1 ADVANCES IN CLIMATE CHANGE RESEARCH 2(3): , DOI: /SP.J POLICY FORUM Metric of Carbon Equity: Carbon Gini Index Based on Historical Cuulative Eission per Capita Fei Teng, Jiankun He, Xunzhang Pan, Chi Zhang Institute of Energy, Environent and Econoy, Tsinghua University, Beijing , China Abstract This paper uses Lorenz curve and Gini index with adjustent to per capita historical cuulative eission to construct carbon Gini index to easure inequality in cliate change area. The analysis shows that 70% of carbon space in the atosphere has been used for unequal distribution, which is alost the sae as that of incoes in a country with the biggest gap between the rich and the poor in the world. The carbon equity should be an urgency and priority in the cliate agenda. Carbon Gini index established in this paper can be used to easure inequality in the distribution of carbon space and provide a quantified indicator for easureent of carbon equity aong different proposals. Keywords: cliate change; carbon equity; long-ter itigation goal; cuulative eission per capita; carbon Gini index Citation: Teng, F., J. He, X. Pan, et al., 2011: Metric of carbon equity: Carbon Gini index based on historical cuulative eission per capita. Adv. Cli. Change Res., 2(3), doi: /SP.J Introduction One of the key issues of addressing cliate change is to enact a reasonable global long ter eission reduction target and ipleent the equal allocation of CO 2 eission space. The quantitative global long ter target will certainly liit the global CO 2 eission space. The unequal allocation of the liited CO 2 eission space would largely restrict the future eission space of developing counties. The earth s atosphere is huan s public natural resource, and reasonable eission space is indispensable for huan developent. Therefore, we should allocate and use the eission space under the principle of global carbon equality. This is the cornerstone of global cooperation in addressing cliate change. Chinese scholars [Chen et al., 2005; Ding et al., 2009; He et al., 2007; 2009] developed the cuulative CO 2 eission per capita index and revealed the different historical responsibilities for developed and developing countries. Moreover, they proposed the guideline based on the principle of cuulative eission per capita convergence. Under this principle, Chinese scholars proposed the carbon budget and carbon eission account ethods [Pan, 2008; PTDRCSCC, 2009] as the eission space allocation syste design. Although cuulative eission per capita reveals the different historical responsibilities for different countries, it cannot provide a coprehensive index which covers every country s cuulative eission per capita, nor can it provide a general easureent of eission space allocation equality. Therefore, any studies used incoe equality easureent ethod, and easured eission equality with different incoe equality index. Hedenus and Azar  easured eission inequality across countries by the well-known Atkinson Received: 26 Deceber 2010 Corresponding author: Fei Teng, 1
2 Fei Teng et al. / Metric of Carbon Equity: Carbon Gini Index Based on Historical Cuulative index. Duro and Padilla  applied the decoposable Theil index of inequality to eissions and showed convincingly that global inequality in per capita eissions was largely due to inequalities in per capita incoe across countries. Heil and Wodon [1997; 2000] used the Gini index to easure the inequality of eission across countries. Groot  established the carbon Lorenz curves and carbon Gini coefficient based on the annual per capita eission. The aforeentioned literatures easured the eission space equality with incoe equality easureent indices, but they were all based on the annual per capita eission. The contribution of this paper is to reestablish the carbon Lorenz curves and Gini indices based on the historical cuulative eission per capita which has essential difference with the annual per capita eission easureent. First, the life tie of greenhouse gas (GHG) in the atosphere is ore than a century; the cuulative eission can show a country s cliate change historical responsibility ore clearly than annual eission. Consequently the historical cuulative eission per capita can represent the carbon equality better. Second, eissions of GHG within a certain period of tie deterine the teperature rise. The equality is to be a easureent of the overall eission allocation in the certain period, rather than that of annual eission allocation. 2 Carbon equality and easureent The essence of carbon equality is to easure the allocation difference of eission space. Although allocation difference is a new topic in cliate change studies, it has been thoroughly investigated in the incoe allocation equality researches [Wan, 2009; Xu, 2008]. The coonly used resident incoe allocation difference indices are variation coefficient, Gini coefficient, Generalized Entropy index, and Atkinson index. The Gini coefficient is the ost widely used index. Such indices are usually used to statically apping the wealth allocation and social stability of a certain country or district. The Lorenz curve was initially proposed by Lorenz in It indicates the relations between population shares and incoe shares. Cuulative incoe shares are on the vertical axis, and cuulative population shares are on the horizontal axis. The curve reflects the relations between incoe shares and population shares. If the population shares are not equal to the incoe shares, inequality exists. If the allocation is perfectly equal, then Lorenz