Increasing energy efficiency is often considered to be one of the main ways of reducing greenhouse gas emissions. However, efficiency gains that reduce the cost of energy services result in energy use rebounding and potential energy use savings being eaten up. Empirical research that quantifies the economy-wide rebound effect while taking the dynamic economic responses to energy efficiency improvements into account is limited. We use a Structural Factor-Augmented Vector Autoregressive model (S-FAVAR) that allows us to track how energy use changes in response to an energy efficiency improvement while accounting for a vast range of potential confounders. We find economy-wide rebound effects of 78% to 101% after two years in France, Germany, Italy, the UK, and the US. This implies that energy efficiency innovations alone may be of limited help in reducing future energy use and emphasizes the importance of tackling carbon emissions directly.