The relationship between obesity of politicians and corruption is correlation, not causation

Not every correlation between two variables represents a causal relationship. Even if we can tell a compelling story about why a change in one variable might cause a change in another, that doesn't make the relationship causal. Sometimes a correlation actually results from something other than the story you tell. Sometimes the correlation is just random noise (a spurious correlation). So, we should be cautious when interpreting correlations.

I was reminded of this when reading this 2021 article by Pavlo Blavatskyy (University of Montpellier), published in the journal Economics of Transition and Institutional Change (sorry, I don't see an ungated version online). The article even generated a small debate, with a comment by György Márk Kis, and then a reply by Blavatskyy, appearing in the same issue of the journal.

In the original article, Blavatskyy looks at the relationship between the body mass index (BMI) of politicians in a country and the Corruption Perceptions Index by Transparency International. The data Blavatskyy uses is for 2017, and the sample of countries is limited to 15 post-Soviet countries (Armenia, Azerbaijan, Belarus, Estonia, Georgia, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, Moldova, Russia, Tajikistan, Turkmenistan, Ukraine, and Uzbekistan). The argument for why this correlation matters is explained in Blavatskyy's reply to Kis:

One common form of corruption/lobbying is inviting governmental officials to lavish banquets with excessive consumption of food and drinks... Corrupt politicians frequenting such banquets might risk gaining extra weight. This ‘hedonic theory of corruption’ postulates the existence of a positive relationship between median body mass index of public officials and the level of grand political corruption in society.

So, Blavatskyy is able to tell a good story for why greater corruption would cause higher BMI among politicians. However, that doesn't mean that the relationship is causal. Even though the correlation between perceived corruption and median politician BMI is clear, from Figure 1 in the original paper:

Low numbers in the Corruption Perceptions Index represent higher levels of perceived corruption. So, this figure shows that countries where the politicians have higher median politician BMI have higher levels of perceived corruption.

Kis took issue with a number of things in the paper. First, why those 15 countries? Why not all countries? Kis shows that if you separate the 15 countries in Blavatskyy's sample by their geographic location, you get different relationships within each subsample. However, the broader question is not what happens when you look at subsamples, but does this relationship hold if you add more countries to the sample? Neither Blavatskyy nor Kis answer that question. We should also wonder whether there is something special about 2017 that leads to this correlation. Does it hold in other years?

In his reply, Blavatskyy doesn't really address those two points (narrow sample, and a single year) in a convincing way. Instead, he narrows the sample even further to look at changes in politician BMI and perceived corruption for just one of the countries in his sample, Ukraine. In that analysis, he again shows a correlation between corruption perceptions and politician BMI, in this case over time for Ukraine. However, that simply raises the question of: why Ukraine? Why didn't he look at other countries in his sample in that way? And just because Ukraine shows a correlation over time, that still doesn't demonstrate a causal relationship.

Kis also takes issue with the machine learning algorithm that Blavatskyy uses to estimate the BMI for politicians in his sample. Kis notes that the accuracy of the algorithm is quite dubious (my words, not Kis's), with:

...errors of at least 5.5 in 21.1% of the time.

That's an error in the estimated BMI of 5.5 in over 20 percent of cases. That extent of measurement error would be problematic. To that, I would add that it is unclear whether the training sample that the machine learning algorithm was trained on included people from post-Soviet countries. The relationship between facial features and BMI could well be ethnic-specific, in ways that systematically bias the results. We have no way of knowing. And Blavatskyy didn't address this point in his reply.

Now, the point of this post is to focus on correlation or causation. From what I have seen, this seems a likely candidate for confounding. There are any number of variables that might increase politician BMI and increase corruption, without corruption being a cause of higher politician BMI. As one example, a country with high inequality might simultaneously have high corruption (with petty officials willing to take bribes to supplement their low incomes) and high politician BMI (since politicians would likely be among the wealthy class in society). Blavatskyy doesn't consider confounding variables such as inequality, or differences in age distribution, or differences in average BMI in the population, or regional differences in diet, in his analysis.

Now, to be fair to Blavatskyy, he doesn't adopt a causal interpretation of his results (except in his response to Kis, as I quoted above). Instead, Blavatskyy argues that, if BMI and perceived corruption are correlated, then we might infer how much corruption is being experienced in a country by looking at the median BMI of its politicians. However, even that inference is problematic, and Blavatskyy should know why. He gives the example of Swiss watches in China as a proxy for corruption, but then notes that:

...the rise of social media and Internet anti-corruption platforms in 2011–2012 made it no longer possible to measure grand political corruption through visible luxury Swiss watches. Luxury Swiss watches could still be a popular expenditure of corrupt governmental officials, but these officials are now more careful not to reveal their Swiss watches to the general public.

When politicians realised that their Swiss watches were giving away their corruption, they stopped showing off their Swiss watches. If politicians realised that their expanding waistlines were giving away their corruption, wouldn't they invest more in personal trainers (or liposuction)? As soon as this correlation was used for inference, the correlation would likely start to break down. This again illustrates the limited usefulness of such proxies.

Correlation does not imply causation. And sometimes, correlation today does not imply correlation in the future. We need to be much more cautious when considering analyses like this one.