Global long-term emission reduction targets need well defined options for equitable allocation of greenhouse gas emissions. Scholars from developing countries put forward the concept of equitable per capita cumulative emission rights. There are four possible operational definitions resulting from this concept. These potential options for allocation of emission rights are expressed with mathematical equations. Through simple simulation, this paper reveals the advantages, disadvantages and characteristics of each option.
climate change ; global long-term target ; per capita historical cumulative emission right ; equitable allocation
The IPCC Assessment Reports on climate change and greenhouse gas (GHG) emissions have promoted the universal adoption of the United Nations Framework Convention on Climate Change (1992) and the Kyoto Protocol (1997) under the United Nations. The ultimate objective of the Convention is to “stabilize GHG concentration in the atmosphere at a level that prevents dangerous anthropogenic interference within the climate system” ① . To achieve this objective, general consensus in the inter-governmental climate change negotiations have already focused on holding the increase in global average temperature below 2°C above pre-industrial levels② . Since deep cuts in global emissions are required to realize this 2°C goal [ IPCC , 2007 ], the remaining GHG emission space in the atmosphere is a rare resource in the future. Therefore, countries are arguing against each other in the current negotiations for a fair and equitable access to the global emission space. To help resolve this dispute, the academic community has put forward various kinds of allocation proposals. Further, studies on sharing the burden of emission reductions, dominated by scholars of developed countries, contribute strongly to the current negotiations. However, Ding et al.  identified various “pitfalls” and inequalities in such allocation schemes. To safeguard legitimate development rights of developing countries, scholars of these countries call for a quantification of historical differentiated responsibilities on GHG emissions and advocate allocation of the remaining carbon budget according to the criteria of population and the climate emission debts of developed countries③ . Building on these ideas, Chinese scholars [ Ding et al ., 2009 ; He et al ., 2009 ; Pan and Chen, 2009 ; Pan and Zheng, 2009 ; RGDRCSCC , 2009 ] put forward the concept of per capita historical cumulative emission rights. They argued that any fair and equitable allocation scheme of global emission space shall guarantee equal or convergent per capita cumulative GHG emission rights for all nations, in an agreed time frame from a certain past year to a certain future year.
To operate the concept of equitable per capita cumulative emission rights, countries would at first agree on a long-term stabilization objective, next define a global emissions trajectory leading to this agreed objective, and then allocate emissions along that trajectory among countries based on the criteria of equitable per capita cumulative emission rights. One fundamental step is to properly calculate per capita cumulative emissions for each nation in the pre-set time frame, which is not easy as population keeps changing over time. Seeing that some studies [ Pan and Chen , 2009 ; WBGU , 2009 ] prefer to employ the so-called “freezing population” approach to calculate per capita cumulative emission, we believe it is not appropriate as the “freezing population” approach deprives the emission rights of vast numbers of population growth after the “population cut-off year”. The current study analyses four kinds of operational definitions of the concept of “equitable per capita cumulative emission rights” taking into account the reality of population change, resulting in four possible emission rights allocation options. Finally, this paper discusses the advantages and disadvantages of the four options with simulation and mathematical analyses, and identifies their influences in emission rights of China.
In sight of the dynamic change of population, we can formulate at least four possible definitions of per capita cumulative emissions, lead to the following four possible options to operate the concept of equitable per capita cumulative emission rights.
Here, per capita cumulative emissions are defined as the sum of annual per capita emissions from the starting year to the last year of the pre-set time frame. So the principle of equitable per capita cumulative emission rights means that the sum of per capita emissions in the pre-set time frame has to be equal for all nations [ Bode , 2004 ]. For any country the following equation (1) is used.
Where t is each year, ranging from the starting year Tb to the end year Tc of the pre-set time frame for the allocation program, Ei (t ) is the GHG emission of country i in year t , Ei (t ) is the global GHG emission in year t , Pi (t ) is the population of country i in year t , and P (t ) is the global population in year t . As the pre-set time frame starts from the past and ends in the future, population for each nation and the global include real population data and ex ante projections.