curve is the straight line with the slope of 45. That is the perfect equal allocation curve (Fig. 1). Based on the Lorenz curve, Gini proposed the equality level easureent index which is called Gini index. Define the area between the actual allocation curve and perfect equal allocation curve as X, the area below the actual allocation curve as Y. Then the Gini index equals to X/(X +Y ). The econoical eaning of Gini index is that the inequality level of the incoe allocation equals to the incoe used for unequal allocation aong total residential incoe. Gini index is a real nuber between 0 and 1. The Gini index for a perfect equal allocation is 0, while the Gini index for a totally unequal allocation is 1. Gini index is a general index, which reveals a general level of the allocation equality. According to the United Nation s definition, Gini index <0.2 represents perfect incoe equality, relative equality, adequate equality, big incoe gap, and above 0.5 represents severe incoe gap. Therefore, the warning level of Gini index is 0.4. This paper uses the above division of Gini index to investigate the carbon inequality issue. How to use Gini index to provide a ore eaningful division is still an issue for further research, since this involves the welfare eanings of the carbon space allocation. Figure 1 Lorenz curve and Gini index
3 136 ADVANCES IN CLIMATE CHANGE RESEARCH Lorenz curve and Gini index reflect the relations between incoe shares and population shares. Whenever the incoe shares and population shares are not equal to each other, inequality exists. The convergence of cuulative per capita proposed by Chinese scholars reflects this principle for equality. This idea applied with the Lorenz curve and Gini index eans that once everyone has the sae cuulative eission space there will be no carbon inequality. Developed countries had eitted large aount of GHG in their industrialization process. The GHG cuulated in the atosphere, not only enhanced the greenhouse effect, but also led to global waring and any other cliate changes. Moreover, GHG eitted by developed countries occupied the eission space and ade developing countries face a ore restricted eission liit. Therefore, Gini index can also easure equality situation of different eission allocation plans. In this application of the Lorenz curve and Gini index, horizontal axis is changed fro households to population, while vertical axis is changed fro incoe to eissions. This paper calculates the carbon equality with historical cuulative eission statistics. Based on such statistics we will establish the carbon Lorenz curve to reflect different countries unequal eission allocation levels. According to carbon Lorenz curve, we can calculate the carbon Gini index to quantitatively easure the eission inequality of different countries. 3 Carbon Lorenz curve and carbon Gini index calculation When investigating different countries historical cuulative eission situation, this paper focuses on the CO 2 eission fro energy activities. Bauert et al.  suggested that CO 2 is the ain GHG, CO 2 eission fro energy activities contribute ore than 2/3 of the world GHG total. This paper calculates the historical cuulative eissions by siply adding the eissions, which is a widely used ethod. In order to understand how the historical cuulative eission per capita Lorenz curve is established, first we define the following variables for country n: G n i is the CO 2 eission in i th year of country n, Pi n is the population of country n in the i th year, p n i = P i n Pi is the population share of country n in the i th year. Considering the period between i th year and j th year, C n ij = j k=i G n k is the historical cuulative CO 2 eission fro i th year to j th year for country n, c n ij = Cn ij Cij is its share of historical cuulative CO 2 eission fro i th year to j th year, and C n ij is its historical cuulative CO 2 eission per capita fro i th year to j th year. C n ij is the ost iportant eission equality easureent index proposed by the authors of this paper. It will also be the basis to sort the data in establishing the Lorenz curve. There are two ways to calculate C n ij. One is to add up the annual eission per capita. Another is to calculate cuulative CO 2 eission Cij n, and then divide Cij n by P j n. Although two ethods yield different values, the results are essentially the sae. Moreover, this paper will use population share. It is not suitable to calculate cuulative populations. Accordingly, we adopt the latter ethod. C n ij = Cn ij P n j (1) Table 1 provides historical cuulative CO 2 eission, population, and the historical cuulative eission per capita for ajor countries between 1850 and All the data were fro Cliate Analysis Indicators Tool (CAIT), Version 7.0 ( ). Fro Table 1 we can see that the USA is the world s largest CO 2 eission country since the industry revolution, its historical cuulative eission is 30% of the world total. The historical cuulative eission per capita for developed countries such as the USA and UK was ore than tens of ties of those for developing counties such as China and India. The historical cuulative eission per capita can reflect the inequality of carbon space allocation. Coparing with developed countries, developing countries industrialization cae late and is on a lower level. Developing countries are allocated with less resource in the constrained carbon space, but they have larger populations in general. As a result, residents in developing countries cannot enjoy equal rights in GHG eission.
