A simple state-contingent pricing rule for complex intertemporal externalities

Some externalities, such as global warming, involve complex relationships between emissions and an environmental state variable, with effects over lags of uncertain length. Coming up with theoretically-motivated and practical policy options in such cases has proven difficult. Deterministic intertemporal general equilibrium models yield what appear to be feasible optimal price paths, but only by assuming away many key uncertainties, nor do they specify how the possibility of new information should affect the policy path. Bayesian models allow limited uncertainty and optimal learning based on observed effects of policy changes, but suggest a discouraging delay before optimal policy can be identified. A full insurance model suggests that risk aversion and 'fat-tailed' probabilities of catastrophe imply an implausibly (or at least impractically) large risk premium, implying that practical policy decisions depend so critically on uncertain parameters as to be unavoidably arbitrary. This paper proposes an entirely new approach based on the observation that the situation giving rise to a complex intertemporal externality also yields an observable state variable that contains information relevant to the identification of the optimal policy path. I derive a simple transformation by which the state variable can yield a good approximation to the optimal externality price. I outline assumptions sufficient to yield the transformation, and present numerical examples that illustrate its ability to follow linear and nonlinear first-best price paths. A specific application to greenhouse gases is proposed.