \left(1 - g _ {\gamma_ {1} ^ {b}}\right) ^ {t}\tag{10}\]

where is the calibrated value of this variable corresponding to the benchmark period.

By considering the more realistic case of making emissions dependent on a particular type of energy production, we curb the close relationship between carbon generation and aggregate output and allow emissions reductions to be achieved not only by reducing output but also by changing inputs.

Firms pay a tax per unit of emissions. The existence of a cost for emitting carbon into the atmosphere creates an incentive to abate emissions. The variable is the fraction of emissions abated by the brown energy producers. We assume that the abatement costs of brown energy producers, , are proportional to energy production,

\[z _ {t} ^ {b} = \theta_ {1} ^ {b} (\mu_ {t} ^ {b}) ^ {\theta_ {2} ^ {b}} v _ {t} ^ {b}\tag{11}\]

The optimization problem faced by the green energy production firms sector can be written as follows:

\[\begin{array}{r l} \max _ {k _ {t - 1} ^ {g}} & P _ {t} ^ {v g} v _ {t} ^ {g} - P _ {t} r _ {t} ^ {g} k _ {t - 1} ^ {g} \\ & v _ {t} ^ {g} = \varsigma_ {t} ^ {g} \left(k _ {t - 1} ^ {g}\right) ^ {\alpha^ {g}} \end{array}\]

Similarly, brown energy producers maximize profits subject to the production and emissions technologies.

\[\max _ {k _ {t - 1} ^ {b}, m _ {t} ^ {b}, \mu_ {t} ^ {b}} P _ {t} ^ {v ^ {b}} v _ {t} ^ {b} - P _ {t} r _ {t} ^ {b} k _ {t - 1} ^ {b} - (1 + \tau_ {t} ^ {m}) P _ {t} ^ {* m ^ {b}} m _ {t} ^ {b} - P _ {t} \tau_ {t} ^ {e} e _ {t} ^ {b} - P _ {t} \theta_ {1} ^ {b} (\mu_ {t} ^ {b}) ^ {\theta_ {2} ^ {b}} v _ {t} ^ {b}\tag{s.t}\]

\[v _ {t} ^ {b} = \left(k _ {t - 1} ^ {b}\right) ^ {\alpha^ {b}} \left(m _ {t} ^ {b}\right) ^ {(1 - \alpha^ {b})}\]

\[e _ {t} ^ {b} = \left(1 - \mu_ {t} ^ {b}\right) \gamma_ {1 t} ^ {b} \left(v _ {t} ^ {b}\right) ^ {1 - \gamma_ {2} ^ {b}}\]

where is the price of type-l energy, is the exogenous price of the imported energy commodity, and is an exogenous price shifter, essentially a change in the international market price of the commodity, or a tariff/subsidy applied to this commodity by the government.

From the above problem optimal decisions about energy production, and emissions are derived. Emissions abatement is guided by the following expression

\[\mu_ {t} ^ {b} = \left[ \frac {\tau_ {t} ^ {e} \gamma_ {1 t} ^ {b}}{\theta_ {1} ^ {b} \theta_ {2} ^ {b}} (v _ {t} ^ {b}) ^ {- \gamma_ {2} ^ {b}} \right] ^ {\frac {1}{\theta_ {2} ^ {b} - 1}}\tag{12}\]

Without internalizing some of the environmental costs of emissions, there are no incentives to reduce emissions, resulting in zero abatements when taxes on emissions (or the price of carbon emissions permits) are zero.

Profits in both sectors are given by

\[\Gamma_ {t} ^ {v ^ {g}} = (1 - \alpha^ {g}) p _ {t} ^ {v ^ {g}} v _ {t} ^ {g}\tag{13}\]

\[\Gamma_ {t} ^ {v ^ {b}} = - \tau_ {t} ^ {e} \gamma_ {2} ^ {b} e _ {t} ^ {b}\tag{14}\]

2..3 Energy suppliers

Energy suppliers package a mix of green and brown energy that they sell to intermediate goods producers at a price of . The packaging technology is given by,

\[v _ {t} ^ {y} = A _ {t} ^ {x} \left[ \theta^ {g} \left(v _ {t} ^ {g}\right) ^ {\frac {\sigma^ {x} - 1}{\sigma^ {x}}} + (1 - \theta^ {g}) \left(v _ {t} ^ {b}\right) ^ {\frac {\sigma^ {x} - 1}{\sigma^ {x}}} \right] ^ {\frac {\sigma^ {x}}{\sigma^ {x} - 1}}\tag{15}\]

where is the total energy supplied, and is the elasticity of substitution between green and brown energy.

Using equations (6) and , the supplied energy package for intermediate production can be written in terms of capital as,

\[v _ {t} ^ {y} = A _ {t} ^ {x} \left[ \theta^ {g} \left(\varsigma_ {t} ^ {g} f ^ {g} (k _ {t} ^ {g})\right) ^ {\frac {\sigma^ {x} - 1}{\sigma^ {x}}} + (1 - \theta^ {g}) \left(f ^ {b} (k _ {t} ^ {b}, m _ {t} ^ {b})\right) ^ {\frac {\sigma^ {x} - 1}{\sigma^ {x}}} \right] ^ {\frac {\sigma^ {x}}{\sigma^ {x} - 1}}\tag{16}\]

Energy packers solve the following optimization problem

\[\min _ {v _ {t} ^ {g}, v _ {t} ^ {b}} p _ {t} ^ {v ^ {g}} v _ {t} ^ {g} + p _ {t} ^ {v ^ {b}} v _ {t} ^ {b}\]

s.t.

\[v _ {t} ^ {y} = A _ {t} ^ {x} \left[ \theta^ {g} \left(v _ {t} ^ {g}\right) ^ {\frac {\sigma^ {x} - 1}{\sigma^ {x}}} + (1 - \theta^ {g}) \left(v _ {t} ^ {b}\right) ^ {\frac {\sigma^ {x} - 1}{\sigma^ {x}}} \right] ^ {\frac {\sigma^ {x}}{\sigma^ {x} - 1}}\tag{17}\]

Under perfect competition, profits in this sector are zero, so the unit cost derived from this problem, , is equal to , the price of one unit of energy mix

\[p _ {t} ^ {v ^ {y}} = \left[ (\theta^ {g}) ^ {\sigma^ {x}} \left(p _ {t} ^ {v ^ {g}}\right) ^ {1 - \sigma^ {x}} + (1 - \theta^ {g}) ^ {\sigma^ {x}} \left(p _ {t} ^ {v ^ {b}}\right) ^ {1 - \sigma^ {x}} \right] ^ {\frac {1}{1 - \sigma^ {x}}}\tag{18}\]

2..3.1 Intermediate non-energy producers

A large number of firms operate under monopolistic competition to produce a differentiated good using capital , labor ), and energy ),

\[y _ {t} (i) = A _ {t} ^ {y} (i) k _ {t - 1} ^ {y} (i) ^ {\alpha^ {y}} h _ {t} (i) ^ {\beta^ {y}} v _ {t} ^ {y} (i) ^ {1 - \alpha^ {y} - \beta^ {y}}\tag{19}\]

where is total factor productivity at the intermediate good firm level. ¹

Firms face a downward-sloping demand curve

\[y _ {t} (i) = \left(\frac {P _ {t} (i)}{P _ {t}}\right) ^ {- \sigma^ {r}} y _ {t}\tag{20}\]

where is aggregate production. They pay a quadratic adjustment cost à la Rotemberg (1982) for changing prices.

¹ Fabra, Lacuesta and Souza (2022) use a similar function for aggregate production with a single energy input.

\[A C _ {t} (i) = \frac {\kappa_ {p}}{2} \left(\frac {P _ {t} (i)}{P _ {t - 1} (i)} - \bar {\pi}\right) ^ {2} P _ {t} y _ {t}\tag{21}\]

The optimization problem for intermediate firms can be written as,

\[\begin{array}{l} \max _ {P _ {t} (i), h _ {t} (i), k _ {t - 1} ^ {y} (i), v _ {t} ^ {y} (i)} \mathbb {E} _ {0} \{\sum_ {t = 0} ^ {\infty} \beta^ {t} \frac {\lambda_ {t}}{\lambda_ {0}} [ \left(\frac {P _ {t} (i)}{P _ {t}}\right) y _ {t} (i) - w _ {t} h _ {t} (i) - r _ {t} ^ {y} k _ {t - 1} ^ {y} (i) \\ - p _ {t} ^ {v ^ {y}} v _ {t} ^ {y} (i) - \frac {\kappa_ {p}}{2} \left(\frac {P _ {t} (i)}{P _ {t - 1} (i)} - \bar {\pi}\right) ^ {2} y _ {t} ] \} \qquad s. t \end{array}\]

\[y _ {t} (i) = \left(\frac {P _ {t} (i)}{P _ {t}}\right) ^ {- \sigma^ {r}} y _ {t}\]

\[y _ {t} (i) = A _ {t} ^ {y} (i) k _ {t} ^ {y} (i) ^ {\alpha^ {y}} h _ {t} (i) ^ {\beta^ {y}} v _ {t} ^ {y} (i) ^ {1 - \alpha^ {y} - \beta^ {y}}\]

We assume a symmetric equilibrium so that firms choose the same price, inputs, and output. Aggregate profits for the intermediate goods producers are:

\[\Gamma_ {t} ^ {y} = y _ {t} \left(1 - m c _ {t} - \frac {\kappa_ {p}}{2} (\pi_ {t} - \bar {\pi}) ^ {2}\right)\tag{22}\]

2..3.2 Final-good firms

The representative final-good firm produces an aggregate good from different varieties using a CES aggregator,

\[y _ {t} = \left[ \int_ {a} ^ {b} y _ {t} (i) ^ {\frac {\sigma^ {r} - 1}{\sigma^ {r}}} d i \right] ^ {\frac {\sigma^ {r}}{\sigma^ {r} - 1}}\tag{23}\]

where represents intermediate goods produced under monopolistic competition.

The optimization problem is,

\[\max _ {y _ {t} (i)} P _ {t} y _ {t} - \int_ {a} ^ {b} P _ {t} (i) y _ {t} (i) d i\tag{24}\]

and profits at this level of production are zero.

2..4 Environmental and economic damage

Emissions feed the atmospheric carbon stock, ,

\[x _ {t} = \eta_ {t} x _ {t - 1} + e _ {t} + e _ {t} ^ {r o w}\tag{25}\]

where are aggregate domestic emissions (brown energy production emissions) and are the (exogenous) emissions of the rest of the world. represents kilotonnes (kt) of atmospheric carbon (GtC) and represents the rate of carbon absorption.

