A Climate Justice Based Model for Carbon Budget Allocation

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A Climate Justice Based Model for Carbon Budget Allocation

https://doi.org/10.21203/rs.3.rs-2484481/v1

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Current Integrated Assessment Models (IAMs) and general carbon budget models do not sufficiently account for climate justice in their allocations of future emissions. To address these limitations, several modeling frameworks such as equal per capita (EPC) and per capita convergence (PCC) that aim to incorporate fairness and justice more comprehensively into emissions attribution and carbon budget allocation have emerged. We propose a novel integrated attribution – allocation (IAA) model construct that robustly incorporates three equity principles of responsibility, capability, and equality into the estimation of carbon budget emissions allocations. Results demonstrate that simple reductions of responsibility for climate action to categories such as global south vs global north and developed vs developing cannot be established a priori as methodologies for fairly and justly assigning emissions rights and mitigation obligations.

Earth and environmental sciences/Climate sciences/Climate change/Attribution

Earth and environmental sciences/Environmental social sciences/Socioeconomic scenarios

The issue of climate justice is receiving increasing attention (Gosseries, 2014; Meyer, 2021; Davidson, 2021). The reality of climate change and its impacts on the planet compel the need for action to mitigate the problems it causes and shift the trajectory towards reaching catastrophic planetary tipping points (Rockstrom et al, 2017). Mitigative actions will require curtailing specific kinds of consumption that generate CO₂ (e.g., the use of fossil fuels for energy and transportation), as well as the avoidance of certain types of exploitation (e.g., conversion of forested lands for non-regenerative use). Adopting these actions could have significant economic implications for the affected regions, and lead to varying levels of severity and impact on human and economic development pathways. This poses questions of equity and fairness both on the scope, scale and impacts of climate action on the affected populations that are not currently being sufficiently addressed by extant models. There is currently no alignment on mitigation pathways, attributions of responsibility for historical emissions and allocations of future emissions that are both fair and just (Rivadeneira & Carton, 2022; Hickel, 2020; Hovi et al, 2012; Davidson, 2021).

Fairness comprises of incorporating into carbon budget allocations the consideration of factors such as historical emissions, differences in current levels of emissions, and differing capacities of societies to cope with reductions in emissions rates (Baskin, 2009; Williges et al, 2022). Climate Justice considerations require that CO₂ budget allocations should not deny societies that have made minimal contributions to the global climate problem historically and currently, the right to development pathways that might lead to an increase in their emissions levels, relative to the status quo while ensuring that global targets for carbon mitigation are met.

Ensuring that fairness and justice are considered in climate budget attribution and allocation models is no trivial task (Baskin, 2009; Keen, 2020; Hickel, 2020). Socolow et al (2012) have gone as far as suggesting that “safety and fairness cannot be achieved simultaneously for strict definitions of both”. Baskin (2009) attributes the lack of alignment around climate action to the absence of robust justice principles in climate policy formulation and posits that there are four factors that must be enabled in a comprehensive climate justice framework, namely: 1) it must lead to dramatic reductions in GHGs 2) should be fair and take account of the varied current and historical responsibilities for emissions, whilst also reflecting differing existing capacities 3) it should not increase inequality and 4) it should not increase the potential for international conflict.

Developing a climate justice compatible carbon allocation model

Integrated Assessment Models (IAMs) combine complex interplays of socio-economic, technological, and biogeochemical variables in their conceptual frameworks but do not sufficiently address questions related to the fairness of adaptation and mitigation strategies (Jafino et al, 2021; Rivadeneira & Carton, 2022). The critiques of IAMs includes the view that they have limited representations of inequality and distributional impacts, foster inequality, promote complacency, reproduce types of economy that are not sustainable and can be unrealistic in their representation of Earth and Human systems and the relation between the two (Jafino et al, 2021; Asefi-Najafabady et al, 2021; Keen, 2020). Furthermore, their reliance on aggregated perspectives of benefits and costs does not permit a clear outlook on burdens and benefits for different actors across time and space, precluding the possibility of comprehensively integrating fairness and justice considerations (Stanton et al, 2009).

