Joint design of emission tax and trading systems

Bernard Caillaud, Gabrielle Demange

06 October 2015



After the disappointing Copenhagen ‘Conference of Parties’ (or COP15) in 2009, the UN has given up on promoting the emergence of a unique carbon price. With the Paris COP21 conference approaching, a large number of economists have signed a ‘call for an ambitious and credible climate agreement in Paris’ in favour of commitments and a unique carbon price.1

The standard economic argument in favour of a unique price, which requires all actors to face an identical marginal cost of pollution, is efficiency. A unique price in a given period can be achieved by imposing a tax or designing an emissions trading system (ETS), also called a ‘cap-and-trade’ system. Both systems produce very different outcomes due to the fluctuations economies are facing. Under a uniform emissions trading system – i.e. one that encompasses all activities – the shocks have no effect on emissions but induce fluctuations in the price and marginal cost of abatement. But under a uniform tax – i.e. a tax applying to all activities – shocks do not affect the marginal cost of abatement but generate a random volume of emissions.  Restricting to a uniform system, one may prefer one or the other, as shown by Weitzman (1974). However, mixing the two systems could smooth the fluctuations in the emissions system’s price and volumes at the cost of departing from the doctrine of a unique carbon price.2 Could this be more efficient than a unique carbon price?


Figure 1. EU emission allowance (EUA) spot price (€/t)

As shown in Figure 1, there is ample evidence of the volatility of the carbon price in the European emissions trading market since 2008, and various studies have empirically analysed its determinants. Chevallier (2011), for example, shows that both industrial production and energy prices have an impact on the European carbon market.

A striking feature, illustrated in Figure 2, is that the production of the firms submitted to the emissions trading system has been much more affected by the 2008 crisis than the others, especially if electricity firms are excluded. Presumably, fluctuations in the carbon price would have been different were the emission trading sector composed differently.

Figure 2. Industrial production

Source: CDC Climat Recherche
Notes: Secteurs EU ETS électricité incluse= EU ETS industries, including electricity.
Secteurs EU ETS hors  électricité= EU ETS Sectors  without electricity.

The regulation should cope with fluctuations

Regulation cannot change too often in order to be integrated by economic agents and to facilitate long-term investment decisions. A stable regulatory framework is even more crucial in the case of pollution, given the difficulties of setting up an international agreement. Yet, though the regulatory framework cannot be contingent on the realisation of shocks that constantly hit the economy, it must take into account firms' reactions to shocks. 

In a recent paper (Caillaud and Demange 2015), we propose a simple normative model that enables us to provide a meaningful discussion about the welfare-maximising design of both fiscal and cap-and-trade instruments under the assumption that the economy is affected by shocks. We analyse how the optimal regulation depends on some parameters reflecting preferences, production, and the structure of the shocks affecting the economy.

The scope

In the static model of Weitzman (1974), we introduce the possibility of the double control mechanism. The mechanism specifies which firms are subjected to a tax and which are subjected to an emissions trading system (what we call the scope of the regulation), as well as the associated tax level and quota allocated to the emissions trading (what we call the policy). The mechanism is decided ex ante, before the realisation of the shocks that affect the firms in the economy. We characterise optimal (or equilibrium) policies for any scope and we explain how the stochastic structure of the shocks influences the optimal design of the scope of the regulatory framework. In particular, we analyse when it is preferable to adopt a uniform system – subjecting all firms to either a cap-and-trade mechanism or a tax on their emissions – or a mixed system in which some firms are regulated through a cap-and-trade mechanism and others through a tax.

The basic forces at play are the following. If climate regulation could be made contingent on shocks, i.e. in a first-best scenario, abatement efforts should be determined so as to equalise marginal abatement costs across firms with the social marginal benefit of abatement. Part of the aggregate shocks should then be absorbed through abatement at the firm level and the coefficient of absorption would be larger the less steep the aggregate marginal abatement cost curve, and the steeper the marginal abatement benefit curve.

