Technological innovations that reduce emissions per output can backfire and may result in countries increasing their emissions. In the case of climate change, assessing the size of this rebound effect requires a fully fledged dynamic analysis since the externality occurs across space and time. Indeed, greenhouse gas (GHGs) emissions are not only transboundary, their persistence in the atmosphere implies that today’s emissions adversely affect current and future generations. The welfare analysis needs to account for the sum of all generations’ welfare. In a dynamic game, the impact of a technological innovation on emissions is ambiguous and depends on the initial stock of pollution. Therefore, relying on a simplified static version of the game or focusing the analysis on the steady state only can be misleading. In the case of climate change, this rebound effect may be strong enough to result in a decrease of welfare. This perverse effect happens for an empirically relevant range of parameters. Our findings advocate for (i) the necessity of a global agreement on mitigating emissions to accompany the implementation of clean technologies and (ii) policies aimed at fostering research and development in innovative clean technologies to target R&D projects on radical technological innovations rather than targeting a wide range of projects with modest objectives.