There has been an increasing focus on the development of more robust distribution models that incorporate fairness and justice into emissions attribution and carbon budget allocations (Hohne et al, 2014; Hickel, 2020; Williges et al, 2022). Hickel (2020) has proposed the fair-shares attribution approach which establishes differentiated national responsibility for climate breakdown consistent with the principles of planetary boundaries and equal access to atmospheric commons. Williges et al (2022) evaluated two commonly utilized allocation mechanisms (per capita convergence, PCC and equal per capita, EPC) and developed a qualified equal per capita allocation approach that incorporates grandfathering to address fairness concerns.

In this work we aim to develop a conceptual framework that comprehensively addresses the challenge of incorporating historical responsibilities for emissions that have contributed to climate damage, the reality of differing current emissions and varying capabilities for addressing climate challenges into an allocation mechanism that generates fair and just carbon emissions budgets. Such a model would integrate the seemingly intractable issues of safety (i.e., maintaining trajectories that keep planetary temperature rise at < 1.5 to 2^oC), fairness, and justice in a single construct.

We establish five principles that serve as the framing basis for our integrated attribution – allocation model. These are:

Individual consumption choices determine the aggregate levels of emissions in any region; hence the per capita emissions of individuals (tCO₂ per capita) are the elemental units that aggregate to regional level emissions
The responsibilities for all emissions attributed to a region must be borne by the population in the region. Responsibility for historical and current emissions are to be borne by the current inhabitants in the region while future emissions are the responsibility of populations within those regions in the relevant future time
Every region has a right to economic and human development with the right to attain widely accepted global milestones for development without encumbrance to the energy pathways utilized to reach that goal. This is a fairness provision that recognizes that most nations that are currently at levels of high development status themselves utilized unfettered energy pathways to attain that status and have no moral right to deny other regions access to such pathways
Prescribed development pathways taken to engage in mitigative climate action should not erode current or future competitive or comparative advantage
Convergence of per capita emissions across geographical regions is necessary to ensure an equitable level of shared responsibility for the global atmospheric commons based on a fair and equitable distribution of emission rights. This aligns with both the equal per capita and per capita convergence principles (Hohne et al, 2014)

These principles if successfully integrated into climate attribution and allocation models have the potential to advance and enhance sustainability of climate policy and provide an objective and equitable basis by which alignment can be readily reached around climate action. They also comprehensively unify the disparate approaches to climate justice such as contraction and convergence of emissions, greenhouse development rights, equal per capita emissions, and individual responsibility for climate action (Baskin, 2009; Williges et al, 2022).

Developing the Integrated Attribution Allocation (IAA) model framework

The global carbon budget provides the maximum value for a range of not-to-be-exceeded emission levels needed to maintain a trajectory towards < 1.5^oC average global temperature rise (Friedlingstein et al, 2021; Matthews et al, 2020). We define the global carbon budget thus:

$$\begin{array}{c}{C}_{G,T}=\sum _{t=1}^{t={T}_{d}}{C}_{G,t} \#1\end{array}$$

Where ${C}_{G,T}$ (GtCO₂) is the global carbon budget over a drawdown period, ${T}_{d}$ and ${C}_{G,t}$ (GtCO₂per year) is the annual global carbon budget.

For any given year, within the drawdown period, we posit that:

$$\begin{array}{c}{C}_{G,t}=\sum {C}_{G,R} \#2\end{array}$$

${C}_{G,R}$ (GtCO₂ per year) is the equitable allocation of carbon emission rights for individual regions. At the global level, the regions of interest are nation states.

The carbon budget in any region is obtained by aggregating per capita emissions (tCO₂ per capita) for the entire population domiciled within that region. Hence, we can define the relationship:

$$\begin{array}{c}{C}_{G,R}={N}_{R}{E}_{G,R } \#3\end{array}$$

Where ${N}_{R}$ is the population living within the region and ${E}_{G,R}$ (tCO₂ per capita) is the average allocated per capita emission for the region.

