Building Climate Coalitions on Preferential Free Trade Agreements

Abstract

In this paper we discuss the endogenous formation of climate coalitions in an issue-linkage regime. In particular, we propose a preferential free trade agreement on which a climate coalition should be built. The basic idea is that the gains of free trade can provide strong incentives for countries to join the coalition. As a framework, a multi-stage strategic trade model is employed in which each country may set an emission cap being effective on a permit market. In addition, a discriminatory import tariff may be imposed on dirty goods. However, at the heart of our approach is a preferential free trade arrangement among the members of a climate coalition leading to a favourable shift in the terms of trade. As a main result, trade liberalisation is found as an institution highly effective in building climate coalitions. In particular, the parametrical simulation of the model shows that participation in joint emission reduction is higher, consumption patterns are more environmentally friendly, and coalitional welfare is much more improved than in case of a single-issue environmental agreement.

Appendix

1.1 Emission Outcomes of the Simulation

See Fig. 2.

Fig. 2

Global emissions in the Stackelberg equilibrium

1.2 Welfare Outcomes of the Simulation

See Figs. 3, 4, 5 and 6.

Fig. 3

Global welfare in the Stackelberg equilibrium

Fig. 4

National welfare in the Stackelberg equilibrium

Fig. 5

Climate damages in the Stackelberg equilibrium

Fig. 6

Consumer welfare in the Stackelberg equilibrium

1.3 Policy Outcomes of the Simulation

See Figs. 7 and 8.

Fig. 7

National emission caps in the Stackelberg equilibrium

Fig. 8

Tariff rates in the Stackelberg equilibrium

1.4 Price Outcomes of the Simulation

See Figs. 9 and 10.

Fig. 9

Permit prices in the Stackelberg equilibrium

Fig. 10

Foreign producer prices of the dirty good in the Stackelberg equilibrium

1.5 Trade Outcomes of the Simulation

See Figs. 11, 12, 13 and 14.

Fig. 11

Terms of trade in the Stackelberg equilibrium

Fig. 12

Individual supplies of the dirty good in the Stackelberg equilibrium

Fig. 13

Inter-group trade patterns for the dirty good in the Stackelberg equilibrium

Fig. 14

Inter-group trade patterns for the clean good in the Stackelberg equilibrium

1.6 Sectoral Patterns of the Simulation

Fig. 15

Production of the dirty good in the Stackelberg equilibrium

Please note that, due to the condition in Eq. (11), consumption of the dirty good corresponds to the national emission outcomes depicted by Fig. 7 (see Figs. 15, 16, 17).

Fig. 16

Production of the clean good in the Stackelberg equilibrium

Fig. 17

Consumption of the clean good in the Stackelberg equilibrium

1.7 Microfoundation of the PPF

The production possibility frontier in (2) can be derived from the following microfoundation. Every country i is endowed with a certain amount of resources ${\bar{r}}$ which can be allocated to the production of a clean good, $r_{x_i}$, and a dirty good, $r_{e_{ij}}$, destined for country j. Thus:

$$\begin{aligned} {\bar{r}} = r_{e_{i1}} + r_{e_{i2}} + \dots + r_{e_{in}} + r_{x_i} \end{aligned}$$

(29)

The production of the clean and dirty good is assumed to be described by the following production functions:

$$\begin{aligned} x^S_i = {\alpha _x}r_{x_i} \qquad \qquad e^S_{ij} = \sqrt{\frac{r_{e_{ij}}}{\alpha _{e_{ij}}}} \end{aligned}$$

(30)

Now, rearranging for the resource variable and substituting into the first equation yields:

$$\begin{aligned} {\bar{r}} = \alpha _{e_{i1}}{(e^S_{i1})}^2 + \dots + \alpha _{e_{in}}{(e^S_{in})}^2 + \frac{x^S_i}{\alpha _x} \end{aligned}$$

(31)

After rearranging the equation above and noting that the maximum producible amount of the clean good, ${\overline{x}}$, is equal to $x({\overline{r}}) = {\alpha _x}{\bar{r}}$ (thus ${\bar{r}} = \frac{{\bar{x}}}{\alpha _x}$), we obtain the equation for the production possibility frontier in (2).

