Precautionary buffers and stochastic dependence in environmental policy

Against a backdrop of rising uncertainty driven by a warming climate, environmental policy has become increasingly reliant on precautionary buffers to safeguard public health, prevent irreversible environmental damages and limit the likelihood of exceeding critical thresholds. These probabilistic constraints are usually implemented under a separability assumption even though outcomes are often dependent. Examples include ambient air pollution and water quality standards, phytosanitary trade measures, and reference points in fisheries management. In this paper, we characterize how stochastic dependence among environmental variables influences environmental policy when the governing regulatory systems use probabilistic precautionary buffers. Our approach builds on Sklar's theorem and the copula representation of multivariate distributions and uses stochastic dependence orderings to compare policy design for different dependence structures including correlated, independent and separable risks. Dependence typically renders policy based on separability suboptimal and we characterize how policy should be adjusted in the presence of correlated risks. We illustrate the theory using fisheries management in the Gulf of Maine, one of the fastest-warming ocean ecosystems on the planet. In its multispecies fishery, even a mild positive correlation between stocks can result in a substantial reduction in effort limits if overfishing is to be avoided.