Regulating Stock Externalities Under Uncertainty

Using a simple analytical model incorporating benefits of a stock, costs of adjusting the stock, and uncertainty in costs, we uncover several important principles governing the choice of price-based policies (e.g., taxes) relative to quantity-based policies (e.g., tradable permits) for controlling stock externalities. Applied to the problem of greenhouse gases and climate change, we find that a price-based instrument generates several times the expected net benefits of a quantity instrument. As in Weitzman (1974), the relative slopes of the marginal benefits and costs of controlling the externality continue to be critical determinants of the efficiency of prices relative to quantities, with flatter marginal benefits and steeper marginal costs favoring prices. But some important adjustments for dynamic effects are necessary, including correlation of cost shocks across time, discounting, stock decay, and the rate of benefits growth. We also demonstrate an important link between instrument choice and policy stringency, based on the observation that both of these elements of policy design depend on the same underlying information, namely the marginal benefit and cost slopes. This result is especially useful when there is disagreement about benefits, since it can be used to restrict the set of efficient policies even in such cases. For negative externalities, we find that less stringent controls and price instruments are both associated with flatter marginal benefits, while aggressive controls and quantity instruments are associated with steeper marginal benefits. Intuitively, damages (marginal benefits) can only be steep enough to recommend quantity controls in the near term if they are steep enough to recommend substantial reductions. Furthermore, as long as the existing stock is large relative to the annual flow, marginal benefits either (i) will appear very flat over range of emissions in a single year, or (ii) will be sufficiently high to warrant near complete abatement. This generic characteristic of what it means to be a stock externality therefore weighs heavily in favor of price instruments for their control, so long as the optimal control falls short of stabilization at the current stock level. In the case of greenhouse gas policy, we show that any benefit slope consistent with quantity controls would imply an optimal emission level of zero. Under more general conditions we further demonstrate that price instruments are preferred in cases where optimal abatement rates are below about 40 percent, unless the initial stock level is small (less than twenty times the flow rate) or benefits and costs diverge quickly (by more than 10 percent annually). This result has important implications for the Kyoto Protocol, which mandates reductions among industrialized countries equal to roughly 5 percent of forecast global emissions. Regardless of one's beliefs about various climate change parameters, these relatively low aggregate abatement levels are inconsistent with quantity-based emission limits.