Three Essays in The Economics of Greenhouse Gas
Emissions’ Mitigation in the Electricity Sector
Thèse Mbea Bell Doctorat en économique Philosophiæ doctor (Ph. D.) Québec, Canada © Mbea Bell, 2018
Three Essays in The Economics of Greenhouse Gas
Emissions’ Mitigation in the Electricity Sector
Thèse
Mbea Bell
Sous la direction de:
Résumé
Face à la menace du changement climatique, il est nécessaire que chaque juridiction politique prenne des mesures rapides et e caces pour réduire ses émissions de gaz à eet de serre (GES). Dans cette problématique, le secteur de la production d'électricité a un rôle central à jouer. D'une part, ce secteur fait partie des principaux responsables des émissions de GES, et d'autre part, ce secteur ore plusieurs solutions alternative pour produire de l'électricité sans émissions telles que des sources renouvelables ou des sources fossiles combinées à la capture et à la séquestration du carbone. Cette thèse examine des solutions économiquement rentables pour réduire les émissions de GES et promouvoir des technologies respectueuses du climat dans le secteur de la production d'électricité. Précisément, elle compare deux instruments dissuasifs : les instruments nanciers visant à mettre un prix sur le carbone (taxe sur le carbone ou marché du carbone) et les normes minimales d'utilisation de sources d'énergies propres. Cette thèse explore également l'enjeu de la promotion des technologies respectueuses du climat par une règle e ciente d'allocation des subventions publiques à ces technologies. Cette thèse se développe en trois essais.
Le premier essai compare une taxe sur les émissions et une norme d'énergie propre en utilisant un modèle d'équilibre général de la production d'électricité. La structure de la production d'électricité comprend deux usines : une qui génère sa production à partir de sources re-nouvelables et l'autre à partir de sources fossiles émettant du CO2. Le modèle est calibré
pour correspondre aux agrégats macroéconomiques sélectionnés de l'économie de la Colombie-Britannique. Le modèle est ensuite utilisé pour mener des expériences conceptuelles qui me-surent le coût économique d'atteindre une cible de réduction des émissions optimale avec un instrument de politique donné contre le coût contrefactuel d'atteindre la même cible avec un autre instrument de politique. L'expérience conduit à la conclusion qu'une taxe sur les émis-sions est plus e cace sur le plan environnemental et moins coûteuse qu'une norme d'énergie propre.
Le deuxième essai enrichit la comparaison entre une norme d'électricité propre et une taxe sur le carbone en ajoutant l'innovation et le pouvoir de marché. Cet essai propose une concur-rence oligopolistique dans la production d'électricité basée sur un jeu non coopératif à 2 étapes entre une usine propre et sa rivale polluante. L'usine polluante peut innover pour réduire ses
émissions, et l'usine propre peut innover pour réduire le désavantage préexistant de ses coûts de production. L'innovation et le pouvoir de marché se combinent pour générer de nouvelles idées, d'abord sur la capacité d'une politique climatique scalement neutre de générer un ef-fet de recyclage des revenus et, d'autre part, sur les mécanismes par lesquels elle augmente le ratio d'énergies propres généré par l'électricité. Le modèle est calibré à des agrégats ma-croéconomiques sélectionnés des États-Unis. Les simulations numériques révèlent de nouvelles sources d'hétérogénéité dans le classement des instruments de politique alternative, qui ont échappé aux lentilles de modèles de compétition parfaite. En particulier, le résultat montre que la norme tend à être un meilleur instrument lorsque (i) le niveau d'ambition de la politique climatique est faible, ou (ii) le niveau de désavantage préexistant des coûts de production de l'usine propre est su samment petit, ou (iii) le coût relatif de l'innovation dans les techno-logies renouvelables est faible. En revanche, la taxe sur le carbone tend à être un meilleur instrument dans les cas inverses.
Le troisième essai examine la problématique de la promotion des technologies respectueuses du climat. Précisément, cet essai détermine une règle e ciente d'allocation des subventions publiques aux investissements entre les technologies renouvelables améliorant la producti-vité et les solutions visant à rendre propre les sources fossiles. Le modèle d'équilibre général sous-jacent comporte un secteur de production d'électricité duopolistique, parallèlement à un secteur de la production d'un bien nal. Les résultats de l'analyse quantitative utilisant la version calibrée du modèle indiquent que, lorsqu'une taxe sur le carbone est utilisée pour en-courager la réduction des émissions, la règle de répartition des subventions rentable est celle qui n'impose pas de punitions multiples sur l'utilisation des ressources fossiles. Par conséquent, lorsque les diérences de coûts d'innovation entre les deux sources technologies respectueuses du climat ne sont pas trop importantes, il est plus rentable d'allouer une plus grande part des subventions aux solutions visant à rendre propre les sources fossiles. En outre, pour atteindre un objectif plus ambitieux de réduction des émissions, il est plus rentable d'augmenter à la fois la taxe carbone et la part des subventions allouées aux technologies visant à rendre propre les sources fossiles.
Abstract
Climate change is one of the biggest challenges that the world is facing. In order to limit global warming, each political jurisdiction must implement a drastic climate policy to mitigate anthropogenic greenhouse gases (GHGs). In this challenge, the electricity generation sector has a central role to play. On the one hand, it is a major contributor to the total GHG emissions, and on the other hand, this sector oers several alternatives for generating electricity without emissions, such as renewable sources or fossil fuel generators equipped with carbon capture and sequestration (CCS) capacity. In three essays, this thesis examines cost-e cient solutions to reducing GHG emissions and promoting climate-friendly technologies in the electricity sector. The rst essay compares an emissions tax and a clean energy standard using a calibrated general equilibrium model of electricity generation. The structure of electricity production features two plants: one that generates its output based on renewable sources and the other based on fossil source emitting CO2. The model is calibrated to match selected macroeconomic
aggregates of the economy of British Columbia. The calibrated model is then used to conduct conceptual experiments that pit the overall cost of achieving the optimal emissions reduction target with a given policy instrument against the counterfactual cost of achieving the same target with an alternative policy instrument. The experiments lead to the conclusion that an emissions tax is more environmentally eective as well as more cost-eective than a clean energy standard.
The second essay extends the comparison between a clean electricity standard and a carbon tax on cost-eectiveness grounds by adding innovation and market power. In our model, a two-stage competition in the electricity sector between a clean plant and its "dirty" rival anchors a two-sector general equilibrium model of climate change intervention. The dirty plant can innovate to reduce its emissions, and the clean plant can innovate to reduce its pre-existing cost-disadvantage. The model is calibrated to selected US macroeconomics aggregates. Results in this essay overturn those obtained in the rst, where perfect competition was the feature of the electricity industry. The second essay thus shows cost-eective choice of climate policy instruments depends on the industrial organization of the electricity sector, as well as on the mechanisms plants use to respond to climate policy.
con-trast, considers a climate policy action aimed, not only at incentivizing abatement, but also at promoting clean electricity solutions to climate change. These solutions have two compet-ing sources. On the one hand, there are climate change solutions consistcompet-ing of technological innovations that mitigate the intermittency and variability problems associated with renew-able sources of electricity. Such solutions, when adequate, reduce the cost-disadvantage of renewable sources at reaching large-scale deployment. On the other hand, there are climate change solutions consisting of carbon abatement technologies that mitigate the trade-o be-tween abatement eort and electricity output among fossil fuel generators. CCS technologies are an essential component of these fossil fuel-based climate change solutions. The main con-tribution of this essay is to show that, in countries with an abundant supply of fossil fuels, subsidizing fossil fuel-based climate change solutions can be an integral part of a cost-eective climate policy action aimed at achieving ambitious emissions reductions.
