Uncertainty over uncertainty in environmental policy adoption: Bayesian learning of unpredictable socioeconomic costs

The socioeconomic impact of pollution naturally comes with uncertainty due to, e.g., current new technological developments in emissions' abatement or demographic changes. On top of that, the trend of the future costs of the environmental damage is unknown: Will global warming dominate or technological advancements prevail? The truth is that we do not know which scenario will be realised and the scientific debate is still open. This paper captures those two layers of uncertainty by developing a real-options-like model in which a decision maker aims at adopting a once-and-for-all costly reduction in the current emissions rate, when the stochastic dynamics of the socioeconomic costs of pollution are subject to Brownian shocks and the drift is an unobservable random variable. By keeping track of the actual evolution of the costs, the decision maker is able to learn the unknown drift and to form a posterior dynamic belief of its true value. The resulting decision maker's timing problem boils down to a truly two-dimensional optimal stopping problem which we address via probabilistic free-boundary methods and a state-space transformation. We completely characterise the solution by showing that the optimal timing for implementing the emissions reduction policy is the first time that the learning process has become “decisive” enough; that is, when it exceeds a time-dependent percentage. This is given in terms of an endogenously determined threshold function, which solves uniquely a nonlinear integral equation. We numerically illustrate our results, discuss the implications of the optimal policy and also perform comparative statics to understand the role of the relevant model's parameters in the optimal policy.