Effective split of an emission budget over the 2010-2050 period

Sharing the emission budget

The modelling of anthropogenic climate change induced by GHG emissions leads to a relatively simple conclusion in terms of the total cumulative amount of GHG emissions over the period 2005-2050, that will remain compatible with an objective of stabilizing the average surface atmospheric temperature around 2oC. We shall call this total amount the global “safety emissions budget”. This budget will depend on the assumed climate sensitivity. In our simulations this will correspond to two possible constraints on the admissible radiative forcing, introduced in the climate module.

In the TIAM simulations the emission budget for the period 2005-2050 is 457 GtC for the 3.5 W/m2 constraint and 570 GtC for the 4.0 W/m2 constraint. We assume that these data will be used to decide on a “safety global emissions budget”, which we set to 519 GtC (approximately the average of both values).

So we assume that, at the forthcoming climate negotiations, it will be recognized that there is sufficient scientific evidence for limiting the total cumulative emissions to this value. Furthermore there is no possibility to argue for a relaxed constraint because of development needs. The constraint is imposed by the earth system dynamics and this system is indifferent to whom is responsible for which part of the global cumulative emissions. From this point of view the forthcoming climate negotiations could be reduced to one simple problem: how should we split the “safety global emissions budget” among the different nations 1.

1. Note that in this model we do not take into account the cost of damage and of adaptation which could be region dependent.

The different splits simulated

Indeed, we shall not consider all the nations in the possible splits and we shall make different groups of nations, also called “coalitions”, sharing some common socio-economic characteristics and also common views on the climate negotiations. IC1 (Industrialized Countries group 1) represents the US coalitions always reluctant to take short-term binding commitments. IC2 (Industrialized Countries group 2) represents mainly European countries and Japan which are in the forefront of climate change negotiations and which have already set up ambitious policies against greenhouse gas emissions. NIC (New Industrialized Countries) corresponds to countries where the GDP per capita is at an intermediate level, and whose economic growth is strong and which contribute already significantly to greenhouse gas emissions but which are reluctant to take into account any action in the middle term against climate change. Finally, DC (Developing Countries) represents countries with low economic development and low greenhouse gas emissions, and which are very sensitive to climate change. Their participation to any agreement against climate change is conditional to financial aid.

In Table 1 we show the different groupings of countries in four “coalitions”. Depending on the model used (TIAM, GEMINI-E3, WITCH) these groupings differ slightly, due to the different geographical granularity of the models. Figure 2 shows the contribution of each coalition in respect to GDP, Population and GHG emissions in 2001 based on GEMINI-E3 figures.

Table 1: The grouping of nations into “coalitions”
Figure 1: Coalition represented in the model - Structural data in 2001

2. See section 3-5 and Drouet et al. (2009) for a technical description of the approach

We have already discussed the different sharing rules that could be adopted to arrive at a “fair split” of the global emissions budget. Using different sharing rules and combining them we have obtained the following possible splits of the global emission budget, as shown in Figure 2.

The first one, called “emissions” corresponds basically to grandfathering and would distribute the emissions budget according to current emission levels. The second one, called “C&C 2050” corresponds to the “contraction and convergence rule” with convergence in 2050, the allocation is based on the integral of emissions on the period 2005 to 2050. The third one is a combination of a rule based on population and a rule based on grandfathering. The fourth one is “C&C alt.” which corresponds to the “contraction and convergence rule” with convergence in 2050 but where the allocation is computed on the period 2005 to 2100. The last one is a mixture of rules based on population (weight 0.5), GDP (the higher the GDP the lower the share; weight 0.25), and grandfathering (weight 0.25). These splits are ranked by increasing value of the share given to DCs, which varies from 26% to 41%.

Figure 2: Different allocations of the global budget

So, there are indeed many different possible allocations of the global safety emissions budget. Using GEMINI-E3 we can evaluate the macro-economic cost for each coalition, of agreeing to one of those sharing rules.

