The size of the economy-wide rebound effect is crucial for estimating the contribution that energy efficiency improvements can make to reducing energy use and greenhouse gas emissions. We provide the first empirical general equilibrium estimate of the economy-wide rebound effect. We use a structural vector autoregressive (SVAR) model that is estimated using search methods developed in machine learning. We apply the SVAR to U.S. monthly and quarterly data, finding that after four years rebound is around 100%. This implies that policies to encourage cost-reducing energy efficiency innovation are not likely to significantly reduce energy use and greenhouse gas emissions.