Wednesday, March 17, 2010

Who cares about the average income!

Many of us think of statistics as basically taking the average of some numbers. Maybe we even think of the normal distribution or ‘the bell curve’ and the concept of standard deviation. In this context, if you say the average height of people in India is around 5’ 5” with a standard deviation of 5”, it’s pretty intuitive what that means – that when you arrive in India you will find most people around 5’5” with some variation this way and that way of mostly 5”. In large part we all look similar and can fit in the same seats, sleep on the same size beds and fit through the same doorways. Instead, imagine if the distribution was not a bell curve but rather looked like this. A decreasing function with a heavy tail.

What this would mean is that most people are less than a foot tall while a few are absolutely enormous 50’ giants (in the heavy tail) with the rest somewhere in between. In this scenario there is no one size fits all and it would be impossible for a randomly selected group to be comfortable sitting at the same sized table. The enormous giants the height of multi-storey apartment buildings would have to live in a different sort of world than their underfoot counterparts. The average height in this distribution is still around 5’5” but knowing this average, and even the standard deviation, would be completely uninformative. Rather what could prepare you for what to expect is to know something about the rate at which the distribution decreases, basically the exponent that describes the relationship.

Now, unlike height distribution, which are bell curves, virtually all over the world the distributions of incomes and wealth display heavy tails. What differs between countries is largely the exponent. So if you knew nothing about India and you wondered what single number would best prepare you for the economic landscape, average income is really quite uninformative. Rather if you knew the exponent, or better still had a good visual of the distribution, you would come prepared to find Mukesh Ambani in a 27 story house on Altamount road surrounded by millions of abysmally poor people with barely a roof over their heads (and a little bit of everything in between). So, particularly from the perspective of understanding poverty, what we should care about is the exponent. Who cares about the average income!

In a separate post I will talk about what gives rise to these different types of distributions and why income and wealth distributions looks like this. Stay tuned.

**Note that if you do decide to delve further into this, most people show heavy tailed distributions in log-log or log-linear scales to emphasize the properties of the tail so make sure you look carefully at the axes.

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