The function representing the impact of the atmospheric carbon stock on total factor productivity is as follows: ²

\[A _ {t} ^ {y} = [ 1 - d _ {0} x _ {t} ^ {d _ {1}} ] \widetilde {A} _ {t} ^ {y}\tag{26}\]

The economic cost of CO2 accumulation is convex, as in Dietz and Stern (2015). Variable is the zero-carbon TFP that evolves exogenously due to exogenous technological progress, represented by . The evolution of is described by the equation:

\[\widetilde {A} _ {t} ^ {y} = \widetilde {A} _ {0} ^ {y} \left(1 + g _ {\widetilde {A}}\right) ^ {t}\tag{27}\]

Here, represents the initial calibrated value of the zero-carbon TFP for the benchmark period.

2..5 The government and the central bank

The central bank follows a standard Taylor’s rule,

\[\frac {r _ {t}}{r} = \left(\frac {r _ {t - 1}}{r}\right) ^ {\rho_ {r}} \left[ \left(\frac {\pi_ {t}}{\pi}\right) ^ {\phi_ {\pi}} \left(\frac {y _ {t}}{y}\right) ^ {\phi_ {y}} \right]\tag{28}\]

where is the policy rate, and and y correspond to the steady state inflation rate and output.

The government finances public spending and green investment subsidies by levying lump sum taxes on households , tariffs on imported energy commodity , and emission taxes on energy-producing firms . So, the budget constrain can be written as,

\[g _ {t} + \tau_ {t} ^ {i g} i _ {t} ^ {g} = \tau_ {t} ^ {h} + \tau_ {t} ^ {m} p _ {t} ^ {* m ^ {b}} m _ {t} ^ {b} + \tau_ {t} ^ {e} e _ {t}\tag{29}\]

Factors contributing to reducing carbon emissions can be divided, as in Burda and

² While the economy’s emissions contribute only to a fraction of global emissions, implying a relatively minor impact on the carbon stock and economic damage from environmental measures, we include this damage function for comprehensive analysis. It also enables us to make comparisons later on regarding emissions reduction scenarios in a coordinated global context, where the rest of the world achieves similar environmental outcomes as our benchmark economy.

Zessner-Spitzenberg (2022), into two blocks. The first block has to do directly with technology improvements in the green energy production sector (changes in or the brown technology of carbon emissions (changes in . The second block implies different instruments of fiscal policy, such as green energy investment subsidies, a tariff on fuel commodities, or a tax on carbon emissions.

2..6 Market clearing

Using the households’ and government budget constraints, the definition of profits at each production level, and some first-order conditions, and assuming a balanced government budget every period , we can derive the expression for aggregate output as follows:

\[y _ {t} = c _ {t} + i _ {t} ^ {y} + i _ {t} ^ {g} + i _ {t} ^ {b} + g _ {t} + p _ {t} ^ {* m ^ {b}} m _ {t} ^ {b} + \theta_ {1} ^ {b} (\mu_ {t} ^ {b}) ^ {\theta_ {2} ^ {b}} v _ {t} ^ {b} + \frac {\kappa_ {p}}{2} (\pi_ {t} - \bar {\pi}) ^ {2} y _ {t}\tag{30}\]

3. Calibration

We calibrate the model annually to replicate some energy and environmental ratios of the Spanish economy in 2010 which is taken as an example in our simulations. In our calibration, we establish a clear distinction between green and brown energy. Specifically, green energy encompasses all forms of energy that do not produce carbon emissions, such as hydraulic, nuclear, and renewable energy. The remaining energy sources, including coalfired energy, combined cycle energy, and cogeneration, are considered dirty or brown. Emissions and air pollution are measured in kilotonnes of carbon, while energy is measured in kilotonnes of oil equivalent. We normalize aggregate GDP to 1 million euros, which allows us to interpret most variables in terms of million euros of production.

Next, we provide a comprehensive overview of the strategy employed to calibrate the parameters in the model. Detailed information on the values used in the model and the pertinent macroeconomic ratios that align with the static solution of the model can be found in Appendix B.

3..1 Parameters from the literature

We adopt a value for the elasticity of substitution between green and brown energy, 3.94, based on Table 2 in Stockl and Zerrahn (2020).³ This elasticity is higher than those estimated by Pageorgiou et al. (2017), which range between 2 and 3.

³ If we consider that the same production services can be obtained from both green and brown energy inputs, we can expect the elasticity of substitution to be very high. However, there are several factors that prevent this elasticity of substitution from being infinite, as discussed by Pageorgiou et al. (2017). Firstly,

For the convex capital adjustment cost function, , we adopt the parameter from Annicchiarico and di Dio (2015). Given the characteristics of energy capital, we assume that the adjustment costs for the capital used in energy production are 1/3 higher than the average adjustment cost for the capital used in the production of goods, leading to . We derive our choice for the value representing energy expenditure as a share of GDP from the Annual Energy Review of the US Energy Information Administration (2022). Based on this report, we set 4

3..2 Parameters from empirical evidence and model equations

We determine the value of based on two shares. First, we consider the share of total energy used for energy production, which was reported as 28% according to Eurostat (2022).⁵ Secondly, according to Red Eléctrica de España (2019),⁶ brown energy accounted for 47% of the total installed energy in 2010. We aim for to be close to the ratio between these two shares. Consequently, we set

We assume that the output-to-capital elasticity in green energy production is the same as in dirty energy production, leading us to set . To determine the depreciation rate of capital used in the production of goods , we refer to the annual accounting depreciation rate applicable in Spain for various types of capital, such as transport, machinery, and non-residential buildings, as documented by Tax Partners (2015). We calculate the weighted average of depreciation rates by considering the proportions of different capital types, relying on Prados de la Escosura (2020) for the required weights. Using the static version of the model equations, we calibrate two additional depreciation rates. This calibration allows us to simultaneously align the energy intensity per unit of GDP and the ratio between the prices of green and brown energy in 2010. As a result, we obtain calibrated values of and . The findings regarding depreciation rates indicate that energy infrastructure generally has a longer useful life compared to standard capital used directly in the production of goods, with capital for dirty energy production having the longest lifespan.

the issue of storage remains a challenge for renewable energy sources, leading to a mismatch between supply and demand during peak periods. Secondly, as renewable energy expands, the marginal productivity decreases, as new installations may be located in less optimal areas for energy generation. Lastly, certain industries still rely on fossil fuels as an energy source, such as cement, steel, ceramics, and transportation.

⁴ In the Energy Overview category, specifically in Section 1.5, the energy expenditure as a share of GDP was reported as 8.1%. Our choice to reduce this percentage for Spain is based on a significantly lower intensity of energy use in Spain relative to the U.S. (9.0% in Spain and 15.0% in the U.S., according to OECD, 2015) Eurostat: Energy Statistics - An Overview 5 Eurostat: Energy Statistics - An Overview

⁶ El Sistema Eléctrico Español. Informe 2019

The time discount rate, is calibrated to ensure that the static version of the model reproduces an annual real interest rate of 4%. This calibration aligns with the recommendation by Nordhaus (2007) to replicate realistic rates of capital return.

To match the ratio of installed green energy to brown energy, based on data from Red Eléctrica de España (2019), we calibrate the distribution parameter in the energy CES composite of goods as . We consider a non-policy benchmark scenario for the year 2010, which implies setting (no taxes or subsidies).⁷ We calibrate to ensure that the static model solution is consistent with the capital-tooutput ratio for goods production.

Given the long-run nature of all the simulations, we set the price stickiness parameter, to virtually 0, enabling full price flexibility. However, the model retains the ability to conduct short-run analysis by modifying this assumption and allowing the Taylor rule to be fully operational in a world of price rigidity.

3..3 Utility function

We set the risk aversion for the utility of consumption, as , consistent with the estimations of the intertemporal elasticity of substitution for consumption in the Spanish economy from Cutanda, Labeaga, and Sanchis-Llopis (2020). The risk aversion for the utility of leisure, denoted as is established at , derived from the average of intertemporal elasticities of substitution for leisure in Spain, as documented in Cutanda and Sanchis Llopis (2022). The parameter which determines the weight of leisure relative to consumption in the utility function, is selected to achieve a target of one-third for working hours in 2010, considering that the total time is normalized to 1.

3..4 Atmospheric carbon accumulation

Atmospheric carbon is driven by total domestic emissions e and exogenous emissions from the rest of the world

\[x _ {t} = \eta x _ {t - 1} + e _ {t} + e ^ {r o w}\tag{31}\]

Here, represents the yearly carbon decay rate, which can be calibrated based on the half-life of atmospheric carbon dioxide. The literature provides varying estimates for this parameter, making it challenging to determine an exact value. Moore and Braswell (1994) estimate the half-life of atmospheric CO2 to range between 19 and 92 years under different assumptions. Heutel (2012) assumes a half-life of 83 years, corresponding to a quarterly parameter η of 0.9979. Other evidence, supported by the NASA indicates that a fraction of fossil carbon dioxide can persist in the atmosphere for hundreds to thousands of years (Archer and Brokvin, 2008; and Archer et al., 2009).

⁷ Environmental taxes still nowadays represent only a modest part of total government revenues and affects a negligible part of emissions (see Delgado-Téllez et al., 2022).

Figure 1: Carbon stock trajectory for constant global emissions at the 2010 global level

Our approach assumes that terrestrial ecosystems absorbed around 30% of global emissions in the long run, a figure consistent with observations over the past 50 years (Brienen et al., 2020). Hence, we set

In 2010, yearly emissions in Spain amounted to 79,381 kt of carbon (or 0.0741 kt per million euros of production) ⁸. This accounted for 0.79% of world emissions. Employing Equation (31), we project the trajectory of carbon stock assuming emissions persist at the 2010 global level and without economic intervention, depicted in Figure 1. The calculated value of η at 0.9964 implies an average atmospheric carbon half-life of approximately 190 years .

⁸ Data from CO2 emissions in IEA-EDGAR CO2 (2022) transformed to carbon emissions.

Figure 2: Economic cost (% of TFP) as a function of atmospheric carbon

3..5 The damage function

We adjust an exponential damage function, , to approximate the laissez-faire damage trajectory as depicted in Figure 6 by Golosov et al (2014b).⁹ The calibrated parameters result in and

Figure 2 represents how this function varies with the stock of atmospheric carbon and specifically marks the values corresponding to the 2010 benchmark year. Atmospheric carbon stock of approximately 776 kt per million GDP corresponds to a loss of TFP of 0.5%. Increasing atmospheric carbon mass by 50% leads to a TFP loss of 1.7%.