Contraction and Convergence [C&C] is the name of the global GHG emissions-management-model introduced by GCI to the UNFCCC negotiation in 1996. Some currect information about the origins, meaning and application of C&C are at these links:


The emission permit supply game

If an international agreement is obtained on a “global safety emissions budget” it should be accompanied by the creation of an international emissions trading system which would permit developing nations to mitigate the cost of switching to cleaner technologies. We also assume that this market will have full banking and borrowing possibilities, which means that each (group of) country could decide how to allocate the among different periods the total allowance obtained in the agreement. In doing so they will play an “oligopoly game” which we describe below.


We consider that, once given a total amount of emissions rights over the period considered, the different groups or “coalitions” of nations will adopt a timing of supply of these rights on the market in such way to maximize their welfare gains. Doing so, the different groups of nations will play a non-cooperative game in the timing of use of their emission rights. In some sense this game is similar to an oligopoly game of exploitation of a nonrenewable resource.

To formulate this game we use GEMINI-E3 which computes the welfare gains associated with the supply of permits by different coalitions. The game is dynamic, since the supplies are determined for each of the four 10-year periods considered. The game is solved, using the oracle based optimization tool (OBOT) which implements the homogenous ACCPM algorithm, where the “oracle” is furnished by GEMINI-E3 2. An equilibrium will be computed for each allocation, or split, of the global safety emissions budget.

Equilibrium solutions

Figure 3 displays the equilibrium global emission profile for the different cases simulated. Among these cases one represents the TIAM baseline emission scenario, the GEMINI-E3 baseline emission scenario. the TIAM 3.5 W/m2 constrained emission scenario and then the emission scenarios for the different splits of the 519 GTC global safety emissions budget. We notice that the emission schedules for the different splits are very similar. This result was expected, because the different allocations will change mainly the financial transfers due to emission rights trading, but not the emissions which, in all cases, will remain determined by the search for the least cost option. This first finding is important because it shows that we can separate the choice of the climate target and the rule for the allocation of quotas. The international negotiation should thus concentrate on this second aspect. We notice that even if our model allows banking and borrowing behaviors all the equilibrium solutions are compatible with the 3.5W/m2 profile computed by TIAM, without overshooting of the worldwide emissions profile after 2050.

Figure 3: Equilibrium total emissions in Mt of CO2-eq

3. The discount factor is equal to 5%.

Figure 4 displays the evolution of the carbon price, according to the different equilibrium solutions computed for the different sharing rules.

Figure 4: Equilibrium carbon prices according to different equilibrium solutions in $ per ton of carbon

Figure 5 displays the surplus (gains or losses) for the different coalitions and the different sharing rules. The figure displays the ratio of the discounted sum of surplus over the period 3, divided by the discounted sum of consumption. It appears that NIC and DC are very sensitive to the allocation rules. NIC, which includes China, always looses much, whereas the group DCS gains substantially in the last three allocations.

The welfare losses of NIC come mainly from the deterioration of terms of trade due to the decrease of worldwide fossil fuel energy consumption. Indeed Russia and the Middle East countries are part of this coalition. It is why, in the negotiation, these countries always claim for financial transfers to compensate these losses of incomes. The situation of DC is more contrasted, the allowances “Emissions” and “C&C 2050” are unfavorable to this coalition, and on the contrary the other rules show substantial welfare gains. The situation of IC1 and IC2 are quite similar, but IC1 always suffers more important welfare loss, this could explain why this coalition is reluctant to any agreement. All this results are coherent with the current positions of countries in front of the climate negotiation. Notice that these allocation rules lead to Nash equilibrium solutions which are not likely to be acceptable to all groups of nations as they always distribute unevenly the welfare losses.

Figure 5: Variations of surpluses for different equilibrium solutions

In order to detect the variations over time in the supply of emission rights we have computed the temporal allocation ratio

which is equal to 0 in period t if the coalition i supplies the same share of rights as it received in the global allocation. Figure 6 displays the values of this ratio for the equilibrium solution corresponding to the “50% Pop-50% Emi” allocation rule.