We further expand the definition of ${E}_{G,R}$ to include three per capita emissions categories that should be incorporated into an equitable and justice-based carbon budget, i.e., historical per capita emissions (${E}_{H,R}$), current per capita emissions (${E}_{C,R}$) and projected future per capita emissions (${E}_{F,R}$). Hence, we have that:

$$\begin{array}{c}{E}_{G,R}=\sum f\left({E}_{C,R}\right)+\sum f\left({E}_{F,R}\right)-\sum f\left({E}_{H,R}\right) \#4\end{array}$$

We can rewrite the formulation in Eq. 4 as:

$$\begin{array}{c}{C}_{G,R}=\sum \theta {N}_{R}{E}_{C,R}+\sum \phi {{N}_{R}E}_{F,R}-\sum {\beta }_{R}{{N}_{R}E}_{H,R} \#5\end{array}$$

Where $\beta$, $\theta$ and $\phi$ are weighting factors whose values reflect the extent to which the historical, current and future economic developmental pathways influence carbon budget allocations.

Equation 5 can also be expressed as:

$$\begin{array}{c}{C}_{G,R}={N}_{R}\left(\sum \theta {E}_{C,R}+\sum \phi {E}_{F,R}-\sum {\beta }_{R}{E}_{H,R}\right) \#6\end{array}$$

The economic underpinnings of${E}_{F}$

The future emissions allocation, ${E}_{F}$ is best aligned with climate justice. It addresses the requirement for climate action to allow poor and developing countries to grow and industrialize without being forced down developmental pathways that erode their competitive advantage and denies them access to energy options that nations that are now at higher levels of economic and human development utilized for attaining their own growth (Baskin, 2009; Davidson, 2021). Such an allowance for the possibility for higher levels of emissions to support development must necessarily be bounded (Fuhr, 2021). We assume that the bounding variable is a per capita level of emissions, ${E}_{T}$ that is functionally correlated with the threshold Gross Domestic Product (GDP) per capita value corresponding to the transition to a high development economy status, $G{DP}_{T}$.

We can redefine the justice based, future emissions allocation as:

$$\begin{array}{c}{E}_{F,R}=f\left\{{E}_{T}-{E}_{R}\right\} \#7\end{array}$$

Where ${E}_{R}$ is the current per capita CO₂ emissions (tCO₂ per capita) for the region and ${E}_{T}$ is the CO₂ emissions per capita level associated with the GDP per capita threshold that marks the transition to developed economy status.

Given the well documented positive relationship between economic growth, energy consumption and CO₂ emissions (Onofrei et al, 2022) we assume that for any region and within a given period, a functional relationship can be established between emissions during that period, $E$ (tCO₂) and GDP (USD) of the form:

$$\begin{array}{c}GDP=kE \#8\end{array}$$

Where $k$ is a transitory constant that establishes the relationship between CO₂ emissions and economic output in the specified region, for the specified period.

Hence, we have that:

$$\begin{array}{c}{E}_{F,R}=f\left\{{E}_{T}-{E}_{R}\right\}=\frac{G{DP}_{T}-G{DP}_{R}}{{k}_{G}} \#9\end{array}$$

Where $G{DP}_{T}$ is the threshold GDP per capita level beyond which a region is considered to have transitioned to a high development status, $G{DP}_{R}$ is the current per capita GDP in the region and ${ k}_{G}$ is a “representative” carbon intensity level used for translating the gap in economic output between $G{DP}_{T}$ and $G{DP}_{R}$ into an emissions equivalent. We assume ${k}_{G}$ to be the inverse of the average global carbon intensity value of GDP (IEA, 2022). The estimate for the average global CO₂ emissions intensity of GDP for the period 2019 to 2021 is 0.26 tCO₂ per $1,000 i.e., ${k}_{G}=$ $3,846 per tCO₂ (IEA, 2022).

Establishing ${GDP}_{T}$

A critical question to be resolved for practical applications of this framework is the question of how ${GDP}_{T}$ gets established and what constitutes an appropriate level of development to set as the high development GDP per capita threshold. There are at least three possible options that can be considered, and these include i) the United Nations definition for high income nations which sets a GNI of >$12,500 as a transitional threshold (Serajuddin & Hamadeh, 2020) ii) setting the threshold as the average GDP per capita for the OECD of >$45,000 (OECD, 2022) and iii) using the average output of >$30,000 GDP per capita observed for most developed economies as the threshold level for economic development (UNCTAD, 2019).

