Carbon Leakages: A General Equilibrium View

Abstract

The effectiveness of unilateral action to curb carbon emissions has been dismissed because of possible “carbon leakages”, this referring to the rise of emissions in non-participating countries. This paper offers a general equilibrium (GE) exploration of the key mechanisms and factors underlying the size of carbon leakages. We developed a two-region, two-goods simplified GE framework, incorporating three types of fossil fuels (coal, oil and low-carbon energy), international trade and capital mobility. The model was designed to make tractable extensive multidimensional sensitivity analysis. The results suggest that the coal supply elasticity plays a critical role, while substitution elasticities between traded goods and international capital mobility appear relatively less influential. The shape of the production function also matters for the size of the leakages. Confirming the results obtained with large computable GE models, for a wide range of parameters’ values carbon leakages appear to be small. Therefore, the argument that unilateral carbon abatement action taken by a large group of countries (such as the Annex 1 group) is flawed by significant carbon leakages is not supported by our sensitivity analysis. The likelihood of small leakages favours in fact the formation of a worldwide coalition to stabilise climate change.

The authors want to thank Graciela Chichilnisky, Jorgen Elmeskov, Peter Sturm and late Alan Manne for discussions and comments on early versions of this work. Anonymous referees also provided very useful suggestions. The views expressed are those of the authors and do not necessarily reflect those of the OECD or its Member countries.

Reprinted with kind permission from the Authors: Originally published in Economic Theory, Volume 49, Number 2, February 2012.

Annex: Specification of the GE Model

This annex provides the list of variables (Table 2), parameters (Table 3) and equations (below) of the simplified GE model used in the paper. All equations are expressed in a linearised growth rate form and variables in per cent changes, except the carbon tax, the price levels and carbon emissions in the base period (the level variables are in bold). The acronym ‘nC’ stands for low-Carbon Energy.

Table 2 List of variables of the GE model

Table 3 List of parameters of the GE model

Energy supply

$$ S_{j.r} = \varepsilon_{j.r} \cdot (P_{j.r} - PVA_{r} ),\quad \text{for}\;j = {\text{coal}},{\text{oil,}}\;{\text{nC}}\quad \text{and}\;r = {\text{Annex1,}}\;{\text{non}\text{-}\text{Annex1}}. $$

(1)

Inter-regional capital allocation

$$ SK_{r} = \text{mig} \cdot (r_{r} - r)\quad \text{with}\quad r = \sum\limits_{r} {shk_{r} \cdot r_{r} } \quad \text{for}\;r = {\text{Annex1,}}\;{\text{non}\text{-}\text{Annex1}}. $$

(2)

Consumer prices of energy (including the carbon tax).Domestic price

$$ \begin{aligned} Pd_{j.r} & = \left[ {\frac{{{\mathbf{Pd}}_{j.r}^{0} \cdot (1 + P_{j.r} ) + \gamma_{j.r} \cdot {\mathbf{CT}}_{r} }}{{{\mathbf{Pd}}_{j.r}^{0} }}} \right] - 1 \\ & \quad \text{for}\;j = {\text{coal,}}\,{\text{oil,}}\;{\text{nC}}\quad \text{and}\quad r = {\text{Annex1,}}\,{\text{non}}\text{-}\text{Annex1}. \\ \end{aligned} $$

(3)

Import price

$$ \begin{aligned} Pm_{j.r} & = \left[ {\frac{{{\mathbf{Pd}}_{j.r}^{0} \cdot (1 + P_{j.r^{\prime}}) + \gamma_{j.r} \cdot {\mathbf{CT}}_{r} }}{{{\mathbf{Pd}}_{j.r}^{0} }}} \right] - 1 \\ & \quad \text{for}\;j = {\text{coal,}}\;{\text{oil}};\;r,\;r^{\prime } = {\text{Annex1,}}\,{\text{non}}\text{-}{\text{Annex1}}\quad \text{and}\;r \ne r^{\prime } . \\ & \quad \text{Note}\;\text{that}\;\text{for}\;{\text{oil}}:P_\text{oil.Annex1} = P_{\text{oil.non}\text{-}{Annex1}} \quad \text{and}\;Pd_{{\text{oil}.r}} = Pm_{{\text{oil}.r}} . \\ \end{aligned} $$

