Impact of international lobby groups on international environmental agreements

Abstract

Economists have long argued over the political economy of tradable emission permits, especially the political pressure of lobby groups on international environmental agreements. However, little attention has been paid to the effects of cross-national lobbying on this market. Here, we examine how an international lobby group can affect national and international climate policies concerning international market for emission permits. It extends the common agency model of policy-making to multiple-agency relationships in the context of international environment agreements. The main questions are (1) to what extent are governments’ rent-seeking incentives affected through international lobbying? (2) how do domestic and global emissions change in the presence of an international lobby group? We present a three-stage non-cooperative game in which international and national lobbies try to influence governments both when the governments decide on the formation of the international market and when each country chooses the number of permits. We find the condition under which the formation of an international lobby group can raise the contributions of national lobbies which support an international market and hence bring more benefits to the government. We also show that domestic and total emission levels not only depend on the aggregate levels of organized stakes in all countries but also on the distribution of stakes among individual lobby groups that form an international lobby group.

Appendix

1.1 Proof of Proposition 1

Given Assumption 1, the existence of a Nash equilibrium is assured by

$$\begin{gathered} SOC_{i} :\left( {\theta_{i} + r_{i} } \right)B_{i}^{ \prime \prime } \left( {\hat{e}_{i} } \right) - \left( {\theta_{i} + d_{i} } \right)D_{i}^{\prime \prime } \left( {\hat{E}} \right) \hfill \\ \quad - \delta_{{ - iM_{ - i} }} D_{ - i}^{\prime \prime } \left( {\hat{E}} \right) + \left( {r_{i} - b_{i} } \right)B_{i}^{\prime \prime } \left( {\hat{e}_{i} } \right) < 0, i = 1,2, \hfill \\ \end{gathered}$$

(A1)

which implies that the problem defined in Eq. (20) is strictly concave.

The uniqueness of the solution to Eq. (22) is assured by the aggregate emissions

$$\hat{E} = \mathop \sum \limits_{i = 1}^{2} B_{i}^{\prime - 1} \left[ {\frac{{\left( {\theta_{i} + d_{i} } \right)}}{{\left( {\theta_{i} + r_{i} } \right)}}D_{i}^{\prime } \left( {\hat{E}} \right) + \frac{{\left( {b_{i} - r_{i} } \right)}}{{\left( {\theta_{i} + r_{i} } \right)}}B_{i}^{\prime \prime } \left( {\widehat{{e_{i} }}} \right)\omega_{i} + \frac{{\delta_{{ - iM_{ - i} }} }}{{\left( {\theta_{i} + r_{i} } \right)}}D_{ - i}^{\prime } \left( {\hat{E}} \right)} \right],\quad i = 1,2,$$

(A2)

which is obtained by summing ${\widehat{e}}_{i}$ over the both countries. As can be seen, the left-hand side of the above equation is strictly increasing in E, while the right-hand side, the inverse function ${B}_{i}^{{{\prime}}-1}$ is strictly and monotonically decreasing in E. Thus, the equilibrium is unique and by replacing this unique level of $\widehat{E}$ into Eq. (22), we obtain the unique Nash equilibrium.

1.2 Proof of Proposition 2

The comparison of equilibrium emission functions under the presence and absence of an international lobby group is more straightforward. In the presence of an international lobby, as indicated by Eq. (22), we have

$$B_{i}^{\prime } \left( {\hat{e}_{i} } \right) = \frac{{\left( {\theta_{i} + d_{i} } \right)}}{{\left( {\theta_{i} + r_{i} } \right)}}D_{i}^{\prime } \left( {\hat{E}} \right) + \frac{{\left( {b_{i} - r_{i} } \right)}}{{\left( {\theta_{i} + r_{i} } \right)}}B_{i}^{\prime \prime } \left( {\hat{e}_{i} } \right)\omega_{i} + \frac{{\delta_{{ - iM_{ - i} }} }}{{\left( {\theta_{i} + r_{i} } \right)}}D_{ - i}^{\prime } \left( {\hat{E}} \right), \forall i$$

(A3)

$$\widehat{E}={\widehat{e}}_{1}+{\widehat{e}}_{2}, i=\mathrm{1,2}.$$

$${\omega }_{i}={\widehat{e}}_{i}.$$

In contrast, in the absence of an international lobby group we have

$$B_{i}^{\prime } \left( {\hat{e}_{i}^{{{\text{NL}}}} } \right) = \frac{{\left( {\theta_{i} + d_{i} } \right)}}{{\left( {\theta_{i} + r_{i} } \right)}}D_{i}^{\prime } \left( {\hat{E}^{{{\text{NL}}}} } \right) + \frac{{\left( {b_{i} - r_{i} } \right)}}{{\left( {\theta_{i} + r_{i} } \right)}}B_{i}^{\prime \prime } \left( {\hat{e}_{i}^{{{\text{NL}}}} } \right)\omega_{i} , \forall i$$

