Raphaël-Homayoun Boroumand

Stéphane Goutte

Thomas Porcher

Thomas F Stocker

How to implement a fair and progressive carbon price to fight climate change?

Keywords: climate, carbon, price, market, tax

The principle of "common but differentiated responsibility", a key concept of the United Nations Framework Convention on Climate Change (UNFCCC), acknowledges the conditions for a generally acceptable and differentiated pricing mechanism on carbon emissions. With reference to this principle, carbon price determination has become one of the necessary instruments to limit global warming to a maximum of 2 °C. In this article, we propose the allocation of a carbon price per country based on the Human Development Index (HDI) and 𝐶0 2 emissions per capita. We demonstrate that under a multilateral framework, the price of carbon would be fixed according to a reference price depending on the HDI and 𝐶0 2 emissions. For example, if a country emits more than the amount allocated to its HDI level, it will have to pay a higher price than the established reference price, and vice versa. Reference prices as functions of HDIs and emissions will be estimated based on a trajectory to reach the target goal of reducing carbon dioxide emissions. A key element of our proposed scheme is that it generates national revenue allowing high-emitting countries a rapid decarbonization and developing countries (with generally lower emissions) accelerated development and early implementation of green infrastructures. Our research goal is related to documenting the benefits of a differentiated and progressive carbon pricing mechanism to ease intergovernmental cooperation.

Introduction

The scientific consensus on global warming is no longer in doubt. The climate emergency is undeniable from now on. The Intergovernmental Panel on Climate Change (IPCC), as the most comprehensive assessment of climate change, affirms that it is extremely likely that human influence has been the dominant cause of the observed warming since the mid-20th century. [START_REF] Ipcc | Summary for Policymakers[END_REF](IPCC, , 2014)). This implies that without major policies aimed at substantially reducing 𝐶0 2 emissions from human activities, the planet's atmosphere could warm by at least 4 °C on average compared to the pre-industrial era. The Paris agreement at COP 21 had raised many hopes. Unlike the Kyoto Protocol, the Paris Agreement is non-binding and is based on the principle of "name and shame game" counting on the reputation of countries vis-à-vis their peers and the public opinion. Each country is expected to present contributions aimed at reducing its 𝐶0 2 emissions and then improve on them over time through a formalized stocktaking process. However, results from the COP 25 in Madrid offer little hope that there is growing commitment from leading 𝐶0 2 emitting countries.

In a global open economy, it is possible to relocate production to countries with lower environmental standards. [START_REF] Almer | Analyzing the Effectiveness of International Environmental Policies: The Case of the Kyoto Protocol[END_REF] argue that an agreement will only be effective if it is global. Indeed, if in an agreement, some countries cooperate while others fail to do so, reduction in the production of tradable goods with high carbon intensity in cooperating countries will reduce the production of goods of these sectors (and therefore 𝐶0 2 emissions). However, this will be largely offset by increased production of these goods in countries that do not have a climate policy. Given that only the total 𝐶0 2 emissions of all countries are relevant to the climate, it has been argued that there is no point in pursuing a policy that simply shifts 𝐶0 2 emissions from cooperating countries to countries that have no climate strategies (see e.g. [START_REF] Hoel | Should a carbon tax be differentiated across sectors[END_REF].

However, following the failure of the Kyoto Protocol (a binding agreement) as well as the less promising beginnings of the Paris Agreement (a non-binding agreement), the global agreements may be regarded as still far from having proven their effectiveness. Tirole (2016) argues that these numerous failures, particularly in the negotiations, are due to the fact that each country is encouraged to behave like a "stowaway" by delaying its reforms with the expectation of better compensations in future negotiations if it does less today. The "polluter pays" principle as a remedy to the problem of free riding demonstrates that each economic player should internalize the negative externalities of their 𝐶0 2 emissions. Following this, an increasing number of studies has argued that a global carbon tax is the best mechanism for managing greenhouse gas emissions even if there are limits to its efficiency (see e.g. [START_REF] Mcevoy | Negotiating a uniform emissions tax in international environmental agreements[END_REF].