⁹ Some researchers prefer utilizing a quadratic damage function. For instance, Heutel (2012) calibrates coefficients within a quadratic damage function based on the DICE-2007 model by Nordhaus (2008). Our setting implies slightly higher damage for a likely range of values for x_t.

3..6 Emissions

According to Heutel (2012) and Annicchiarico and Di Dio (2015), aggregate emissions are an increasing and (possibly) concave function of GDP:

\[e _ {t} ^ {b} = (1 - \mu_ {t} ^ {b}) \gamma_ {1} y _ {t} ^ {1 - \gamma_ {2}}\]

Here, represents the fraction of emissions optimally abated by the economy, which is zero in the benchmark scenario of no carbon taxation. In our model, we link aggregate emissions to brown energy, resulting in the equation:

\[e _ {t} ^ {b} = \left(1 - \mu_ {t} ^ {b}\right) \gamma_ {1} ^ {b} \left(v _ {t} ^ {b}\right) ^ {1 - \gamma_ {2} ^ {b}}\]

\[\gamma_ {1} ^ {b} = \frac {e _ {2 0 1 0} ^ {b}}{\left(v _ {2 0 1 0} ^ {b}\right) ^ {1 - \gamma_ {2} ^ {b}}}\tag{32}\]

To ensure consistency with the observed emissions, zero abatement, and brown energy production in 2010, should satisfy the equation:

Figure 3: Emissions as a function of dirty energy production

Heutel (2012) takes and . However, Annicchiarico and Di Dio (2015) assume that . We also adopt , and obtain from equation (32), because it is consistent with the empirical evidence for the Spanish economy from 1985 to 2005 when the contribution of renewable energy to the production of primary energy was below 5%. During this period, the ratio of CO2 emissions to GDP was relatively constant and the contribution of oil, gas, and coal was also steady, around 80% (the remaining 15% obtained from nuclear and hydroelectric sources), suggesting that the elasticity of emissions to dirty energy production was close to 1.0,

Sen and Vollebergh (2018) estimate that an increase of 1 e in energy taxes imposed on each tonne of CO2 leads to a long-run reduction in emissions from energy consumption by 0.73%. However, Metcalf (2019) obtains a larger 10-year elasticity of emissions to carbon taxes (-1.11). We check with our model that increasing the price of the commodity used to produce brown energy by 1% would result in a long-term emission drop of 0.97%. The relationship between emissions and normalized brown energy output is illustrated in Figure 3.

3..7 Abatement costs

The ratio represents the cost, relative to total output, of abating a fraction of emissions. Heutel (2012) assumes a parameter elasticity of the cost of abatement, based on Nordhaus (2008). We adopt the same elasticity for our equation (11). Regarding the scale coefficient, Heutel (2012) sets , indicating that eliminating emissions would cost 5.6% of GDP, but this cost is allowed to decrease over time to 3.92% within 50 years. However, Annicchiarico and Di Dio (2015) assume . To reconcile these differences, we choose such that it results in a cost of 12% of GDP for , which is the average between Heutel (2012) and Annicchiarico and Di Dio (2015). This yields a value of in our model because we write this cost in terms of brown energy production.

Figure 4 illustrates the relationship between the cost and the percentage of abated emissions for the baseline level of dirty energy production. Note that due to the uncertainty surrounding these and other energy and environmental parameters, we conduct a sensitivity analysis at the end of the next section, where we significantly vary their values.

4. Results

We use the model to evaluate the economic consequences of implementing various mitigation policies to meet the 2050 emission targets in Spain. First, we establish a baseline scenario for Spanish emissions between 2010 and 2050, assuming no policy intervention and maintaining constant annual carbon emissions worldwide at their 2010 levels. To achieve this, we calibrate the growth rate of specific exogenous technological variables by referencing observed changes in Spain’s GDP, carbon emissions, and the proportion of green to brown energy production from 2010 to 2019.

4..1 Baseline scenario: 2010-2019

Between 2010 and 2019, Spain’s real GDP increased by 10.6%, while carbon emissions decreased by 11.8% and the ratio of green energy production to brown energy increased by 14.5%. We attribute these changes to different types of technological progress, specifically, technological progress that increases total factor productivity , technological progress that reduces emissions per unit of energy production , and technological progress biased towards green energy production . It should be noted that this approach provides an upper-bound estimate of the potential impact of technological progress on decarbonization during the studied period. This is because we do not account for other regulatory or fiscal mitigation policies implemented between 2010 and 2019.¹⁰

Figure 4: Abatement costs as a function of the abatement share of emissions

To calibrate the composition of the three sources of technical progress that best account for these observed changes, we introduce unanticipated series for , and over a 10-period span from 2010 to 2019. Each series has a different constant growth rate (technology progress), and these growth rates are calibrated such that when the three unanticipated series, starting from their initial calibrated values and are included together in the model, the dynamic solution matches the observed global rates of GDP growth, carbon emissions reduction, and the relative increase in green energy production between 2010 and 2019.

The results are presented in Table 1. The observed increase in GDP, the decrease in emissions, and the increase in the ratio of green to brown energy production during the period are consistent with an annual growth rate of 1.21% for TFP, 1.79% for green energy bias technology, and 1.68% for emissions efficiency. Notably, the technological progress that increases the efficiency of emissions makes the largest individual contribution to the decline in emissions. However, technological progress that increases TFP increases emissions at a rate of 0.69% per year.

¹⁰ See footnote 7.

Table 1: Technology growth, individual contribution to emissions reduction, and matched growth rates (all in annual %). Source: National Institute of Statistics (Spain), Crippa et al (2022), IEA-EDGAR (2022) and our own analysis.

Figure 5 provides an overview of how the model captures the decline in emissions when considering the three types of technological progress. Taking into account only the evolution of the TFP would lead to an increase in carbon emissions. This highlights the relevance of green technology and emissions efficiency in the process of decarbonization.

4..2 Baseline scenario: 2019-2200

We utilize the calibrated growth rates of technological progress from Table 1 as annual inputs for simulating the model again. This enables us to project the dynamic trajectory of a vector of endogenous variables from 2019 to 2200, referred to as the baseline path,

Figure 6a visually depicts the emission trajectory from 2019 to 2050 under the baseline scenario. It also presents two alternative scenarios considering varied paths for technological progress. In the optimistic scenario, we enhance the growth rates of exogenous green-biased technological progress and emissions efficiency by one-third, while keeping the total factor productivity (TFP) growth rate unchanged. Conversely, in the pessimistic scenario, we reduce these growth rates by one-third.

These definitions of optimistic and pessimistic scenarios significantly impact the evolution of emissions. Furthermore, it is evident that the decline in emissions loses momentum over time.

Figure 5: Observed and projected evolution of emissions, comparing the actual trend since 2010 to a model scenario with TFP growth and decarbonization. Source: IEA-EDGAR (2022) and own analysis Table 2: Required emissions reduction in 2050 to achieve the emissions target (percentage decrease with respect to 2019)

This projection of emissions goes hand in hand with the corresponding projections of macroeconomic, energy, and environmental variables in the model. Figure 6b displays the evolution of GDP in the three scenarios considered. In the baseline scenario, GDP exhibits an average growth rate of 1.3%. However, the different technological scenarios of environmental technology have a relatively minor effect on economic performance¹¹. Figure 6c highlights the progressive increase in the ratio of green to brown energy production driven by technological advancements. By 2050, this ratio is projected to increase to 1.9 under the baseline scenario.

¹¹ Remember that our study focuses on the internal response within Spanish emissions while keeping emissions in the rest of the world constant. An examination of a coordinated strategy, where emissions in the rest of the world change proportionally to those in Spain, is detailed in Section 4..4.

(a) Projected carbon emissions (kt)

(b) Projected GDP

(c) Projected ratio of green to brown energy Figure 6: Baseline, optimistic and pessimistic scenarios 2019-2050

To set the emissions target we take into account that during decades natural carbon sinks have captured about 30% of global emissions, coinciding with most of the estimates.¹² Extrapolating to Spain, we assume that reducing overall emissions by about 70% of the 2019 emissions is required to achieve the Paris Agreement’s goal of net-zero greenhouse gas emissions by 2050. Taking into account the Spanish carbon emissions in 2019 under the baseline scenario, we set an emission target of 20,997 kt of carbon.

Table 2 presents the percentage reduction in emissions from 2019 to 2050 attributed solely to the expected behavior of the technology in each of the three scenarios. It also includes the additional effort required, beyond the projected 2050 values for technology, to meet the emission reduction target. In the baseline scenario, the anticipated technological advances between 2019 and 2050 are projected to achieve a reduction of 32.1% in emissions compared to 2019 levels. This represents a significant contribution to the overall target of 70% reduction. However, it leaves an additional 37.9% reduction to be achieved through mitigation policies, which will be examined in detail in the following sections. In the pessimistic scenario, a greater proportion (54.6%) of emissions reduction depends on mitigation policies, as expected technological advances in decarbonization alone are insufficient to offset emissions driven by economic growth.

4..3 Mitigation plans

The Paris Agreement calls upon each country to develop its post-2020 climate actions, referred to as Nationally Determined Contributions (NDCs). Meanwhile, within the European Union, the Fit-for-55 package proposes strategies to achieve ambitious climate objectives.

In this section, we delve into the economic implications of diverse mitigation strategies aimed at achieving a predetermined percentage reduction in emissions. To ensure a fair comparison of different plans and their economic impacts, we maintain consistency in the following manner: all examined plans, regardless of technological developments, strive for a long-term emissions reduction equal to the additional effort detailed in Table 2. In essence, we calculate the change in the policy instrument that, without considering technological changes, would result in the same steady-state alteration in emissions. It is important to note that this comparative strategy does not imply that the various policy mitigation plans scrutinized here will achieve the Net Zero Emissions (NZE) target by

¹² See Brienen et al. (2020)

2050 (refer to section 4..4 for further exploration of this aspect).