Estimating ${E}_{C}$

For fairness, the level of net current emissions per capita, ${E}_{C}$ should reflect the difference between current emissions from that region, ${E}_{R}$ and a fairness based budgetary allocation based on the available global carbon budget, ${E}_{B,R}$.

Hence, we define the relationship:

$$\begin{array}{c}{{E}_{C,R}=E}_{B,R}-{E}_{R} \#10\end{array}$$

${E}_{B,R}$ , which is the gross annual per capita carbon allocation is determined by proportionally assigning every global citizen equal emissions allocation from the global carbon budget over a defined drawdown period. Hence, we have that:

$$\begin{array}{c}\left(\frac{{N}_{R}}{{N}_{T}}\right)\frac{{C}_{G,t}}{{N}_{R}}={E}_{B,R} \#11\end{array}$$

Where ${N}_{T}$ is the global population, ${N}_{R}$ is the regional population, ${C}_{G,t}$ is the annual global carbon budget, and ${E}_{B,R}$ is the gross annual per capita emissions allocation.

We can therefore rearrange the global carbon allocation budget, ${C}_{G,t}$ as:

$$\begin{array}{c}{C}_{G,t}=\sum \theta {N}_{R}f\left\{{E}_{B,R}-{E}_{R}\right\}+\sum {{\phi }_{R}N}_{R}\left(\frac{G{DP}_{T}-G{DP}_{R}}{{k}_{G}}\right)-\sum {{\beta N}_{R}E}_{H,R} \#12\end{array}$$

Specifying Time Horizons

There are two-time horizons of interest. The first is the drawdown period, ${T}_{d}$, which is the time over which the available carbon budget is to be applied. The second is the historical emissions coverage horizon, which is the time span for which historical emissions are to be considered and requires the definition of a start time, ${T}_{s}$, and a baseline time, ${T}_{b}$.

Estimating ${E}_{H}$

In this conceptual framework, the responsibility for historical carbon emissions generated in any region is assumed to be borne by the extant populations domiciled in those regions. This is consistent with principles of reparative justice and is supported by the reality that current inhabitants of those regions that have contributed the most to the addition of carbon to the atmosphere experience relatively higher standards of living and economic attainment that have been made possible by developmental pathways that are directly linked to the historical release of higher-than-average CO₂ emissions into the atmosphere from those regions (Chapman and Ahmed, 2021).

Defining ${C}_{H,R}$ as the cumulative value of atmospheric CO₂ emissions in a region from a starting period, ${T}_{s}$ through to a defined baseline period ${T}_{b}$, then the per capita historical emissions in that region, ${E}_{H,R}$ for a specified drawdown period, ${T}_{d}$ can be defined as:

$$\begin{array}{c}\frac{{C}_{H,R}}{{N}_{R}}\left(\frac{1}{{T}_{d}}\right)={E}_{H,R} \#13\end{array}$$

${N}_{R}$ is as previously defined.

Reviewing model conditionalities and constraints

$\beta$ , $\theta$ and $\phi$ can range from $0 to \infty$. They are expected to vary as economic, development and environmental conditions change
${E}_{T}$ , ${k}_{G}$, and ${GDP}_{T}$ have values ≥ 0, that can change over time
Given that ${E}_{F,R}=\frac{G{DP}_{T}-G{DP}_{R}}{{k}_{G}}$then we have that as ${k}_{G}$ $\to \infty$, $\frac{G{DP}_{T}-G{DP}_{R}}{{k}_{G}}\to 0$; and ${E}_{F,R}\approx 0$. This represents conditions in which the region has a high rate of economic output per ton of CO₂ emitted i.e., a high energy productivity economy
Solution sets that reduce inequality are preferred. The coefficient of variation for the allocated per capita emissions, ${E}_{G,R}$ represents a suitable equality criterion (Bendel et al, 1989).
We assume a historical emissions coverage horizon that spans, ${T}_{s}=1750$ and ${T}_{b}=2019$, except stated otherwise
Convergence values of 2 tCO₂ per capita are set for all instances where ${E}_{B,R}<2$ and a positive carbon budget is to be allocated. For instances where the carbon budget is negative, no convergence values are specified.