To set a price for 𝐶0 2 emissions that is compatible with the objective of the Paris agreement, i.e. the warming must be kept well below 2°C relative to pre-industrial levels, there are two economic instruments: a carbon tax or a carbon market. In 1920, the celebrated Economist Pigou proposed a tax to protect environmental goods. Fundamentally, a carbon tax requires that countries agree on a minimum price for their 𝐶0 2 emissions and that each country collects the corresponding sums on its territory. This tax could then be readjusted with reference to a trajectory of reduction in 𝐶0 2 emissions in accordance with the climate emergency. On the other hand, another way of pricing carbon is an emission permit market [START_REF] Crocker | The structuring of atmospheric pollution control systems[END_REF][START_REF] Dales | Pollution, property & prices[END_REF].

In the first place, an emission permit market creates scarcity by capping authorized emissions.

Once the carbon constraint is defined, emissions are capped with the aim of reaching ideally 1.5 degrees maximum by 2100, then it is possible to exchange rights to pollute. The climate ambition is set by the world carbon budget and the trading of permits is supposed to ensure the economic efficiency of the methods used to achieve these objectives [START_REF] De Perthuis | Le climat, à quel prix ? Odile Jacob[END_REF]. As part of the fight against acid rain, a market for rights to emit 𝑆0 2 and NOx emissions into the atmosphere was successfully launched to reduce emissions from 20 million tonnes to 10 million from 1995. Conversely, the European carbon market (EU ETS) has not demonstrated its capacity to deliver an appropriate long-term price signal for a low carbon economy resilient to climate change even if jurisdictions around the world are learning from each other [START_REF] Narassimhan | Carbon pricing in practice: a review of existing emissions trading systems[END_REF]. 𝐶0 2 emissions quotas have been over-allocated and the price per tonne of 𝐶0 2 has dropped from 30 euros to a floor of 5 euros between 2005 and 2014 even if the price is higher in 2020. The European Commission has planned to review the market rules and set up an obligation for the purchase of emission rights by companies instead of their free allocation by the States. [START_REF] Chevallier | Carbon price drivers: an updated literature review[END_REF] demonstrates that some fundamental principles have now been identified and confirmed by numerous empirical studies such as regulatory and political questions, market fundamentals (including the emissions/ceiling ratio, the role of fuel substitution, the weather conditions) and macroeconomic activity. More research is needed on adjusting the carbon price to the global economic recession.

According to [START_REF] Weitzman | Can Negotiating a Uniform Carbon Price Help to Internalize the Global Warming Externality[END_REF], the price of carbon must be unique and perceived by the country in which carbon dioxide is actually released into the atmosphere. Further, given that all 𝐶0 2 molecules, whether emitted in the United States or in Bangladesh, have the same negative impact on the climate, [START_REF] Gollier | Negotiating effective institutions against climate change[END_REF] argue that an effective international agreement should create a grand coalition in which all countries and all regions will be encouraged to set the same carbon price in their jurisdiction and a price trajectory that scientists consider consistent with the very maximum 2°C objective. Hourcade and Gilotte (2000) show that the price mechanism gives rise to difficulties, some of which are comparable to those based on quotas. Based on a theoretical model that captures the main practical aspects of climate policies, they demonstrate that an efficient allocation is obtained through differentiated taxes and that a uniform tax would only be appropriate if it was applied with transfers between countries. Lastly, [START_REF] Edenhofer | Closing the Emission Price Gap[END_REF] demonstrate that the incentives to set emission pricing differs among countries. For example, climate damages and reduced air pollution appear to be the main motivation for pricing emissions in China, while for the United States and the European Union, public revenue generation dominates.

Although a consensus seems to be reached on the necessity to set a price on carbon, the most appropriate method is still debated. The failure of the European carbon market is evident that the formation of a market and the determination of a price are not natural but result from underlying power relations between economic agents and the establishment of an effective regulation beyond the concept of the supposedly Invisible hand. Negotiating a uniform carbon price between developed and developing countries with historical differences in climate impact lead to an impasse, as shown by the failures of several UN climate conferences (COPs).