(A4)

$${\widehat{E}}^{\mathrm{NL}}={{\widehat{e}}_{i}}^{\mathrm{NL}}+{{\widehat{e}}_{-i}}^{\mathrm{NL}}, i=\mathrm{1,2}.$$

$${{\omega }_{i}}^{\mathrm{NL}}={{\widehat{\mathrm{e}}}_{i}}^{NL},$$

where the superscript “NL” refers to the presence of only national lobbying. It implies that ${{\widehat{e}}_{i}}^{\mathrm{NL}}<{\widehat{e}}_{i} \forall i$.

1.3 Proof of Corollary 1

Using the following abbreviation:

$$\tau_{i} = SOC_{i} \times SOC_{ - i} + \left( {\left( {\theta_{i} + d_{i} } \right)D_{i}^{\prime \prime } \left( E \right) + \delta_{{ - iM_{ - i} }} D_{ - i}^{\prime \prime } \left( E \right)} \right)^{2} > 0$$

(A5)

We derive

$$\frac{{d\omega_{i} }}{{dx_{i} }} = - \frac{{{\text{SOC}}_{ - i} }}{{\tau_{i} }}. \frac{{\partial {\text{FOC}}_{i} }}{{\partial x_{i} }},$$

(A6a)

$$\frac{{d\omega_{ - i} }}{{dx_{i} }} = - \frac{{\left( {\theta_{ - i} + d_{ - i} } \right)D_{ - i}^{\prime \prime } \left( {\hat{E}} \right) + \delta_{{iM_{i} }} D_{i}^{\prime \prime } \left( {\hat{E}} \right)}}{{\tau_{i} }}. \frac{{\partial {\text{FOC}}_{i} }}{{\partial x_{i} }},$$

(A6b)

$$\frac{dE}{{dx_{i} }} = - \frac{{SOC_{ - i} + \left( {\theta_{ - i} + d_{ - i} } \right)D_{ - i}^{^{\prime\prime}} \left( {\hat{E}} \right) + \delta_{{iM_{i} }} D_{i}^{^{\prime\prime}} \left( {\hat{E}} \right)}}{{\tau_{i} }}. \frac{{\partial {\text{FOC}}_{i} }}{{\partial x_{i} }},$$

(A6c)

$$\frac{{d\omega_{i} }}{{dx_{ - i} }} = - \frac{{\left( {\theta_{i} + d_{i} } \right)D_{i}^{^{\prime\prime}} \left( {\hat{E}} \right) + \delta_{{ - iM_{ - i} }} D_{ - i}^{^{\prime\prime}} \left( {\hat{E}} \right)}}{{\tau_{ - i} }}. \frac{{\partial {\text{FOC}}_{ - i} }}{{\partial x_{ - i} }},$$

(A6d)

$$\frac{{d\omega_{ - i} }}{{dx_{ - i} }} = - \frac{{{\text{SOC}}_{i} }}{{\tau_{ - i} }}. \frac{{\partial {\text{FOC}}_{ - i} }}{{\partial x_{ - i} }},$$

(A6e)

$$\frac{dE}{{dx_{ - i} }} = - \frac{{{\text{SOC}}_{i} + \left( {\theta_{i} + d_{i} } \right)D_{i}^{^{\prime\prime}} \left( {\hat{E}} \right) + \delta_{{ - iM_{ - i} }} D_{ - i}^{^{\prime\prime}} \left( {\hat{E}} \right)}}{{\tau_{ - i} }}. \frac{{\partial {\text{FOC}}_{ - i} }}{{\partial x_{ - i} }},$$

(A6f)

where $x\epsilon \left\{\theta ,b,d\right\}$. Then, $(\frac{\partial {\mathrm{FOC}}_{i}}{\partial {x}_{i}})$ in the two cases ${r}_{i}={b}_{i}$ and ${r}_{i}={d}_{i}$ are

$$\frac{{\partial {\text{FOC}}_{i}^{{r_{i} = b_{i} , r_{i} = d_{i} }} }}{{\partial \theta_{i} }} = B_{i}^{^{\prime}} \left( {e_{i} } \right) - D_{i}^{^{\prime}} \left( E \right),$$

