The optimal time path for carbon abatement and carbon sequestration under uncertainty: The case of stochastic targeted stock

We explore the optimal time path of carbon sequestration and carbon abatement in stabilizing CO2 levels under uncertainty of climate impacts. Using a two-period sequential decision making model, we analytically derive optimal rates for the two control variables, abatement and sequestration rates. Uncertainty is assumed to affect the desired future stabilization level of the CO2 stock but is resolved prior to the decision on how much to control the stock in the second period. Contrary to recent numerical studies, we find that uncertainty can make it optimal to use carbon sequestration either earlier or later depending on the relative rates of change in both marginal cost curves and on the amount of land that can be converted to forest. Comparative statics suggest that an increase in the discount factor could either increase or decrease the optimal rate of sequestration in the first period depending on the expected rate of change of the marginal cost of sequestration in the second period and on future benefits of current sequestration.