Defining a fair and progressive carbon price to fight climate heating

Setting a single carbon price that satisfies all stakeholders seems unrealistic. How could the European market mechanism be reproduced on a global scale in the negotiations (notably with the very powerful emerging countries) to fix a uniform carbon price? This is particularly irrelevant given that the OECD countries account for about 2/3 of 𝐶0 2 emissions in the 20th century while they represent only 15% of the world population. This climate debt has been at the heart of the deadlock in negotiations at the various climate summits. Under these conditions, it is difficult to compel emerging or developing countries to accept a price of 𝐶0 2 equivalent to that of industrialized countries when the latter were able to develop economically without considering the carbon footprint of their economic growth. However, it is basically the climate debt of developed countries with regard to developing countries that makes the generalized application of a single, high carbon price unrealistic operationally. If countries choose the option of a uniform price, it will most likely be too low in order to satisfy all stakeholders. Consequently, its inefficiency will be comparable to that of the European carbon market.

One method could be to allocate a carbon price per country based on the HDI (Human Development Index) and 𝐶0 2 emissions per capita. Under the aegis of a multilateral organization, the carbon price would thus be set according to a reference price depending on the HDI and the emissions of 𝐶0 2 . For example, if a country emits more 𝐶0 2 than the amount allocated according to its HDI level, it will have to pay a higher price than the established reference price, and vice versa. Apparently, the benchmark prices as functions of HDIs and emissions will be estimated according to a trajectory allowing to reach the target objective of reduction of carbon dioxide emissions.

The proposed methodology for estimating a fair carbon price offers several advantages. For instance, the empirical feature permits the identification of a reference scale of carbon prices according to various levels of economic development. Indeed, the principle would be a progressive price based on HDI thresholds. The underlying idea is that of a correlation up to a certain level of development between 𝐶0 2 emissions and the HDI. As such, a "poor" country does not have to pay a high carbon price when it begins to develop economically. As it takes off economically, its 𝐶0 2 emissions and its carbon price will increase jointly. Even more, the escalation in the price of carbon will also encourage it to make significant and rapid use of clean energies in its energy mix and to invest in low-carbon infrastructures for a green growth. Finally, "rich" countries with a high HDI and a largely service-oriented economy will pay a high price for carbon and will be encouraged to accelerate their energy transition to a low carbon economy resilient to climate change. By considering existing development inequalities, this mechanism fully adheres to the principle of "common but differentiated responsibility" of the climate convention. It also allows us to get out of the current binary and obsolete vision in which industrialized countries and developing countries have climate divergences. We provide a pricing mechanism in which emerging countries will be more encouraged to cooperate because they retain (although temporary) their competitive advantage compared to industrialized countries.

Lastly, among wealthy countries, those who emit more emissions than necessary will pay a very high price for carbon. A simple comparison of the top 20 countries by HDI reveals that some countries have significant differences in 𝐶0 2 emissions for globally similar living standards. For example, France emits 4.6 tonnes of 𝐶0 2 /inhabitant compared to 16.5 tonnes of 𝐶0 2 for an American in 2014. At the same time, their HDIs remain fairly close with 0.88 for France and 0.91 for the United States. In this case, the price of US carbon would be more expensive than in France.

This mechanism would also serve as an instrument so that competitiveness is no more a pretext for climate inaction. Indeed, the most sober production systems will have a lower 𝐶0 2 price and therefore higher competitiveness.

Discussion

A differentiated and progressive price for carbon has the potential to simplify negotiations and probably make it easier to find an agreement. It would also be fairer given its likelihood of placing higher impact on developed countries which have a greater climate debt than emerging countries.

But rather than favoring transfers between countries via the funding of the green fund, the carbon tax allows the States which implement it to recover the revenue it generates for reallocation to ecological projects. It therefore appears preferable in comparison to the funding of the climate adaptation fund which would go to the biggest polluters. Here, [START_REF] Chancel | Carbon and inequality from Kyoto to Paris: Trends in the global inequality of carbon emissions (1998-2013) and prospects for an equitable adaptation fund[END_REF] note that out of the 150 billion dollars necessary for the climate adaptation fund, 85 billion is projected to come from North America (about 0.5% of its GDP) whereas 24 billion is expected from Europe (about 0.2% of its GDP). Such transfers, although necessary, appear to be difficult to implement, Electronic copy available at: https://ssrn.com/abstract=3603275 as shown by the lack of ambition on the part of rich countries to finance the climate adaptation fund. For instance, in 2016, the sums promised were less than 10 billion dollars.