1.8 Policy Benchmarks

1.8.1 Business as Usual

For deriving the optimal policy decisions in the BAU scenario, $m=0$ is set in the welfare function above. After that, the optimal BAU emission caps are obtained through consideration of the following optimality conditions for a Nash equilibrium:

$$\begin{aligned} \frac{\partial W_i}{\partial e_i} = 0 \quad \wedge \quad \frac{\partial W_i}{\partial t_i} = 0 \qquad \qquad {\text {for }} \forall i \end{aligned}$$

(32)

Noting that $e_i = e_j$ and $t_i = t_j, \forall i,j$ because of symmetry, we get a system of two equations with the solution given by (19) and (20).

1.8.2 Social Planner

The SP scenario in turn is obtained by setting $m=n$. In this case, a global free trade area is implemented where tariffs do not play a role anymore. Analytically, this step is justified by the fact that, for $m=n$, tariffs are a free parameter. This can be seen by looking at the supply functions of the producers in (6a) and (6b) in which the tariffs appear. If one brings everything to a common denominator in the conditions for the Nash equilibrium, the tariff rates disappear. Therefore, we can set $t_i=0$ and use symmetry again to derive (21).

1.9 Stackelberg Equilibrium

The Stackelberg equilibrium conditions can be derived as usual by backward induction. The decision of the fringe decision is characterised by the following set of equations.

$$\begin{aligned} \frac{\partial W_i}{\partial e_i} = 0 \quad \wedge \quad \frac{\partial W_i}{\partial t_i} = 0 \qquad \qquad {\text {for }} \forall i \not \in C \end{aligned}$$

(33)

In order to derive the reaction functions of the fringe countries, we can exploit the symmmetry of the fringe nations. Thus, we can set $e_F = e_i, \forall i$ and $t_F = t_i, \forall i$. Analytically, this conforms to the structural symmetry of the equilibrium conditions of the fringe countries. By this we can reduce the number of equations to two and solve for the fringe reaction:

$$\begin{aligned} e_F= & {} \frac{(a-\delta \sum _{i = 1}^m e_i)(2 \alpha ^* + (n-1)\alpha _H)}{2 \alpha ^*(b + \delta (n - m) +2 \alpha _H) + (n-1)(b + \delta (n - m))\alpha _H} \end{aligned}$$

(34)

$$\begin{aligned} t_F= & {} \frac{2(a-\delta \sum _{i = 1}^m e_i)\alpha ^*\alpha _H}{2 \alpha ^*(b + \delta (n - m) +2 \alpha _H) + (n-1)(b + \delta (n - m))\alpha _H} \end{aligned}$$

(35)

Substituting the fringe reaction functions into the welfare functions, we can derive the following first order conditions for the coalition decisions $\forall k \in C$:

$$\begin{aligned} \frac{\partial W_C}{\partial e_k}&= \sum _{i \in C} \frac{\partial W_i}{\partial e_k} = \frac{\partial W_k}{\partial e_k} + \sum _{i \in C \wedge i \not = k} \frac{\partial W_i}{\partial e_k} = 0 \nonumber \\ \frac{\partial W_C}{\partial t_k}&= \sum _{i \in C} \frac{\partial W_i}{\partial t_k} = \frac{\partial W_k}{\partial t_k} + \sum _{i \in C \wedge i \not = k} \frac{\partial W_i}{\partial t_k} = 0 \end{aligned}$$

(36)

For $i = k$ in the above sums we get:

$$\begin{aligned} \frac{\partial W_k}{\partial e_k}&= \frac{\partial x^D_k}{\partial e_k} + a - b e_k - \delta \left( \sum _{i \in C} e_i + (n-m)e_F\right) \left( 1 + (n-m)\frac{\partial e_F}{\partial e_k}\right) \nonumber \\ \frac{\partial W_k}{\partial t_k}&= \frac{\partial x^D_k}{\partial t_k} \nonumber \\ \frac{\partial x^D_k}{\partial e_k}&= \frac{\partial x^S_k}{\partial e_k} + \left( \frac{\partial p_k}{\partial e_k}e_{kk} + p_k \frac{\partial e_{kk}}{\partial p_k} \frac{\partial p_k}{\partial e_k}\right) + (n - m)\left( \frac{\partial p_F}{\partial e_k} e_{kF} + p_F\frac{\partial e_{kF}}{\partial e_k}\right) - \left( \frac{\partial p_k}{\partial e_k}e_k + p_k\right) \nonumber \\ \frac{\partial x^D_k}{\partial t_k}&= \frac{\partial x^S_k}{\partial t_k} + \left( \frac{\partial p_k}{\partial t_k}e_{kk} + p_k \frac{\partial e_{kk}}{\partial t_k}\right) - \frac{\partial p_k}{\partial t_k} e_k \nonumber \\ \frac{\partial x^S_k}{\partial e_k}&= -2\alpha _H e_{kk} \frac{\partial e_{kk}}{\partial p_k} \frac{\partial p_k}{\partial e_k} - 2(n-m)\alpha ^* e_{kF}\frac{\partial e_{kF}}{\partial e_k} \nonumber \\ \frac{\partial x^S_k}{\partial t_k}&= -2\alpha _H e_{kk} \frac{\partial e_{kk}}{\partial t_k} \end{aligned}$$

