Integrating the rebound effect: accurate predictors for upgrading domestic heating

<div><p>One particular definition of the ‘rebound effect’ has won acceptance for its conceptual clarity and mathematical robustness: the energy efficiency elasticity of demand for energy services. This is formulated as a partial differential, and its structure enables transformations with price and energy elasticities. However, when considering heating energy efficiency upgrades of homes, the mathematical predictions can be unreliable because these upgrades involve large changes in efficiency, energy and energy services, whereas differential calculus only holds true for very small changes. This could be one reason why existing estimates of rebound effects are so diverse. This paper shows how this limitation can be remedied, using the German housing stock as a case study. A curve of consumption/efficiency for this stock is derived from empirical studies and, based on the mathematical definition of the rebound effect, a rebound effect relation is derived from this. This curve is then integrated over the likely ranges of energy efficiency upgrades that would correspond to the government's policy of reducing consumption by 80%. The model is found to be mathematically coherent, and suggests energy service rebounds of 28–39% for the German stock as a whole if the 80% goal is achieved.</p>