Table des matières
Résumé iii
Abstract v
Table des matières vii
Liste des tableaux ix
Liste des gures x
Remerciements xiii
Introduction 1
1 Between Fiscal Instruments and Intensity Standards : What Best
Pro-motes A Cost-Eective Decarbonization ? 5
1.1 Introduction. . . 1
1.2 The Economic Environment . . . 5
1.3 Quantitative Analysis . . . 18
1.4 Concluding Remarks . . . 28
2 Market Power, Innovation, and Instrument Choice for Climate Policy 30 2.1 Introduction. . . 1
2.2 The Environment . . . 5
2.3 Analytics . . . 12
2.4 Quantitative analysis . . . 19
2.5 Conclusion . . . 34
3 No Double Jeopardy : Subsidy-Allocation Rule for Investments in Clean Electricity Solutions 36 3.1 Introduction. . . 1
3.2 A Model of Electricity Generation . . . 3
3.3 Quantitative Analysis . . . 13
3.4 Conclusion . . . 26
Conclusion 28
B Annexe Chapitre 2 35
B.1 Appendix B.1 . . . 35
B.2 Appendix B.2 . . . 37
C Annexe Chapitre 3 39
Liste des tableaux
1.1 Calibration . . . 20
1.2 Environmental Laissez-Faire Outcomes . . . 23
1.3 The Eects of Optimal Emissions Tax (φ = 2). . . 25
1.4 The Eects of Optimal Standard Mandate (φ = 2) . . . 26
2.1 Calibration . . . 21
2.2 Key Baseline Values . . . 21
2.3 Baseline Simulation (κ = 0.1) . . . 23
2.4 New Laissez-Faire Values . . . 25
3.1 Calibration . . . 15
3.2 Baseline Key Values . . . 15
3.3 Cost-Eective Subsidy-Allocation Rule . . . 22
3.4 Dierences in Innovation Costs and Cost-Eective Subsidy Allocation Rule . . 24
3.5 New Laissez-Faire Values . . . 25
Liste des gures
1.1 Wage Rate Level Under Alternative Policy Instruments . . . 21
1.2 Tax Revenue Under Alternative Policy Instruments . . . 22
1.3 Equilibrium Emissions under Alternative Policy Instruments . . . 22
1.4 Emissions Policy and Income Tax Interactions under Revenue-Neutrality . . . . 24
1.5 Relative Cost-Eectiveness . . . 27
2.1 Instruments' Levels : CT vs. Standard . . . 26
2.2 Income Tax Rate Comparison of CT vs. Standard for various levels of κ and φ 27 2.3 Plant c's Pro t : CT vs Standard . . . 28
2.4 Plant d's Pro t : CT vs Standard . . . 28
2.5 Plants' innovation Eorts : CT vs. Standard . . . 29
2.6 Plants' Individual Output Levels : CT vs. Standard. . . 30
2.7 Electricity Price : CT vs. Standard . . . 31
2.8 Total Electricity Output : CT vs. Standard . . . 31
2.9 Climate Policy and Welfare : CT vs. Standard. . . 32
2.10 Welfare Eects : CT vs. Standard, for ρd= 0.005 . . . 34
2.11 Welfare Eects : CT vs. Standard, for ρd= 0.01 . . . 34
2.12 Welfare Eects : CT vs. Standard, for ρd= 0.015 . . . 34
3.1 Climate Policy and Plants' Innovation Eorts . . . 17
3.2 Clean Electricity Output. . . 19
3.3 Electricity Price and Total Output . . . 19
3.4 Climate Policy and Fiscal Policy . . . 20
3.5 Cost-Eective Subsidy Allocation Rule . . . 22
3.6 Dierences in Innovation Costs and Cost-Eective Subisidy Allocation Rule . . 23
There's one issue that will de ne the contours of this century more dramatically than any other, and that is the urgent and growing threat of a changing climate.
Barack Obama, President of the United States of America (2009-2017)
Remerciements
Je tiens tout d'abord à remercier Dieu, le Tout puissant de m'avoir permis de faire cette thèse. Plusieurs personnes ont contribué à l'aboutissement de cette thèse. Je remercie sincèrement mon directeur de recherche le professeur Sylvain Dessy pour m'avoir encadré tout au long de cette thèse. Premièrement, il m'a permis d'intégrer le programme de doctorat en tant que directeur de programme. Ensuite, en tant que directeur de recherche, il m'a formé à la recherche en économie, il a été extrêmement disponible et m'a soutenu du début à la n de ma rédaction.
Je remercie les professeurs du département d'économique pour la formation qu'ils m'ont ap-portée. Je tiens particulièrement à remercier les professeurs Markus Herrmann, Philippe Barla, Martino Pelli, Vincent Boucher et Bruno Larue pour leurs commentaires constructifs sur ma recherche. Je remercie également les professeurs Carlos Ordás Criado, Charles Bellemare et Ar-naud Dellis. Je remercie le directeur du programme de doctorat, le professeur Stephen Gordon, le directeur du département le professeur Guy Lacroix, ainsi que son prédécesseur l'honorable Jean-Yves Duclos.
Je suis reconnaissant pour le soutien nancier que j'ai reçu de la Fondation de l'Université Laval, de la Faculté des Sciences sociales, du département d'économique et du Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques. Je remercie sincèrement mes superviseurs au Ministère de l'Énergie et des Ressources naturelles du Québec Madame Caroline Davoine et Monsieur Lamine Touré, mon superviseur à L'École nationale d'administration publique Monsieur Alexandru Gurau, ainsi que toute l'équipe de l'analyse des marchés du Québec de la Société canadienne d'hypothèque et du logement, en particulier Messieurs David L'Heureux, Nicolas Bernatchez et Madame Elisabeth Koulouris.
Je remercie tous les camarades que j'ai eus au doctorat en particulier mes promotionnaires Gilles Koumou, Aimé Simplice Nono, Sétou Diarra, Ali Yedan, Jean Armand Gnagne et Isaora Zefania Dialahy, j'ai appris énormément à travers nos discutions. Je remercie particulièrement Gilles pour sa disponibilité et ses conseils pour l'utilisation des logiciels Matlab et Latex. Je remercie tous les autres doctorants que j'ai côtoyés notamment André-Marie Taptué, Safa Ragued, Bodel Aymele, Abdellah Manadir, Marie Albertine Djuikom et Carole Kempa. Je
remercie Annie Gignac et toute l'équipe du Service de placement de l'Université Laval. Je remercie également tous mes amis qui m'ont toujours encouragé et soutenu en particulier Cédric Tinfa et Salomon Grunitzky.
En terminant, je remercie de tout c÷ur ma conjointe Alexandra Tchuam pour son soutien indéfectible. Je remercie in niment mon père le professeur Joseph Martin Bell et ma mère Rose pour avoir tout mis en place pour que j'aie la meilleure éducation possible, mon frère Tjomb et le reste de ma famille pour tout le soutien et les encouragements qu'ils m'ont apportés.
Introduction
Climate change is one of the biggest challenges facing the world. The Paris Agreement on climate change (2015) set the target of limiting global warming to less than 2 degrees Celsius by the end of the century compared to its preindustrial level. In order to meet this ambitious objective, each political jurisdiction must implement a drastic climate policy to mitigate an-thropogenic greenhouse gases (GHGs). The electricity sector is a major contributor to GHG emissions. For example, the US Environmental Protection Authority (EPA) estimated that in 2015, the electricity production which generated 29% of all GHG emissions held the largest share of GHG emissions in the US, and 67% of this production came from burning fossil fuels. Given the predominance of fossil-based sources in this sector, an important eort is needed to transform the way heat and electricity are generated (Popp,2010). However, climate policy action is no `free lunch'. Choosing the instrument that minimizes the cost of this "lunch" is, therefore, of paramount importance for progress needed to mitigate anthropogenic climate change.
This thesis examines cost-e cient solutions to reduce GHG emissions and promote climate-friendly technologies in the electricity sector. In fact, a complete climate policy in the elec-tricity generation sector features a tool to dissuade rms from emitting GHG and a policy to promote innovation of climate-friendly technologies (Popp,2006;Kalkuhl et al.,2015). On the dissuasive side, there are two main types of policy instruments : scal-based instruments (e.g., carbon tax and cap-and-trade) and intensity standard mandates (e.g., clean energy stan-dards). Each of these instruments can ful ll the target of reducing emissions through dierent mechanisms. Fiscal instruments make electricity producers internalize the cost of emissions, in addition to generating tax revenue that may be recycled to reduce a pre-existing tax (e.g., income or corporate taxes). Environmental economists tend to view these elements formali-zing the superiority of scal instruments over intensity standards (Holland et al., 2009). Yet, because they impose a lower bound on the ratio of clean, over total energy generated, standard mandates are a more precise form of intervention. Moreover, some studies show that standards tend to impose less distortion in the economy, which makes them a cost-eective instrument when lower emissions reduction is required (Goulder et al., 2016). However, existing studies examining the important issue of instrument choice for climate policy either rely on perfectly competitive models, abstract away from dierences in productivity between competing sources
of electricity or side step the potential role of innovation as a potential channel for the eect of climate policy.