(37)

where

$$\begin{aligned} \frac{\partial e_{kF}}{\partial e_k}&= \frac{\partial e_{kF}}{\partial p_F}\left( \frac{\partial p_F}{\partial e_F}\frac{\partial e_F}{\partial e_k} + \frac{\partial p_F}{\partial t_F}\frac{\partial t_F}{\partial e_k}\right) + \frac{\partial e_{kF}}{\partial t_F}\frac{\partial t_F}{\partial e_k} \\ \frac{\partial e_{kk}}{\partial t_k}&= \frac{\partial e_{kk}}{\partial p_k}\frac{\partial p_k}{\partial t_k} + \frac{\partial e_{kk}}{\partial t_k} \end{aligned}$$

and $e_{kF} := e_{kj}$, $p_F := p_j$, and $t_f := t_j$, $\forall j \not \in C$ because of the symmetric reactions of the fringe countries.

Now, for $i \not = k$ in the above sums we have:

$$\begin{aligned} \frac{\partial W_i}{\partial e_k}&= \frac{\partial x^D_i}{\partial e_k} - \delta \left( \sum _{i \in C} e_i + (n-m)e_F\right) \left( 1 + (n-m)\frac{\partial e_F}{\partial e_k}\right) \nonumber \\ \frac{\partial W_i}{\partial t_k}&= \frac{\partial x^D_i}{\partial t_k} \nonumber \\ \frac{\partial x^D_i}{\partial e_k}&= \frac{\partial x^S_i}{\partial e_k} + \left( \frac{\partial p_k}{\partial e_k}e_{ik} + p_k \frac{\partial e_{ik}}{\partial p_k} \frac{\partial p_k}{\partial e_k}\right) + (n - m)\left( \frac{\partial p_F}{\partial e_k} e_{iF} + p_F\frac{\partial e_{iF}}{\partial e_k}\right) \nonumber \\ \frac{\partial x^D_i}{\partial t_k}&= \frac{\partial x^S_i}{\partial t_k} + \left( \frac{\partial p_k}{\partial t_k}e_{ik} + p_k \frac{\partial e_{ik}}{\partial t_k}\right) \nonumber \\ \frac{\partial x^S_k}{\partial e_k}&= -2\alpha ^* e_{ik} \frac{\partial e_{ik}}{\partial p_k} \frac{\partial p_k}{\partial e_k} - 2(n-m)\alpha ^* e_{iF}\frac{\partial e_{iF}}{\partial e_k} \nonumber \\ \frac{\partial x^S_i}{\partial t_k}&= -2\alpha ^* e_{ik} \frac{\partial e_{ik}}{\partial t_k} \end{aligned}$$

(38)

where

$$\begin{aligned} \frac{\partial e_{iF}}{\partial e_k}&= \frac{\partial e_{iF}}{\partial p_F}\left( \frac{\partial p_F}{\partial e_F}\frac{\partial e_F}{\partial e_k} + \frac{\partial p_F}{\partial t_F}\frac{\partial t_F}{\partial e_k}\right) + \frac{\partial e_{iF}}{\partial t_F}\frac{\partial t_F}{\partial e_k} \\ \frac{\partial e_{ik}}{\partial t_k}&= \frac{\partial e_{ik}}{\partial p_k}\frac{\partial p_k}{\partial t_k} + \frac{\partial e_{ik}}{\partial t_k} \end{aligned}$$

and $e_{iF} := e_{ij}$, $\forall i \not \in C$ for similar reasons as above.

It is possible to use the symmetry among the coalition countries to reduce the first order conditions of the coalition to two equations and solve them for $e_c := e_i$ and $t_c := t_{i},$$\forall i \in C$. This step results in rational functions for $e_c$ and $t_c$, where the numerator of $e_c$ and $t_c$ are polynomials of third degree and second degree in m, respectively, and the denominators are polynomials of third degree each. Since the coefficients of the powers of m are quite complex multivariate polynomials in the parameters, we decided to proceed numerically in the evaluation of the model.