Omitting the question of inequalities within developed countries, carbon pricing implies to tax carbon emissions more heavily. However, the purchasing power of certain population groups is likely to be impacted more strongly by higher taxes. For instance, the movement of "Yellow vests" in France started due to the increase in the carbon tax on automotive fuels. Fuel taxation can be perceived as unfair because it does not take into account the differences in terms of public transportation between notably rural and urban populations. Depending on their living areas (city centers, suburbs, rural zones), not all citizens have the choice between using their car or using public transportation. For example, in Paris region, the rate of private vehicle usage is estimated as about 13% compared to almost 80% in other regions. This difference is explained by the fact that residents in Paris benefit from a large supply of transportation facilities unlike other residents of other French regions [START_REF] Boroumand | Worker mobility and the purchase of low CO2 emission vehicles in France: a datamining approach[END_REF]. Furthermore, the effectiveness of taxes also depends on the elasticity of user demand (Porcher, Porcher, 2017) and on financial compensation measures for low-income households.

Furthermore, the potential of a carbon tax policy in China has been analyzed by some studies (See e.g. [START_REF] Yang | Regional disparities in carbon dioxide reduction from china's unifrom carbon tax : a perspective on interfactor / interfuel substitution[END_REF]. They demonstrate that the inelastic demand for fuel and the heterogeneity of industrialization and urbanization processes across regions limit the effectiveness of the carbon tax. For example, the regions in the municipalities and the North-West could also reduce their 𝐶0 2 emissions by more than 3%. In contrast, the Midland and North West regions have the potential to reduce their 𝐶0 2 emissions by respectively 1.6% and 0.92%. To be accepted at international and national level, the determination of a fair carbon tax must therefore consider development inequalities on a global scale as well as heterogeneity in terms of mobility infrastructures within a country. Contrarily, despite an acceptance at a global scale, there would be imminent difficulties in implementation at the national level. This is consistent with the lessons of the Kyoto Protocol in which a national implementation was not feasible even after the United States ratification of the agreement.

Electronic copy available at: https://ssrn.com/abstract=3603275

Electronic copy available at: https://ssrn.com/abstract=3603275

Conclusion and policy implications

The global effect of an emitted CO2 molecule is independent of the type of source, its location and the time of emission. However, there are important economic, social and moral differences between different sources of CO2 emissions. For example, a CO2 emission caused by enhanced sustainable economic activity in a developing country is associated with a clear net benefit, whereas the same emission from heating poorly constructed houses in a rich country is a waste.

Although both emissions contribute equally to global warming, and must be avoided, it is clear that the former helps to reach several of the Sustainable Development Goals of the UN whereas the latter simply increases the challenge to reach them.

Against this background, imposing a carbon price at a global level when the majority of 𝐶0 2 emissions are not subject to any constraint must take into account its realities. A differentiated and progressive carbon pricing mechanism would more easily encourage governments to cooperate since it takes into account the differences in development between countries. Furthermore, each country recovers the amount of budgetary revenue and therefore is free to organize transfers of goods inside its economy.

Conversely, the low funding of the climate fund is an evident fact that countries are reluctant to set up transfers between countries. However, putting a price on carbon will not be the miracle cure for saving the climate, a global public good. Even under the best conditions, its effectiveness remains insufficient. For instance, there are many economic situations where the price signal fails to capture the expected effect, causing distrust among the populations concerned (e.g. the demonstrations of the "Yellow vests" in France). For fighting efficiently against global warming, there is a need for massive investments in clean energies as well as the thermal renovation of buildings. A systematic consideration of the climate impact of all economic agents is crucial to break the link between economic growth and carbon emissions. The planet is at a critical point which imposes a major change in production processes and consumption behaviors. Incentivebased mechanisms such as carbon pricing are necessary but not sufficient to meet this challenge.

Electronic copy available at: https://ssrn.com/abstract=3603275