While the global per capita cumulative emissions for the whole pre-set time frame is calculated as the benchmark, the per capita cumulative emissions of any country should not exceed this benchmark. Annual testing at begin of each year after the entry-into-force year T0 of the allocation program would be employed to insure this rule. For each nation under test, we can trace its actual trajectory of per capita emissions from the starting year of the pre-set time frame till the testing year, by simply assuming that this nation’s per capita emissions will converge linearly at during the remainder of the pre-set time frame, we can calculate this nation’s per capita cumulative emissions for the entire pre-set time frame. If this value exceeds the benchmark, the per capita emissions of this country under test are required being reduced linearly down to while its emission quota for every year since then is multiplied by the projected population for each year. If it does not exceed the benchmark, no constraints will be imposed on the country for the coming year.
Per capita cumulative emissions are here defined as the quotient of cumulative emissions for each country and its cumulative population within the pre-set time frame. Based on this definition and the principle of equitable per capita cumulative emission rights, for any country the following equation (2) is used.
Equation (2) implies people (wherever and whenever they live) enjoy the same emission rights per year. Therefore, for each nation i, its deserved emission rights for the whole pre-set time frame are calculated as follows.
Here, we define the disposable remaining emission quota Q (i , T ) of the country i at the year T (T0 ≤ T ≤ Tc ). The quota is equal to its deserved emission rights minus the emissions which already occurred from the starting year Tb to the year T .
The disposable remaining emission quota Q (i , T0 ) of the country i at the entry-into-force year T0 is then estimated in accordance to the following formula.
In option 3, the principle of equitable per capita cumulative emission rights is defined as that each person in any country in year t enjoys the same emission rights equivalent to the global per capita emissions for that year, i.e., the deserved emission rights of any country i for the whole pre-set time frame are equal to the sum of products of the global per capita emissions and a dynamic population of that country.
The disposable remaining emission quota Q (i , T0 ) of each country is then estimated in accordance to the following formula.
Here the estimation of per capita cumulative emissions is defined as the cumulative emissions of a country divided by a fixed population of a certain year. Based on this definition and the principle of equitable per capita cumulative emission rights, the following formula is used for any country i .
where is the “population cut-off year”, and populations are notionally “freezing population” for years beyond the cut-off year at the values for the year . Note that this assumption does not necessarily mean there is no population change beyond the cut-off year, it merely implies that any newly added population after the “population cut-off year” will not be granted any emission rights.
Finally, the disposable remaining emission quota Q (i , T0 ) of each country should be calculated according to the following formula.
The suggestion of a “freezing population” comes from the “Contraction and Convergence” solution put forward by the Global Commons Institute [ GCI , 1997 ]. Both the global carbon budget based on per capita cumulative emissions presented by Pan and Chen  and the global emission budget based on historical responsibility put forward by WBGU  employ the “freezing population” approach. It is argued that the purpose of this “freezing population” method is to reduce any incentive for a particular nation to increase their population and thereby their emissions allocation.
The mathematical equations of the above mentioned four options for per capita cumulative emission rights show the basic characteristics of each option. To evaluate the advantages and disadvantages of each option, a simple simulation is taken and the results are discussed.
Input data for the simulation include population and emission data for each country and the world, as well as assumptions about the pre-set time frame and the entry-into-force year of the allocation program.
Referring to the assumptions about the pre-set time frame and the entry-into-force year of the allocation program, it must be noted that the selection of the starting year Tb of the pre-set time frame has a great influence on the historical responsibilities of each nation on GHG emissions and their emission allocation. In the inter-governmental climate change negotiations at the “Technical Briefing on Historical Responsibility as a Guide to Future Action to Address Climate Change” held at the Sixth Meeting of AWG-LCA on June 4, 2009, India and China suggested to quantify historical differentiated responsibilities since 1850 when GHG concentrations began to increase above “natural” levels due to increasing influences of industrialization. Unfortunately, no population data for those years are available. Here, for better data support, we assume that the starting year of the pre-set time frame is 1900, the end year Tc is 2050, while the year T0 of the allocation program is 2013 which is just subsequent to the first commitment period of the Kyoto Protocol .
