We compare taxes and quotas when firms and the regulator have asymmetric information about abatement costs. Damages are caused by a stock pollutant. Uncertainty enters multiplicatively, i.e. it affects the slope rather than the intercept of abatement costs. We calibrate the model using cost and damage estimates of greenhouse gases. As with additive uncertainty, taxes dominate quotas. The advantage of taxes is much greater with mulitiplicative, compared to additive uncertainty.