The size of the economy-wide rebound effect is crucial for estimating the contribution that energy efficiency improvements can make to reducing greenhouse gas emissions and for understanding the drivers of energy use. Existing estimates, which vary widely, are based on computable general equilibrium models or partial equilibrium econometric estimates. The former depend on many a priori assumptions and the parameter values adopted, and the latter do not include all mechanisms that might increase or reduce the rebound and mostly do not credibly identify the rebound effect. Using a structural vector autoregressive (SVAR) model, we identify the dynamic causal impact of structural shocks, including an energy efficiency shock, applying identification methods developed in machine learning. In this manner, we are able to estimate the rebound effect with a minimum of a priori assumptions. 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 in the long run.