(A7a)

$$\frac{{\partial {\text{FOC}}_{i}^{{r_{i} = b_{i} }} }}{{\partial b_{i} }} = B_{i}^{^{\prime}} \left( {e_{i} } \right),\quad \frac{{\partial {\text{FOC}}_{i}^{{r_{i} = d_{i} }} }}{{\partial b_{i} }} = - B_{i}^{^{\prime\prime}} \left( {e_{i} } \right)\omega_{i} ,$$

(A7b)

$$\begin{gathered} \frac{{\partial {\text{FOC}}_{i}^{{r_{i} = b_{i} }} }}{{\partial d_{i} }} = - D_{i}^{^{\prime}} \left( E \right), \hfill \\ \quad \frac{{\partial {\text{FOC}}_{i}^{{r_{i} = d_{i} }} }}{{\partial d_{i} }} = B_{i}^{^{\prime}} \left( {e_{i} } \right) - D_{i}^{^{\prime}} \left( E \right) + B_{i}^{^{\prime\prime}} \left( {e_{i} } \right)\omega_{i} , \hfill \\ \end{gathered}$$

(A7c)

$$\frac{{\partial {\text{FOC}}_{i}^{{r_{i} = b_{i} ,r_{i} = d_{i} }} }}{{\partial \delta_{{ - iM_{ - i} }} }} = - D_{ - i}^{^{\prime}} \left( E \right).$$

(A7d)

For determining the signs of (A7c), we applied the first-order condition when ${\mathrm{r}}_{\mathrm{i}}={d}_{i}$:

$$\left[ {B_{i}^{^{\prime}} \left( {e_{i} } \right) - D_{i}^{^{\prime}} \left( E \right)} \right] = \frac{{\left( {b_{i} - d_{i} } \right)}}{{(\theta_{i} + d_{i} )}}\omega_{i} B_{i}^{^{\prime\prime}} \left( {\omega_{i} } \right) + \frac{{\delta_{{ - iM_{ - i} }} }}{{(\theta_{i} + d_{i} )}}D_{ - i}^{^{\prime}} \left( E \right),$$

(A8)

which implies that ${B}_{i}^{{{\prime}}}\left({e}_{i}\right)-{D}_{i}^{{{\prime}}}\left(E\right)>0$ ⟺ ${d}_{i}>{b}_{i}$.

By re-writing again the first-order condition, we have

$$B_{i}^{^{\prime\prime}} \left( {e_{i} } \right)\omega_{i} = \frac{{b_{i} }}{{d_{i} }}B_{i}^{^{\prime\prime}} \left( {e_{i} } \right)\omega_{i} - \left( {\frac{{\theta_{i} }}{{d_{i} }} + 1} \right)(B_{i}^{^{\prime}} \left( {e_{i} } \right) - D_{i}^{^{\prime}} \left( E \right)) + \frac{{\delta_{{ - iM_{ - i} }} }}{{d_{i} }}D_{ - i}^{^{\prime}} \left( E \right),$$

(A9)

which enables us immediately to evaluate the sign of $\frac{\partial {{\text{FOC}}}_{{i}}^{{{r}}_{{i}}={{d}}_{{i}}}}{\partial {{d}}_{{i}}}$. Hence, even if ${{B}}_{{i}}^{{{\prime}}}\left({{e}}_{{i}}\right)-{{D}}_{{i}}^{{{\prime}}}\left({E}\right)>0$, we yield

$$B_{i}^{^{\prime\prime}} \left( {e_{i} } \right)\omega_{i} < - \left( {B_{i}^{^{\prime}} \left( {e_{i} } \right) - D_{i}^{^{\prime}} \left( E \right)} \right) \Rightarrow \frac{{\partial FOC_{i}^{{r_{i} = d_{i} }} }}{{\partial d_{i} }} < 0,$$

(A10)

1.4 Proof of Proposition 3

Given assumption 1, the existence of a Nash equilibrium is assured by

$$\begin{gathered} SOC_{i} : p^{^{\prime}} \left( {\hat{E}} \right)\left[ {2\theta_{i} + 2r_{i} - (\theta_{i} + b_{i} )e_{i}^{^{\prime}} \left( {\hat{E}} \right) - \gamma_{{ - iM_{ - i} }} e_{ - i}^{^{\prime}} \left( {\hat{E}} \right)} \right] \hfill \\ \quad - \left( {\theta_{i} + d_{i} } \right)D_{i}^{^{\prime\prime}} \left( {\hat{E}} \right) - \delta_{{ - iM_{ - i} }} D^{\prime\prime}_{ - i} \left( E \right) < 0, i = 1,2, \hfill \\ \end{gathered}$$

(A11)

which implies that the problem defined in Eq. (25) is strictly concave.

