The concept of ecological debt: some steps towards an enriched sustainability paradigm

Abstract

In this paper, we elaborate on the concept of ecological debt. Starting from the enriching environmental justice perspectives, this grass-roots concept has to offer to sustainability discourse, a broad conceptual discussion is presented resulting in a working definition for ecological debt. In elaborating on this definition, we try both to accommodate these enriching perspectives and to offer a more robust conceptualisation that is applicable in international sustainability discourse. Also, a scientifically sound methodology is presented which allows quantifying different aspects of ecological debt. Finally, both the conceptual analysis as well as the quantification method is applied to the case of climate change.

Appendices

Annex: calculation methodology

This annex deals with the mathematical details of calculating the Historical Carbon Debt (HCD), the Generational Carbon Debt (GCD) and the total Carbon Debt (CD) of a country, according to the two models introduced in the paper. For model 1, we start from defining the total Carbon Debt, then indicating how it can be split up into a Historical and a Generational Carbon Debt. In the case of model 2, we go the other way around, beginning with definitions for the HCD and GCD which taken together make up the total CD.

Model 1

2.1 The total Carbon Debt (CD)

In the case of model 1, the Carbon Debt is the cumulative amount of CO₂ a country has emitted over time above the sustainable level. In a more formal way, the carbon debt of a country c, CD _c , can be expressed as

$$ {\text{CD}}_{c} = \sum\limits_{i = \sigma }^{\varepsilon } {\left[ {e_{c} \left( i \right) - {\frac{{{\text{Pop}}_{c} \left( i \right)}}{{{\text{Pop}}_{w} \left( i \right)}}}s_{w} \left( i \right)} \right]} $$

(1)

where σ is the start year, ε the end year of accounting, Pop _c (i) is country c’s population for year i, Pop _w (i) is the world year i population, e _c (i) is country i’s CO₂ emissions from year i and s _w (i) is the world sustainable level for year i. The carbon debt can be positive or negative. Countries with a positive CD are debtors, those with a negative CD are creditors. Summing the CD _c over all countries gives the carbon debt of the world as a whole, CD _w , i.e.

$$ \sum\limits_{c} {{\text{CD}}_{c} = \sum\limits_{i = \sigma }^{\varepsilon } {\left[ {\sum\limits_{c} {e_{c} \left( i \right)} - {\frac{{\sum\limits_{c} {{\text{Pop}}_{c} \left( i \right)} }}{{{\text{Pop}}_{w} \left( i \right)}}}s_{w} \left( i \right)} \right]} } $$

which immediately gives

$$ {\text{CD}}_{w} = \sum\limits_{i = \sigma }^{\varepsilon } {\left[ {e_{w} \left( i \right) - s_{w} \left( i \right)} \right]} . $$

(2)

2.2 The Historical Carbon Debt (HCD)

In model 1, splitting the CD _c of a particular country in a HCD _c and a GCD _c is based on the HCD_debtors/CD_debtors ratio of all debtor countries as a whole, and the latter is determined as follows. Consider all carbon creditors, i.e. all countries which have a negative CD _c . According to model 1, these countries should be compensated for exactly the amount of carbon credit they total. Also according model 1, this total amount of carbon credit equals the total amount of HCD_debtors of all debtor countries together, i.e.

$$ {\text{HCD}}_{\text{debtors}} = - \sum\limits_{\text{creditors}}^{{}} {{\text{CD}}_{\text{creditors}} } . $$

In this way, the HCD_debtors/CD_debtors ratio is determined for all debtor countries as a whole. This ratio can than be used to determine the HCD _c for every individual debtor country; every debtor country thus having the same HCD _c /CD _c (= HCD_debtors/CD_debtors) ratio.

$$ {\text{HCD}}_{c} = {\frac{{{\text{HCD}}_{\text{debtors}} }}{{{\text{CD}}_{\text{debtors}} }}}{\text{CD}}_{c} . $$

(3)

2.3 The Generational Carbon Debt (GCD)

The rest of a debtor country’s CD _c is then regarded as carbon debt towards future generations, i.e. the GCD _c

$$ {\text{GCD}}_{c} = {\text{CD}}_{c} - {\text{HCD}}_{c} . $$

HCD _c being determined according to Eq. 3. In this model, carbon creditors will have a negative HCD _c (credit) and no GCD _c ; carbon debtors will have a positive HCD _c and a positive GCD _c adding up to a positive CD _c ; the HCD _c /CD _c ratio of an individual country being determined by the HCD_debtors/CD_debtors ratio of all debtor countries together. The sum of all HCD _c over all countries is of course equal to zero.

Model 2

3.1 The Historical Carbon Debt (HCD)

In this model, the HCD deals with over-emissions with respect to the world average per capita emissions. The Historical Carbon Debt is thus the amount of CO₂ a country has emitted over time in excess of the world average per capita emissions. In a more formal way, the Historical Carbon Debt of a country c, HCD _c , can be expressed as:

$$ {\text{HCD}}_{c} = \sum\limits_{i = \sigma }^{\varepsilon } {\left[ {e_{c} \left( i \right) - {\frac{{{\text{Pop}}_{c} \left( i \right)}}{{{\text{Pop}}_{w} \left( i \right)}}}e_{w} \left( i \right)} \right]} $$

(4)

where σ is the start year, ε the end year of accounting, Pop _c (i) is country c’s population for year i, Pop _w (i) is the world year i population, e _c (i) and e _w (i) are country i’s and world CO₂ emissions from year i.

It should be mentioned that the HCD can be positive or negative. Countries with a positive HCD are considered to be in debt with countries that have a negative HCD. Note that the sum of HCD over all countries is equal to zero.

3.2 The Generational Carbon Debt (GCD)

The Generational Carbon Debt concerns that part of over-emissions with respect to a sustainable level that does not fall under the historical carbon debt. The Generational Carbon Debt is thus the cumulative amount of CO₂ a country has emitted over time above the sustainable level, taking into account only that part of CO₂ emissions that does not overshoot the world average per capita emissions (as that part is contained in the HCD). In a more formal way, the Generational Carbon Debt of a country c, GCD _c , can be expressed as

$$ {\text{GCD}}_{c} = \sum\limits_{i = \sigma }^{\varepsilon } {{\text{GCD}}_{c} \left( i \right)} $$

(5)

with:

$$ {\text{GCD}}_{c} \left( i \right) = {\frac{{{\text{Pop}}_{c} \left( i \right)}}{{{\text{Pop}}_{w} \left( i \right)}}}\left( {e_{w} \left( i \right) - e_{\text{sust}} \left( i \right)} \right) $$

where σ is the start year, ε is the end year of accounting, Pop _c (i) is country c’s population for year i, Pop _w (i) is the world year i population, e _c (i) and e _w (i) are country i’s and world CO₂ emissions from year i, and e _sust(i) is the sustainable level for year i. Note that in this case, every country has a positive GCD _c (i) in proportion to its share in the world’s population. This is in line with the argument made in the paper that once the HCD _c (i) is compensated for, we deal with a notional average consumer.

3.3 The total Carbon Debt (CD)

The total Carbon Debt of a country, CD _c , is of course determined by the sum of the HCD and GCD, i.e.

$$ {\text{CD}}_{c} = {\text{HCD}}_{c} + {\text{GCD}}_{c} . $$

(6)

Making use of Eqs. 1, 4, 5 and 6, it is easily verified that the total carbon debt calculated according to model 2 is identical to the total carbon debt according to model 1.