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Monday, March 13, 2006

Correlation and Causality 

Veer Bothra of Mobile Pundit (a must-read blog) posts an e-mail exchange in which Atanu Dey explains brilliantly well something that all of us, especially those of us with an interest in policy, should keep in mind: the difference between correlation and causality.
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.
In my opinion, it is the lack of understanding of this difference which leads people to waste so much time and resources fixing problems like the digital divide (which assumes a causal relationship between telecom and economic growth in developing countries, with scant evidence), when in fact those resources could be used so much more efficiently in public health or primary education.

In other news, Dr James Reese is hosting Atanu and my friend and co-blogger, Edward Hugh in a Radio Economics segment on the Indian Economy.
Topics covered include: Indian development options; should India be treated as a single country; should India concentrate on services as an engine of growth; the role of public education in economic development; what role should the Indian government play in economic development, and what is their current 5 year plan; and prospects for the next 10 years.