We assume that all mitigation strategies considered in this analysis are initially unanticipated, meaning they were not pre-planned or expected in advance. Consequently, there is no economic response to these strategies prior to their implementation. However, once enacted, these strategies are perceived by agents as being in place indefinitely. This conceptual framework for the plans aligns with ambitious European environmental objectives that require significant policy efforts, particularly front-loaded ones (see Delgado-T’ellez et 2022, and Emambakhsh et , 2023).¹³ Once we ascertain from the comparative strategy the magnitude of the unanticipated permanent change in the exogenous variable, we incorporate the sequence of unanticipated technology shocks into the model and simulate the path of endogenous variables to obtain the baseline plus policy scenario, denoted as

By comparing the expected evolution of relevant variables with and without the implementation of these plans, we assess both the transitional effects of the policy from 2019 to 2050 and its long-run effects by 2200. With this analysis, we aim to shed light on the potential economic implications of various mitigation strategies in bridging the emissions gap and achieving the objectives set forth in the Paris Agreement.

4..3.1 Increase in the price of imported commodity

Brown energy production relies on an imported fossil fuel commodity, represented by (such as oil or gas). The price of this commodity, , is determined in international markets and is considered exogenous in our model. Additionally, the government has the option to apply a tariff on imports of this commodity or impose a tax/subsidy on its use.

The first strategy we study is related to the price of the imported commodity used to produce energy. We assume that this price (relative to CPI) is pushed up, and the fiscal authority ensures that the relative price will stabilize at this level in the future. Depending on the international evolution of this price, the fiscal authority may need to impose taxes on the use of the commodity in some years and provide subsidies in others.

According to our findings, the price of the commodity (relative to the CPI) necessary to achieve ex ante the emissions target would sustainably increase by 58%. Figure 7a illustrates the resulting emissions reduction resulting from the fiscal strategy of raising and maintaining a high relative price for imported fuel commodities. Additionally, Figure 7b displays the trajectories of the ratio of brown to green energy production in the

¹³ For simulations, we utilize Dynare 5.4 and Dynare 6.0 running on Matlab R2019a.

Table 3: Macroeconomic average effects of various mitigation plans during the period 2019-2050, expressed as average percentage deviations from accumulated baseline paths, except for abatement which is represented as the percentage reduction of accumulated emissions

baseline and under this specific policy.

Table 3 presents the average effects during the period 2019-2050 relative to the baseline technology evolution. Consider and as the dynamic paths of a variable belonging to vectors and , respectively. The average relative effect is computed as follows:

\[\hat {x} _ {T} ^ {a v} = \frac {\sum_ {t = 2 0 1 9} ^ {T} x _ {t} ^ {b + p} - \sum_ {t = 2 0 1 9} ^ {T} x _ {t} ^ {b}}{\sum_ {t = 2 0 1 9} ^ {T} x _ {t} ^ {b}}\tag{33}\]

where

This strategy reduces brown energy production during the 2019-2050 period by roughly 30% on average, increases green energy production by more than and increases the cost of the energy mix by 13%. The total reduction in emissions over the period is 29%, while the cumulative loss of GDP is calculated to be about 1 percentage point. Although the 2030 intermediate objective, established under the European Green Deal, is anticipated to be significantly met¹⁴ (96%), the accomplishment towards the 2050 Net Zero Emissions (NZE) target stands at 82%.

Figure 8 shows the percentage deviations of a selection of variables from baseline every year from 2019 to 2100. The last subplot in the figure displays the welfare dynamics in terms of the percentage consumption required to compensate for the loss in utility. Specifically, it shows the (minus) percentage reduction in consumption that would leave households equally well-off before (baseline scenario) and after the change in the policy (baseline plus policy scenario), with a negative sign indicating a reduction in welfare. Except for a decrease in the welfare cost during the 2020s decade, the welfare cost progressively increases over time, projecting a potential loss of approximately 2.5% in terms of equivalent consumption by 2050.

¹⁴ Under the European Green Deal, Member States committed to reducing EU greenhouse gas emissions by 55% compared with 1990 levels by 2030.

(a) Carbon emissions. Baseline and increase in the price of imported fuels

(b) Brown to green energy production. Baseline and increase in the price of imported fuels. Figure 7: Increase in the price of fossil fuels

This strategy entails a significant substitution of brown energy for green energy, leading to a higher price for the energy mix. However, the macroeconomic impact is relatively modest. By 2050, it is projected that GDP will be 1.1% lower compared to the baseline scenario, and consumption is expected to decrease by 1.2%.

Figure 9 illustrates the comprehensive emissions trajectory until 2200. Carbon emissions persistently decrease over time, and by 2200, the economy is projected to be emissionsfree.

Table 4 compares average welfare changes relative to different technology progress scenarios for various mitigation plans in terms of equivalent consumption. More particularly, it shows

\[\bar {\omega} _ {T} ^ {s} = \sum_ {t = 2 0 1 9} ^ {T} \frac {\omega_ {t} ^ {s + p}}{T + 1 - 2 0 1 9} - \sum_ {t = 2 0 1 9} ^ {T} \frac {\omega_ {t} ^ {s}}{T + 1 - 2 0 1 9}\tag{34}\]

The variable stands for the welfare change at period t, measured as a percentage change in equivalent consumption with respect to the initial steady state, within technology scenario s (s = baseline, optimistic, pessimistic) and mitigation policy p. Correspondingly, signifies the welfare change in terms of percentage equivalent consumption relative to the initial steady state under technology scenario s. The period T can represent either the year 2050 or the very distant year 2200.

The table’s top section concerns the period from 2019 to 2050, offering insights into the transition welfare changes. The bottom part delineates the long-term projections spanning until 2200. Additionally, it details the scale of the policy instrument employed to achieve the emission target.

The results indicate a decline in welfare during the period 2019-2050 for the baseline scenario, with an average reduction of -1.6% in terms of equivalent consumption. In the long run, this reduction widens to about -14%. The long-term welfare costs reflect the implementation of the policy under the assumption of no climate actions by the rest of the world, coupled with the relatively modest influence of the Spanish economy on global emissions. Therefore, implementing the policy in isolation does not sufficiently mitigate the persistent costs linked to the ongoing increase in atmospheric carbon stock.¹⁵ In the pessimistic scenario, the projected 2019-2050 welfare loss is around -2.5%, while in the optimistic scenario, it is only about -0.9%. In the optimistic scenario, the commodity price would increase by only 31%, while in the pessimistic scenario, the increase would exceed 100%. These findings highlight the significant influence of decarbonization technologies on the overall cost of the mitigation policies.

Figure 8: Dynamic macroeconomic effects of a permanent unanticipated increase in the commodity prices (percentage deviations with respect to the baseline period)

¹⁵ We deal with this issue in section 4..4.

Figure 9: Dynamic trajectory of emissions after an increase in the commodity price. Baseline and baseline + policy scenarios.

4..3.2 Subsidies to green investment

So far, the model has operated under the assumption that the subsidy rate for green investment, denoted by the exogenous variable , starts at zero. Now, this rate is increased once and for all to ensure the ex ante (without taking into account the evolution of technology) attainment in the long-term of the reduction targets outlined in Table 2, even without technological changes.

In the baseline scenario, the subsidy amounts to 62% of the investment cost, resulting in an increase of 2.6 percentage points of GDP per year in government budget costs by 2050.¹⁶ This cost is financed by a lump-sum tax in the model economy. Figures 10a and 10b illustrate the projected paths for emissions and the relative production of brown to green production, respectively, from 2019 to 2050. By 2050, this strategy will achieve approximately 79% of the target reduction in emissions, which is reached 12 years later.

Table 3 indicates that during the 2019-2050 period, contrary to the previous mitigation strategy, a dynamic scheme of subsidies for green investment promotes GDP growth, resulting in an average 1.7% higher GDP between 2019 and 2050 compared to the baseline scenario. Green energy production augments by that year around 43% on average compared to the baseline, while brown energy decreases by more than 15%. The price of green energy experiences a significant drop of around 13%. This is an economy where a substantial amount of resources is allocated to green investment, driving economic growth without reducing energy intensity, but negatively impacting aggregate consumption, leisure, and welfare over some decades (see Figure 11).

¹⁶ These figures can be compared with the current level of climate-related public investment in Europe, which currently stands at around 1 percent of GDP (see Delgado-Téllez et al., 2022)

(a) Carbon emissions. Baseline and subsidies to green investment.

(b) Brown to green energy production. Baseline and subsidies to green investment. Figure 10: Subsidies to green investment

Table 4: Welfare effects of mitigation plans from 2019-2050 and 2019-2200, expressed as average percentage changes in equivalent consumption (negative values = loss, positive values = gain)

The economy experiences a significant average increase in energy consumption of over 14%, driven primarily by the higher supply of non-polluting green energy. On average, there is a reduction of approximately 14% in emissions over the period. However, as we mentioned, this strategy does not lead to a reduction in energy intensity (energy use over GDP).

Despite the uptick in GDP and energy intensity, Table 4 indicates an average cumulative welfare decline of nearly 1.1% in terms of consumption during the projected baseline period. This decline primarily results from reduced consumption and increased working hours. However, in the long run, welfare notably rebounds as the favorable impacts of increased capital in the economy manifest in heightened consumption. Yet, if advancements in decarbonization technology fall below a certain threshold, the effort required in terms of consumption to subsidize green investment escalates significantly, multiplying by three the transitional welfare loss. Interestingly, although this policy, combined with the optimistic technology scenario, minimizes welfare costs between 2019 and 2050, it could result in the smallest welfare increase in the long run compared to the baseline or pessimistic scenarios. This outcome is attributed to the comparatively more restrained investment incentives resulting from the policy.

Figure 11: Dynamic macroeconomic effects of a permanent unanticipated increase in the subsidy to green investment (percentage deviations with respect to the baseline period)

4..3.3 Emission taxes

In this scenario, emission taxes (τ^e) increase permanently from 2019 onwards to achieve ex ante emissions target in the long run. We find that raising this tax by 83 e per tonne of carbon (at 2010 prices) would attain this goal. In the optimistic scenario, the tax would be set at 44 e, while in the pessimistic scenario, it would be 152 e. These numbers fall within a wide range of values reported in the literature. For example, Dietz and Stern (2015) suggest a range of $32-103/tCO2 ¹⁷ (at 2012 prices) in 2015, increasing to $82- 260/tCO2 over the course of two decades. Delft (2010), based on a meta-analysis of various studies, indicates that CO2 taxes could range from as low as 20 e/tCO2 to as high as 180 e/tCO2 in 2050 (at 2012 prices). Golosov et al. (2014), with a discount rate similar to Nordhaus, suggests an optimal tax slightly under 60 e per tonne of carbon, nearly double that of Nordhaus (see Nordhaus and Boyer, 2000). Using the same model as Golosov et al. (2014), but with a calibration that takes into account the world stock of carbon in the atmosphere and the world GDP both in 2019, Andrés et al. (2023) obtain an optimal carbon tax of $105. OECD (2021) proposes three carbon price benchmarks ranging from 30 e/tCO2 to 120 e/tCO2. According to the High-Level Commission on Carbon Pricing (2017), the price signals necessary to decarbonize electricity generation and heavy industry by 2030 would fall within the range of 30US$/tCO2 to 100US$/tCO2. Delgado-Téllez et al. estimate that an increase of carbon rates by e10 per tonne of CO2 is estimated to reduce emissions by 7.3% in the long term.

