(Un)fair Delegation: Exploring the Strategic Use of Equity Rules in International Climate Negotiations

Abstract

We provide a new approach for identifying a strategic use of equity arguments in international (climate) negotiations. We first develop a theoretical model of strategic delegation which accounts for both environmental as well as equity preferences. We show that the strategic use of equity arguments qualitatively depends on the extent to which environmental preferences can be misrepresented: representatives from different countries may be expected to have similar equity views rather than widely differing perceptions of a fair share. Based on survey data on climate negotiations, we then provide empirical evidence for differences between equity preferences of citizens from Germany, China, and the U.S. and the perceived view on the position of their respective countries.

Appendices

Appendix 1: Descriptions of Burden Sharing Rules

2004 survey among agents involved in international climate policy:

• Polluter-pays rule (Principle of equal ratio between abatement costs and emissions): This means that a country whose greenhouse gas emissions amount to x% of the global greenhouse gas emissions should bear x% of the global abatement costs for reductions of greenhouse gas emissions.

• Ability-to-pay rule (Principle of equal ratio between abatement costs and GDP): This means that a country whose GDP amounts to x% of the global gross product should bear x% of the global abatement costs for reductions of greenhouse gas emissions.

• Egalitarian rule (Principle of equal per capita emissions): This means that a country whose population amounts to x% of the global population should get x% of the global entitlements for greenhouse gas emissions.

• Sovereignty rule (Principle of equal percentage reduction of current emissions): This means that a country whose greenhouse gas emissions amount to x% of the global greenhouse gas emissions should get x% of the global entitlements for greenhouse gas emissions.

2013 survey among citizens:

• Polluter-pays rule Every country has to bear costs according to the emissions it causes (hence countries causing higher emissions have a higher share of the costs).

• Ability-to-pay rule Every country has to bear costs according to its economic strength (hence richer countries have a higher share of the costs).

• Egalitarian rule Every country is allowed to produce the same amount of emissions per capita (hence countries with currently high emissions per capita have higher costs).

• Sovereignty rule Every country is allowed to produce the same share of global emissions as in the past (hence the proportional reduction of emissions is the same for every country).

Appendix 2: Mathematical Derivations

1.1 Derivation of Condition (6)

We know that

$$\begin{aligned} \frac{1}{\kappa _i}\frac{u_i^R(a_i, A)- u_i^R(0,0)}{c+\mu _i^R f_j^{R,'}}=\frac{1}{\kappa _i}\frac{\theta _i^R B(A)-c a_i-\mu _i^R f_i^R}{c+\mu _i^R f_i^{R,'}}=:\lambda \end{aligned}$$

is identical for all i. Therefore,

$$\begin{aligned} a_i (c+\mu _i^R f_i^{R,'})= & {} \theta _i^R B(A)-\mu _i^R (f_i^{R}-f_i^{R,'}a_i)-\kappa _i \lambda (c+\mu _i^R f_i^{R,'}) \end{aligned}$$

(11)

$$\begin{aligned} A=\sum _j a_j= & {} \sum _j \frac{\theta _j^R B(A)-\mu _j^R (f_j^{R}-f_j^{R,'}a_j)}{(c+\mu _j^R f_j^{R,'})}-\underbrace{\sum _j \kappa _j}_{=1} \lambda \nonumber \\ \lambda= & {} -A+\sum _j \frac{\theta _j^R B(A)-\mu _j^R (f_j^{R}-f_j^{R,'}a_j)}{(c+\mu _j^R f_j^{R,'})} \end{aligned}$$

(12)

Reinserting $\lambda$ from (12) into (11) immediately yields (6). $\square$

1.2 Proof of Proposition 1

For our first order linear approximation, for given parameters $\mu _j$, $\beta _j^{f,R}$, $\theta _j$, condition (5) already determines the aggregate abatement level A.

