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Clean-Development Investments: An Incentive-Compatible CGE Modelling Framework

An Erratum to this article was published on 18 March 2015


Emissions offset schemes, such as the Clean Development Mechanism established under the Kyoto Protocol and sectoral crediting schemes which are currently discussed as a new market-based mechanism within the United Nations Framework Convention on Climate Change, allow industrialized Annex I countries to offset part of their domestic emissions by investing in emissions-reduction measures in developing non-Annex I countries. Here we present a novel modelling framework for offset schemes which can be used in computable general equilibrium models to quantify the sector-specific and macroeconomic impacts of clean-development investments. Compared to conventional approaches that mimic offset schemes as sectoral emissions trading, our framework adopts a micro-consistent representation of an offset scheme’s incentive structure and its investment characteristics. In our empirical application, we show that incentive compatibility implies that the offset-generating sectors do not suffer, and that overall cost savings from the offset scheme tend to be lower than suggested by conventional modelling approaches.

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  1. The latest Conferences of the Parties in Copenhagen (COP 15), Cancún (COP 16), Durban (COP 17), and Doha (COP 18) have brought about only a voluntary pledge-and-review system. Although some developing countries, such as India and China, have made voluntary pledges, they have not adopted legally binding emissions-reduction commitments.

  2. The CDM has two main purposes (Article 12.2 Kyoto Protocol). For Annex I countries its purpose is to increase the cost-efficiency of fulfilling their emissions reduction commitments made under the Kyoto Protocol by utilizing low-cost abatement options in non-Annex I countries. For non-Annex I countries its purpose is to spur sustainable development by financing projects that reduce emissions and support development.

  3. In contrast to the CDM Programme of Activities (PoA) and Nationally Appropriate Mitigation Actions (NAMAs), the UNFCCC has not formally defined sectoral CDM measures, despite extensive discussions (Sterk and Wittneben 2006; Paulsson 2009). However, consultations on a new market-based mechanism (NMM) which may take the form of a sectoral crediting or sectoral trading scheme were initiated during the 17th Conference of the Parties (COP 17) in 2011 (Michaelowa 2012).

  4. There also exist other offset mechanisms which transfer clean-development investments within one country, such as Australia’s Carbon Farming Initiative, or which transfer investments from one Annex I country to another, such as Joint Implementation. Although this study’s focus is on clean-development investments by industrialized countries in developing countries, its general methodology could as well be applied to other offset mechanisms.

  5. A substantial body of literature has formed around the CDM which analyses and proposes ways to hold the CDM in line with its dual purpose of enabling cost-efficient (regionally flexible) emissions reduction for Annex I countries and of spurring sustainable development through CDM investment in non-Annex I countries (e.g. Ellis et al. 2007; Boyd et al. 2009; Lecocq and Ambrosi 2007).

  6. A political rather than technical reason for constraining the trade of emissions allowances between Annex I and non-Annex I countries is to represent the supplementarity requirement laid out in the Marrakech Accords to the Kyoto Protocol. Those accords state that the use of each of the flexible mechanisms (ETS, CDM, JI) shall be supplemental to domestic action and that domestic action shall thus constitute a significant effort made by each Party included in Annex I to meet its quantified emissions limitation and reduction commitments. Supplementarity constraints are also part of various national climate policy strategies such as the EU Climate Action and Renewable Energy Package (EU 2008).

  7. In general, CDM buyers have two markets in which to purchase CERs, the primary and the secondary market (see World Bank 2013). In the primary market, the investor and project developer agree on a price for the expected future credits from a CDM project. The resulting contract, which is known as an Emissions Reduction Purchase Agreement (ERPA), is similar to a project-finance agreement and can vary from case to case. The secondary CER (sCER) market is used for trading credits which are already delivered or with a guarantee of delivery or compensation if the contract is broken. In contrast to the primary market, the secondary one has an observable price (which is higher than the price in the primary CER market due to lower risks for the buyer).

