Does a Clean Development Mechanism Facilitate International Environmental Agreements?

Abstract

When politicians negotiate in international climate conventions they may suffer from incomplete information for each other’s preferences for reaching an agreement. As is known, this may cause failure to reach an efficient cooperative agreement. We study the role of cross border abatement provisions in the likelihood of such failure. For instance, the clean development mechanism was introduced in the context of the Kyoto Protocol to allow countries to make efficiency-enhancing use of cross-country low-cost mitigation opportunities. We use a simple bargaining framework to uncover why this mechanism may reduce the likelihood of reaching an efficient cooperative climate agreement.

Appendix: S is the Proposer

The Appendix discusses the case in which S makes an ultimatum offer to N. This offer consists of a transfer t from S to N as a compensation for N to implement the efficient amount of abatement. For space considerations we concentrate on the case of interior solutions.

If the offer is rejected then players N and S choose the amounts of mitigation that maximize their own rents and no transfers are paid. These amounts of mitigation are $\left( m_{{ NN}}^{1},m_{{ SS}}^{*}\right)$ or $\left( m_{{ NN}}^{2},m_{{ NS}}^{2},m_{{ SS}}^{*}\right)$, depending on the regime. If the offer is accepted then $\left( m_{{ NN}}^{3},m_{{ NS}}^{3},m_{{ SS}}^{*}\right)$ is implemented and country S pays t to country N. The net benefits for proposer S change from $\theta _{S}^{i}$ to $\theta _{S}^{3}+\sigma -t$ and N’s payoff changes from $\theta _{N}^{i}$ to $\theta _{N}^{3}+t+\nu$. Player N accepts the offer if $\theta _{N}^{3}+t+\nu -\theta _{N}^{i}\ge 0$, or

$$\begin{aligned} \nu \ge \theta _{N}^{i}-\left( \theta _{N}^{3}+t\right) \end{aligned}$$

(13)

for $i\in \{1,2\}$. This inequality describes a one-to-one relationship between t and the critical $\nu$ such that N accepts the transfer demanded if the transfer is at least equal to the t that solves (13) with equality. We denote this critical $\nu ^{i}$ as a function of t as

$$\begin{aligned} \nu ^{i}(t)=\theta _{N}^{i}-\theta _{N}^{3}-t\quad \text {for}\quad i\in \{1,2\}. \end{aligned}$$

(14)

This function is linear in t and has a slope of $-1$.

The bargaining-success probability as a function of t is $1-G\left( \theta _{N} ^{i}-\theta _{N}^{3}-t\right)$. Proposer S chooses t to maximize

$$\begin{aligned} E\pi _{S,i}=\left( \theta _{S}^{3}+\sigma -t-\theta _{S}^{i}\right) \cdot \left[ 1-G\left( \theta _{N}^{i}-\theta _{N}^{3}-t\right) \right] . \end{aligned}$$

This expected payoff is the product of S’s actual gain in case of successful bargaining, times the probability of acceptance of the proposal. Differentiating with respect to t yields a first-order condition which can be rewritten as

$$\begin{aligned} \frac{1-G\left( \theta _{N}^{i}-\theta _{N}^{3}-t\right) }{G^{\prime }\left( \theta _{N}^{i} -\theta _{N}^{3}-t\right) }=\theta _{S}^{3}+\sigma -t-\theta _{S}^{i}. \end{aligned}$$

(15)

If this condition has an interior solution, we denote it by ${\hat{t}} ^{i}(\sigma )$ to distinguish it from the function $t^{i}(\nu )$ in the previous section. Note that the left-hand side is weakly increasing in the transfer offered (due to Assumption (HR) of a non-increasing hazard rate), and the right-hand side is strictly monotonically decreasing in the transfer. Accordingly, there is at most one transfer level ${\hat{t}}^{i}(\sigma )$ that fulfills this first-order condition for each regime i and a given $\sigma$. We further note that

$$\begin{aligned} {\hat{t}}^{1}(\sigma )>{\hat{t}}^{2}(\sigma ) \end{aligned}$$

(16)

Recall the one-to-one correspondence between t and a value of $\nu$ such that responder N accepts transfer offer t if $\nu >\nu ^{i}(t)$ and rejects the transfer offer if N’s true value of $\nu$ is smaller than $\nu ^{i}(t)$ in the interior range of $({\underline{\nu }},{\bar{\nu }})$. With a mild abuse of notation, let $\nu ^{i}(t)$ denote the political benefit necessary to make country N indifferent between accepting and rejecting offer t in regime i. As shown by (14), the respective functions $\nu ^{i}(t)$ are linear and have a slope of −1. Further, $\nu ^{2}(t)-\nu ^{1}(t)=\theta _{N} ^{2}-\theta _{N}^{1}>0$. Together with (16) and (14) this implies

$$\begin{aligned} \nu ^{1}({\hat{t}}^{1}(\sigma ))<\nu ^{2}({\hat{t}}^{2}(\sigma ))\text {. } \end{aligned}$$

The probability of bargaining failure is higher if cross-border abatement opportunities are available in the non-cooperative fallback.