The Kaya equation: The equation that complicates our decarbonization

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Understanding the roots of CO2 emissions

To act effectively against climate change, we must first understand its root causes. Greenhouse gas emissions, mainly carbon dioxide (CO2), are not the result of chance, but the direct consequence of our economic and energy activities.

The Kaya equation, named after the Japanese economist Yoichi Kaya (1934-2020), offers a clear mathematical framework for decomposing this complex phenomenon into key factors. This relation is not a predictive model, but an accounting identity that allows us to analyze the possible levers of action against climate change.

This identity, developed at the end of the 20th century, has become a fundamental tool for the IPCC (Intergovernmental Panel on Climate Change) and policymakers. It allows modeling future emission scenarios and identifying possible levers of action.

The Kaya formula

The Kaya equation establishes a multiplicative relationship between global CO2 emissions and four socio-economic and technological factors: \( \text{CO2} = \text{Population} \times \frac{\text{GDP}}{\text{Population}} \times \frac{\text{Energy}}{\text{GDP}} \times \frac{\text{CO2}}{\text{Energy}} \)

For greater clarity, it is often rewritten by defining intermediate ratios: \( \text{CO2 emissions} = \text{P} \times \text{g} \times \text{e} \times \text{f} \)

• P: Population (number of inhabitants).
• g: GDP per capita (economic wealth/prosperity).
• e: Energy intensity (amount of energy consumed per unit of GDP). This is an indicator of the energy efficiency of an economy.
• f: Carbon intensity of energy (amount of CO2 emitted per unit of energy consumed). This factor depends on the energy mix (combination of energy sources used (coal, gas, oil, nuclear, renewables…)).

N.B.:
The Kaya equation is an identity, not an equation in the strict sense. This means it is always true by mathematical construction; it serves to organize thought and quantify the relative contributions of each factor, and not to predict the future deterministically.

The four levers of climate action

The strength of the Kaya equation is that it highlights the four major levers on which it is possible to act to reduce CO2 emissions:

1. Population (P): A delicate and long-term lever, linked to demographic, education and health policies. Population growth mechanically amplifies the other factors.

2. Prosperity per capita (g): Reducing this factor means giving up economic growth, a politically and socially complex option. The challenge is rather to decouple growth from emissions.

3. Energy intensity (e): This is the lever of energy efficiency. Reducing 'e' means producing the same wealth with less energy, thanks to technological innovation (buildings, transport, industry) and behavioral changes.

4. Carbon intensity of energy (f): This is the most powerful and direct lever. Reducing 'f' implies decarbonizing the energy mix by replacing fossil fuels (coal, oil, gas) with low-carbon energies (renewables, nuclear).

Limits and criticisms of the model: Its simplicity is also its weakness

While the Kaya equation is a valuable pedagogical and analytical tool, it has certain limitations.

It focuses solely on energy-related CO2, leaving aside other greenhouse gases (water vapor, methane, nitrous oxide) or emissions linked to land use (deforestation). The simplicity of this identity does not account for the complex interactions and feedbacks (positive or negative) between factors. For example, energy efficiency gains (lower 'e') can sometimes lead to increased consumption (rebound effect (phenomenon where efficiency gains lead to an increase in overall resource consumption)), partially canceling out the benefit. Likewise, an increase in temperature due to CO2 emissions can increase the concentration of water vapor in the atmosphere (a powerful greenhouse gas), creating a positive feedback that amplifies the initial warming, a phenomenon the equation does not capture. It says nothing about the technical, economic or political feasibility of reducing each factor.

The factorization implicitly assumes that population, wealth, energy intensity and carbon intensity are independent. In reality, these variables are strongly coupled.

From theory to practice: the Kaya equation facing climate objectives

A compass for IPCC scenarios

Despite its limitations, the Kaya equation structures the construction of emission scenarios used by the IPCC to project climate evolution. The different scenarios (SSP1-1.9, SSP2-4.5, SSP5-8.5…) correspond to contrasting trajectories for each of the four factors. For example, the very ambitious SSP1-1.9 scenario assumes a population (P) that peaks and then declines slightly, moderate but sustainability-oriented economic growth (g), a very rapid improvement in energy efficiency (e) and an extremely rapid decarbonization of the energy system (f). Conversely, a high-emission scenario like SSP5-8.5 projects strong growth in P and g, combined with limited progress on e and f, leading to a very high P×g×e×f product.

The scale of the challenge in figures

A strong mitigation scenario (limiting warming to 1.5°C) necessarily implies a very rapid and deep decrease in carbon intensity (f) and energy intensity (e), partially offsetting the expected growth in population (P) and wealth per capita (g). For example, to halve global emissions by 2050 compared to 2020, while assuming moderate growth in P (about +20%) and g (about +80%), calculations show that energy intensity (e) would need to be reduced by about 40% and, above all, carbon intensity (f) divided by more than 4. This concretely illustrates the equation: CO2 = P×g×e×f must decrease by half, despite the increase in P and g, thanks to drastic reductions in e and f.

Although these figures may seem discouraging, they define a precise framework for action. The decline in energy intensity is already underway in many countries thanks to technological progress, and the decarbonization potential of the energy mix (lower 'f') is immense with renewable energies and nuclear power. The challenge is less technological than political and economic: it is about carrying out this transition at an unprecedented speed and scale.

Which levers are truly actionable?

• Most actionable lever: Carbon intensity (f)
  Decarbonizing the energy mix is technologically mature (solar, wind, nuclear) and economically viable. It is the lever on which the international community agrees most, through agreements on renewable energies.
• Very actionable lever: Energy intensity (e)
  Energy efficiency technologies exist (insulation, high-performance engines, LEDs). The main obstacle is economic (initial cost) and regulatory (building standards).
• Partially actionable lever: Prosperity (g)
  Decoupling economic growth from emissions is possible, but politically sensitive. Sufficiency (consuming less but better) is an accepted concept, but its large-scale implementation faces enormous cultural and economic resistance.
• Little directly actionable lever: Population (P)
  Acting on demography raises major ethical questions and is a long-term matter. Positive measures (education, women's empowerment, health) are effective but slow. No coercive policy is acceptable in a democratic framework and human rights.

Thus, the realistic climate strategy focuses mainly on an accelerated transformation of factors 'e' and 'f', while accompanying a natural evolution of 'P' and orienting growth 'g' toward more sober models. The Kaya equation shows that success relies on an exponential improvement in our energy efficiency and the cleanliness of our energy.