The uniqueness of the solution to Eq. (27) is assured by the aggregate emissions

$$2p\left( E \right) = \mathop \sum \limits_{i = 1}^{2} \frac{{\left( {\theta_{i} + d_{i} } \right)}}{{\left( {\theta_{i} + r_{i} } \right)}}D_{i}^{^{\prime}} \left( {\hat{E}} \right) + p^{\prime}\left( E \right)\mathop \sum \limits_{i = 1}^{2} \frac{{\delta_{{ - iM_{ - i} }} }}{{\left( {\theta_{i} + r_{i} } \right)}}D_{i}^{^{\prime}} \left( {\hat{E}} \right),$$

(A12)

which is obtained by summing ${\widehat{e}}_{i}$ over the both countries. As can be seen, the left-hand side of the above equation is strictly increasing in E, while the right-hand side is strictly and monotonically decreasing in E. Thus, the equilibrium is unique. When we replace this unique level of $\widehat{\mathrm{E}}$ into equation Eq. (27), we obtain the unique Nash equilibrium.

1.5 Proof of Proposition 4

The determination of how the presence of an international lobby group affects the policy choices can be illustrated by comparisons of the best response functions. In the presence of an international lobby, as indicated by Eq. (27), we have

$$\begin{gathered} p\left( {\hat{E}^{I} } \right) + p^{\prime}\left( {\hat{E}^{I} } \right)\left( {\omega_{i} - e_{i} \left( {\hat{E}} \right)} \right) = \frac{1}{{\left( {\theta_{i} + r_{i} } \right)}}\left[ \left( {\theta_{i} + d_{i} } \right)D_{i}^{^{\prime}} \left( {\hat{E}^{I} } \right) + \left( {b_{i} - r_{i} } \right)p^{^{\prime}} \left( {\hat{E}^{I} } \right)e_{i} \left( {\hat{E}^{I} } \right) + \delta_{{ - iM_{ - i} }} D_{ - i}^{^{\prime}} \left( {\hat{E}^{I} } \right) + \left( {\gamma_{{ - iM_{ - i} }} e_{ - i} - \rho_{{ - iM_{ - i} }} \omega_{ - i} } \right)p^{\prime}\left( {\hat{E}^{I} } \right) \hfill \right],\forall i \hfill \\ \end{gathered}$$

(A13)

$$\hat{E}^{I} = e_{1} \left( {\hat{E}^{I} } \right) + e_{2} \left( {\hat{E}^{I} } \right) = \omega_{1} + \omega_{2} .$$

Conversely, in the absence of an international lobby group, we have

$$p\left( {\hat{E}_{NL}^{I} } \right) + p^{\prime}\left( {\hat{E}_{NL}^{I} } \right)\left( {\omega_{i} - e_{i} \left( {\hat{E}_{NL}^{I} } \right)} \right) = \frac{1}{{\left( {\theta_{i} + r_{i} } \right)}}\left[ {\left( {\theta_{i} + d_{i} } \right)D_{i}^{^{\prime}} \left( {\hat{E}_{NL}^{I} } \right) + \left( {b_{i} - r_{i} } \right)p^{^{\prime}} \left( {\hat{E}_{NL}^{I} } \right)e_{i} \left( {\hat{E}_{NL}^{I} } \right)} \right], \forall i$$

(A14)

$${\hat{\text{E}}}_{NL}^{I} = e_{1} \left( {{\hat{\text{E}}}_{NL}^{I} } \right) + e_{2} \left( {{\hat{\text{E}}}_{NL}^{I} } \right) = \omega_{1} + \omega_{2} ,$$

where the subscript “NL” refers to the presence of only national lobbying. This implies that

$${\delta }_{-i{M}_{-i}}{\mathrm{D}}_{-\mathrm{i}}^{{^{\prime}}}\left({\widehat{E}}^{I}\right)+\left({\gamma }_{-i{M}_{-i}}{\mathrm{e}}_{-\mathrm{i}}-{\uprho }_{-{\mathrm{iM}}_{-\mathrm{i}}}{\upomega }_{-\mathrm{i}}\right){\mathrm{p}}^{{^{\prime}}}\left({\widehat{E}}^{I}\right)\mathop \lesseqgtr 0\iff {\widehat{E}}^{I}\mathop \lesseqgtr {\widehat{\mathrm{E}}}_{NL}^{I}.$$