The optimal tax rate and emissions trading quota are determined so as to replicate the first-best optimum in expected terms. Expected marginal abatement costs, that is, the tax rate and the expected price on the emissions trading market, are equalised to their first-best value. Expected net emissions are equalised to their first-best optimal value as well.

So, the precise definition of the scope of the regulatory framework, i.e. of the industries to be included in the emissions trading system and of those to be taxed, only affects social welfare through the fluctuations due to the shocks. The optimal scope should then be designed so as to replicate as closely as possible the emissions fluctuations corresponding to the first-best allocation, given that all fluctuations in emissions are generated by firms subject to the tax. A uniform emissions trading system, in which all firms are subject to the trading regulation, eradicates all fluctuations, while a uniform tax system induces all shocks to be passed on in emissions fluctuations. Comparing both systems amounts to assessing the relative slopes of the marginal abatement cost and benefit curves, as in Weitzman (1974). Improving on either system requires an analysis of mixed systems, with a non-degenerate emissions trading sector and a non-degenerate taxed sector, and calibration of the taxed sector so that the shocks that affect it are sufficiently correlated with the partially dampened aggregate shocks as required in the first-best. But doing so creates a wedge between the marginal abatement cost of emissions trading firms and taxed firms, hence a social loss due to the misallocation of abatement efforts across firms. The optimal scope optimally balances these effects.   

Non-cooperative design of regulatory frameworks

Using this framework, we address the issue of the non-cooperative design of emissions trading in various areas worldwide. We consider a world consisting of several areas, in which each area uses a double control mechanism. The non-cooperative outcome is compared to the first-best emissions levels for the global economy and the corresponding inefficiency that results, i.e. excess in emissions worldwide, is precisely analysed.

Moreover, we analyse the proposal of linking emissions trading. The linking between California’s and Quebec’s emissions trading systems was the first to be implemented in January 2014. Several possibilities are currently under debate to link the EU’s emissions trading system and the Swiss system, or even New Zealand’s system after the failed attempt with the Australian one. We analyse a specific form of linking that we call ‘emissions trading merging’. Under a merged emissions trading system, each local authority sells the same quantity of permits as in the separate regime, but there is full convertibility of allowances across areas and, consequently, a unique price of allowances across areas. We provide a strong Pareto argument in favour of merging emissions trading systems. Such a move benefits both areas, even without implementing transfers across them or changing the sovereign decisions with respect to the fiscal instruments. We precisely characterise these benefits for each area; they are proportional to the square of the difference between the emissions trading price under merging and the emissions trading price in the area under a separate regime. Within each area, there are possible losers – for example, the firms, if the emissions trading price in the area is lower than in other emissions trading systems under a separate regime – but they may be compensated within the area by adequate transfers due to the extra resources collected by the government.


Caillaud, B and G Demange (2015), “Joint Design of Emission Tax and Trading Systems”, CEPR DP10671

Chevallier, J (2011), "A Model of Carbon Price Interactions with Macroeconomic and Energy Dynamics,'' Energy Economics, 33(6), 1295-1312.

Mandell, S (2008), "Optimal Mix of Emissions Taxes and Cap-and-Trade," Journal of Environmental Economics and Management, 56(2), 131-140.

Weitzman, M L (1974), "Prices vs. Quantities," The Review of Economic Studies,  41(4), 477-491.


2 Mandell (2008) analyses this question in the restricted framework in which there is a single common shock affecting all firms.



Topics:  Taxation

Tags:  emission trading system, Cap-and-trade, economic shocks, carbon price, climate regulation

Senior Research Officer, Ecole des Ponts - ParisTech; Associate Chair, Paris School of Economics; Research Fellow, CEPR

Directeur de recherches, l'Ecole des Hautes Etudes en Sciences Sociales (EHESS); Associate Chair, Paris School of Economics