(4)

Composite energy prices

$$ \begin{aligned} PC_{j.r} & = \alpha d{}_{j.r}\,.\,Pd_{j.r} + \alpha m_{j.r} \,.\,Pm_{j.r} \\ & \quad \text{for}\;j = {\text{coal,}}\;{\text{oil}},\,{\text{nC}}\quad \text{and}\;r = {\text{Annex1,}}\;{\text{non}\text{-}\text{Annex1}}. \\ & \quad \text{Note}\;\text{that}\;\text{for}\;{\text{nC}}:\;PC_{nC.r} = Pd{}_{nC.r} \\ \end{aligned} $$

(5)

$$ PE_{r} = \sum\limits_{j} {\alpha_{j.r} \cdot PC_{j.r} \quad \text{for}\;j = {\text{coal,}}\,{\text{oil}},\,{\text{nC}}\quad \text{and}\;r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}} $$

(6)

Composite factor prices

$$ PVA_{r} = \alpha L_{r} .w_{r} + \alpha K_{r} .r_{r} \quad \text{for}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. $$

(7)

Producer price of the non-Energy good

$$ P_{r} = \alpha E_{r} .PE_{r} + \alpha VA_{r} .PVA_{r} \quad \text{for}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. $$

(8)

Consumption of the non-Energy good

$$ \begin{aligned} C_{{r,r^{{\prime }} }} & = - \sigma_{r} .P_{{r^{{\prime }} }} + (\sigma_{r} - 1) \cdot PC_{r} + Y_{r}\\ & \quad \text{for}\;r\;\text{and}\;r^{{\prime }} = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. \\ & \quad \text{and}\;\text{with}\;PC_{r} = \beta_{r.r} .P_{r} + \beta_{{r.r^{{\prime }} }} \,.\,P_{{r^{{\prime }} }} \\ \end{aligned} $$

(9)

Output of the non-Energy good

$$ X_{r} = \sum\limits_{{r^{\prime}}} {\delta_{{r.r^{\prime } }} \, \cdot \,C_{{r.r^{\prime } }} \text{for}\;r\;\text{and}\;r^{\prime } = {\text{Annex1,}}\,{\text{non}}\text{-}{\text{Annex1}}.} $$

(10)

Total Energy demand

$$ E_{r} = - \kappa_{r} \,.\,PE_{r} + \kappa_{r} \,.\,P_{r} + X_{r} \quad \text{for}\;r = {\text{Annex1,}}\;{\text{non}\text{-}\text{Annex1}} $$

(11)

Total demand of the composite Factor (K, L)

$$ VA_{r} = - \kappa_{r} .PVA_{r} + \kappa_{r} \,.\,P_{r} + X_{r} \quad \text{for}\;r = {\text{Annex1,}}\;{\text{non}\text{-}\text{Annex1}} $$

(12)

Factor demands

$$ L_{r} = - w_{r} + PVA_{r} + VA_{r} \quad \text{for}\;r = {\text{Annex1,}}\;{\text{non}\text{-}\text{Annex1}} $$

(13a)

$$ K_{r} = - r_{r} + PVA_{r} + VA_{r} \quad \text{for}\;r = {\text{Annex1,}}\;{\text{non}\text{-}\text{Annex1}} $$

(13b)

Fuel specific demands

$$ \begin{aligned} E_{j.r} & = - \varphi_{r} \,.\,PC_{j.r} + \varphi_{r} \,.\,PE_{r} + E_{r} \\ & \quad \text{for}\;j = {\text{coal,}}\,{\text{oil}},\,{\text{nC}}\quad \text{and}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. \\ \end{aligned} $$