¹⁷ To convert Euros per unit of carbon into Euros per unit of CO2, we must divide the tax by 3.67.

(a) Carbon emissions. Baseline and emission taxes

Figure 12: Emission taxes (b) Brown to green energy production. Baseline and emission taxes.

Figure 12 shows the path for emissions and the relative production of brown to green energy in relation to the baseline scenario, while Figure 13 represents the year-toyear percentage deviation of a set of variables with respect to the baseline. By 2050, GDP will decrease 0.7% with respect to the projected value in the baseline, dirty energy will fall by 26%, and green energy will increase by 6%. In 2050, a 76% of the target reduction is reached, and the full target is attained forty years latter.

Table 3 presents the average macroeconomic effects of the emission taxing plan from 2019 to 2050. The plan has a reduced impact on overall GDP, resulting in only a 0.4% average decrease over the period.¹⁸ There is virtually no impact on aggregate consumption (-0.2%). Notably, firms respond to the increased taxes by investing in abatement measures that would account for a 9% reduction in accumulated emissions during the period. Figure 14 shows the dynamics of abatement in the long run. The heavily front-loaded policy initiates a rapid increase in abatement efforts, yet this response diminishes progressively over time.

The negative impacts on welfare during the period 2019-2050 are relatively small, not exceeding 1 percent point in terms of equivalent consumption, even in the pessimistic scenario, as shown in Table 4. However, in the long run, welfare experiences a decline in terms of equivalent consumption that can range from -5% in the optimistic scenario to -16% in the pessimistic scenario.

The comparison of welfare with the previous plans makes evident that emission taxes have the least detrimental impact until 2050. On the other hand, subsidies on green investment are found to be the most beneficial for long-term welfare. Figure 13 illustrates that once taxes on carbon increase, the negative effects on GDP, consumption, and welfare persist over an extended period of time.

¹⁸ A moderate impact of emissions taxes on GDP is also found in Delgado-Téllez et al., 2022.

Figure 13: Dynamic macroeconomic effects of a permanent unanticipated increase in the tax to emissions (percentage deviations with respect to the baseline period)

4..3.4 Emission taxes to subsidize green investment

Subsidies for green investment in the above exercise are financed through lump sum taxes. Additionally, government revenues from carbon taxes are returned to households through transfers. In this section, we examine the consequences of using carbon taxes to subsidize green investment. For this purpose, we assume that all revenues generated from taxing carbon emissions are utilized by the government to subsidize investment in green energy production.

Figure 14: Emissions tax: percentage abatement 2019-2200

Once again, we assume a sudden increase in taxes to achieve the ex ante emission target in the long run. The emission tax in the technology baseline necessary to do so is 58 e, compared to 83 e when taxes are rebated to households as lump-sum transfers. This lower tax level is still effective in achieving the ex ante desired emissions reduction in the long run.

Moreover, the average subsidy for green investment totals 20% of the investment cost. This figure is slightly below recent findings by Darvas and Wolff (2021), who find that EU governments are willing to provide around 28% of the required funding for energy and transport investments in the energy transition.

Figure 15 depicts the evolution of emissions and the relative production of green to brown energy. Despite the significant fall in emissions, the impact on accumulated GDP during the transition period is virtually nil, as shown in Figure 16.

The final column in Table 3 indicates that the macro effects of this policy are consistent with those of subsidies on green investment and taxes on carbon implemented separately. This combination of emission taxes and green investment subsidies accounts for 89% of the emissions reduction compatible with the Green Deal target, and for the 77% of the NZE target. Furthermore, as shown in Table 4, this strategy mitigates most of the short-term welfare costs associated with financing green investment through lump sum taxes, as well as the long-term welfare costs of increasing carbon taxes and redistributing the revenues through transfers to households.

Comparing all the strategies, it can be concluded that this particular approach strikes a balance between short and long-term effects. It takes into consideration both immediate welfare concerns and the broader, long-term objectives of emission reduction and sustainable economic growth to a reasonable extent. Although this strategy in our model entails a relatively low welfare cost, it implies that the revenue from environmental taxation cannot be used to offset the unequal impact of these measures across households in the economy. The redistribution issue stands not only as an additional means to enhance welfare but, as emphasized by Blanchard, Gollier, and Tirole (2023), any effective environmental policy should encompass a redistribution component to mitigate the political costs associated with its implementation.

4..4 Full emissions target by 2050

In the preceding section, we established a metric for comparing various mitigation policies. Nevertheless, as emphasized earlier, none of the proposed plans thus far are entirely capable of timely achieving the 2050 Net Zero Emissions (NZE) target.

This section aims to address several pivotal inquiries: What level of emissions tax would be necessary to successfully achieve the NZE target by 2050? What would be the corresponding welfare transition cost? Furthermore, in a scenario where the rest of the world reduces emissions at a pace akin to Spain’s, what are the anticipated long-term benefits of this policy? We delve into these questions to offer comprehensive insights.

We now adopt a more realistic emissions tax scheme that increases linearly until 2050 and remains constant at this level thereafter. This tax trajectory is announced and fully anticipated by economic agents. Tax revenues are returned as lump-sum transfers to households. We simulate this anticipated policy alongside a sequence of unanticipated technological shocks corresponding to our baseline technology scenario.

The rest of the world’s emissions were considered exogenous and constant so far. Now, we also consider a scenario where the rest of the world reduces emissions at the same rate as simulated in our economy while maintaining a constant ratio e We refer to this as a coordinated scenario. This term serves as a simplified representation of a fully general equilibrium coordinated scenario, wherein the costs incurred by the rest of the world due to mitigation policies would probably negatively affect the Spanish economy through various channels. Consequently, we interpret the coordinated welfare results as an upper bound.

Our results are displayed in Figure 17. Emissions taxes increase to a level of 227 e per tonne of carbon in 2050 to achieve NZE. Because the small weight of Spain in total emissions, the impact of the measure on the evolution of the global atmospheric carbon is negligible.

(a) Carbon emissions. Baseline and emission taxes to subsidize green investment

(b) Brown to green energy production. Baseline and emission taxes to subsidize green investment. Figure 15: Emission taxes used to subsidize green investment

Figure 16: Dynamic macroeconomic effects of a permanent unanticipated increase in the tax to emissions used to subsidize green investment (percentage deviations with respect to the baseline period)

Using a standard assumption in the literature¹⁹, we establish a mapping between the evolution of carbon atmospheric stock and temperature using the following expression:

\[T _ {t} = \lambda \frac {\log (\frac {x _ {t}}{\bar {x}})}{\log (2)}\tag{35}\]

Here, x¯ stands for the pre-industrial atmospheric carbon concentration, and λ represents the sensitivity parameter of temperature to carbon stock. While a common value in the literature has been , we find that a value of better fits the historical relationship between carbon concentration and temperature since 1850.

¹⁹ See Golsov et al. (2014).

Figure 17: Dynamic trajectory of emissions after an increase in emissions taxes. Baseline and baseline + policy scenarios (left scale). Taxes (right scale)

Using this formula in a non-coordinated strategy, the temperature is projected to increase by 1.8 degrees Celsius above pre-industrial levels by , and by over 3.5 degrees Celsius by 2200 (Figure 18 and Table 5).

As a result of the economic impact of this policy, the average welfare loss relative to the technology baseline is estimated at -0.44% in terms of equivalent consumption during the period 2019-2050, and -19.11% between 2019 and 2200 (Figure 19 and Table 5).

In a coordinated scenario, the global emissions reduction gradually alters the trajectory of atmospheric carbon several decades into the implementation of the policy. Consequently, the increase in temperature above pre-idustrial levels will remain below 1.5 degrees Celsius by 2050 with excess temperature effectively reverting to almost preindustrial levels by 2200. The beneficial impact on welfare is apparent, as depicted in Figure 19, although it takes several decades to materialize. In the very long run, there is an average welfare increase of 60% between 2019 and 2200 (refer to Table 5).

²⁰ The temperature is considered to have been 1.1 degrees Celsius above pre-industrial levels in 2019.

4..5 Sensitivity analysis

In this section, we perform a robustness analysis of our findings by exploring the impact of different parameter changes within the environmental block of the model. To enable straightforward comparisons among these varied parameter settings, our emphasis will be on achieving the previously discussed full emissions target by 2050, accomplished via emissions taxation. As part of this approach, taxes will progressively rise in a linear fashion until 2050 and maintain a constant level thereafter for the long term.

Table 6 showcases the results concerning the average welfare impact during the transition period from 2019 to 2050. Initially, we present the welfare effects and the carbon tax projected for 2050 in the benchmark default case, as depicted in Table 5. This scenario reflects the parameter settings employed thus far and represents the nocoordination scenario. Within this context, the estimated welfare loss amounts to -0.44 percentage points in equivalent consumption between 2019 and 2050.

Next, we explore the scenario where the shift from dirty energy to clean energy becomes more challenging by reducing the elasticity of substitution between brown and green energy. Specifically, we halve the elasticity from the benchmark value of to , aligning it more closely with the findings of Papageorgiou et al. (2017). To calculate the average welfare loss, we utilize expression (34), modifying the parameter in both the baseline and the baseline plus policy cases. This adjustment results in an increased carbon tax of 412 e per tonne of carbon by 2050. Consequently, welfare deteriorates compared to the benchmark scenario during the transition period, experiencing an average decrease of 0.55 percent.

When firms face a reduced elasticity of costs in relation to the share of abated emissions , the costs of abatement for these firms may increase or decrease based on the initial value of . With lower initial values of , a decrease in amplifies the cost for the same change in . In our table, we have halved the value of from the benchmark of 2.8 to 1.4. This adjustment elevates the carbon tax to per tonne of carbon, which is 60 e higher than the baseline. However, this change does not affect the average welfare during this period.