The rst two essays of this thesis build around the existing literature by exploring the implica-tions of incorporating these realistic features of electricity generaimplica-tions. However, the choice of climate instruments need not be restricted to dissuasive instruments such as carbon pricing or intensity standards, especially if more ambitious emissions reductions are to be achieved. In-deed, there is evidence that a cost-eective rapid displacement of fossil fuel generation by low carbon alternatives is not possible without major breakthroughs in deployment technologies for large-scale renewable generation (Böhringer,2014). Moreover, there is substantial evidence showing that fossil fuel sources have the potential to contribute technological sound clean electricity solutions to climate change, for example, through innovations in carbon capture and storage (CCS) technologies.
I consider this possibility in my Ph.D. thesis and explore the issue of how to promote clean electricity solutions to climate change. In its 2015 issue of World Energy Report, the Inter-national Energy Agency (IEA) points to the urgency for countries to put in place domestic energy systems consistent with an emissions reduction trajectory that climate change research indicates would give an 80% chance of limiting average global temperature increase to 2 de-grees Celsius. Technological advances in this sector thus are seen as an essential part of the solution to the climate change problem. However, neither carbon-free electricity sources, such as wind and solar, nor alternative technological solutions, such as the CCS, are currently cost-competitive for large-scale electricity generation (Barrett,2009). Furthermore, the incentives provided by private markets for electricity innovation lead to underinvestment due to exter-nalities (Popp, 2010), which calls for supporting public investments, if climate change goals are to be achieved. Since public funds have an opportunity cost to be justi ed, and important research question is : What is the cost-eective allocation of public subsidies between clean technologies that increase the productivity of renewable sources and those that enhance clean electricity generation by fossil fuel sources ? Addressing this issue is the purpose of my third essay.
Throughout this thesis, I use general equilibrium models. This approach is relevant if one is to take full account of the constituents of the social cost of climate policy. Moreover, in two of the three essays, I embed imperfect competition into this framework, which takes the form of an oligopolistic market structure in the electricity sector, with a two-stage competition. Tech-nically, embedding a two-stage non-cooperative game in a general equilibrium model amounts to combining strategic and non-strategic elements in the de nition of the equilibrium of the economy, which calls for extra care, as to how this equilibrium is de ned and characterized. I calibrate all the theoretical models used, with selected macroeconomic aggregates of Bri-tish Columbia and the USA. This computational strategy allows me to conduct quantitative analyses that provide numerical answers to the relevant research questions.
I consider this Ph.D. thesis as both very important and scienti cally relevant to addressing the pressing issue of anthropogenic climate change. First, it sheds light on the determinants of a cost-eective choice of policy instruments likely to dissuade emissions and promote climate-friendly technologies in the electricity generationthe biggest emitting sector worldwide. Se-cond, it also sheds light on the principle underlying a cost-eective allocation of investment subsidies to competing sources of clean electricity solutions to climate change, highlighting the interactions between dissuasive instruments (e.g., the carbon tax), and those promoting best-practice (e.g., subsidies). Overall, my thesis contributes to the environmental economics literature focusing on emissions mitigation policy in the electricity sector, aside from the glo-bal or collective bene ts of mitigating climate change (e.g., Montero et al. (2002); Goulder and Parry (2008);Marron et al. (2015);Goulder et al. (2016);Lazkano et al. (2017)). It also contributes to the growing literature on clean energy solutions to anthropogenic climate change (e.g., Popp(2006);Gerlagh and Van der Zwaan(2006);Popp(2010);Lilliestam et al. (2012);
Kalkuhl et al. (2015); Lazkano et al. (2017)). My contribution to this literature spans three essays.
The rst essay compares an emissions tax and a clean energy standard using a calibrated gene-ral equilibrium model of electricity generation. The structure of electricity production features two plants : one that generates its output based on renewable sources and the other based on fossil source emitting CO2. The model is calibrated to match selected macroeconomic
aggre-gates of the economy of British Columbia, the rst North America's political jurisdiction to introduce a carbon tax. The calibrated model is then used to conduct conceptual experiments that pit the overall cost of achieving optimal emissions reduction target with a given policy instrument against the counterfactual cost of achieving the same target with an alternative policy instrument. The experiment leads to the conclusion that an emissions tax is more en-vironmentally eective as well as more cost-eective than a clean energy standard. Compared to the existing literature, this essay preserves the perfectly competitive environment under-lying existing studies of instrument choice but adds the feature of dierences in costs between renewable and fossil fuel-based generation technologies.
The second essay extends the comparison between a clean electricity standard and a carbon tax on cost-eectiveness grounds by adding innovation and market power. In fact, a two-stage competition in the electricity sector between a clean plant and its "dirty" rival anchors a two-sector general equilibrium model of climate change intervention. The dirty plant can innovate to reduce its emissions, and the clean plant can innovate to reduce its pre-existing cost-disadvantage. Innovation and market power combine to generate new insights, rst on the ability of revenue-neutral climate policy to generate a revenue-recycling eect, and second, on the mechanisms through which it increases the ratio of clean, over total, electricity generated. The model is calibrated to selected US macroeconomics aggregates. Numerical simulations uncover new sources of heterogeneity in the ranking of alternative policy instruments, which
evaded the lenses of perfect competition models. In particular, pre-existing plant-speci c dif-ferences in production and innovation costs emerge as key factors controlling this ranking. Unlike the existing literature on instrument choice, this essay relaxes the assumption of per-fect competition in the electricity sector. It also extends this literature to include the feature of technological innovations in the electricity sector.
The third essay examines the issue of how to promote climate-friendly technologies. Preci-sely, this essay analyzes the cost-eective rule for allocating investment subsidies between productivity-enhancing renewable technologies and fossil fuel-based carbon mitigation solu-tions. The underlying general equilibrium model features a duopolistic electricity generation sector, alongside a nal-good sector. A quantitative macro-analysis using the calibrated ver-sion of the model indicates that, when a carbon tax is used to incentivize abatement, the cost-eective subsidy allocation rule is one that in icts no multiple punishments (no `double jeopardy') on fossil fuel power sources. Consequently, when dierences in innovation costs between the two sources of clean electricity solutions to climate change are not too large, it is more cost-eective to allocate a greater share of subsidies to carbon mitigation solutions. Moreover, to reach a more ambitious emissions reduction target, it is more cost-eective to increase both the carbon tax and the share of subsidies allocated to fossil fuel sources.
Chapitre 1
Between Fiscal Instruments and
Intensity Standards : What Best
Promotes A Cost-Eective
Decarbonization ?
AbstractFiscal instruments are increasingly becoming the centerpiece of eorts to reduce greenhouse gases in many political jurisdictions, but are still debated on cost-eectiveness grounds. This paper compares an emissions tax and a clean energy standard using a calibrated general equilibrium model of electricity generation. Our comparative cost-eectiveness analysis is grounded in a four-step thought experiment that pits the overall cost of achieving an optimal emissions reduction target with a given policy instrument against the counterfactual cost of achieving the same target with an alternative policy instrument. The experiment leads to the conclusion that an emissions tax is more environmentally eective as well as more cost-eective than a clean energy standard.
JEL : Q42, Q43, Q52, Q53, Q58 ; Keywords : Greenhouse gases, scal instruments, intensity standards, cost-eectiveness, calibration.
