Economists have speculated that the welfare gains from technological innovation that reduces the future costs of environmental protection could be a lot more important than the "Pigouvian" welfare gains over time from correcting a pollution externality. If so, then a primary concern in the design of environmental policies should be the impact on induced innovation, and a potentially strong case could be made for additional instruments such as research subsidies. This paper examines the magnitude of the welfare gains from innovation relative to the discounted Pigouvian welfare gains, using a dynamic social planning model in which research and development (R&D) augments a knowledge stock that reduces future pollution abatement costs. We find that the discounted welfare gains from innovation are typically smaller and perhaps much smaller than the discounted Pigouvian welfare gains. This is because the longrun gain to innovation is bounded by the maximum reduction in abatement costs and, since R&D is costly, it takes time to accumulate enough knowledge to substantially reduce abatement costs. Only in cases when innovation substantially reduces abatement costs quickly (by roughly 50% within 10 years) and the Pigouvian amount of abatement is initially modest, can the welfare gains from innovation exceed the welfare gains from pollution control. These results apply for both flow and stock pollutants, and for linear and convex environmental damage functions. Our results suggest that spurring technological innovation should not be emphasized at the expense of achieving the optimal amount of pollution control. More generally, our results appear to have implications for a broad range of policy issues. They suggest that the welfare gains from innovation that reduces the costs of supplying any public good (defense, crime prevention, infrastructure, etc.) may be fairly small relative to those from providing the optimal amount of the public good over time.