The values of the parameters for the damage function are subject to high uncertainty. Therefore, we consider the case where the marginal damage to a change in atmospheric carbon stock is halved compared to the benchmark value. Specifically, we divide by 2. Despite this alteration, both the carbon price and welfare remain unaffected. This is attributed to the reduced impact of marginal damage, indicating that energy production has a less adverse effect on productivity, both before and after the implementation of carbon taxing. Moreover, considering Spain’s limited influence on the global carbon stock, this parameter adjustment has minimal impact on both carbon pricing and welfare.

Figure 18: Temperature evolution (above pre-industrial levels) between non-coordinated and coordinated scenarios

Figure 19: Welfare evolution between non-coordinated and coordinated scenarios

We also examine the implications of doubling the marginal effect of dirty energy production on emissions via the parameter . This adjustment amplifies the influence of a carbon price increase on promoting abatement, as described by Equation 12. With heightened taxes, the relatively costlier dirty energy production becomes less appealing, prompting a more pronounced shift from dirty to cleaner energy sources. Table 6 illustrates that, in this scenario, the carbon tax by 2050 is half of the benchmark. However, despite this change, welfare remains unaffected.

Table 5: Average welfare effects and temperature comparison (above pre-industrial levels) between non-coordinated and coordinated scenarios.

Commencing with a lower elasticity of production to energy (1-α^y-β^y) reduces the welfare cost of achieving NZE. This circumstance arises from the fact that, in this scenario, the same level of emissions is produced using less energy, implying that brown energy is more polluting ²¹. Substituting brown energy with green energy would consequently result in a more substantial reduction in emissions.

To gauge the impact of technology, we investigate a scenario where we switch off all three sources of technological progress. In this instance, the sole method to attain the 70% emission reduction by 2050 is through taxes. Consequently, the carbon tax will climb to 324 e, resulting in an average transition welfare decline of -0.65% in equivalent consumption.

Lastly, we reduce the value of the discount rate β from 4% to 2%. This adjustment causes the emission tax to rise to 313 e. However, the welfare cost decreases to -0.08%.

Although average welfare provides an overview, it conceals the trend in welfare losses over time. To offer a detailed insight into welfare’s sensitivity to changes in environmental parameters, Figure 20 illustrates the period-to-period evolution of welfare losses. It showcases the benchmark scenario and the four scenarios from Table 6 that exhibit the most significant deviations in average welfare compared to the benchmark.

²¹ Calibrated emissions remain constant -equivalent to the observed ones- regardless of the values of the parameters and .

Table 6: Change in welfare and carbon tax to different environmental settings

As expected due to the escalating trend in emission taxes, welfare effects depict a significant and persistent decline that extends well beyond the year 2050. By that juncture, the benchmark scenario records a welfare loss surpassing 1.5 percentage points (pp) in equivalent consumption. The sensitivity analysis uncovers a reduction of 0.6 pp in welfare loss by that year due to a lower elasticity of production to energy, an additional 0.4 pp welfare loss in the absence of technological growth, and a 0.7 pp increase in welfare loss when the elasticity of substitution between brown and green energy is more constrained.

Overall, the robustness analysis demonstrates that the welfare costs associated with transitioning to Net Zero Emissions (NZE) remain manageable across a wide range of simulation configurations.

Figure 20: Welfare evolution under different environmental parameters

5. Conclusions

In this paper, we have proposed an environmental dynamic general equilibrium model to assess the welfare effects of energy transition policies, such as those geared to reduce carbon emissions through environmental taxation, investing in green technologies, or a combination of both. Starting from a central scenario characterized by a trend of environmentally friendly technological progress, zero-emission taxes and incentives to green investment, as well as current oil prices, we have simulated the effort required to achieve NZE under different mitigation strategies and assessing their welfare and macroeconomic consequences.

Maintaining or accelerating current emission-saving technological progress would reduce carbon emissions by one third by 2050 with respect to 2019. Policies heavily frontloaded to rapidly mitigate carbon emissions may demonstrate effectiveness in reaching the intermediate 2030 Green Deal target. However, they fall short of meeting the 2050 Net Zero Emissions (NZE). For example, a once-and-for-all subsidy on green energy investment of approximately 60% on green energy investment, equivalent to 2.6 percentage points of GDP per year in government budget costs, would result in reaching 92% of the intermediate 2030 target but only 80% of the 2050 NZE target.

The welfare effects significantly vary between the short to medium and the very long term, particularly among different mitigation policies. Thus, elevating fossil fuel prices to deter their usage results in the highest welfare costs in both the transition to 2050 and in the long run. Conversely, emissions taxes prove to be the most favorable policy in terms of welfare during the transition to 2050, while green investment subsidies exhibit substantial welfare gains in the very long term, even without a globally coordinated emissions reduction policy.

To attain Net Zero Emissions (NZE) fully, a gradual increase in the carbon tax to a steady state level of per tonne of carbon (at 2010 prices) is needed. The average welfare loss resulting from this policy is calculated at a very manageable -0.44% in terms of equivalent consumption during the period 2019-2050. However, it escalates to -19.11% in the very long run (between 2019 and 2200). When the government reallocates revenues from carbon taxes towards green investment subsidies, the required increase in the tax to achieve the emission target is significantly lower. Additionally, this policy leads to a more balanced welfare effect between the short and long run.

Our findings highlight the significance of global coordination in mitigation policies. Through a simple exercise, we demonstrate that a coordinated policy possesses the potential to entirely reverse the long-term adverse effects of emission taxes, transforming them from negative to largely positive impacts. This transformation occurs via a substantial reversal in the global temperature trend.

Overall, our paper underscores the utility of eDGE models for assessing the welfare and macroeconomic consequences of various mitigation policies across different scenarios and assumptions, particularly in light of the uncertainties surrounding energy transition, technological advancements, and climate change.

