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

Abstract

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.

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. Macro output:

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

  (5)

• 2. Energy:

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

  (6)

• 3. Energy demand:

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

  (7)

• 4. Armington aggregate (in final consumption):

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

  (8)

• 5. Welfare (utility):

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

  (9)

Market-Clearing Conditions

• 6. Output:

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

  (10)

• 7. Energy:

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

  (11)

• 8. Energy demand:

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

  (12)

• 9. Labor:

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

  (13)

• 10. Capital:

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

  (14)

• 11. Fossil-fuel resources:

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

  (15)

• 12. Armington:

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

  (16)

• 13. Welfare:

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

  (17)

• 14. Emissions (applies to emissions-regulating regions only):

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

  (18)

Constraints

• 15. Emissions (applies to emissions-regulating regions only):

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

  (19)

• 16. Offset scheme’s incentive compatibility:

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

  (20)

• 17. Offset scheme’s budget balance:

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

  (21)

Income Balance

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

(22)