A Graphical Look at the Kaya Identity

I decided to write this after reading two posts by Willis Eschenbach and numerous comments on Watts Up With That (update: see also a reply from Roger Pielke Jr). My post uses graphs to show how the Kaya identity can help to identify the factors underlying a country’s CO2 emissions.

What is the Kaya Identity?

The Kaya Identity is a way of looking at the factors that affect CO2 emissions. It includes four factors and can be written as follows:

CO2 emissions = Population x Standard of living x Energy intensity of the economy x Carbon intensity of energy
Factor 1 Factor 2 Factor 3 Factor 4
Population GDP per capita Energy per unit of GDP CO2 per unit of Energy

Taking each factor in turn, why should they affect CO2 emissions?

Factor 1, Population. It is reasonable to expect that CO2 emissions will be related to population – other things being equal, a country with a large population will have more cars, more houses, more factories, and so on, than a smaller one simply because it has more people. However, the graph below (Figure 1) shows that while there is a relationship between population and CO2 emissions, it is clearly not the whole story.

Figure 1 (updated). CO2>/sub> emissions versus population. Source World Bank Indicators.

Figure 1 (updated). CO2 emissions versus population, 2010 data. Source World Bank Indicators.

To compare countries with different populations, it is useful to divide both sides of the Kaya identity by population, and calculate CO2 per capita (CO2/Population).

CO2 emissions per capita = 1 x Standard of living x Energy intensity of the economy x Carbon intensity of energy
Factor 1 Factor 2 Factor 3 Factor 4
GDP per capita Energy per unit of GDP CO2 per unit of Energy

Factor 2, Standard of Living: Now, if population were the only factor affecting CO2 emissions, CO2 emissions per capita would be constant regardless of GDP per capita (Figure 2).

Figure 2.

Figure 2.

However assuming that GDP per capita has no effect on CO2 emissions leads to the ridiculous conclusion that a country with very low (or zero) per capita wealth will have the same CO2 emissions as one with great wealth, assuming equal populations. In fact we expect that per capita CO2 emissions will increase with wealth. People with higher per capita GDP consume more, travel more, build more and manufacture more, on average, than people with low per capita GDP. In that case we predict a linear relationship between per capita CO2 and per capita GDP (Figure 3), consistent with first two factors of the Kaya identity.

Figure 3.

Figure 3.

So what do the real-world data look like? Here are the UNEP data from 2005 for per capita CO2 emissions and per capita GDP. It certainly looks more like Figure 3 than Figure 2, but countries do not all lie on a single straight line.

CO2 per capita against GDP per capita (Source UNEP 2005).

Figure 4. CO2 per capita against GDP per capita (Source UNEP 2005).

Factors 3 and 4: So, the fact that countries do not all lie on a single straight line shows that population and GDP per capita do not completely explain the CO2 emissions of different countries. Uncertainties in the estimates of CO2 emissions, GDP and population play a part in the scatter, but we must also think about Factors 3 and 4 in the Kaya identity, that is, Energy intensity of the economy and Carbon intensity of energy.

Countries lying above the straight line have higher CO2 emissions per unit of GDP than those on the line, while those below the line have lower CO2 emissions. We can see this in the graph below (Figure 5), the two ‘off-diagonal’ countries have respectively higher and lower CO2 emissions than predicted by their population and per capita GDP. Countries lying on the line all have the same ‘average’ values of Factors 3 and 4 (or, strictly speaking, the product of those factors).

Figure 5.

Figure 5.

Only a detailed understanding of each country’s economy can establish the relative importance of Factor 3 and Factor 4 effects. For example, Factor 3 could depend on the level of heavy industry contributions to GDP (high energy/GDP) versus service economy (low energy/GDP) and how energy-efficient each process is. And Factor 4 (CO2/Energy) will depend on how energy is generated in the country, whether there is a ‘high-’ or ‘low-carbon’ mix of fuel sources. One could also include in Factor 4 net emissions of CO2 and other greenhouse gases unrelated to energy generation – though such measurements are not consistent between countries, and are not usually included in international comparisons.

Although we can’t disentangle factors 3 and 4 by looking at the graphs above, they are the factors are important to policymakers. As Roger Pielke Jr argues, Factors 1 (population) and 2 (standard of living) are not ones that policymakers can or wish to reduce (Pielke’s Iron Law of climate policy). Factors 3 ‘energy efficiency’ and 4 ‘low-carbon technology’ are factors that policies may be able to affect. Policymakers can use the Kaya Identity to see how their country performs relative to others after taking population and wealth into account, and track how their policies affect their country’s position. I discuss Factors 3 and 4 in my next post.


7 thoughts on “A Graphical Look at the Kaya Identity

  1. Has the question of how many angels can dance on the head of a pin been settled yet?

    • That question was settled conclusively in Good Omens by Neil Gaiman and Terry Pratchett:

      “Firstly, angels simply don’t dance. It’s one of the distinguishing characteristics that marks an angel. They may listen appreciatively to the Music of the Spheres, but they don’t feel the urge to get down and boogie to it. So, none.

      At least, nearly none. Aziraphale had learned to gavotte in a discreet gentlemen’s club in Portland Place, in the late 1880s, and while he had initially taken to it like a duck to merchant banking, after a while he had become quite good at it, and was quite put out when, some decades later, the gavotte went out of style for good.

      So providing the dance was a gavotte, and providing that he had a suitable partner (also able, for the sake of arguement, both to gavotte, and to dance it on the head of a pin), the answer is a straightforward one.”

  2. Pingback: Kaya Identity part II – and a ‘diamond law’? | My Garden Pond

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