A marginal change of the representative’s preference parameter affects utility of a given citizen as follows:

$$\begin{aligned} \frac{du_i}{d(\cdot )}=\left[ \frac{\partial u_i}{\partial A}+\frac{\partial u_i}{\partial a_i}\frac{\partial a_i}{\partial A}\right] \frac{\partial A}{\partial (\cdot )}+\frac{\partial u_i}{\partial a_i}\left[ \frac{\partial a_i}{\partial (\cdot )}\right] \end{aligned}$$

where $(\cdot )$ serves as a placeholder for any of the respective parameters. Using (5) and (6), we can rewrite

$$\begin{aligned} \frac{\partial u_i}{\partial A}+\frac{\partial u_i}{\partial a_i}\frac{\partial a_i}{\partial A}= & {} \theta _i B'(A)+\mu _i f_i^{'} \beta _i^{f}- (c+\mu _i f_i^{'})\frac{\theta _i^R B'(A)+\mu _i^R f_i^{R,'} \beta _i^{f,R}}{c+\mu _i^R f_i^{R,'}}\nonumber \\= & {} (c+\mu _i f_i^{'}) \left[ \frac{\theta _i B'(A)+\mu _i f_i^{'} \beta _i^{f}}{c+\mu _i f_i^{'}}-\frac{\theta _i^R B'(A)+\mu _i^R f_i^{R,'} \beta _i^{f,R}}{c+\mu _i^R f_i^{R,'}}\right] \nonumber \\=: & {} (c+\mu _i f_i^{'}) X_i \end{aligned}$$

(13)

where $X_i$ reflects the differences in the preferences of the delegate R, $(\theta _i^R,\beta _i^{f,R},\mu _i^R)$, and those of the citizen $(\theta _i,\beta _i^f,\mu _i)$.

Therefore,

$$\begin{aligned} \frac{1}{c+\mu _i f_i^{'}}\frac{du_i}{d(\cdot )}=X_i \frac{\partial A}{\partial (\cdot )}-\frac{\partial a_i}{\partial (\cdot )} \end{aligned}$$

Now, with (5) we get:

$$\begin{aligned} \frac{\partial A}{\partial \theta _i^R}= & {} \frac{1}{\sum _j \frac{-\theta _j^R B''(A)}{c+\mu _j^R f_j^{R,'}}} \frac{B'(A)}{c+\mu _i^R f_i^{R,'}} \end{aligned}$$

(14)

$$\begin{aligned} \frac{\partial A}{\partial \beta _i^{f,R}}= & {} \frac{1}{\sum _j \frac{-\theta _j^R B''(A)}{c+\mu _j^R f_j^{R,'}}} \mu _i^R \frac{f_i^{R,'}(c+\mu _i^R f_i^{R,'})-f_i^{R,''} A(\beta _i^{f,R}c-\theta _i^R B'(A))}{(c+\mu _i^R f_i^{R,'})^2}\end{aligned}$$

(15)

$$\begin{aligned} \frac{\partial A}{\partial \mu _i^{R}}= & {} \frac{1}{\sum _j \frac{-\theta _j^R B''(A)}{c+\mu _j^R f_j^{R,'}}} \frac{f_i^{R,'}(\beta _i^{f,R}c-\theta _i^R B'(A))}{(c+\mu _i^R f_i^{R,'})^2} \end{aligned}$$

(16)

Similarly, with (6) and given that $f_i^R-f_i^{R,'}a_i=f({\bar{a}}_i-\beta _i^{f,R}{\bar{A}})-f'({\bar{a}}_i-\beta _i^{f,R}{\bar{A}}){\bar{a}}_i$ at the equilibrium abatement levels, we obtain:

$$\begin{aligned} \frac{\partial a_i}{\partial \theta _i^R}= & {} (1-\kappa _i) \frac{B(A)}{c+\mu _i^R f_i^{R,'}}\end{aligned}$$

(17)

$$\begin{aligned} \frac{\partial a_i}{\partial \beta _i^{f,R}}= & {} (1-\kappa _i) \mu _i^R A \frac{f_i^{R,'}(c+\mu _i^R f_i^{R,'})+f_i^{R,''}(\theta _i^R B(A)-c a_i-\mu _i^R f_i)}{(c+\mu _i^R f_i^{R,'})^2}\end{aligned}$$