1.1 Introduction
The centerpiece of a public policy aimed at reducing emissions of greenhouse gases (GHG) is the instrument used to implement it. Yet, as political leaders trumpet their commitment to mitigate GHG emissions in their respective jurisdictions, at the research front, the issue of which policy instrument is the most cost-eective remains a hotly contested area of discussion. There are two main types of policy instruments : scal-based instrumentse.g., emissions taxes and cap-and-trade and intensity standard mandatese.g., clean energy standards (hereafter Standard). Recent focus has been on the relative merit of scal instruments, and on how the revenue they raise can be recycled into the tax system to enhance their attractiveness. Despite this attractive feature of scal instruments of emissions mitigation, concerns remain over the magnitude of the overall burden they place on the economy. On the one hand, unlike a intensity standard mandate, a scal instrument raises revenue which can be recycled into the system to reduce pre-existing distortions from non-environmental policies (Goulder,2013;Goulder et al.,
2016;Marron et al.,2015) . But on the other hand, a scal instrument is more distortionary than a intensity standard mandate (Goulder et al.,2016). In the absence of revenue-recycling, the overall burden on the economy is therefore arguably higher when GHG emissions are mitigated with a scal instrument rather than with a intensity standard mandate. Even after the revenue-recycling eect is accounted for, it remains unclear which of these two types of instruments ends up placing the lowest overall burden on the economy. In their treatment of this issue, existing workse.g.,Goulder et al.(2016) reach inconclusive results. Each of the two types of instruments can dominate the other, depending on the emissions reduction target considered. Yet, the common denominator of existing cost-eectiveness analyses is that they compare the two types of policy instruments within a range of emissions reduction targets that includes those that are not necessarily politically feasible. This raises the important issue of whether restricting the comparison between instrument of emissions mitigation within the range of those that are politically feasible can remove this inconclusivess.
This paper advances the idea that when comparisons between an emissions tax and a Stan-dard are restricted to levels of emissions reduction that are optimal from the viewpoint of a benevolent utilitarian regulator, the former dominates the later on grounds of both environ-mental eectiveness and cost-eectiveness. We justify this restriction by the fact that, in the real world, emissions reduction targets are not implementable unless they win political sup-port from stakeholders. This raises the relevance of cost-eectiveness analyses that generate a ranking of policy instruments based upon a range of politically feasible emissions reduction targets, but also raises the important issue of how to measure cost-eectiveness in this context. To address this issue, we develop a one-sector general equilibrium model, from which we draw the ingredients of our cost-eectiveness analysis. Our model focuses on electricity-related GHG emissions. The focus on the electricity or power generation sector is motivated by the fact that this sector is a prominent source of GHG emissions. For example, in 2013, the US
Environ-mental Protection Authority (EPA) estimated that the power generation sector accounted for 31 % of all GHG emissions in the US. Furthermore, this sector is also one where intensity standard mandates are still very prominent instruments of emissions mitigation. For example, in the United States, intensity standards are used at the federal level and in 29 States, whereas in Canada, they are used at the federal level (OECD 2015).
There are three important features in our model. First, electricity generation has a constant-elasticity-of-substitution in emitting sourcese.g., coal plants and clean power sources e.g., windmills and solar panels. Calibration of the model will quantitatively determine the degree of substitutability of these two sources of electricity at the economy-wide level, along with other relevant parameters. Second, households in our model care about a public good e.g., clean air, the quantity of which is negatively aected by GHG emissions (Parry et al.,
2015). Third, consumption of electricity is subject to a subsistence requirement. The addition of a subsistence requirement as a feature of electricity consumption is justi ed by the fact that, in almost all countries, electricity is directly linked to household subsistence activities, as it is used to power household appliances like televisions, fans, radios, and in some climates, the heating system. It also plays an essential role in the provision of healthcare services, the operation of public transportation systemse.g., subway trains, and the production of good and services in general. A high frequency of power outages can therefore create havoc in the economy. This implies that there exists a minimum level of electricity consumption below which households' subsistence will be at stake. The last two features of our model provide a justi cation for both the desirability of emissions mitigation eort aside from the collective bene ts of arresting climate change at the global level, and the requirement that the regulator's emissions mitigation eort be politically feasible.
For the purpose of this study, therefore, we de ne an optimal emissions reduction target as one that is achieved by maximizing utilitarian social welfare over all households. In this context, a policy instrument will be said to be cost-eective, if the welfamaximizing emissions re-duction target it induces cannot be replicated by another instrument at an overall lower cost to the economy. Our cost-eectiveness analysis requires that we de ne and characterize the measure of the economic cost induced by each policy instrument of emissions mitigation. We select this measure based upon the qualitative predictions of our model. Indeed, our theoretical model makes a number of qualitative predictions. First, emissions mitigation policy tends to reduce the real return to laborthe only source of income for households in our model, and to increase labor supply, irrespective of the type of instrument implementing it. Second, and more importantly, our model also predicts that emissions mitigation policy tends to reduce after-tax per capita income, irrespective of the type of instrument implementing it. On this evidence, the reduction in after-tax per capita income induced by an emissions mitigation policy is a good measure of the overall economic cost of implementing it.
eco-nomic cost of achieving an optimal emissions reduction target with a given policy instrument against the counterfactual cost of achieving this target of emissions reduction through an al-ternative policy instrument. The thought experiment proceeds in four steps. In the rst step, we calibrate the model to match selected macroeconomic aggregates of the economy of the Canadian province of British Columbiathe rst North America's political jurisdiction to introduce a carbon tax. We derive some quantitative predictions with respect to the eects of varying the intensity of the emissions mitigation eort, for a given policy instrument. We show that the calibrated model replicates the qualitative predictions of the theoretical model. In the second step of our thought experiment, we use the calibrated model to quantitatively determine the optimal income tax rate under the counterfactual scenario of complete environ-mental policy inaction. We also compute the associated optimal levels of per capita after-tax income and GHG emissions, respectively. We interpret the outcomes of this counterfactual laissez-faire as a benchmark or reference case, against which we measure the environmental eectiveness of a given policy instrument, as well as its cost-eectiveness.
In the third step, we quantitatively determine the optimal emissions mitigation eort with alternative policy instruments, as an integral part of a revenue-neutral optimal scal reform. This allows us to compute, for each policy instrument, the optimal level of per capita after-tax income, and GHG emissions. We combine these variables with those obtained in step two of the experiment to compute the optimal emissions reduction target associated with each instrument as the dierence between the optimal level of GHG emissions under complete policy inaction and the corresponding level obtained with a given instrument. We interpret this dierence as a measure of the environmental eectiveness of this policy instrument. We also compute the overall cost to the economy of mitigating GHG emissions with a given policy instrument as the dierence between the optimal level of per capita after-tax income under the counterfactual laissez-faire and the corresponding gure obtained with this policy instrument. We complete the thought experiment in the fourth and nal step, by pitting the overall cost to the economy of reaching an optimal level of emissions reduction target with a given po-licy instrument against the counterfactual overall cost to the economy of reaching this target with an alternative policy instrument. First, starting with the Standard, we ask if the op-timal emissions reduction target it induces can be replicated by a revenue-neutral emissions tax with an overall lower cost to the economy. To address this question, we solve a system of two equations in two unknowns, including the counterfactual levels of the emissions tax and income tax rate, respectively. The emissions tax thus obtained is used to compute the counterfactual overall cost to the economy of using this alternative instrument to replicate the optimal emissions reduction level achieved with Standard mandate. Second, reversing this process and starting with the emissions tax instead, we follow the same computational steps as in the case of the Standard. We repeat both case scenarios of this last step of our thought experiment for various levels of the relative cost-disadvantage of switching the economy from
GHG-emitting power sources to clean sources. We do so in order to assess whether the level of the cost-disadvantage of switching the economy to clean power sources in uences the ranking of alternative policy instruments. We rst show that for all levels of this cost-disadvantage, an emissions tax is always more environmentally eective than a Standard mandate, owing to the fact the latter, unlike the former, does not generate revenue. We then show that for all levels of this cost-disadvantage, a revenue-neutral emissions tax replicates the Standard's optimal emissions reduction target at a signi cantly lower cost to the economy. In contrast, for all levels of this cost-disadvantage, a revenue-neutral Standard can only replicate an emis-sions tax's optimal emisemis-sions reduction target at a signi cantly higher cost to the economy. On the basis of the thought experiment thus outlined, we conclude that an emissions tax is relatively more cost-eective than a Standard mandate. This nding is important because it suggests that global eorts to reduce electricity-related emissions of greenhouse gases can be enhanced if all political jurisdictions implement their emissions mitigation eorts with scal instruments, instead of intensity mandates.