References

1. Aguirre, A., J.C. Conesa, and F. Valero (2018): "The Role of Fiscal Policy in Energy Transition: A General Equilibrium Analysis". Energy Policy, vol. 116, pp. 70-79.
2. Andrés, J. , J.M. Barrutiabengoa, J. Cubero y R. Doménech (2013): "Social Welfare and the Social Cost of Carbon". BBVA Research WP230405. http://t.ly/D0SpW
3. Annicchiarico, B. and F. Di Dio (2015): "Environmental policy and macroeconomic dynamics in a new Keynesian model". Journal of Environmental Economics and Management, vol. 69, pp. 1-21.
4. Annicchiarico, B., Carattini, S, Fischer, C., and G. Heutel (2021): "Business cycles and environmental Policy: Literature Review and Policy Implications". NBER Working Paper N^o 29032.
5. Annicchiarico, B.; Carattini, S.; Fischer, C.; and G. Heutel (2022): "Business cycles and environmental policy: A primer." Environmental and Energy Policy and the Economy, 3(1), 221-253.
6. Archer, D.; Eby, M.; Brovkin, V.; Ridgwell, A.; Cao, L.; Mikolajewicz, U.; Caldeira, K.; Matsumoto, K.; Munhoven, G.; Montenegro, A. and K. Tokos (2009): "Atmospheric Lifetime of Fossil Fuel Carbon Dioxide", Annual Review of Earth and Planetary Sciences 37, 11734.
7. Archer, D. and V. Brovkin (2008): "The millennial atmospheric lifetime of anthropogenic CO2", Climatic Change 90, 283297
8. Batten , S. (2018): "Climate change and the macroeconomy: a critical review". Bank of England, Staff Working Paper No. 706.
9. Blanchard, O.; Gollier, C.; and J. Tirole (2023): "The Portfolio of Economic Policies Needed to Fight Climate Change". Annual Review of Economics, 15, 689-722.
10. Boscá, J. E., Doménech, R, Ferri, J., Mendez-Marcano, R., and J. Rubio-Ramírez (2020): ""Financial and fiscal shocks in the great recession and recovery of the Spanish economy," European Economic Review, vol. 127.
11. Brienen, R. J. W., Caldwell, L., Duchesne, L., Voelker, S., Barichivich, J., Baliva, J. Ceccantini, G., Di Filippo, A.; Helama, S., Locosselli, G. M., Lopez, G. M., Piovesan, G., Schöngart, J., Villalba, R. and E. Gloor (2020): Forest carbon sink neutralized by ervasive growth-lifespan trade-offs", Nature Communications, pp. 1-10.
12. Burda, M. and L. Zessner-Spitzenberg (eds) (2022): "DP17368 Greenhouse Gas Mitigation and Price-driven Growth in a Baumol-Solow-Swan Economy", CEPR Press Discussion Paper No. 17368.
13. CE Delft (2010): Shadow Prices Handbook: Valuation and weighting of emissions and environmental impacts.
14. Crippa M., Guizzardi D., Banja M., Solazzo E., Muntean M., Schaaf E., Pagani F., Monforti-Ferrario F., Olivier, J.G.J., Quadrelli, R., Grassi, G., Rossi, S., Oom, D., Branco, A., San-Miguel, J., and E. Vignati (2022): CO2 emissions of all world countries - 2022 Report, EUR 31182 EN, Publications Office of the European Union.
15. Cutanda, A.; Labeaga, J.M; and J. Sanchis-Llopis (2020): "Aggregation biases in empirical Euler consumption equations: evidence from Spanish data", Empirical Economics, 58, 957977.
16. Cutanda, A. and J. Sanchis-Llopis (2022): "Human capital and the intertemporal substitution for leisure: empirical evidence for Spain", Portuguese Economic Journal, 22, s 377396.
17. Darvas, Z. and G. Wolf (2021): "A green fiscal pact: climate investment in times of budget consolidation", Policy Contribution, 18/2021, Bruegel.
18. Delgado-Téllez, M. M. Ferdinandusse and C. Nerlich (2022): "Fiscal policies to mitigate climate change in the euro area", ECB Economic Bulletin, Issue 6/2022.
19. Demaria, F., Scheneider, F., Sekulova, F., and J. Martinez-Alier (2013): "What is Degrowth? From an Activist Slogan to a Social Movement" Environmental Values, vol. 22, pp. 191215.
20. Dietz, S. and N. Stern (2015): "Endogenous Growth, Convexity of Damage and Climate Risk: How Nordhaus’ Framework Supports Deep Cuts in Carbon Emissions". The Economic Journal, vol. 125(583), pp. 574-620.
21. Emambakhsh, T.; Fuchs, M.; Kordel, S.; Kouratzoglou, C.; Lelli, C.; Pizzeghello, R.; Salleo, C.; and M. Spaggiari (2023): "The Road to Paris: Stress Testing the Transition Towards a Net-Zero Economy" . ECB Occasional Paper No. 2023/328.
22. Eurostat (2022): Energy statistics - an overview. Primary Energy Production. website: https://shorturl.at/kmX36
23. Evroux, C., Spinaci. S. and A. Widuto (2023): "From growth to ’beyond growth’: Concepts and challenges". EPRS / European Parliamentary Research Service.
24. Fabra, N., Lacuesta A. and M. Souza (2022): "The implicit cost of carbon abatement during the COVID-19 pandemic". European Economic Review, vol. 147, 104165.
25. Fried, S. (2018): "Climate Policy and Innovation: A Quantitative Macroeconomic Analysis", American Economic Journal: Macroeconomics, 10(1): 90118.
26. Golosov, M., Tsyvinski, A. and I. Werning (2014): "A Welfare-Based Approach to Climate Policy." American Economic Review, vol. 104(5), pp. 555-559.
27. Golosov, M., Hassler, J, Krusell, P. and A. Tsyvinski (2014b): "Optimal taxes on fossil fuel in general equilibrium", Econometrica, vol. 82(1), pp. 41-88.
28. Heutel, G. (2012): "How should environmental policy respond to business cycles? Optimal policy under persistent productivity shocks", Review od Economic Dynamics, vol. 15, 244-264.
29. High-Level Commission on Carbon Prices (2017): Report of the High-Level Commission on Carbon Prices. World Bank, Washington, DC.
30. Intergovernmental Panel on Climate Change (IPCC) (2018): "IPCC, 2018: Global Warming of 1.5^◦ C. An IPCC Special Report on the impacts of global warming of 1.5^◦C above pre-industrial levels and related global greenhouse gas emission pathways, in the context of strengthening the global response to the threat of climate change, sustainable development, and efforts to eradicate poverty". Masson-Delmotte, V., P. Zhai, H.-O. Pörtner, D. Roberts, J. Skea, P.R. Shukla, A. Pirani, W. Moufouma-Okia, C. Péan, R. Pidcock, S. Connors, J.B.R. Matthews, Y. Chen, X. Zhou, M.I. Gomis, E. Lonnoy, T. Maycock, M. Tignor, and T. Waterfield (eds.). Cambridge University Press, Cambridge, UK and New York, NY, USA.
31. IPCC (2023): Climate Change 2023 Synthesis Report Summary for Policymakers. https://bit.ly/3P64mUU International Energy Agency (IEA) (2020): "Net Zero by 2050: A Roadmap for the Global Energy Sector". IEA.
32. IEA-EDGAR (2022): IEA-EDGAR CO2, a component of the EDGAR (Emissions Database for Global Atmospheric Research) Community GHGV. website: https://edgar.jrc.ec.europa.eu/report_2022
33. International Monetary Fund (2019): "How to Mitigate Climate Change", International Monetary Fund, Fiscal Monitor, 2019.
34. Jackson A. and J. Jackson (2021): "Modelling energy transition risk: The impact of declining energy return on investment (EROI)", Ecological Economics, vol. 185.
35. Lüthi, D.; Le Floch, M.; Bereiter, B.; Blunier, T.; Barnola, JM.; Siegenthaler, U.; Raynaud, D.; Jouzel, J.; Fischer, H.; Kawamura, K.; Stocker, TF. (2008): "High-resolution carbon dioxide concentration record 650,000-800,000 years before present" Nature, vol 453, pp 379382
36. Marron, D.B. and E.J. Toder (2014): “Tax Policy Issues in Designing a Carbon Tax”. American Economic Review P&P, vol. 104(5), pp. 563-68.
37. Metcalf. G. E. (2019): “On the Economics of a Carbon Tax for the United States ”. Brookings Papers on Economic Activity, BPEA Conference Drafts.
38. Moore, B. and B. H. Braswell (1994): "The lifetime of excess atmospheric carbon dioxide", Global Biogeochemical Cycles, vol. 8(1), pp. 23-38.
39. Nakicenovic, N., and R. Swart (2000): "Special Report on Emissions Scenarios: A Special Report of Working Group III of the Intergovernmental Panel on Climate Change". Cambridge University Press.
40. Nordhaus, W. D. (1991): "To Slow or Not to Slow: The Economics of the Greenhouse Effect." The Economic Journal, vol. 101(407), pp. 920-937.
41. Nordhaus, W. D. (2007): "A Review of the Stern Review on the Economics of Climate Change". Journal of
42. Economic Literature, vol. XLV, pp. 686-702
43. Nordhaus, W. D. (2007b): "To Tax or Not to Tax: The Case for a Carbon Tax" Review of Environmental Economics and Policy, 1(1), pp. 2644.
44. Nordhaus, W. D. (2008): A Question of Balance: Weighing the Options on Global Warming Policies. New Haven: Yale University Press, 2008.
45. OECD (2015): "Energy intensity and mix", in Environment at a Glance 2015: OECD Indicators, OECD Publishing, Paris.
46. OECD (2021): Effective Carbon Rates 2021, OECD Publishing, Paris.
47. Papageorgiou, C., Saam, M. and P. Schulte (2017): "Substitution between Clean and Dirty Energy Inputs: A Macroeconomic Perspective." The Review of Economics and Statistics, vol. 99(2), pp. 281-290.
48. Prados de la Escosura. L. (2020): "Capital in Spain, 1850-2019". Working Papers in Economic History N^o 2020-09. Instituto Figuerola de Historia y Ciencias Sociales. Universidad Carlos III de Madrid.
49. Red Eléctrica de España (2019): El Sistema Eléctrico Español. Informe 2019. website: https://shorturl.at/mnGO2
50. Rotemberg, J. J. (1982): "Sticky Prices in the United States". Journal of Political Economy, vol. 90(6), pp. 1187- 1211.
51. Semmler, W., Braga, J.P., Lichtenberger, A., Toure, T. and E. Hayde (2021): "Fiscal Policies for a Low-Carbon Economy". International Bank for Reconstruction and Development / The World Bank.
52. Sen, S., and H. Vollebergh (2018): "The effectiveness of taxing the carbon content of energy consumption". Journal of Environmental Economics and Management, 92, pp.74-99.
53. Stock J.H. and D. Stuart (2021): "Emissions and Electricity Price Effects of a Small Carbon Tax Combined with Renewable Tax Credit Extensions". Working Paper. Harvard University.
54. Stockl, F. and A. Zerrahn (2020): "Substituting Clean for Dirty Energy: A Bottom-Up Analysis". Discussion Papers N^o 1885, Deutsches Institut für Wirtschaftsforschung (DIW), Berlin.
55. Tax Partners (2015): Assets Depreciation Rates in Spain. website: https://t.ly/gPcT
56. United Nations Framework Convention on Climate Change (UNFCCC) (2015): Paris Agreement. United Nations.
57. U.S Energy Information Administration (2022): Annual Energy Review. Energy Overview. Section 1.5. Table 1.7. website: https://www.eia.gov/totalenergy/data/annual/

Appendix A The complete Model

In this Appendix, we show all the equations of the model

\[\lambda_ {t} = \frac {1}{c _ {t} ^ {\sigma}}\tag{36}\]

\[\kappa_ {L} h _ {t} ^ {\varphi} = \lambda_ {t} w _ {t}\tag{37}\]

\[\lambda_ {t} = \beta \mathbb {E} _ {t} \left(\lambda_ {t + 1} \frac {r _ {t}}{\pi_ {t + 1}}\right)\tag{38}\]

\[q _ {t} ^ {s} = \beta \mathbb {E} _ {t} \left\{\left(\frac {\lambda_ {t + 1}}{\lambda_ {t}} [ r _ {t + 1} ^ {s} + (1 - \delta_ {s}) q _ {t + 1} ^ {s} ]\right) \right\} \quad \text { for } s = \{y, g, b \}\tag{39}\]

\[1 - \tau_ {t} ^ {i ^ {s}} = q _ {t} ^ {s} \left[ 1 - \kappa_ {I} ^ {s} \left(\frac {i _ {t} ^ {s}}{i _ {t - 1} ^ {s}}\right) \left(\frac {i _ {t} ^ {s}}{i _ {t - 1} ^ {s}} - 1\right) - \frac {\kappa_ {I} ^ {s}}{2} \left(\frac {i _ {t} ^ {s}}{i _ {t - 1} ^ {s}} - 1\right) ^ {2} \right]\]

\[+ \kappa_ {I} ^ {s} \beta \mathbb {E} _ {t} \left\{q _ {t + 1} ^ {s} \frac {\lambda_ {t + 1}}{\lambda_ {t}} \left[ \left(\frac {i _ {t + 1} ^ {s}}{i _ {t} ^ {s}} - 1\right) \left(\frac {i _ {t + 1} ^ {s}}{i _ {t} ^ {s}}\right) ^ {2} \right] \right\} \quad \text {for s = \{y,g,b\} and \tau_{t} ^{is} = 0 for s = \{y,b\}}\tag{40}\]

\[k _ {t} ^ {y} = (1 - \delta_ {y}) k _ {t - 1} ^ {y} + \left[ 1 - \frac {\kappa_ {I} ^ {y}}{2} \left(\frac {i _ {t} ^ {y}}{i _ {t - 1} ^ {y}} - 1\right) ^ {2} \right] i _ {t} ^ {y}\tag{41}\]

\[k _ {t} ^ {g} = (1 - \delta_ {g}) k _ {t - 1} ^ {g} + \left[ 1 - \frac {\kappa_ {I} ^ {g}}{2} \left(\frac {i _ {t} ^ {g}}{i _ {t - 1} ^ {g}} - 1\right) ^ {2} \right] i _ {t} ^ {g}\tag{42}\]

\[k _ {t} ^ {b} = (1 - \delta_ {b}) k _ {t - 1} ^ {b} + \left[ 1 - \frac {\kappa_ {I} ^ {b}}{2} \left(\frac {i _ {t} ^ {b}}{i _ {t - 1} ^ {b}} - 1\right) ^ {2} \right] i _ {t} ^ {b}\tag{43}\]

\[v _ {t} ^ {g} = \varsigma_ {t} ^ {g} \left(k _ {t - 1} ^ {g}\right) ^ {\alpha^ {g}}\tag{44}\]

