Optimal Management of Environmental Externalities with Time Lags and Uncertainty

Many environmental externalities occur with time lags that can range from a few days to several centuries in length, and many of these externalities are also subject to uncertainty. In this paper, we examine the key features of an optimal policy to manage environmental externalities that are both lagged and stochastic. We develop a two-period, two-polluter model and obtain closed-form solutions for optimal emissions levels under different combinations of damage functions and stochastic processes. These solutions show that it is not obvious whether greater control should be exerted on polluters that generate externalities with longer lags or on polluters that generate externalities with shorter lags. We find that the optimal ranking of polluters with respect to the length of the time lag associated with their externality will depend on (a) the discount rate, (b) conditional expectations of future states of the polluted resource, (c) persistence of the pollutant, and (d) initial conditions.