Our study contributes to the environmental economics literature focusing on emissions miti-gation policy, aside from the global or collective bene ts of mitigating climate change (e.g.,
Goulder (1995);Parry et al. (1999);Bento and Jacobsen(2007);Fullerton and Heutel (2007);
Holland et al.(2009);Krupnick and Parry(2012);Goulder(2013);Parry et al. (2015);Ambec and Ehlers (2016); Marron et al. (2015); Goulder et al. (2016)). However, the closest analy-sis to ours is Goulder et al.(2016) who contrast the performances of a carbon tax a scal instrument and a Standard mandate, subject to the constraints that (i) both these emissions mitigation instruments are used to reach the same emissions reduction target and (ii) both are revenue-neutral. In this context, they highlight factors that cause the Standard to dominate the carbon tax, as the most cost-eective instrument of emissions mitigation. While retaining some of the features of Goulder et al. (2016), including revenue-neutrality of emissions mitigation policy, our model nevertheless diers from their in several respects. First, unlikeGoulder et al.
(2016), we restrict comparisons between alternative policy instruments to emissions reduction targets that are optimal from the viewpoint of a benevolent Utilitarian regulator. This allows our measure of cost-eectiveness to bear on the reality that to be implementable, a regulator's desired level of emissions reduction must win political support. Second, as in (Parry et al.,
2015), our model captures the harmful eects of GHG emissions (for example in the form of poor air quality), and link them to the level of provision of a public good say, clean air. This causes households to care about emissions abatement, a feature which has implications for the desired level of emissions reduction. Third, an important departure fromGoulder et al.(2016) is the introduction of a subsistence requirement for electricity consumption. The incorporation of this real-world feature of electricity consumption not only enhances our model's connection to reality, but it also alters households' consumption-leisure trade-o in a way that impacts the indirect revenue eect of emissions mitigation policy. In particular, unlike inGoulder et al.
rate must rise to keep revenue invariant at the optimum, under revenue-neutrality of scal reforms. Finally, unlike Goulder et al. (2016), we treat the level of cost-disadvantage of swit-ching to clean sources of electricity generation as exogenous. This modeling strategy allows us to assess the potential role played by the relative cost-disadvantage of making the economy switch to clean power sources in the ranking of alternative policy instruments. Overall, these four distinguishing features of our model position this study as a complement toGoulder et al.
(2016).
The rest of the paper is organized as follows. Section 2 presents the analytical model as well as the main features of equilibrium. Section 3 presents the quantitative analysis and the results of the associated thought experiments. Section 4 oers conclusions. Finally, tables are included in the Appendix section.
1.2 The Economic Environment
We develop a theory of GHG emissions and abatement emphasizing three main features. First, households face a subsistence requirement for electricity consumption. Second, at the economy-wide level, electricity generation has a constant-elasticity-of substitution between GHG-emitting sources coal plants and clean, renewable sourcese.g., windmills and solar panels. Third, rms face a cost-disadvantage of switching from GHG-emitting to clean sources of electricity generation. We use this theory as a basis for comparing an emissions tax and a Standard mandate on the ground of cost-eectiveness.
1.2.1 General Description
The economy consists of three types of agents : a stand-in rm which produces electricity (the numeraire) using labor and a composite power inpute.g., fossil fuel, solar panels, etc., a stand-in household who splits its time between labor supply and leisure, and a regulator endowed with the power of coercion and taxation, who supplies a public goode.g., clean air to the stand-in household. The regulator is concerned about GHG emissions because they reduce the quantity of the public good available to the stand-in household, and thus may seek to mitigate emissions, either through an emissions tax or Standard. We abstract from physical capital and aggregate uncertainty in this economy.
A. Household's Problem
The stand-in household derives utility from consumption of the numeraire, c, leisure, l, and a public good, G. The utility function representing these preferences is given by :
where c > 0 denotes a subsistence requirement for electricity consumption, σ > 0 and µ > 0 measure the relative contribution of leisure and clean air to the the stand-in household's utility, respectively.
The quantity of clean air, G, depends negatively of the national level of GHG emissions, E, and positively on the level of public investment in the provision of better air quality or provision of medical solutions to poor air quality problems (e.g., healthcare facilities). The quantity of clean air thus has the following speci cation :
G := T
1 + E, (1.2)
where T denotes both the level of public investment and total revenue under a balanced-budget legislation. The stand-in household receives an after-tax wage rate (1 − τω)ω in exchange for
one unit of labor services delivered to the stand-in rm, where τω denotes the income tax rate
whose level is determined optimally by the regulator, and ω, the wage rate which equals the real return to labor under perfect competition. Consumption of the numeraire thus is subject to the following budget constraint :
c ≤ (1 − τω) (1 − l) ω (1.3)
where 1 − l denotes household's time allocated to labor. The stand-in household takes G, ω and τω as given, and chooses leisure l to solve the following problem :
max
l {(1 − µ) [ln ((1 − τω) (1 − l) ω − c) + σ ln l] + µ ln G}
We denote as L (τe ω, ω) the policy rule derived from this problem. B. Firm's Problem
At the economy-wide level, electricity output is Cobb-Douglas in labor, N, and a composite power input. We assume that at the economy-wide level, the composite electricity-generating input is constant-elasticity-of-substitution in clean sources, Xc, and dirty, or GHG-emitting
sources, Xd. Thus aggregate production of electricity can be described as follows :
Y = AN1−α[(Xc)ρ+ (Xd)ρ]
α
ρ , (1.4)
where A denotes total factor productivity, ρ, a parameter that controls the elasticity of sub-stitution between the clean power source and dirty power source at the economy-wide level, and α ∈ (0, 1), the share of the composite input in the output. Our calibration procedure, described in the next section, allows for the parameters of the function in (1.4) as well as preference parameters to be determined by a set of calibration targets in British Columbia's data.
We assume that the cost of generating one unit of electricity from a clean source (respectively, dirty source) is exogenously given by κc (respectively, κd). These per unit costs measure not
just the price of the equipment (such as wind turbines or coal), but also local maintenance, storage technology, grid connection, and other operational costs. We also assume that κc >
κdi.e., there is a cost-disadvantage of switching from the dirty to the clean power source.
This assumption is based upon the fact that the various ways of generating electricity exhibit signi cantly dierent costs, with the cleaner ways being in general more costly than the dirtier ways. This cost-disadvantage of clean electricity varies from one location to another depending on the type of power source (either solar-based or wind-based). For example, since areas near the Equator get more sunlight than the areas near the poles, the cost-disadvantage of generating solar-based energy may be higher in the latter than in the former. Another element that increases the cost-disadvantage of generating electricity with clean power sources is its variability at dierent time periods (daytime vs. nighttime, or winter vs. summer), which raises storage capacity and management issues. In its 2010 Edition of Projected Cost of Electricity, the US International Energy Agency (IEA) reveals that the median levelized cost of producing baseload power from natural gas, coal and atomic plants (dirtier sources of electricity) was about $100 a megawatt-hour compared with about $500 for solar-based electricity a 5-to-1 dierence. To keep the focus on the relative cost-disadvantage of switching to clean power sources, we de ne the level of this cost disadvantage as
φ = κc κd
, (1.5)
and normalize κdto one.
