My colleague Veer Bothra is the Mobile Pundit. Recently he discussed teledensity and GDP growth where he quoted an email exchange from me on the distinction between correlation and causation. Here it is for the record:
Correlation and causation are not the same thing.
If you observe there is a relationship between the shoe size of a person and the size of his vocabulary – and note that there is a positive correlation in that the larger the shoe size, the larger the vocabulary – then you could falsely reason that having big feet causes larger vocabulary. The two are correlated but not causally related. There are other variables: older children have bigger feet and also bigger vocabularies.
There are lots of correlated variables in the world. Some of these correlations have causal connections as well. In some cases the direction of causation is evident, and in some cases it is difficult to figure out. In some other cases, the causation could be bi-directional.
For instance, number of forest fires in a month and average temperatures of the month are positively correlated. It is easy to see that hot weather causes forest fires, and not the other way around–forest fires do not raise the average temperature of the month.
Now suppose we note the positive correlation between the presense of riot police and riots. Again the direction is easy to spot: clearly, riot police do not cause riots; riots cause riot police to appear. Or the presense of firemen and fires: fires cause firemen to appear, rather than the other way around.
Now bidirectional causal links: chicken and eggs. Chickens causes eggs; but eggs cause chickens as well. So which is the cause and which the effect? That is the most famous chicken and egg problem: which came first?
The vicious cycle is similar. If you are poor, you cannot good education; if you are not well educated, you cannot get a good job and hence you are poor, and so on. Or if you are poor, you cannot afford nutritious food and therefore your health is poor and so you cannot hold on to a good job and therefore you are poor, etc.
Now cell phones and growth in GDP is positively correlated. For every 1 percent increase in teledensity, the GDP growth rate goes up 0.6 percent. (Figures for illustration only.) It is not easy to tease out which direction the causal relationship is, if at all there is a causal relationship.
There need not be a causal relationship, merely a correlation. For instance, more cell phones and more GDP could be both due to the underlying factor that the country has suddenly become very very successful in BPO services.
Even if cell phones adoption and GDP growth rates are causally related, it is not at all evident which way the causality holds: it could be that GDP growth increased per capita incomes so that people could afford phones; or it could be the other way around, that more people having phones made them more productive and this pushed up the GDP. Or both.