Improvements in energy efficiency usually induce increases in the demand for energy services so that the energy savings are less than the improvement in efficiency. This rebound effect may be magnified or reduced by further adjustments across the economy. The size of the economy-wide rebound effect is crucial for estimating the contribution energy efficiency improvements can make to reducing greenhouse gas emissions and for understanding the drivers of energy use. Existing estimates are based on CGE models or partial equilibrium econometric estimates. We use structural vector autoregressions to identify the dynamic causal impact of structural energy efficiency shocks using search methods developed in machine learning. This allows us to estimate the economy-wide rebound effect with a minimum of a priori assumptions. We apply the SVAR to US data, finding that the rebound to energy efficiency specific shocks is close to 100 per cent.