Figure 6: Temporal allocation ratios for the “50% Pop-50% Emi” rule

We see that the industrialized countries tend to supply more than their shares in the early periods and less than their shares in the three last periods. Figures 7 and 8 display this ratio for the other allocation rules. They all show a similar behavior for the industrialized countries.

Figure 7: Temporal allocation ratios for the “50% Pop-25% Emi-25% GDP” and “C&C-alt.” rules
Figure 8: Temporal allocation ratios for the “C&C-2050” and “Emissions” rules

A fair split of the global emission budget

The different allocations or splits of the global safety emissions budget were obtained from a priori “fairness” or “equity” rules. We can also search for a splitting rule which tends to equalize the burden, expressed in terms of loss of surplus. Figure 9 displays a split of the global budget (called Min Surplus) which, at equilibrium tends to equalize the losses of surplus (in % of household final consumption), as shown in Figures 10. This allocation was obtained by trial and error direct search.

Figure 9: Allocation which tends to equalize surplus losses in % of Household Final Consumption: Split of total budget

We summarize the allocations for the different equity rules in Table 2.

Table 2: Allocations for different equity rules : Split of total budget
Figure 10: Variation of surplus for different allocation rules

We notice that this allocation is relatively similar to the one resulting from the C&C-2050 rule. Nevertheless it gives slightly more (44%) to the group NIC and this equalizes the percentage of surplus losses, at the expense of the group IC2 (which includes EU).

This result shows that even if standard allocations proposed by literature fail to find an acceptable agreement for all parties, we can find an allocation which could conduct to a stable and acceptable agreement. In comparison with the other allocations that we have tested the allocation “Min max loss of Surplus” has the following features:

  • It gives an overcompensation to the region NIC, compensating mainly the loss of revenue coming from the decrease of fossil fuel consumption;
  • It is rather generous to the region IC1 to compensate its dependence to oil consumption;
  • By contrast, the allocation to IC2 is slightly more restrictive as it takes into account the actual energy efficiency of these countries;
  • Finally, the allowance to DC is less important than those coming from rules giving an important weight to the population;

Remarks and policy insights

This simulation exercise has mobilized three models: (i) TIAM has been used to obtain an indication concerning the likely “global safety emissions budget” that will be imposed as a constraint to the whole planet earth system if one does not want to suffer a temperature increase of more than 2oC; this has permitted us to define a global cumulative emissions amount of 519 GtC for the period 2005-2050, which will be a constraint imposed on all participants in a climate change international agreement; (ii) GEMINI-E3 has been used to compute the macro-economic effect of any allocation of this global amount to four different groups of countries; (iii) OBOT, using GEMINI-E3 as an “oracle” has permitted us to compute a timing of the supply of emission rights or quotas which constitutes a Nash equilibrium in a game similar to an oligopoly exploiting a nonrenewable resource.

Using this simulation approach we have been able to explore the consequences of sharing the global safety emissions budget according to different equity rules. We find several policy insights:

  • The worldwide emission profile is not dependent to the allocation rule; in any case the global emission profile is always determined by the search for the least cost option.
  • No standard allowance founded on existing propositions would allow to obtain an agreement. In each case a coalition is strongly penalized or on the contrary strongly favored. In a certain way, this finding summarizes the current difficulty of the climate negotiations.
  • However it has been possible to identify a split which would equalize the burden to the different groups of countries, expressed in surplus losses in % of household final consumption. This solution could be able to find an agreement acceptable by all parties; this split is 17% for IC1 (which includes USA, Australia, Canada), 9% for IC2 (which includes EU), 44% for NIC (which includes China), 30 % for DC (which includes India).

In summary, by giving around 75% of emissions rights to NIC and DC countries and installing an international emissions trading system with full banking and borrowing over the horizon 2050 we could find an agreement which seems to be acceptable by all parties.