Abstract A zero-carbon society requires dramatic change everywhere including in buildings, a large and politically sensitive sector. Technical possibilities exist but implementation is slow. Policies include many hard-to-evaluate regulations and may suffer from rebound mechanisms. We use dynamic econometric analysis of European macro data for the period 1990–2018 to systematically examine the importance of changes in energy prices and income on residential energy demand. We find a long-run price elasticity of −0.5. The total long-run income elasticity is around 0.9, but if we control for the increase in income that goes towards larger homes and other factors, the income elasticity is 0.2. These findings have practical implications for climate policy and the EU buildings and energy policy framework.