(18)

$$\begin{aligned} \frac{\partial a_i}{\partial \mu _i^{R}}= & {} -(1-\kappa _i) \frac{-f_i^{R,'}(\theta _i^R B(A)-c a_i)-c f_i^R}{(c+\mu _i^R f_i^{R,'})^2} \end{aligned}$$

(19)

Combining these equations and denoting $L:=\sum _j \frac{-\theta _j^R B''(A)}{c+\mu _j^R f_j^{R,'}}>0$, we therefore obtain:

$$\begin{aligned} \frac{c+\mu _i^R f_i^{R,'}}{c+\mu _i f_i^{'}}\frac{du_i}{d\theta _i^R}= & {} \frac{X_i}{L} B'(A)-(1-\kappa _i)B(A) \end{aligned}$$

(20)

$$\begin{aligned} \frac{c+\mu _i^R f_i^{R,'}}{c+\mu _i f_i^{'}}\frac{du_i}{d\beta _i^{f,R}}= & {} \frac{X_i}{L} \mu _i^R \frac{f_i^{R,'}(c+\mu _i^R f_i^{R,'})-f_i^{R,''} A(\beta _i^{f,R}c-\theta _i^R B'(A))}{(c+\mu _i^R f_i^{R,'})}\nonumber \\&- (1-\kappa _i)\mu _i^R A \frac{f_i^{R,'}(c+\mu _i^R f_i^{R,'})+f_i^{R,''}(\theta _i^R B(A)-c a_i-\mu _i^R f_i)}{(c+\mu _i^R f_i^{R,'})} \end{aligned}$$

(21)

$$\begin{aligned} \frac{c+\mu _i^R f_i^{R,'}}{c+\mu _i f_i^{'}}\frac{du_i}{d \mu _i^{R}}= & {} \frac{X_i}{L} \frac{f_i^{R,'}(\beta _i^{f,R}c-\theta _i^R B'(A))}{(c+\mu _i^R f_i^{R,'})}\nonumber \\&\quad -\,(1-\kappa _i)\frac{-f_i^{R,'}(\theta _i^R B(A)-c a_i)-c f_i^R}{(c+\mu _i^R f_i^{R,'})} \end{aligned}$$

(22)

Note that at $(\theta _i^R,\beta _i^{f,R},\mu _i^R)=(\theta _i,\beta _i^f,\mu _i)$, we obtain $X_i=0$ such that we immediately obtain:

$$\begin{aligned} \frac{c+\mu _i^R f_i^{R,'}}{c+\mu _i f_i^{'}}\frac{du_i}{d\theta _i^R}= & {} -(1-\kappa _i)B(A)<0\\ \frac{c+\mu _i^R f_i^{R,'}}{c+\mu _i f_i^{'}}\frac{du_i}{d\beta _i^{f,R}}= & {} -(1-\kappa _i)\mu _i^R A \frac{f_i^{R,'}(c+\mu _i^R f_i^{R,'})+f_i^{R,''}(\theta _i^R B(A)-c {\bar{a}}_i-\mu _i^R f_i)}{(c+\mu _i^R f_i^{R,'})}<0\\ \frac{c+\mu _i^R f_i^{R,'}}{c+\mu _i f_i^{'}}\frac{du_i}{d \mu _i^{R}}= & {} -(1-\kappa _i)\frac{-f_i^{R,'}(\theta _i^R B(A)-c{\bar{a}}_i)-c f_i^R}{(c+\mu _i^R f_i^{R,'})}>0 \end{aligned}$$

where the latter two follow from $\theta _i^R B(A)-c a_i>\theta _i^R B(A)-c a_i-\mu _i^R f_i=u_i^R(a_i,A)-u_i^R(0,0)>0$. This immediately proves the claims in Proposition 1. $\square$