4 Fei Teng et al. / Metric of Carbon Equity: Carbon Gini Index Based on Historical Cuulative Table 1 Historical cuulative eission of ajor countries fro 1850 to 2006 (data source: CAIT V7.0) Country Historical cuulative Historical cuulative Population in 2006 Population Historical cuulative Annex I CO 2 eission (Mt) CO 2 share (%) (10 3 ) share (%) CO 2 eission per (Y/N) capita (t per capita) UK 68, , ,133.0 Y USA 333, , ,125.6 Y Gerany 80, , Y Russian Fed 93, , Y Australia 12, , Y France 32, , Y Japan 44, , Y South Africa 12, , N Mexico 11, , N China 99, ,304, N Brazil 9, , N India 27, ,094, N When we focus on the CO 2 eission fro i th year to j th year for each country, in order to construct the Lorenz curve, we need to sort the countries in ascending order by their historical cuulative eissions per capita C n ij and assign a sequence nuber s. After sorting the countries in ascending order, set cuulative population of j th year on the horizontal axis, and set cuulative historical cuulative eission per capita fro i th year to j th year on the vertical axis. It should be noted that cuulative in this context is referring to suing up of eissions by those countries whose sequence nuber is less than s. Therefore, the coordinates (p s, c s ) refer to p s = p t j, c s = c t ij. t s t s Connecting the different countries points in the coordinate syste with a sooth curve, we established the Lorenz curve based on the historical cuulative eission per capita fro i th year to j th year. Figure 2 shows the carbon Lorenz curve started fro 1850 and lists the positions of different countries. As the carbon Lorenz curve is sorted by the historical cuulative eission per capita, the country s position is closer to the upright, the higher its historical cuulative eission per capita is, the bigger historical responsibility that country should take in cliate change issue. Moreover, fro Figure 2 we can learn that developing countries have 82% population of the world, but they contributed erely 25% cuulative eission of world s total. On the other hand, developed countries have 18% population of the world, but their cuulative eissions account for 75% of the world s total. Figure 2 year Carbon Lorenz curve using 1850 as starting Based on the carbon Lorenz curve, we can calculate the carbon Gini index. Siilar to the incoe Gini index calculation, we use two ethods. One is the area ethod; the other is ean variance ethod. The area ethod is derived straightly fro the definition of Gini index. As entioned before, since (X + Y )=0.5, we have G = X X + Y = 0.5 Y 0.5 = 1 2Y (2) The ain difference between various area calculation ethods is in the calculation of area Y. One way is to select a suitable fitting Lorenz curve, and then use integration to calculate the area. Another way is to divide Y into several trapezoids. The su of the trapezoidal area is a close approxiation to the area Y (Fig. 3).