  8. An alternative way of expressing this condition is that the profits per unit of output for the offset-generating firm are kept at the level they would be without the offset mechanism, with profits being expressed as: \(\pi =( {1+\mu } )pq-( {1+\tau } )p_E E\).

  9. In the mixed complementarity formulation of our equilibrium model, this arbitrage condition is associated with the endogenous subsidy rate \(\mu \).

  10. The CDM budget constraint is associated, in complementarity, with the shadow emissions tax \(\tau \).

  11. The unit-cost function of the IET-type representation of offset schemes is equivalent to Eq. (2) with the output subsidy rate set to zero (\(\mu =0\)), and with the emissions price (\(\tau \)) determined as the shadow price of the emissions cap of the multi-regional IET which includes the offset-generating countries (sectors).

  12. A more detailed technical description is provided in Böhringer et al. (2011).

  13. \(\hbox {CO}_{2}\) emissions are linked in fixed proportions to the use of fossil fuels, with \(\hbox {CO}_{2}\) coefficients differentiated by the specific fuel’s carbon content.

  14. The clean-development investments emerging from this welfare-maximization rule can be considered an upper bound from a game-theoretical perspective. The optimal investment level would be reduced if the offset-generating countries could exercise bargaining power and, as a result, receive a larger share of the cost savings that accrue to Annex I countries due to the offset mechanism. This would reduce the attractiveness of the offset scheme for Annex I countries and therefore the optimal level of clean-development investments.

  15. Detailed information on the type of CDM projects can be found at (accessed 05/27/2012).

  16. Clean-development investments in the IET scenario are used by the non-Annex I countries’ representative agent to maximise consumption, which directly affects welfare measured in terms of equivalent variation of income. In contrast, clean-development investments in the ICC scenario are used to compensate the offset-generating electricity sector for its increase in production costs and therefore do not enter the representative agent’s budget. The main benefit for non-Annex I countries in the ICC scenario (and one of the benefits in the IET scenario) therefore stems from improvements in their terms of trade: the decrease of import demand and increase of export prices in Annex I countries observed in the REF scenario is less drastic in the ICC and IET scenarios due to the availability of emissions offsets.

  17. An emissions-reduction target in Annex I countries of 10 % is broadly in line with the Kyoto Protocol’s initial emissions-reduction target of 5.2 % below 1990 levels (which correspond to reducing emissions by about 10 % below 2004 levels). A target of 30 % is closer to the range of emissions reductions (25–40 % below 1990 levels) that are needed to stabilize global emissions at 450 ppm (see e.g. Levin and Bradley 2010).

  18. Underlying the greater welfare gains for non-Annex I countries in the IET representation are greater clean-development investments driven by greater abatement obligations and higher domestic \(\hbox {CO}_{2}\) prices in Annex I countries. Compared to the main scenarios, the clean-development investments and their inter-scenario differences more than double in the high-reduction scenarios (to USD 44 billion in the IET scenario and to USD 23 billion in the ICC scenario). The increase in clean-development investments in the IET scenario more than offsets the negative terms-of-trade effects from Annex I countries’ unilateral abatement policies, something which is not the case for a 10 % reduction target.

  19. The relative output changes between the IET and ICC scenarios in the offset-generating sector in non-Annex I countries (as defined in Table 2) are \(-\)4.1 and \(-\)14.4 % for a 10 and 30 % emissions-reduction target, respectively.


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Correspondence to Marco Springmann.

