From the Guardian Unlimited: China overtakes US as world's biggest CO2 emitter

China has overtaken the United States as the world's biggest producer of carbon dioxide, the chief greenhouse gas, figures released today show. Check out the rest of the story.

All of this stuff reminds me of something that I read a few years ago, especially about how the United State's emissions aren't really a problem, so long as GDP continues to grow.The above chart is something that I've seen before (in various different forms) to show that the impact of CO2 emissions aren't really as bad as some people think they are (since relative growth of GDP is apparently what is required). I mean, look at the chart: China's line is negative, the US's line is negative. In fact all lines are basically negative, except India, which is starting to go negative. (Of course, China is also starting to go positive.)

The problem with the above graph (and ones like it) is that the graph says NOTHING about absolute CO2 emissions. It only says that the relative growth of CO2 emissions for all the countries shown have grown slower than that of GDP. However, all this means is that if a country has a 2% GDP growth rate, so long as the CO2 emissions don't increase by more than 2%, no net "growth" occurs.

Stepping back and looking at the growth rates of CO2 emissions for each country shown above, one can see that, in fact, China, India, and the United States have had net CO2 emission growth over the period of 1969 - 2003. Meanwhile, the CO2 emissions of Germany and the United Kingdom have diminished slightly. Mexico's CO2 emissions over the same period also increased slightly.

How can this be? I mean, the above graph shows one thing, this graph shows a completely different message. One might say that this is one example of how graphs can be misleading, unless you are careful in understanding what a graph actually is illustrating.

The first graph is showing the relative amount of two things: GDP and CO2 emissions. To make the first graph, the value of CO2 emissions is divided by the value of GDP. But are these two amounts (GDP and CO2 emissions) actually correlated? If they are correlated, are the amounts just as correlated across different countries? These are both important questions to ask when looking at these sorts of comparisons (especially before slapping them together and putting them on a graph).

When you look at the graph of CO2 emissions over time, you should be very comfortable about making direct comparisons between countries, since both variables (time and tons of CO2 emissions) affect all countries in the same way. Time (indicated as years along the X-axis) is the same from country to country; the year 1990 in the United Kingdom is directly and completely equivalent to the year 1990 in China, the United States, etc. Similarly, a metric ton of CO2 emitted in one country is directly and completely equivalent to a metric ton of CO2 emitted in another country. The importance of knowing that both time and CO2 emissions are "equally equal" in all countries means that a person looking at the second graph can immediately state (without any hesitation) that the rise of CO2 emissions in China can be compared to the much smaller rise of Mexican CO2 emissions (assuming that you can trust the data sources). These statements may seem to be overly-pedantic on my part to bring up, but they are important to understand when moving on to the next paragraph.

IF you wish to accurately state that the two amounts (GDP and CO2 emissions) really are comparable as a consistent relationship between countries, the slopes of each line should be statistically insignificant from each other. One way to see if this is even conceivable, you can first graph them. Here, I graphed GDP directly against CO2 emissions. On the Y-axis, the GDP values are shown on a logarithmic scale (only to show the relatively small GDP values of Mexico, India, and about half of China's data). The values on the X-axis show the amount of CO2 emissions on a linear scale.

As we can see, the slope of China and the slope of the United States appear similar to each other. Likewise, the slopes of India and Mexico appear similar to each other, and those of the United Kingdom and Germany also appear similar to each other. However, the China and United States slopes are not similar at all to those of the United Kingdom and Germany (the prior are both "positive slopes" and the latter are both "negative slopes"), and are not very similar to those of India and Mexico (although all four slopes are positive slopes).

How do these visual estimations relate to numerical values? In calculating the slopes, I did a few things. First, I took the logarithm of the GDP values. This process - a type of "power transformation" - was done to make the data fit more toward a straight line. Next, I divided the value of CO2 emissions by 100,000. This was done because the values of CO2 emissions are roughly 100,000 times greater than those of the logarithm-transformed GDP values. (If the CO2 emission values were not divided by 100,000, the slope values I would be showing you would be several decimal places to the right of the initial zero.) Then I used MS Excel's in-built slope calculation tool to find each country's GDP-to-CO2 emission relation slope (the thing we are looking for in order to justify comparing countries against each other).

Here are the results:
Country: Slope
China : 1.512
USA : 0.865
Germany: -2.975
India : 2.280
Mexico: 5.446
United Kingdom: -6.427

These numbers basically support the statement made a few paragraphs above: China and the USA have similar slopes; Germany and the United Kingdom have similar slopes; and India and Mexico have similar slopes. I could go on to show just how similar these slopes are to each other by doing different sorts of ANCOVA analyses, but I think you get the idea of how these slopes relate to each other. (If such analyses were conducted, however, it might be shown that none of the slopes are actually statistically similar enough to each other to make even paired comparisons.)

So, going back to why I came down this road in the first place, can one really justify the use of the first graph (or ones like it)? I would argue that, NO, you cannot just take CO2 emissions and divide them by GDP. You cannot do it because the relationship between these two variables are NOT equal between all countries. Just look at the slopes of China and Germany. Although many people are "comfortable" with the concept of GDP, you cannot make the statement that GDP can (or should) be directly and implicitly related to CO2 emissions.

The thing about CO2 is that it is the absolute magnitude of CO2 emissions that are the important thing to consider. You can (and many people do) make CO2 emissions per capita analyses (since the existence of a single individual in one country is equally identical the existence of a single individual in another country). You can also do CO2 emissions based on sectors of a nation's economy (e.g., %CO2 emissions from industry, transportation, etc). If this is done, you assume (especially when comparing across countries) that the definitions of economic sectors of "industry", "transportation", etc. are effectively identical across the countries you are comparing. You can even do CO2 emissions based on wealth within a country (e.g., %CO2 emissions from the richest 20% of a nation).

I hope that I was able to show that when you see graphs of CO2 emissions divided against GDP (without any explicit statement that these values are somehow normalized) that you take them with such a large pinch of salt that you find the whole thing as unpalatable as I do.

The Gristmill posted a follow-up article about the China passing the US story.