(14)

Demands for domestic and imported coal

$$ Ed_{{\text{coal}.r}} = - \sigma_{{\text{coal}.r}} \,.\,Pd_{{\text{coal}.r}} + \sigma_{{\text{coal}.r}} PC_{{\text{coal}.r}} + E_{{\text{coal}.r}} \quad \text{for}\;r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}} . $$

(15a)

$$ Em_{{\text{coal}.r}} = - \sigma_{{\text{coal}.r}} \,.\,Pm_{{\text{coal}.r}} + \sigma_{{\text{coal}.r}} PC_{{\text{coal}.r}} + E_{{\text{coal}.r}} \quad \text{for}\;r = {\text{Annex1,}}\;{\text{non}\text{-}\text{Annex1}} . $$

(15b)

Coal supply

$$ X_{{\text{coal}.r}} = shd_{{\text{coal}.r}} \,.\,Ed_{{\text{coal}.r}} + she_{{\text{coal}.r}} \,.\,Em_{{\text{coal}.r^{{\prime }} }} \quad \text{for}\;r \ne r^{{\prime }} = {\text{Annex1,}}\;{\text{non}\text{-}\text{Annex1}}. $$

(16)

World production of oil

$$ X_{\text{oil}} = \sum\limits_{r} {shd_{{\text{oil}.r}} } \,.\,E_{oil.r} \quad \text{for}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. $$

(17)

Carbon emissions

$$ \begin{aligned} CEM_{r} = \sum\limits_{j} {\gamma_{j.r} \,.\,\chi_{j.r} \,.\,E_{j.r} } \\ & \quad \text{for}\;j = {\text{coal,}}\,{\text{oil}},\,{\text{nC}}\quad \text{and}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. \\ \end{aligned} $$

(18)

Carbon tax revenues (in percentage of base-year GDP)

$$ RCTAX_{r} = \frac{{(1 + CEM_{r} )\,.\,{\mathbf{CEM}}_{r}^{0} \,.\,{\mathbf{CT}}_{r} }}{{{\mathbf{Y}}_{r}^{0} }}\quad \text{for}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. $$

(19)

Regional incomes

$$ \begin{aligned} Y_{r} & = (shL_{r} \,.\,w_{r} ) + shK_{r} \,.\,(r_{r} + SK_{r} ) + \sum\limits_{j} {sh_{j.r} \,.\,(P_{j.r} + S_{j.r} )} + RCTAX_{r} \\ & \quad \text{for}\;j = {\text{coal,}}\,{\text{oil,}}\,{\text{nC}}\quad \text{and}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}} \\ \end{aligned} $$

(20)

Market-clearing price of coal

$$ P_{{\text{coal}.r}} \quad \text{such}\;\text{as}\quad S_{coal.r} = E_{coal.r} \quad \text{for}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. $$

(21)

Market-clearing international price of oil

$$ \begin{aligned} P_{\text{oil}} \quad \text{such}\;\text{as}\quad X_{\text{oil}} & = \sum\limits_{r} {shs_{{\text{oil}.r}} \,.\,S_{oil.r} \quad \text{and}\quad P_{oil.r} = P_{oil} } \\ & \quad \text{for}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. \\ \end{aligned} $$

(22)

Market-clearing price of the low-carbon energy

$$ P_{nC.r} \quad \text{such}\;\text{as}\quad S_{nC.r} = E_{nC.r} \quad \text{for}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}} . $$

(23)

Market-clearing price of labour

$$ w_{r} \quad \text{such}\;\text{as}\quad L_{r} = 0\quad \text{for}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. $$

(24)

Market-clearing price of Capital

$$ r_{r} \quad \text{such}\;\text{as}\quad K_{r} = SK_{r} \quad \text{for}\quad r = {\text{Annex1,}}\,{\text{non}\text{-}\text{Annex1}}. $$

(25)