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Appendix A: Algebraic Model Summary

Appendix A: Algebraic Model Summary

Following Mathiesen (1985), Cottle et al. (1992) and Rutherford (1995), an economic equilibrium can be expressed as a mixed complementarity problem where inequalities are associated with decision variables. The inequalities correspond to the two classes of conditions associated with a general equilibrium: (i) exhaustion of product (zero profit) conditions for constant-returns-to-scale producers, and (ii) market clearance for all goods and factors. The former class determines activity levels, and the latter determines price levels. In equilibrium, each of these variables is linked to one inequality condition: an activity level to an exhaustion of product constraint and a commodity price to a market clearance condition. Furthermore, income balances keep economic agents on their budget lines. In the following, we state the equilibrium conditions for our stylized CGE model of Sect. 3. Tables 3, 4, 5, 6, 7 and 8 provide an overview of the symbols and notation used. For a convenient calibration of functional forms based on an initially balanced dataset we make use of the calibrated share form (see Böhringer et al. 2003). Numerically, the model is implemented in the general algebraic modelling system GAMS and solved using PATH (Dirkse and Ferris 1995).

Table 3 Activity variables
Table 4 Price variables
Table 5 Additional variables
Table 6 Cost shares
Table 7 Endowments
Table 8 Elasticities

Zero-Profit Conditions

  1. 1.

    Macro output:

    $$\begin{aligned} \left( {\theta _{r}^{E} (p_{r}^{ED} (1+\tau _r ))^{1-\sigma }+\left( {1-\theta _{r}^{E} } \right) \left( {v_{r}^{\theta _{r}^{K} } w_r^{(1-\theta _{r}^{K} )} } \right) ^{1-\sigma }} \right) ^{\frac{1}{1-\sigma }}\ge p_{r}^{Y} (1+\mu _r ) \,\, \bot \,\, y_r\nonumber \\ \end{aligned}$$
  2. 2.


    $$\begin{aligned} \left( {\theta _{r}^{R} v_{r}^{1-\eta } +\left( {1-\theta _r^{ER} } \right) q_r^{1-\eta } } \right) ^{\frac{1}{1-\eta }}\ge p^{E}\,\, \bot \,\, y_{r}^{E} \end{aligned}$$
  3. 3.

    Energy demand:

    $$\begin{aligned} p^{E}+p^{{CO}_2 }\ge {p}_{r}^{ED} \,\, \bot \,\, y_r^{ED} \end{aligned}$$
  4. 4.

    Armington aggregate (in final consumption):

    $$\begin{aligned} \left( \mathop \sum \limits _s \theta _{sr}^Y p_r^{1-\gamma } \right) ^{\frac{1}{1-\gamma }}\ge p_{r}^{A} \,\, \bot \,\, y_{r}^{A} \end{aligned}$$
  5. 5.

    Welfare (utility):

    $$\begin{aligned} w_r^{\theta _r^{LW} } p_{r}^{A} {^{(1-\theta _r^{LW} )}}\ge p_{r}^{W} \,\, \bot \,\, y_{r}^W \end{aligned}$$

Market-Clearing Conditions

  1. 6.


    $$\begin{aligned} Y_r \ge \mathop \sum \limits _s \overline{ {c_{rs}}} A_{s} \left( {\frac{p_{s}^{A} }{p_{r}^{Y} }} \right) ^{\gamma } \,\, \bot \,\, p_{r}^{Y} \end{aligned}$$
  2. 7.


    $$\begin{aligned} \mathop \sum \limits _r y_{r}^{E} \ge \mathop \sum \limits _r y_{r}^{ED} \,\, \bot \,\, p^{E} \end{aligned}$$
  3. 8.

    Energy demand:

    $$\begin{aligned} y_r^{ED} \ge \overline{{ed_r }} y_{r} \left( {\frac{\left( {1+\mu _r } \right) p_{r}^{Y} }{\left( {1+\tau _r } \right) p_r^{ED} }} \right) ^{\sigma } \,\, \bot \,\, p_{r}^{ED} \end{aligned}$$
  4. 9.


    $$\begin{aligned} \overline{ {L_r }} \ge \overline{{ls_r }} \frac{y_r^W p_r^W }{w_r }+\overline{{l_r }} y_r \left( {\frac{p_r^Y \left( {1+\mu _r } \right) }{v_r^{\theta _r^K } w_r^{1-\theta _r^K } }} \right) ^{\sigma }\frac{v_r^{\theta _r^K } w_r^{\left( {1-\theta _r^K } \right) } }{w_{r} } \,\, \bot \,\, w_r \end{aligned}$$
  5. 10.