Case Studies

The following section will demonstrate the use of the model using fifteen (15) case studies. Historical carbon emissions data is sourced from Ritchie et al (2020). All other data is sourced from the World Bank (World Bank, 2022). The case studies address one or more of these conditions:

1. For twelve cases (Cases 1 through 13) a carbon budget of 500 GtCO₂ is specified. The carbon budget represents the total amount of permissible CO₂ emissions to limit global warming within ≤ 1.5^oC (Xu and Ramanathan, 2017; Matthews et al, 2020).

2. For two cases (cases 14 and 15) a carbon reduction target of -500 GtCO₂. These scenarios are intended to demonstrate the model’s capacity for carbon mitigation allocation which could be relevant in future periods where humanity has exhausted the carbon budget and a net reduction in atmospheric carbon is required to mitigate global warming

3. Setting constraints on the maximum emissions allocation in each region, ${{E}}_{{G},{R}}$ (see Table 1)

4. Setting the drawdown period, ${T}_{d}$ (see Table 1)

5. Setting the historical emissions coverage horizon by varying ${T}_{s}$ while maintaining ${T}_{b}=2019$ (see Table 1).

6. Specifying the threshold GDP per capita level, ${GDP}_{T}$ to which developing nations can aspire using unfettered development pathways (see Table 1)

Table 1 contains a summary of all the conditions used in each of the 15 case scenarios. For each case, the generalized reduced gradient (GRG) non-linear optimization routine is used to solve for a set of $\beta$, $\theta$, $\phi$ values that satisfy the requirements which in all cases is allocating a specified annual global carbon budget on an equitable basis across all regions, subject to specific constraints. The GRG routine evaluates the gradient of the objective function as the input values change and reaches a local optimum solution when the partial derivative equals zero (Lasdon et al, 1978; Fylstra et al, 1998). We note that the use of the GRG approach does not preclude the existence of other values of $\beta$, $\theta$, $\phi$ that satisfy the model’s objective function within the specified constraints since it returns local optima. For the GRG approach, the starting values for $\beta$, $\theta$, $\phi$ can have an impact on the local optima that meet the model specifications. We utilize starting values for the solver routine of $\beta =1$, $\theta =1$, $and \phi =1$ in all cases.

Table 1

Summary table of key variables in all the evaluated case examples
Cases	${G}{{D}{P}}_{{T}}$ per capita	Constraints	Drawdown (T_d, yrs.)	${{T}}_{{s}}$	${{T}}_{{b}}$	${{C}}_{{G},{T}}$ GtCO₂
Case 1	$12,500	None	10	1750	2019	500
Case 2	$30,000	None	10	1750	2019	500
Case 3	$45,000	None	10	1750	2019	500
Case 4	$12,500	Minimize Coef. of Var	10	1750	2019	500
Case 5	$30,000	Minimize Coef. of Var	10	1750	2019	500
Case 6	$45,000	Minimize Coef. of Var	10	1750	2019	500
Case 7	$12,500	Minimize Coef. of Var	30	1750	2019	500
Case 8	$30,000	Minimize Coef. of Var	30	1750	2019	500
Case 9	$45,000	Minimize Coef. of Var	30	1750	2019	500
Case 10	$30,000	Minimize Coef. of Var	100	1750	2019	500
Case 11	$30,000	Minimize Coef. of Var	30	1850	2019	500
Case 12	$30,000	Minimize Coef. of Var	30	1950	2019	500
Case 13	$30,000	Minimize Coef. of Var	30	1990	2019	500
Case 14	$30,000	None	10	1750	2019	-500
Case 15	$30,000	None	30	1750	2019	-500

The determination of a preferred state between two states that satisfy the model will require the setting of additional constraints such as the selection of the state that has the minimum value for the coefficient of variation for the objective function, ${E}_{G,R}$ (Bendel et al, 1989). Generally, a lower coefficient of variation suggests that less “inequality” exists within the sample set.