\[v _ {t} ^ {b} = \varsigma_ {t} ^ {b} \left(k _ {t - 1} ^ {b}\right) ^ {\alpha^ {b}} \left(m _ {t} ^ {b}\right) ^ {1 - \alpha^ {b}}\tag{45}\]

\[e _ {t} ^ {b} = \left(1 - \mu_ {t} ^ {b}\right) \gamma_ {1 t} ^ {b} \left(v _ {t} ^ {b}\right) ^ {1 - \gamma_ {2} ^ {b}}\tag{46}\]

\[z _ {t} ^ {b} = \theta_ {1} ^ {b} (\mu_ {t} ^ {b}) ^ {\theta_ {2} ^ {b}} v _ {t} ^ {b}\tag{47}\]

\[p _ {t} ^ {v ^ {g}} = \frac {r _ {t} ^ {g}}{\alpha^ {g} \varsigma_ {t} ^ {g}} \left(k _ {t - 1} ^ {g}\right) ^ {1 - \alpha^ {g}}\tag{48}\]

\[p _ {t} ^ {v ^ {b}} = \frac {r _ {t} ^ {b}}{\alpha^ {b} \varsigma_ {t} ^ {b}} \left(\frac {k _ {t - 1} ^ {b}}{m _ {t} ^ {b}}\right) ^ {1 - \alpha^ {b}} + \frac {\tau_ {t} ^ {e} (1 - \mu_ {t} ^ {b}) \gamma_ {1 t} ^ {b} (1 - \gamma_ {2} ^ {b})}{(v _ {t} ^ {b}) ^ {\gamma_ {2} ^ {b}}} + \theta_ {1} ^ {b} (\mu_ {t} ^ {b}) ^ {\theta_ {2} ^ {b}}\tag{49}\]

\[p _ {t} ^ {v ^ {b}} = \frac {(1 + \tau_ {t} ^ {m}) p _ {t} ^ {* m ^ {b}}}{(1 - \alpha^ {b}) \varsigma_ {t} ^ {b}} \left(\frac {m _ {t} ^ {b}}{k _ {t - 1} ^ {b}}\right) ^ {\alpha^ {b}} + \frac {\tau_ {t} ^ {e} (1 - \mu_ {t} ^ {b}) \gamma_ {1 t} ^ {b} (1 - \gamma_ {2} ^ {b})}{(v _ {t} ^ {b}) ^ {\gamma_ {2} ^ {b}}} + \theta_ {1} ^ {b} (\mu_ {t} ^ {b}) ^ {\theta_ {2} ^ {b}}\tag{50}\]

\[\mu_ {t} ^ {b} = \left[ \frac {\tau_ {t} ^ {e} \gamma_ {1 t} ^ {b}}{\theta_ {1} ^ {b} \theta_ {2} ^ {b}} (v _ {t} ^ {b}) ^ {- \gamma_ {2} ^ {b}} \right] ^ {\frac {1}{\theta_ {2} ^ {b} - 1}}\tag{51}\]

\[e _ {t} = e _ {t} ^ {b}\tag{52}\]

\[\tilde {v} _ {t} ^ {y} = \left[ \theta^ {g} \left(v _ {t} ^ {g}\right) ^ {\frac {\sigma^ {x} - 1}{\sigma^ {x}}} + (1 - \theta^ {g}) \left(v _ {t} ^ {b}\right) ^ {\frac {\sigma^ {x} - 1}{\sigma^ {x}}} \right] ^ {\frac {\sigma^ {x}}{\sigma^ {x} - 1}}\tag{53}\]

\[v _ {t} ^ {y} = A _ {t} ^ {x} \tilde {v} _ {t} ^ {y}\tag{54}\]

\[v _ {t} ^ {g} = (\theta^ {g}) ^ {\sigma^ {x}} \left(\frac {p _ {t} ^ {v ^ {g}}}{p _ {t} ^ {v ^ {y}}}\right) ^ {- \sigma^ {x}} \frac {v _ {t} ^ {y}}{(A _ {t} ^ {x}) ^ {1 - \sigma^ {x}}}\tag{55}\]

\[v _ {t} ^ {b} = (1 - \theta^ {g}) ^ {\sigma^ {x}} \left(\frac {p _ {t} ^ {v ^ {b}}}{p _ {t} ^ {v ^ {y}}}\right) ^ {- \sigma^ {x}} \frac {v _ {t} ^ {y}}{(A _ {t} ^ {x}) ^ {1 - \sigma^ {x}}}\tag{56}\]

\[\left(\pi_ {t} - \bar {\pi}\right) \pi_ {t} = \frac {(1 - \sigma^ {r})}{\kappa_ {p}} + \frac {\sigma^ {r}}{\kappa_ {p}} m c _ {t} + \beta \mathbb {E} _ {t} \frac {\lambda_ {t + 1}}{\lambda_ {t}} \left(\pi_ {t + 1} - \bar {\pi}\right) \pi_ {t + 1} \frac {y _ {t + 1}}{y _ {t}}\tag{57}\]

\[r _ {t} ^ {y} = \alpha^ {y} m c _ {t} \frac {y _ {t}}{k _ {t - 1} ^ {y}}\tag{58}\]

\[w _ {t} = \beta^ {y} m c _ {t} \frac {y _ {t}}{h _ {t}}\tag{59}\]

\[p _ {t} ^ {v ^ {y}} = (1 - \alpha^ {y} - \beta^ {y}) m c _ {t} \frac {y _ {t}}{v _ {t} ^ {y}}\tag{60}\]

\[y _ {t} = A _ {t} ^ {y} \left(k _ {t - 1} ^ {y}\right) ^ {\alpha^ {y}} h _ {t} ^ {\beta^ {y}} \left(A _ {t} ^ {x} \tilde {v} _ {t} ^ {y}\right) ^ {1 - \alpha^ {y} - \beta^ {y}}\tag{61}\]

\[\Gamma_ {t} ^ {y} = y _ {t} \left(1 - m c _ {t} - \frac {\kappa_ {p}}{2} \left(\pi_ {t} - - \bar {\pi}\right) ^ {2}\right)\tag{62}\]

\[\Gamma_ {t} ^ {v ^ {g}} = (1 - \alpha^ {g}) p _ {t} ^ {v ^ {g}} v _ {t} ^ {g}\tag{63}\]

\[\Gamma_ {t} ^ {v ^ {b}} = - \tau_ {t} ^ {e} \gamma_ {2} ^ {b} e _ {t} ^ {b}\tag{64}\]

\[x _ {t} = \eta x _ {t - 1} + e _ {t} + e _ {t} ^ {r o w}\tag{65}\]

\[A _ {t} ^ {y} = [ 1 - (d _ {0} + d _ {1} x _ {t} + d _ {2} x _ {t} ^ {2}) ] \tilde {A} _ {t} ^ {y}\tag{66}\]

\[g _ {t} + \tau_ {t} ^ {i g} i _ {t} ^ {g} = \tau_ {t} ^ {h} + \tau_ {t} ^ {m} p _ {t} ^ {* m ^ {b}} m _ {t} ^ {b} + \tau_ {t} ^ {e} e _ {t}\tag{67}\]

\[\frac {r _ {t}}{r} = \left(\frac {r _ {t - 1}}{r}\right) ^ {\rho_ {r}} \left[ \left(\frac {\pi_ {t} ^ {E Z}}{\pi^ {E Z}}\right) ^ {\phi_ {\pi}} \left(\frac {y _ {t} ^ {E Z}}{y ^ {E Z}}\right) ^ {\phi_ {y}} \right] \exp \left(\nu_ {t} ^ {r}\right)\tag{68}\]

\[\pi_ {t} ^ {E Z} = 0. 1 \pi_ {t} + 0. 9 \pi_ {t} ^ {* ^ {R E Z}}\tag{69}\]

\[y _ {t} ^ {E Z} = 0. 1 y _ {t} + 0. 9 y _ {t} ^ {* ^ {R E Z}}\tag{70}\]

\[y _ {t} = c _ {t} + i _ {t} ^ {y} + i _ {t} ^ {g} + i _ {t} ^ {b} + g _ {t} + p _ {t} ^ {* m ^ {b}} m _ {t} ^ {b} + \theta_ {1} ^ {b} (\mu_ {t} ^ {b}) ^ {\theta_ {2} ^ {b}} v _ {t} ^ {b} + \frac {\kappa_ {p}}{2} (\pi_ {t} - \bar {\pi}) ^ {2} y _ {t}\tag{71}\]

\[U _ {t} = \left(\frac {c _ {t} ^ {1 - \sigma}}{1 - \sigma} - \kappa_ {L} \frac {h _ {t} ^ {1 + \varphi}}{1 + \varphi}\right)\tag{72}\]

\[W _ {t} = U _ {t} + \beta \mathbb {E} _ {t} W _ {t + 1}\tag{73}\]

40 equations for 40 variables (definitions not included):

TRANSITIONING TO NET-ZERO: WELFARE ASSESSMENT

\[\begin{array}{r} \lambda_ {t}, c _ {t}, h _ {t}, w _ {t}, r _ {t}, \pi_ {t}, q _ {t} ^ {y}, q _ {t} ^ {g}, q _ {t} ^ {b}, r _ {t} ^ {y}, r _ {t} ^ {g}, r _ {t} ^ {b}, i _ {t} ^ {y}, i _ {t} ^ {g}, i _ {t} ^ {b}, k _ {t} ^ {y}, k _ {t} ^ {g}, k _ {t} ^ {b}, m _ {t} ^ {b}, v _ {t} ^ {g}, v _ {t} ^ {b}, v _ {t} ^ {y}, \tilde {v} _ {t} ^ {y}, e _ {t} ^ {b}, e _ {t}, \mu_ {t} ^ {b}, \\ z _ {t} ^ {b}, p _ {t} ^ {v ^ {g}}, p _ {t} ^ {v ^ {b}}, p _ {t} ^ {v ^ {y}}, m c _ {t}, y _ {t}, A _ {t} ^ {y}, \Gamma_ {t} ^ {y}, x _ {t}, \tau_ {t} ^ {h}, U _ {t}, W _ {t} \end{array}\]

Appendix B Parameter values and macroeconomic ratios

This appendix presents the values of the parameters and exogenous variables used in the model (Table B1) as well as the performance of the model in matching selected energy and macroeconomic ratios (Table B2).

TRANSITIONING TO NET-ZERO: WELFARE ASSESSMENT

Table B1: Value of the parameters and benchmark values of the exogenous variables

Table B2: Energy and macroeconomic ratios