An infinite-horizon model of dynamic membership of international environmental agreements

Much of the literature on international environmental agreements (IEAs) uses static models, although most important transboundary pollution problems involve stock pollutants. The few papers that study IEAs using models of stock pollutants do not allow for the possibility that membership of the IEA may change endogenously over time. In this paper we analyse a simple infinite-horizon version of the static model of self-enforcing IEAs, in which damage costs increase with the stock of pollution, and countries decide each period whether to join an IEA. Using a quadratic approximation of the value function of the representative country we show that there exists a steady-state stock of pollution with corresponding steady-state IEA membership, and that as the stock rises towards steady state the IEA membership falls. Moreover, we find that the greater is the cost of damage, and hence the greater are the potential gains from cooperation, the smaller is the membership of a self-enforcing IEA.