    $$\begin{aligned} \overline{{K_r }} \ge \overline{{f_r }} y_{r}^{E} \left( {\frac{p^{E}}{v_r }} \right) ^{\eta }+\overline{{k_r }} y_r \left( {\frac{p_r^Y \left( {1+\mu _r } \right) }{v_r^{\theta _r^K } w_r ^{\left( {1-\theta _r^K } \right) }}} \right) ^{\sigma }\frac{v_r^{\theta _r^K } w_r^{\left( {1-\theta _r^K } \right) } }{v_r }\,\, \bot \,\, v_r \end{aligned}$$
  6. 11.

    Fossil-fuel resources:

    $$\begin{aligned} \overline{Q_r } \ge \overline{Q_r } y_r^E \left( {\frac{p^{E}}{q_r }} \right) ^{\eta }\,\, \bot \,\, q_r \end{aligned}$$
  7. 12.


    $$\begin{aligned} \mathop \sum \limits _s c_{sr} y_{r}^{A} \ge \mathop \sum \limits _s c_{sr} y_r^W \frac{p_r^w }{p_r^A } \,\, \bot \,\, p_r^A \end{aligned}$$
  8. 13.


    $$\begin{aligned} y_r^W \left( \mathop \sum \limits _s c_{sr} +\overline{{ls_r }} \right) \ge \frac{RA_r }{p_r^W }\,\, \bot \,\, p_r^W \end{aligned}$$
  9. 14.

    Emissions (applies to emissions-regulating regions only):

    $$\begin{aligned} \overline{{CO}_2} \ge \mathop \sum \limits _r y_{r}^{ED} \,\, \bot \,\, p^{{CO}_2 } \end{aligned}$$


  1. 15.

    Emissions (applies to emissions-regulating regions only):

    $$\begin{aligned} \overline{{CO}_{2r} } {CO}_{2r} \ge y_r^{ED} \,\, \bot \,\, {CO}_{2r} \end{aligned}$$
  2. 16.

    Offset scheme’s incentive compatibility:

    $$\begin{aligned}&\left( \theta _E p_E^{1-\sigma }+( 1-\theta _E) ( {p_K^\vartheta p_L^{1-\vartheta } } )^{1-\sigma } \right) ^{\frac{1}{1-\sigma }} \nonumber \\&\quad \ge \frac{1}{1+\mu }\left( \theta _E (p_E ( {1+\tau } ))^{1-\sigma }+(1-\theta _E) ( {p_K^\vartheta p_L^{1-\vartheta } })^{1-\sigma } \right) ^{\frac{1}{1-\sigma }} \bot \quad \mu _r \end{aligned}$$
  3. 17.

    Offset scheme’s budget balance:

    $$\begin{aligned} \mu _{r} p_{r}^{Y} y_{r} -\tau _r p^{E}y_r^{ED} \ge w_r \mathop \sum \limits _s T_{sr} \,\, \bot \,\, \tau _r \end{aligned}$$

Income Balance

$$\begin{aligned} RA_r&= \overline{Q_r } q_r +\overline{{K_r }} v_r +\overline{{L_r }} w_r +p^{{CO}_2 }\overline{{CO}_{2r} } {CO}_{2r} +w_r \mathop \sum \limits _s T_{sr} \nonumber \\&-\mathop \sum \limits _s w_s T_{rs} +\tau _r y_r^{ED} p_r^{ED} -\mu _r y_r p_r^y \,\, \bot \,\, RA_r \end{aligned}$$

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Böhringer, C., Rutherford, T.F. & Springmann, M. Clean-Development Investments: An Incentive-Compatible CGE Modelling Framework. Environ Resource Econ 60, 633–651 (2015).

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  • Clean Development Mechanism
  • Clean-development investments
  • Climate finance
  • Computable general equilibrium modelling

JEL Classification

  • C68
  • Q58