Population data Pi (t ) and P (t ) for 1900–1949 is estimated from historical population statistics from the Populstat website ④ ; population data for 1950–2005 comes from the UN Statistics Division Demographic Yearbook system since 1948 ⑤ ; population projection for 2006–2050 is taken from the UN median population forecasts (UN Department of Economic and Social Affairs, 2008 ). Whilst the UN data is available in five year intervals, population values for other interim years are interpolated.
Yearly emissions of the world and each country from the starting year Tb until the entry-into-force year are produced as follows. The data on global emissions and energy-related CO2 emissions of 185 countries for 1900–2005, comes from the climate analysis indicator tools developed by the World Resources Institute⑥ . Emission data for 2006–2012 is estimated by the time series extrapolation models, whilst the regression functions may be different for each nation depending on their emission trends from 1990 to 2005. Please note that in this simple simulation, only data on the energy-related CO2 emissions is used to estimate the results of each option. This is because that among the six kinds of human-induced GHGs specified in the Kyoto Protocol , CO2 (in particular resulting from human enery consumption) is the most important emission source with minimum uncertainty in data and has a close relationship with economic development.
The global emission control pathway from the entry-into-force year to the end year E (t ) (2013–2050) is assumed based on the 2°C threshold and the CO2 emissions pathways of mitigation scenarios for a 450 μ mol (mol CO2 -eq)−1 stabilization target recommended by the IPCC  . Figure 1 shows the pre-set global energy emission control path and global per capita emission trajectory.
The pre-set global energy emission control path and per capita emissions
Simulation results show that option 1 cannot achieve the pre-set global emission reduction path (Fig. 2 ). In particular, the sum of annual emission rights of each country will gradually reach and further exceed the global emissions limit, thus the original goal of limiting temperature rise will not be achieved. Based on this, option 1 is rejected. Options 2, 3 and 4 are able to ensure that the sum of deserved emission rights of the countries for the whole pre-set time frame equals the total permitted carbon budget in the same period, and that the sum of each country’s disposal remaining emission quota equals the global remaining carbon budget for the period from the entry-into-force year to the end year of the pre-set time frame. However, in order to strictly follow the pre-set global emission control pathway, additional measures are needed to restrain each country’s annual emissions in option 2, 3 and 4. If the remaining emission quota Q (i , T ) of each country is taken as a weight to divide global annual emission quota E (T ) for each country as expressed in equation (10) , the annual emission control targets for each country could be identified, and thus the pre-set global emission control path would be strictly followed.
Outcomes of option 1 and the pre-set global energy emission control path
A prerequisite to any incentives for a particular country to deliberately increase its population for additional emission rights is that the obtained marginal emission rights for a newborn population be larger than the country’s per capita emission level at the year when this person is born. In addition, the cumulative emission rights accrued for the newborn population in their lifetime must be larger than their cumulative “business as usual” emission demand during the same period. Otherwise, this country must make extra reduction efforts for newly added population.
However, the simulation shows that the marginal emission rights per new person per year for any country under option 2 range at about 2.99 t CO2 . In option 3, this value decreases over time from 4.09 t CO2 in 2013 to 1.31 t CO2 in 2050. The results of the simulation reveal that only a few countries meet the prerequisite of stimulating population growth for additional emission rights in the early stage when the allocation program becomes effective under a relatively strict global emission control path⑦ . The number of these countries is likely to reduce over time, taking into account their increasing per capita emission demands versus the decreasing annual marginal emission rights per person. Therefore, the effects of incentives for population growth for more emissions allocation are overestimated by the “freezing population” assumption in option 4. In view of a significant increase in the world population due to non-climate change factors⑧ , these anticipated population growth are entitled to their deserved emission rights. Therefore, option 2 and 3 make more sense than option 4.
Option 2 implies that people, wherever and whenever they live, enjoy the same emission rights each year. Option 3 implies that every year each person in any country enjoys the same emission rights equivalent to the global per capita emissions for that year. Both options are based on crucial reasons. If we only consider their impacts on emission rights of a specific country, it mainly depends on whether its population trajectory is consistent with the pre-set global per capita emission trajectory for the entire time period. For example, option 3 would give a country more emission rights in case that the two trajectories coincide with each other with increasing or decreasing trends.
