Kaya decomposition (or Kaya identity) is a way to understand the CO₂ emissions in terms of the following components: human population, GDP per capita, energy intensity (per unit of GDP), and carbon intensity (emissions per unit of energy consumed). It is depicted as a percentage growth compared to the previous year.
Below you can select a country and inspect the Kaya decomposition of its carbon emissions. For comparison, we also depict the measured CO₂ emissions from fossil fuel combustion.
Please note that the graphic depends on available data. For some countries, some components might be available only for some years or be missing entirely.
For a larger view or if the applet does not load properly, click here.
Italy
Let us look at the Kaya decomposition for Italy. We can see a positive trend in reducing the fossil CO₂. However, the largest drops are caused by global events (e.g., the financial crisis in 2008 has an effect in 2009, the Covid-19 pandemic in 2020). Moreover, the big drops are compensated by an increase the year after (recall that the data show a percentage change compared to the previous year).
The population has not seen any significant increase since 1991, and it has been declining in the last ten years. That agrees with the known problem of Italy, low number of children, which is clearly not outweighted by the number of immigrants.
On the positive side, GDP/Population has been increasing in the last ten years (with the exception of the pandemic year 2020) while both Energy/GDP and CO₂/Energy keep decreasing. It means that Italy is producing more while using less energy per unit of product, and the energy is overall greener.
Math behind the decomposition
The idea behind the Kaya decomposition is the following identity: \[F = P \cdot \frac{G}{P} \cdot \frac{E}{G} \cdot \frac{F}{E}\] Here:
- \(F\) is the CO₂ emissions from human sources;
- \(P\) denotes the population;
- \(G\) stands for the GDP; and
- \(E\) is the energy consumption.
Now observe the identity from the mathematical point of view: almost everything on the right side cancels out, and we are left with \(F=F\). That explains why the identity is valid. However, we can now reinterpret the factors of the product:
- \(P\) is still the population;
- \(\frac{G}{P}\), i.e., the GDP divided by the population, measures the GDP per capita;
- \(\frac{E}{G}\), i.e., the energy consumption divided by the GDP, measures how much energy is consumed per each unit of GDP, so we call it the energy intensity of GDP;
- \(\frac{F}{E}\), i.e., the amount of the CO₂ emissions divided by the energy consumption, measures how many carbon emissions are produced per each unit of energy, and we call it the emission intensity of energy.
So we understand the Kaya identity, but how does it relate to the plot? In the identity, we have a product of four components. We could depict the product of two numbers as an area, but for the product of four components we would need at least four dimensions. So instead, we use the log-linearization trick: it includes taking a logarithm of both sides of the identity and then differentiating the new equation. The logarithm translates multiplication into addition, and through the differentiation we obtain the growth. The downside is that we end up with an approximation instead of the equality we had. But the upside is that we can now easily compare values that were originally in different units. This (roughly) explains why it makes sense to sum the percentage growth of the four components.
Data sources