This paper looks at the growing concern over Greenhouse Gas emissions and the resulting human induced climate change. The background to a cost-benefit approach is sketched in terms of the scientific understanding and expected impacts. Then the theory behind a cost-benefit approach is explained and some of the studies and their results are critically presented. In the final section the concern for future generations is raised and a cost-benefit approach is shown to violate a right of the innocent to be free from harm. The conclusion is that economics cannot calculate the damages and the cost-benefit approach cannot therefore answer the question of how much to reduce Greenhouse Gases. Instead a range of no regrets policy actions are recommended along with changing how the deliberate creation of future harm of the innocent is treated both in economics and public policy. This is a paper from the Ecological Economics discussion paper series edited by Clive L. Spash and run from Stirling University from 1994 to 1996. This particular paper was published as: Cost-Benefit Analysis of the Greenhouse Effect. In Nick Hanley and Clive L. Spash (1993) Cost-Benefit Analysis and the Environment. Aldershot, England, Edward Elgar Chapter 13.