Let us denote as θ ∈ {0, τe, ¯xc} both the regulator's emissions reduction eort and the policy
instrument she uses. In particular, θ = 0 means the regulator makes no eort to reduce GHG emissions ; θ = τe means her eort takes the form of an emissions tax levied on each unit of
GHG emitted by the stand-in rm ; θ = ¯xc means this eort takes the form of a mandated
minimum ratio of clean to total power-generating inputs used, ¯xc ∈ [0, 1]. We thus follow
Goulder et al. (2016) in referring to ¯xc as the clean energy standard, according to which
the stand-in rm's choice of power-generation inputs combination (Xc, Xd) must satisfy the
following constraint :
Xc
Xc+ Xd
≥ ¯xc. (1.6)
Given the regulator's emissions mitigation eort, θ, and assuming that the Standard intensity is binding whenever in eect, the stand-in rm's pro t can be expressed as follows :
π (θ) = AN1−α[(Xc)ρ+ (Xd)ρ] α ρ − ωN − φX c− Xd if θ = 0 AN1−α[(Xc)ρ+ (Xd)ρ] α ρ − ωN − φXc− X d− τeE if θ = τe AN1−α[ξ (¯xc) X]α− ωN − ζ (¯xc) X if θ = ¯xc , (1.7)
where E denotes the total level of emissions, and X := Xc+ Xd; ξ (¯xc) := [(¯xc)ρ+ (1 − ¯xc)ρ]
1
ρ; ζ (φ, ¯x
c) := 1 + (φ − 1)¯xc.
Following Bento and Jacobsen (2007), we assume that the emissions level is proportional to the quantity used of the dirty power-generating input, Xd:
E = βXd, (1.8)
where β > 0. The stand-in rm takes the regulator's emissions mitigation eort, θ, and the relative cost-disadvantage of generating electricity with the clean power-generating input, φ, as given when choosing its optimal inputs' levels by maximizing (1.7).
1.2.2 Equilibrium Analysis
Given the income tax system, τω, and the regulator's emissions mitigation eort, θ, an
equi-librium is an allocation {l∗, X∗
c, Xd∗, N∗} and a wage rate ω∗, such that l∗ solves the stand-in
household's problem, the vector (X∗
c, Xd∗, N
∗) solves the stand-in rm's pro t-maximization
problem, and the labor market clears. We characterize this equilibrium below.
First, given the regulator's emissions mitigation eort, θ, pro t-maximization under perfect competition yields the market-clearing wage rate, ω∗ = ω (θ), the level of emissions, E∗ =
E (θ), and the ratio of clean to total power-generating input xc(θ) = Xc/X, as follows : ω (θ) = e A (1 + [ϕ (0)]ρ)α¯ if θ = 0 e A (1 + [ϕ (τe)]ρ)α¯ if θ = τe ¯ A " [(¯xc)ρ+ (1 − ¯xc)ρ] 1 ρ (φ − 1) ¯xc+ 1 #1−αα if θ = ¯xc (1.9) E (θ) = χ (0) (1 + [ϕ (0)]ρ)α¯N (0, τω) if θ = 0 χ (τe) (1 + [ϕ (τe)]ρ)α¯N (τe, τω) if θ = τe ¯ β (1 − ¯xc) " [(¯xc)ρ+ (1 − ¯xc)ρ] α ρ [(φ − 1) ¯xc+ 1] #1−α1 N (¯xc, τω) if θ = ¯xc (1.10) xc(θ) = ϕ (0) 1 + ϕ (0) if θ = 0 ϕ (τe) 1 + ϕ (τe) if θ = τ e ¯ xc if θ = ¯xc (1.11)
where N = 1 − l∗ equals to the total supply of labor by the stand-in household under
market-clearing, and ¯ A := (1 − α) (ααA)1−α1 ; A := (1 − α)e α φ α A 1−α1 ; β = β (αA)¯ 1−α1 .; ¯ α := (1 − ρ) α (1 − α) ρ ϕ (τe) := φ 1 + βτe 1 1−ρ χ (τe) = αA φ 1 1−α ϕ (τe) .
Observe that the Standard intensity ¯xcis never binding unless the following condition
¯ xc≥
ϕ (0)
1 + ϕ (0) (1.12)
is satis ed. The right-hand side of this inequality denotes the ratio of clean to total power-generating input under the laissez-faire regime (i.e., θ = 0).
A classic exercise is to explore potential sources of similarities/dissimilarities between the eects of an emissions tax and of a Standard. First, from (1.9), taking the partial derivative of ω (θ) with respect to θ 6= 0 yields
∂ω ∂θ = ρ ¯α eA (1 + [ϕ (τe)]ρ)α−1¯ [ϕ (τe)]ρ−1 ∂ϕ ∂τe if θ = τe [(¯xc)ρ+ (1 − ¯xc)ρ] 1−ρ ρ [(φ − 1) ¯xc+ 1]2 h (¯xc)ρ−1− φ (1 − ¯xc)ρ−1 i if θ = ¯xc . (1.13)
Since by construction ∂ϕ/∂τe < 0, it clearly follows from (1.13) that for the emissions tax
regime, ∂ω/∂τe < 0. Under a Standard mandate, it can be seen by inspection of (1.13) that
the eect of the intensity standard, ¯xc, on the real wage, ω, is strictly positive if and only if
(¯xc)ρ−1− φ (1 − ¯xc)ρ−1> 0, (1.14)
and negative if and only if the reverse is true. Observe, however, that in order for condition (1.14) to hold, it must be that
¯ xc<
1 1 + ϕ (0),
which is impossible since φ ≥ 1, and the Standard intensity is binding, as implied by (1.12). Therefore it follows that under condition (1.12), ∂ω/∂¯xc< 0as well. We have just established
the following result :
Proposition 1. Under condition (1.12), the regulator's emissions mitigation eort reduces the wage rate, irrespective of the policy instrument implementing it.
Proposition 1 implies that ω (θ) < ω (0), for θ 6= 0. In other words, the regulator's emis-sions mitigation eort imposes an implicit tax on labor, irrespective of the policy instrument implementing this eort.
Second, expression (1.10) shows there are two dierent channels for the impact of the regu-lator's emissions mitigation eort, a direct channel, and an indirect channel working through households' labor supply, N (θ, τω). It is through this latter channel that the subsistence
requi-rement for electricity consumption impacts the level of emissions. Indeed, as we show below, through the labor supply channel, both the emissions tax and a Standard tend to push emis-sions up because they force households to supply more labor, on subsistence grounds in the face of reduced labor wage.
Given the tax system as determined by the marginal income tax rate, τω, and the regulator's
emissions mitigation eort, θ, the stand-in household's equilibrium labor supply, N (θ, τω) =
as follows : N (θ, τω) = 1 1 + σ 1 + σc (1 − τω) ω (0) if θ = 0 1 1 + σ 1 + σc (1 − τω) ω (τe) if θ = τe 1 1 + σ 1 + σc (1 − τω) ω (¯xc) if θ = ¯xc (1.15) R (θ, τω) = 1 1 + σ[(1 − τω) ω (0) + σc] if θ = 0 1 1 + σ[(1 − τω) ω (τe) + σc] if θ = τe 1 1 + σ[(1 − τω) ω (¯xc) + σc] if θ = ¯xc (1.16)
Expressions (1.15) and (1.16) show that both the pre-existing labor income tax and the emis-sions mitigation eort are distortionary. One can see from (1.15) the implication of introdu-cing a subsistence requirement for electricity consumption, c. Because of it, any exogenous increase (respectively, decrease) in the wage rate reduces (respectively, increases) labor supply (N ≡ 1 − l).
How does the regulator's emissions mitigation eort aect labor supply and household dis-posable income ? Are there similarities/dissimilarities between a Standard and an emissions tax ? To address these questions, we assume for now that emissions mitigation does not aect the income tax rate, τω, i.e., it is not revenue-neutral. Under this condition, the following
Proposition, which obtains as an implication of Proposition 1, summarizes our answer to the aforementioned questions :
Proposition 2. Under condition (1.12), a non-revenue-neutral emissions mitigation eort increases households' labor supply, while also reducing their disposable income, irrespective of the policy instrument implementing it.
Proposition 2 implies that (i) N (θ, τω) > N (0, τω) and (ii) R (θ, τω) < R (0, τω), for all
θ 6= 0. The rst part of this proposition is a direct implication of the incorporation of a subsistence requirement for electricity consumption. The second part highlights the burden the regulator's emissions mitigation eort places on the economy. Indeed, it suggests that protecting the environment is no free lunch, as pointed out by Fullerton and Metcalf (1997). Part (ii) of Proposition 2 implies that both policy instruments place a burden in the economy in the form of a decrease in the stand-in household's after-tax incomewhich, in this case of
homogenous households, can be interpreted as after-tax per capita income. It thus suggests that the negative eect induced by emissions mitigation policy on after-tax per capita income, R (θ, τω), is an adequate measure of the economic cost of this policy.
