Kaya identity



It was developed by Japanese economist Yoichi Kaya.

\(F\) is global CO2 emissions from human sources, \(P\) is global population, \(G\) is GPD, \(E\) is global energy consumption. \[ F = P \times \frac{G}{P} \times \frac{E}{G} \times \frac{F}{E} \]

The fractional terms correspond to well studied quantities:

  • \(G/P\) is the GDP per capita
  • \(E/G\) is the energy intensity of the GDP
  • \(F/E\) is the carbon footprint of energy


This identity is simply a rewrite of \(F=F\) in terms of commonly used quantities to highlight several levers one could act on to reduce CO2 emissions. According to this identity, to reduce CO2 emissions one could either:

  • Reduce the population (e.g. through family planning, or birth planning programs like China’s one-child policy). Policies directly acting on demographics are often regarded as invasive and too restrictive, particularly in liberal democracies.
  • Reduce GDP per capita. This corresponds to a recession, and probably impoverishment of parts of population. Western democracies are also generally against the idea of limited or negative growth.
  • Energy intensity of GDP is a tricky quantity, influenced by many factors. These factors range from general standards of living and weather to technological advancement, energy mix and economic specificity of a country. It is probably where politician can act the most, but also where it is the hardest to predict the result of any given policy.
  • Carbon footprint of energy corresponds to the amount of CO2 emitted to produce energy. It depends on the source of energy. Fossil fuels such as oil, coal and natural gas have high carbon footprints while solar energy, wind energy and nuclear energy have much lower carbon footprints — but other types of footprints possibly relevant to a policymaker.
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