This study examined the causal relations among per capita CO2 emissions, per capita income, non-fossil fuels electricity production, and energy productivity for the Spanish economy (1970–2017) using structural equation modeling with quadratic effects and introducing the fundamentals of the derived demand to formulate a novel approach. The relationships revealed statistical significance with a scale effect between income per capita and the level of per capita CO2 emissions. There is also a structural effect, dominated by a higher share of non-fossil fuel electricity production, and a technical effect associated with a reduction in energy intensity due to a sustained increase in capital formation and a policy of higher energy prices in the long term. Thus, climate change policies must be based on a sustained effort to modify the energy supply, in addition to an accumulation of capital stock and a sustained policy of keeping relative energy prices, at least in the transition phase to more environment-friendly energy production.