What a difference carbon leakage correction makes!

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In this paper, we investigate the effect of carbon leakage correction when turning from a production-based to a consumption-based approach. We consider six different regulatory regimes. For calculating carbon leakage corrections, we employ the Leontief Inverse derived from WIOD input/output tables. To account for country-specific characteristics we use OECD data. As modelling technique, we apply a non-parametric productivity estimation approach (Data Envelopment Analysis) to calculate relative efficiency scores of countries’ environmental performance to take their heterogeneity into account. The results suggest that irrespective of the chosen policy regime, the correction for carbon leakage will always lead to a significant reduction of emissions. The average effect of leakage correction amounts to 37% less CO2 emissions.

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Fig. 1
Fig. 2


  1. 1.

    When two developed Annex B countries jointly carry out a venture to reduce emissions, the initiating country gets credited for the reduction of emissions realized in the other country.

  2. 2.

    This mechanism is similar to the Joint Implementation mechanism but focusses on the emission reduction in developing countries. Thus Annex B countries can use these projects for compliance at home. Compare Newell et al. (2013).

  3. 3.

    Compare Aldy et al. (2003, p. 1).

  4. 4.

    This includes developed countries as well as countries in transition according to the Framework Convention on Climate Change (FCCC); an agreement on greenhouse gas emissions reached in Rio de Janeiro, Brazil, at the United Nations Conference on Environment and Development, in 1992.

  5. 5.

    The concept of natural disposability implies that a decision making unit (a country) decreases a directional vector of inputs in order to decrease a directional vector of undesirable outputs. The concept of managerial disposability implicates that a decision making unit may increase a directional vector of inputs to advance technology in order to decrease a directional vector of undesirable outputs. See Sueyoshi and Goto (2012a, 2013) for more details.

  6. 6.

    All vectors are strictly positive, which means that there is no DMU with a zero entry neither in inputs nor in outputs. This must hold in all models.

  7. 7.

    We follow standard procedures to set this scalar to a very small non-Archimedian number (𝜖 = 10− 6).

  8. 8.

    Compare e.g. Sueyoshi and Goto (2012b).

  9. 9.

    The distinction between CRS and VRS is neglected, as it does not help understanding.

  10. 10.

    The corresponding DEA models, i. e. linear programs, were discussed in the subsection above.

  11. 11.

    In Regime I CRS and Regime I VRS, CO2 emissions will be considered as inputs, even if it technically is an output, though a bad one. Because the objective is to minimize emissions per unit good output (Y ) and the underlying DEA model in Regime I implicitly minimizes inputs per unit good output, emissions treated as inputs are minimized, too.

  12. 12.

    The increase in good output is pegged to a reduction in bad outputs (CO2 emissions). The higher α, the more weight is put on the reduction of emissions. With α = − 1, the increase in good output by ξ% would allow for an increase in bad output by ξ% (no decoupling). With − 1 < α ≤ 0, a relative decoupling is assumed. The increase in good output would nevertheless go along with an increase in bad output, although with a lower ratio between bad and good output. In case of an absolute decoupling (α > 0), the increase in good output requires an absolute reduction of overall emissions in order to reach the frontier.

  13. 13.

    This is tantamount to saying an economic actor is innovating.

  14. 14.

    Assuming constant returns to scale, i. e. country size remains unconsidered, the inequality labeled VRS-condition in the above models such as in Eq. 1 is ignored.

  15. 15.

    The DEA model with constant returns to scale was introduced by Charnes et al. (1978). Since then it has become known as the CCR model, according to author initials.

  16. 16.

    With this information, we will calculate below the CO2 emissions of the country assuming an efficiency score 𝜃 = 100%.

  17. 17.

    Note that for small values it is easy to approximate the inefficiency \(\xi =|1-B^{*}_{B}/B_{B}|=|1-Y^{*}_{B}/Y_{B}|=5.9\%\).

  18. 18.

    Compare also Fig. 1a.

  19. 19.

    In most studies, the emission of greenhouse gases, proxied by carbon dioxide, is considered as bad output. Aside from carbon dioxide, also other greenhouse gases exist such as methane (CH4) or nitrous oxide (N2O), which contribute to global warming. Carbon dioxide, however, is the main polluter among all greenhouse gases. According to the IPCC, carbon dioxide makes about three quarters of all greenhouse gas emissions. For simplicity, we confine bad output to the emission of CO2, in our study. This indeed is a simplification, because the interdependency between different kinds of gases is not linear. For a discussion of this topic see e. g. Wagner and De Preux (2016).

  20. 20.

    The production of nuclear waste also is a bad output. In account of not all countries being endowed with nuclear power, nuclear waste is generated only in countries with nuclear power. For technical reasons, as DEA requires positive vectors in inputs, good as well as in bad outputs, nuclear waste cannot enter the models as a bad output. Alternatively, we summarize all non-renewable electrical energy production capacities under the variable FOS.

  21. 21.

    For further details, see Timmer et al. (2014).

  22. 22.

    For a concise summary see Peters and Hertwich (2008).

  23. 23.

    As Wiedmann (2009) points out, the first estimation of pollution contained in international trade goes back to Walter (1973).

  24. 24.

    The construction of the WIOD tables is explained in detail by Dietzenbacher et al. (2013).

  25. 25.

    See Table A2 in the appendix of Timmer et al. (2014).

  26. 26.

    Compare e. g. Peters (2008) for further details.

  27. 27.

    The calculations are also based on the WIOD tables.

  28. 28.

    As far as fossil energy production is concerned, it is impossible that any technical progress will manage to reduce CO2 to zero, because the energy contained in fossil energy sources is bound to carbon which will always lead to CO2 emissions when extracting the energy. Excluding FOS from our analysis would change the results fundamentally, since there would also be a benchmark country specializing in fossil energy production.

  29. 29.

    Note that the potential reduction of CO2 emissions is always calculated relative to the actual production-based CO2 emissions for the sake of comparability. We could certainly also use the consumption-based CO2 account as a base.

  30. 30.

    Also here, we use the actual production-based CO2 quantities as a base to calculate the relative reduction of CO2 emissions.

  31. 31.

    The asterisk is placeholder for the respective variable CO2,GDP,FOS,CAP, or POP; u and c stand for the scenario with uncorrected and corrected values, respectively.

  32. 32.

    As an example, the total absolute reduction of CO2 emissions across all countries divided by their actual total production-based CO2 emissions yields − 37% lower emissions in comparison to the base value (= total sum of CO2 emissions of all countries). Subtracting the respective number in part II (= − 14%) from the number in part I (= − 48) yields − 34.

  33. 33.

    The values of part III in column ΔCO2 are equivalent to the leakage correction values of the last column (labeled All) in Table 9.

  34. 34.

    The differences refer to average changes in CO2 across all six scenarios.

  35. 35.

    This includes nuclear power capacities. See above for the technical reasons, why we subsume nuclear power under the variable FOS.

  36. 36.

    In the above regimes, the directional loss function stipulates that an increase of one unit in output must go along with a unit decrease in bad output, if the respective regimes’ parameter a was set to unity. This parameter certainly is subject to negotiation.


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Grebel, T. What a difference carbon leakage correction makes!. J Evol Econ 29, 939–971 (2019).

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  • Energy efficiency
  • CO2-emissions
  • DEA
  • Benchmarking

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  • Q56
  • Q58