1.3 Derivation of (7) and (8)

We first derive (7). Using (20) and (21), we obtain at $\frac{du_i}{d\theta _i^R}=0$:

$$\begin{aligned}&B'(A)\frac{(c+\mu _i^R f_i^{R,'})^2}{c+\mu _i f_i^{'}}\frac{du_i}{d\beta _i^{f,R}}\nonumber \\&\quad =(1-\kappa _i)\mu _i^R\left[ B(A)[f_i^{R,'}(c+\mu _i^R f_i^{R,'})-f_i^{R,''} A(\beta _i^{f,R}c-\theta _i^R B'(A))]\right. \nonumber \\&\qquad \left. -\,B'(A)A [f_i^{R,'}(c+\mu _i^R f_i^{R,'})+ f_i^{R,''}(\theta _i^R B(A)-c a_i-\mu _i^R f_i)]\right] \nonumber \\&\quad =(1-\kappa _i)\mu _i^R\left[ (B(A)-B'(A)A)f_i^{R,'}(c+\mu _i^R f_i^{R,'})\right. \nonumber \\&\left. \qquad - f_i^{R,''}A[B(A)(\beta _i^{f,R}c-\theta _i^R B'(A))]+B'(A)(\theta _i^R B(A)-c a_i-\mu _i^R f_i)]\right] \nonumber \\&\quad =(1-\kappa _i)\mu _i^R\left[ (B(A)-B'(A)A)f_i^{R,'}(c+\mu _i^R f_i^{R,'})\right. \nonumber \\&\qquad \left. +\, f_i^{R,''}A[-B(A)\beta _i^{f,R}c+B'(A)(c a_i+\mu _i^R f_i)]\right] \nonumber \\&\quad =(1-\kappa _i)\mu _i^R[\underbrace{(B(A)-B'(A)A)}_{>0}f_i^{R,'}(c+\mu _i^R f_i^{R,'})\\&\qquad +\,f_i^{R,''}B'(A)A(c\underbrace{(a_i- \eta _B\beta _i^{f,R}A)}_{>0}+\mu _i^R f_i)]]\nonumber \\&\quad >0 \end{aligned}$$

Turning to (8), and again using (20) and (22), we obtain at $\frac{du_i}{d\theta _i^R}=0$:

$$\begin{aligned}&B'(A)\frac{(c+\mu _i^R f_i^{R,'})^2}{c+\mu _i f_i^{'}}\frac{du_i}{d{\hat{\mu }}_i^{R}}\nonumber \\&\quad = B'(A)\frac{X_i}{L} [f_i^{R,'}(\beta _i^{f,R}c-\theta _i^R B'(A))]-(1-\kappa _i)B'(A)[-f_i^{R,'}(\theta _i^R B(A)-c a_i)-c f_i^R]\nonumber \\&\quad =(1-\kappa _i)\left[ B(A) f_i^{R,'}(\beta _i^{f,R}c-\theta _i^R B'(A))+B'(A) f_i^{R,'}(\theta _i^R B(A)-c a_i)+B'(A) c f_i^R\right] \nonumber \\&\quad =(1-\kappa _i)\left[ B(A) f_i^{R,'}\beta _i^{f,R}c-B'(A) f_i^{R,'} c a_i+B'(A) c f_i^R\right] \nonumber \\&\quad =(1-\kappa _i)B'(A)f_i^{R,'}c\left[ \eta _B \beta _i^{f,R}A- a_i+ \eta _f (a_i-\beta _i^{f,R}A)\right] \nonumber \\&\quad =(1-\kappa _i)B'(A)f_i^{R,'}c\left[ (\eta _f-1)a_i-(\eta _f-\eta _B) \beta _i^{f,R}A)\right] \end{aligned}$$

$\square$

Appendix 3: Tables

Table 1 Summary statistics of estimation samples

Table 2 Parameter estimates and marginal/discrete probability effects in random and fixed effects models for the EU and Germany

Table 3 Parameter estimates and marginal/discrete probability effects in random and fixed effects models for G77/China

Table 4 Parameter estimates and marginal/discrete probability effects in random and fixed effects models for the U.S

Table 5 Average discrete probability and interaction effects in random effects probit models

Table 6 Difference between citizens’ equity preferences and observed positions of parties

Table 7 Description of (a) dependent and explanatory variables and (b) explanatory variables in Sect. 3.3

Table 8 Means (standard deviations) of dependent and explanatory variables in Sect. 3.3, restricted to estimation sample

Table 9 Parameter estimates in binary probit models for Germany

Table 10 Parameter estimates in binary probit models for China

Table 11 Parameter estimates in binary probit models for the U.S