Creating a marketplace for emissions to fund global carbon mitigation

While the model provides “fair” allocations of emissions rights, most nations are going to be unable to reach their allotted specific carbon allocations quickly. Their ability to utilize the allocations will be affected by factors such as local politics, access to capital, policy, infrastructure, and entrepreneurial readiness. Should such nations be allowed to defer those emissions till some future time when they can utilize it, or should it be a use it or lose it proposition, given that there are immediate needs by other nations for those emissions right? While there might be debate about what is to be done with unused emissions rights, what is clear is that those emissions have a value that is bounded between two realities. The lower bound is the value of the offset emissions to the nations to which they have been allocated based on their current emissions to GDP ratio, and the upper bound is the value of the opportunity cost of the reduced per capita emissions value to those economies that are assigned a lower allocation than their current emission levels. This model can therefore define the emissions volumes that can be traded in a global carbon market and provide a fair means for determining which nations come to the market with surplus or deficit emissions allocations. Funds from such a marketplace can also be used to finance global climate mitigation programs.

Measures of fairness

Statistical variables such as coefficient of variance, skewness and Gini coefficients have been used as estimates of inequality. We posit that a sustainable allocation framework should ensure that there is more equality, not less, as regions adopt and operationalize their carbon budget allocations. In this paper we have used the coefficient of variance of ${E}_{G,R}$, as a fairness condition. Future work will evaluate the extent to which other measures of inequality are relevant to consider as metrics for evaluating equality and fairness. The obvious impact of the specification of equality as a model constraint is the tightening of the spread in ${E}_{G,R}$ between regions (see Table 3).

This paper presents a robust theoretical framework for incorporating climate justice into the attribution and allocation of CO₂ emissions. It comprehensively addresses all of Baskin’s four considerations for climate justice (Baskin, 2009). It also resolves what Tavoni et al (2012) had suggested was an impossible task, i.e., achieving safety and fairness for strict definitions of both, in the attribution and allocation of CO₂ emissions. The model can also be utilized in determining emissions allocations even in a Net Zero regime, in which net negative global emissions would be required to avoid hitting planetary tipping points. The model also decouples designations of development and economic status of countries from allocation outcomes. The model can also be utilized for allocating carbon budgets at sub-national levels once the national level budget is established. The approach offers several levers that can serve as a basis for objectively modeling policy implications for human and economic development across regions and can be readily integrated into existing IAMs.

At the UN climate summit in Copenhagen in 2008, “rich” nations made a pledge to commit $100 billion a year to less wealthy nations by 2020 in support of climate actions that enhance adaptation and mitigate further rises in temperature. Nearly a decade and a half later, this commitment is still not being met and there continues to be uncertainty about how the global carbon removal initiative will be funded. At issue is what the obligations of the “rich” countries should be and what is in or out of scope. What our conceptual approach indicates is that from a climate fairness perspective, it is not only the so called “rich” countries that should have obligations. As can be seen in Figs. 1–3, the allocations of emissions for the three cases depicted does not lend itself to simple categorizations by geographic regions. Hence this model avoids a major drawback in many attribution and allocation models which label climate obligations as an issue of “west vs east”, “global South vs global North”, “developed vs developing” or any of the other categorizing labels that have made global mobilization for climate action difficult. We believe that the absence of a priori categorizations of regions as the basis of climate responsibility in our model, meets Baskin’s requirement that an appropriate climate justice model should help to reduce the likelihood for international conflict (Baskin, 2009).

We conceive of the possibility that future policy development efforts and climate negotiations could be spent in determining the $\beta$, $\theta$, $\phi$, ${E}_{T}$, ${k}_{T}$, and ${GDP}_{T}$ values that should be utilized in carbon budget allocation model to enable global CO₂ reduction targets to be met.

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A Climate Justice Based Model for Carbon Budget Allocation

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