5 138 ADVANCES IN CLIMATE CHANGE RESEARCH Figure 3 ethod Carbon Gini index calculation using trapezoid We assued that there are S countries and we can divide the total area into S trapezoids. Y = S A s = s=1 S s=1 = 1 2 (c s 1 + c s )(p s p s 1 ) 2 S (c s 1 + c s )p s j (3) s=1 Apparently, when S is big enough, the result above is alost the sae as real value. Another coonly used ethod is ean difference ethod. We define the absolute ean variance as = E C a ij C b ij, relative ean variance as /C ij, where a and b is the sequence nuber of two different countries, and C ij is the historical cuulative world eission per capita. Gini index is the half of the relative ean variance. Therefore, G = E Ca ij C b p ij a j pb j Ca ij C b ij a b = 2C ij 2 C (4) ij p j and carbon Gini index to quantitatively analyze the ipact of the starting year on historical responsibility. Figure 4 shows the carbon Lorenz curves with different starting years. Table 2 shows carbon Gini index results with different starting years in various calculation ethods. We can see that different calculation ethods do not affect the carbon Gini index value uch, but the different starting years have big influence on the carbon Gini index value. The latter the starting year, the lower the carbon Gini index is. That eans as the starting years becoe bigger, the carbon space allocation inequality would be concealed. On the global level, carbon Gini index does not change uch when coparing the 1850 starting year calculation with the 1900 starting year calculation. But the 1950 starting year calculation and 1990 starting year calculation largely underestiate the carbon inequality. The 1950 calculation results in a 4% underestiation of the carbon space allocation inequality, while the 1990 calculation accounts for a 14% underestiation of the carbon space allocation inequality. Fro 1850 to 2006, 70% of the cuulative eission space has been allocated unequally, but when starting fro 1990 this figure decreases to 60%. No atter what the starting year is, the inequality of carbon space allocation needs to be concerned. According to the World Bank statistics, three countries incoe Gini indices are above 0.6 in the 182 countries in the world. The biggest incoe gap is in Naibia which has the incoe Gini index of The Gini index of carbon space allocation is 0.70 if the starting year is The covariance Eq. derived fro Eq. (4). (5) in the following can be 1 G = C [2cov(C a ij, p ij p a ) cov(c a ij, p a j )] (5) j One of the ost iportant things in carbon equality and carbon budget is to set the starting year. Many researches confired that the earlier the starting year was, the ore historical responsibility is reflected. But they did not provide a quantitative analysis of the various starting years ipacts on the historical responsibility. In this paper we try to use the carbon Lorenz Figure 4 years Carbon Lorenz curve by using different starting
6 Fei Teng et al. / Metric of Carbon Equity: Carbon Gini Index Based on Historical Cuulative Table 2 Carbon Gini index based on the historical cuulative eission per capita Calculation ethod Fitting ethod Trapezoid area ethod Gini ean difference ethod Covariance ethod Even if 1990 is used as the starting year, the carbon Gini index can still reach 0.60 which is on the sae level as countries with the largest incoe gaps. 4 Conclusions Econoics and sociology are focused ore on the inequality in ters of econoical paraeters, especially the incoe inequality, since incoe is a key factor which deterines the welfare. In the field of cliate change, the unequal allocation of carbon eission space is an issue of great iportance, but the study of the easure of this inequality is rather liited in both theory and application. The quantification of the carbon allocation inequality has great significance. Through the quantification, we can investigate an inequality issue in cliate change fro a different angle or underlying layer. For exaple, easuring the inequality level and trends will be beneficial to look for the root cause of the inequality. The incoe allocation related literatures have provided any eaningful indices and tools for inequality research. With soe adjustent, such indices and tools can be applied to the eission space allocation related carbon inequality issue. In this paper, based on the historical cuulative eission per capita, the authors established the carbon Lorenz curve and carbon Gini index to quantitatively analyze the eission space allocation inequality issue. Several iplications of the historical cuulative eission per capita based on carbon Gini index proposed by the authors in this paper are the following: 1) historical cuulative eission per capita based carbon Gini index reflects the severe inequality of current eission allocation in a ore general way, it helps policy akers and the public to know the eission allocation inequality level; 2) carbon Gini index can not only be used to analyze the current situation of the eission space allocation inequality, but also can be eployed to copare the eission space allocation inequality of different future allocation plans, thus it can reveal the equality raification of different future eission allocation plans and provide guidelines in establishing future allocation plans; and 3) by using the carbon Gini index and carbon Lorenz curve, we can further understand the deep-seated factors in carbon inequality by factor decoposition. The result of the carbon Gini index based on the historical cuulative eission per capita shows that current eission space allocation is severely unequal. The inequality situation is on the sae level as a country with the biggest incoe gap. In the calculation period, carbon Gini index reaches 0.70 which is far beyond the warning level in the case of incoe inequality. This result indicates that 70% of the world total eission space is allocated unequally and such space has been excessively occupied by developed countries. The carbon Gini index has confired that developed countries had excessively occupied the eission space. According to the principle of UNFCCC, developed countries should take the lead to reduce their eissions to redress the unequal situation. The selection of starting year has great influence on the carbon Gini index. The inequality of carbon space allocation has been concealed as the starting year becoes ore recent. However, even year 1990 is used as the starting year, the carbon Gini index can still reach 0.60 which is far beyond the warning line. Carbon Gini index can be used as a static index to easure the inequality of eission allocation. It also provides a quantitative index for international carbon equality discussion. At present, any institutes and scholars have proposed various plans to allocate future CO 2 eission space. It is difficult to copare different plans. The carbon Gini index presented in this paper can reveal the equality iplication of different allocation plans, and copare and contrast different
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