We showed in (1.10) above that households' labor supply behavior aects emissions. Given this labor supply behavior as described in Proposition 2, and using (1.9), we arrive at the following equilibrium level of emissions :
E (θ, τω) = αϕ (0) (1 + σ) (1 − α) φ ω (0) + σc 1 − τω if θ = 0 αϕ (τe) (1 + σ) (1 − α) φ ω (τe) + σc 1 − τω if θ = τe e β (1 − ¯xc) (1 + σ) ζ (¯xc) ω (¯xc) + σc (1 − τω) if θ = ¯xc (1.17) where e β := αβ 1 − α.
With expression (1.17), we are now ready to characterize the impact emissions mitigation policy has on the level of GHG emissions. Partially dierentiating this expression with respect to θ 6= 0, taking into consideration the fact that ϕ0(τ
e) < 0 and ζ0(¯xc) > 0 by construction,
yields the following result, as an implication of Proposition 1 :
Proposition 3. Under condition (1.12), increasing the level of θ ∈ {τe, ¯xc} reduces the
equi-librium level of GHG emissions.
Proposition 3 states that E (θ, τω) < E (0, τω) for all θ 6= 0, implying that both policy
instru-ments are eective in mitigating GHG emissions. This implies that the dierence E (0, τω) −
E (θ, τω) corresponds to the level of emissions reduction brought about the policy instrument
θ ∈ {τe, ¯xc}.
1.2.3 The Regulator's Policy Objective
The government may levy up to two kinds of taxes to nance its expenditures. On the one hand, he levies an income tax at a at rate, τω. Given our normalization of the population
size, and given the regulator's emissions reduction eort, θ, total pre-tax households' income amounts to ω (θ) N (θ, τω). As households represent the only tax base for the income tax, total
tax revenue is τωω (θ) N (θ, τω). When θ = τe, the emissions tax becomes another source of
(1.17), we arrive at the following expressions for total scal revenue : T (θ, τω) := τω 1 + σ ω (0) + σc 1 − τω if θ = 0 τω 1 + σ ω (τe) + σc 1 − τω 1 + ατeϕ (τe) τω(1 − α) φ if θ = τe τω 1 + σ ω (¯xc) + σc 1 − τω if θ = ¯xc . (1.18)
Note that unlike the emissions tax, the Standard is not a direct source of revenue for the regulator. Therefore, since by Proposition 1 the inequality ω (¯xc) < ω (0)holds, it follows by
inspection of (1.18) that for a given income tax rate, τω, a Standard reduces scal revenue :
T (¯xc, τω) < T (0, τω). In the case of the emissions tax, partially dierentiating (1.18) with
respect to τe, rearranging terms, yields :
∂T ∂τe = τω 1 + σ 1 +ατ¯ eϕ (τe) τω ∂ω ∂τe + α ¯¯ϕ (τe) [1 − ρ (1 + βτe)] (1 − ρ) τω ω (τe) + σc 1 − τω (1.19) where ¯ α := α τω(1 − α) φ ; ϕ (τe) := φ2−ρ1 1 + βτe !2−ρ1−ρ .
Since by Proposition 1, ∂ω/∂τe< 0, it follows that the sign of the partial derivative, ∂T/∂τe,
is ambiguous. Hence the following result :
Proposition 4. Under condition (1.12), a non-revenue-neutral Standard causes a reduction in tax revenue (i.e., T (¯xc, τω) < T (0, τω)). Furthermore, if
ρ > 1 1 + βτe
, (1.20)
then an emissions tax also causes the tax revenue to decrease (i.e., T (τe, τω) < T (0, τω)).
Proposition 4 thus raises the possibility that both policy instruments may have a negative (instead of a positive) revenue-recycling eect under the requirement of revenue-neutrality of emissions mitigation policy. However, note that while this possibility turns out to be a certainty in the case of a Standard, in the case of an emissions tax, its realization depends on a condition (1.20) being satis ed. Since the level of the emissions tax, τe, is determined by a
Utilitarian welfare-maximizing regulator, it is not clear whether condition (1.20) is necessarily satis ed at the optimum. In what follows, we analytically explore the possibility of a positive revenue-recycling eect.
De nition 1 : The regulator's emissions mitigation eort, θ 6= {τe, ¯xc}, is said to
be revenue-neutral if and only if it induces a scal reform, τω,such that :
where τ∗
ω denotes the optimal or welfare-maximizing tax rate under the
laissez-faire regime.
Expression (1.21) implies a relationship between θ and τω, for all θ 6= 0. Using (1.18) we can
rewrite this identity as follows : ∆ (θ, τω) := T (θ, τω) − T (0, τω∗) ≡ 0, where
∆ (θ, τω) = τω 1 + σ ω (τe) + σc 1 − τω 1 + ατeϕ (τe) τω(1 − α) φ − T (0, τω∗) if θ = τe τω 1 + σ ω (¯xc) + σc 1 − τω − T (0, τω∗) if θ = ¯xc (1.22)
Totally dierentiating (1.22) yields :
dτω dθ = −∂T ∂τe /∂T ∂τω if θ = τe −τω ∂ω ∂ ¯xc ω (¯xc) + σc 1 − τω 2 − τω 1 − τω −1 if θ = ¯xc (1.23) where ∂T ∂τω = σc (1 − τω)2 τω+ ατeϕ (τe) (1 − α) φ + ω (τe) + σc 1 − τω > 0
and ∂T/∂τe is as characterized in (1.19) above. Consider rst a Standard regime. Observe
from (1.23) that ω (¯xc) + σc 1 − τω 2 − τω 1 − τω > 0. Furthermore, by Proposition 1, ∂ω/∂¯xc< 0. Therefore, we have that
dτω
d¯xc
> 0.
Next, consider an emissions tax. From Proposition 4, we know that if condition (1.20) holds, then ∂T ∂τe < 0, in which case, dτω dτe > 0
as well. We have just established the following Proposition :
Proposition 5. Under conditions (1.12) and (1.20), a revenue-neutral Standard causes the income tax rate to increase, as does a revenue-neutral emissions tax. However, if
ρ < 1 1 + βτe (1.24) and ∂ω ∂τe > −α ¯¯ϕ (τe) [1 − ρ (1 + βτe)] [τω+ ¯ατeϕ (τe)] (1 − ρ) ω (τe) + σc 1 − τω , (1.25)
Conditions (1.24) and (1.25) are necessary and su cient conditions for a revenue-neutral emissions tax to induce a decrease in the level of the income tax rate, τω. Proposition 5
implies that a revenue-neutral Standard unambiguously induces a rise in the income tax rate, because it raises no revenue of itself, while it indirectly causes the level of scal revenue to decrease. Note, however, that the advantage of the emissions tax over a Standard mandate is not set in stone. Instead, it hinges on conditions (1.24) and (1.25) being satis ed in the real world. Whether or not this is indeed the case will only become clear in our quantitative analysis to follow.
Next, moving on to the regulator's policy objective, it is important to recall that in this study, we follow a large body of the literature on optimal public policy in assuming that the regulator sets the optimal level of her chosen emissions mitigation eort so as to maximize Utilitarian social welfare over all households represented in our model by the stand-in household. The regulator's objective thus is obtained from (1.1), by substituting in the stand-in household's optimal consumption-leisure allocation, as follows :
W (θ, τω) = (1 − µ) [(1 + σ) ln [(1 − τω) ω (θ) − c] − σ ln (1 − τω) ω (θ)]
+ µ ln T (θ, τω)
1 + E (θ)+ γ (1.26)
where
γ := (1 − µ) [σ ln σ − (1 + σ) ln (1 + σ)] .
The regulator's choice variables thus include her emissions mitigation eort, θ, and the income tax rate, τω, under revenue-neutrality.