The disposable remaining emission quota of some major countries in 2013–2050 estimated by options 2, 3 and 4 are shown in Table 1 . The findings show that China will receive more emission rights under option 3, followed by option 2. Option 4, which is based on “freezing population” of each country at the values for the year 2012, gives the lowest emission rights to China, because of the emission rights of newly added population in China being deprived notably. This estimated deprivation of emission rights of a country that practices the world most rigorous birth control program questions the use of the “freezing population” assumption. Table 1 also shows that, based on “equitable per capita cumulative emission rights”, most developed countries, plus several non-Annex I countries whose per capita emissions are already above world average, would be allocated negative quantities of emission rights due to their high historical responsibilities.
|Country||Option 2||Option 3||Option 4|
Though, lacking political acceptability, these results offer another perspective for the political bargaining process on the standard for fair and equitable access to the global atmospheric space.
The intergovernmental climate change negotiations support the political bargaining and scientific studies for the standard for fair and equitable access to the global atmospheric space. Thus an allocation proposal for equitable per capita cumulative emission rights has been put forward by developing countries. The main feature of this proposal is that per capita cumulative GHG emission rights in an agreed time frame from a certain past year to a certain future year, has to be equal for all countries. Therefore proper calculation of per capita cumulative emissions for each nation in the pre-set time frame is fundamental for the allocation program but not easily achieved as the population keeps changing over time.
Taking into account the reality of population change, four kinds of operational definitions of the concept of “equitable per capita cumulative emission rights” are presented, resulting in four possible emission rights allocation options. Option 1 assumes that the sum of per capita emissions in the pre-set time frame has to be equal for all nations. Option 2 implies that people, wherever and whenever they live, enjoy the same emission rights per year. Option 3 assumes that every year each person in any country enjoys the same emission rights equivalent to the global per capita emissions for that year. In option 4, the “freezing population” approach is applied, which implies that any newly added population after the “population cut-off year” has no emission rights.
Simulations and mathematical analysis show that among the four possible options, option 1 must be rejected due to its design, as it fails to achieve the pre-set global emission control pathway. Under relatively strict global emission control path, option 4 is questionable due to over-estimated effects of incentives for population growth for more emissions allocation. Option 2 and option 3 are well explained. From the perspective of China, option 3 results in the highest emission rights, followed by option 2. Simulation results also show that based on “equitable per capita cumulative emission rights”, most developed countries, plus several non-Annex I countries whose per capita emissions are already above world average, would be allocated negative quantities of emission rights due to their high historical responsibilities.
This study was supported by the 2009 special study project employing basic scientific research fund of the Academy of Macroeconomic Research of NDRC. Any opinion expressed in this paper is the personal view of the authors and not to be imputed to any other person or entity. All errors are the authors’ sole responsibility.
①. Article 2 of the United Nations Framework Convention on Climate Change
②. In international climate change negotiations, no more than 2°C rise of global average temperature compared with that of preindustrialization period has gained strong consensus. The Copenhagen Accord in 2009 and the Cancun Agreement in 2010 have reconfirmed this consensus
③. The Sixth Meeting of AWG-LCA held the “Technical Briefing on Historical Responsibility as a Guide to Future Action to Address Climate Change” on June 4, 2009. The delegates from developing countries including China and India suggested addressing the issue of common but differentiated responsibility and curbing global GHG emissions in terms of “per capita cumulative emissions”. Their presentations are available on http://unfccc.int/meetings/ad_hoc_working_groups/lca/items/4891.php
⑤. United Nations Statistics Division, http://unstats.un.org/unsd/demographic/products/dyb/dyb2.htm
⑦. Global per capita energy-related CO2 emission has been rising over the past years to 4.38 t per capita in 2007 (to 11.21 t per capita for Annex I parties and to 2.56 t per capita for non-Annex I parties)
⑧. According to UN “World Population Prospects: The 2008 Revision”, world population in 40 years will rise from 6.9 billion to 8—11 billion by 2050 with a median at 9.2 billion