We compare taxes and quotas when firms' and the regulator have asymmetric information about the slope of firms' abatement costs. Damages are caused by a stock pollutant. We calibrate the model using cost and damage estimates of greenhouse gasses. Taxes dominate quotas, as with additive uncertainty. This model with multiplicative uncertainty allows us to compare expected stock levels under the two policies, and to investigate the importance of stock size and the magnitude of uncertainty on the policy ranking.