1.2.4 The Thought Experiment
In this sub-section we describe the analytical process underlying our quantitative assessment of the best policy instrument for mitigating GHG emissions. In the environmental economics literature, the comparison between several policy instruments of emissions mitigation is often carried on the basis of their relative cost-eectiveness. Krupnick and Parry (2012) de ne a cost-eective policy instrument as one that achieves a given level of emissions reduction at the lowest overall cost to the economy, after accounting for the regulator's use of scal revenue potentially raised. This implies that the policy instrument is revenue-neutral. However, in a departure from Krupnick and Parry(2012), we assess the cost-eectiveness of a given policy instrument only for optimal emissions reduction levels. This guarantees that the emissions reduction level for which a given policy is cost-eective is indeed implementable by a benevolent Utilitarian regulator.
De nition 2 : A policy instrument is said to be cost-eective, if the optimal emissions reduction level achieved through it cannot be replicated by any other revenue-neutral instrument at an overall lower cost to the economy. To compare an emissions tax to a Standard, we design a thought experiment which proceeds in four steps. First, we calibrate the model parameters such that the equilibrium of our model matches selected data from the Canadian Province of British Columbia. In a second step we determine the optimal scal policy under the laissez-faire regimeunderstood as one where there is complete inaction vis-a-vis GHG emissions. This amounts to setting θ = 0, and using (1.26) to quantitatively determine
ˆ
τω0= arg max
τω
W (0, τω)
We repeat this step for various levels of the cost-disadvantage, φ, of switching the economy from fossil fuel-based sources of electricity generation to clean, renewable sources. This allows us to later check whether this cost-disadvantage matters for the choice of the best policy instrument for mitigating GHG emissions. The purpose of this second step is to provide quantitative values for the optimal pair, Eφ 0, ˆτω0 , Rφ 0, ˆτω0 , Tφ 0, ˆτω0
, which form the benchmark against which we quantitatively assess the cost-eectiveness of a given policy instrument. The terms Eφ 0, ˆτω0 , Rφ 0, ˆτω0 , and Tφ 0, ˆτω0
denote, for each level of φ, the optimal levels of GHG emissions, the after-tax per capita income, and total scal revenue respectively, under the laissez-faire regime corresponding to θ = 0.
In a third step, we compute the optimal revenue-neutral policy mix consisting of an emissions mitigation action, θ ∈ {τe, xc}, and an income tax rate, τω. In other words, we use (1.26) to
quantitatively determine ˆθ, ˆτω = arg max (θ,τω) W (θ, τω) s.t.(1.21)
In doing so, care is taken to distinguish between an emissions tax ( ˆθ = ˆτe) and a Standard
mandate (ˆθ =xb¯c). Each policy instrument is set at its optimal levelde ned as one maximizes Utilitarian social welfare. As in the aforementioned second step, we repeat this optimization for various levels of φ. For each such level, we use the optimal level ˆθ ∈ ˆτe,bx¯c
to compute the associated optimal levels of GHG emissions, Eφ ˆθ, ˆτω, and the per capita after-tax income,
Rφ ˆθ, ˆτω.
For a given policy instrument, θ, we de ne its measure of environmental eectiveness, ∆φ ˆθ, ˆτω,
as the gap between the optimal level of emissions under laissez-faire, Eφ 0, ˆτω0
, and the cor-responding optimal level when the regulator chooses to mitigate GHG emissions with this
instrument, Eφ ˆθ, ˆτω : ∆φ ˆθ, ˆτω = Eφ 0, ˆτω0 − Eφ ˆθ, ˆτω . (1.27)
Therefore, we shall say that a revenue-neutral policy instrument θ is more environmentally eective than another revenue-neutral instrument, θ0 6= θ if and only if, given φ,
∆φ ˆθ, ˆτωe > ∆φ ˆθ0, ˆτω0 , where θ, θ0 ∈ {τ
e, ¯xc} and variable with (ˆ) are evaluated at the optimum.
In the fourth and nal step of our thought experiment, we carry out a cost-eectiveness analy-sis. First, from the outcome of the third step of our thought experiment, we compute the overall cost to the economy of achieving an optimal emissions reduction, ∆φ ˆθ, ˆτω, with the policy
instrument θ. For a given policy instrument θ, and a level of cost-disadvantage, φ, of switching the economy to clean-power sources, we measure this overall cost (denoted as Cφ ˆθ, ˆτω)
by the gap between the after-tax per capita income under laissez-faire, Rφ 0, ˆτω0
, and the corresponding gure when the regulator chooses to mitigate emissions with this instrument, Rφ ˆθ, ˆτω : Cφ ˆθ, ˆτω = Rφ 0, ˆτω0 − Rφ ˆθ, ˆτω , (1.28) where again, ˆθ ∈ ˆτe,bx¯c .
Second, assume that the regulator chose to mitigate emissions using a revenue-neutral ins-trument θ, and, at the optimum, achieved a level of emissions reduction, ∆φ ˆθ, ˆτω, relative
to the laissez-faire benchmark. Next, compute the counterfactual overall cost to the economy of replicating this optimal emissions reduction with an alternative revenue-neutral instrument θ06= θinstead, with θ, θ0 ∈ {τe, ¯xc}. To compute this counterfactual, we rst solve the following
system of two equations in two unknowns for θ0 and τ ω : Eφ 0, ˆτω0 − Eφ(θ0, τω) = ∆φ ˆθ, ˆτω Tφ(θ0, τω) = Tφ 0, ˆτω0 (1.29) The rst equation of this system corresponds to the requirement that the alternative policy instrument θ0 achieves the same level of emissions reduction as the instrument θ evaluated
at the optimum. The second equation corresponds to the requirement that the alternative emissions mitigation policy, θ0,be revenue-neutral. The pair
e
θ0,τeω0 is the unique solution to this system, for a given value of φ.
Next given the solution,θe0, e
τω0, to the system of equations in (1.29), we compute the counter-factual overall cost to the economy of replicating the optimal emissions reduction, ∆φ ˆθ, ˆτω,
capita income under laissez-fairedenoted as Rφ(0, τω∗), and the counterfactual after-tax
per capita income that obtained when ∆φ ˆθ, ˆτω is replicated by θ0denoted as Rφ
e θ0,τeω0 : Cφ e θ0,eτω = Rφ(0, τω∗) − Rφ e θ0,τeω0. (1.30)
Therefore, a revenue-neutral emissions mitigation policy instrument θ ∈ {τe, ¯xc} is said to be
relatively more cost-eective than another revenue-neutral instrument θ0 6= θ if and only if
∆φ θ0, τω0 ≡ ∆φ ˆθ, ˆτω and Cφ ˆθ, ˆτω < Cφ θ0, τω0 where θ, θ0 ∈ {τ e, ¯xc}.
The next section characterizes all these experiments.
1.3 Quantitative Analysis
The model is parameterized such that the equilibrium matches selected observations from the economy of the Canadian Province of British of Columbia (hereafter BC for short) on the share of total carbon tax revenue, as well as the share of clean over total energy. The goal of this calibration exercise is to enable us to perform a series of counterfactual experiments necessary to compare an emissions tax with a Standard on the basis of both environmental eectiveness and cost-eectiveness.
1.3.1 Calibration
We calibrate parameter values of our economy to represent as close as possible relevant fea-tures of BC's economy in the period 2012-2014. We need to choose values for the following parameters : c, µ, σ (preferences), α, ρ, A (technology), β (emissions technology), φ (energy costs), τω, τe (income tax and emissions tax).
A number of these parameters have direct empirical counterparts whose values can be selected without solving the model. Without loss of generality, we set the total factor productivity A = 100. The existing literature (e.g., Restuccia and Urrutia (2004)) often normalized this factor to unity. We chose to set A = 100 for two reasons. First, this choice does not aect the comparison between the two policy tools. Second, this choice allow us to appropriately scale variables so that their values match the data as closely as possible.
In practice, the cost of electricity generation from any given power source is hard to measure, as this cost includes more than just the price of the equipment or material involved (e.g., coal price or solar panels' price). In its 2010 Edition of Projected Cost of Electricity, the EIA estimates the levelized equivalent of the cost disadvantage of generating electricity with clean power sources to range from 2 to about 6, depending on the type of clean power source
