Friday, March 09, 2012

World Bank Poverty Stats

I have been doing some comparisons and calculations ever since the World Bank came out with this release.,,contentMDK:23130032~pagePK:64257043~piPK:437376~theSitePK:4607,00.html

Though the $1.25/day (@2005 PPP rates) is the 'line' of absolute poverty, I'm somewhat more interested in the $2/day line. The release itself mentions that the progress on this (still fairly modest) indicator has been markedly less successful – but the absolute percentages and numbers are still quite shocking.

For instance in 2010, by World Bank's estimates, 32.7% of India's population was below $1.25/day and 68.7% below $2/day. While the first figure is understandable (though certainly not an acceptable state of affairs), the second figure is truly staggering.

In 2005 PPP terms, $1 was equal to Rs. 11.4 in rural areas and Rs. 17.2 in urban areas. This roughly corresponds to a weighted average of Rs. 16, nationally, given the urban-rural size of economy splits.,,contentMDK:21880725~pagePK:141137~piPK:141127~theSitePK:295584,00.html

$2/day then, means Rs.32/day, again at 2005 prices. Total consumer price inflation in India between 2005 and 2010 was 53%, so this now converts to Rs.49/day at 2010 prices.

This is, of course, consumption. Income would be somewhat higher – say by 25% (implying a savings rate of 20%, fairly optimistic for a person living at that level of income)? So, Rs. 61/day then. Or, Rs. 22,000/annum, rounded to the nearest thousand. Now this is where my disbelief kicks in. India's per capita income in 2010 was Rs 55,000 (again, rounded to the nearest thousand). So, by the World bank's estimates, a full 69% of the Indian population earns less than 40% of the national mean?!

I tried to do a simple stress test this figure – using the World Bank's Gini figures. The intuition is simple, given poverty headcount ratios and per capita incomes, one can create lower bounds on the Gini coefficient of a country. See this link for how the Gini coefficient is calculated.

In this instance, the stat claims that 69% of India earns less than (an average of) Rs. 22000/ annum. Let's say they all have an income of 22,000 per annum (thus understating inequality and the Gini). Then the other side of this divide (31%) has an average income of Rs 128,000/annum (to make an average of Rs 55,000 per annum). Let's say they all earn thsi same average income. So now, we have divided everyone in India in two separate sets, with perfect equality within each of the sets.

This division implies that the bottom 69% of India earns (at most) 28% of India's income and the top 31% earns (at least) 72% of India's income. This is an extremely simplistic piece-wise linear representation of the population-income Lorenz Curve, but it provides an implied lower bound of the Gini. The area under the curve (with coordinates of (0,0), (0.69, 0.28) and (1,1)) is 0.295, implying a Gini of ((0.5-0.295)/0.5) = 41%. To reiterate, this is just the lower bound. The World Bank Gini coefficient for India in 2010, however, is just 37.

If you separate the population into four distinct sets - at the world bank lines of $1/day (17% of India's population below this), $1.25/day (33% below this) and $2/day (69% below this), you get a lower bound on the Gini of 51!

Now I understand that these are based on very rough calculations and assumptions, but given that I am only trying to establish a lower bound with fairly conservative assumptions (about the savings rate, about intra-population equal distribution of income within the two separate populations identified), the 69% figure doesn't seem to pass the 'smell test'.

If India's poverty stats are indeed correct, then we'd be almost as unequal as Brazil and much more unequal than China. But India's inequality stats belie that. Which of these numbers is incorrect? My hypothesis suggests the $2/day figure of 69% is over-stated, but there could be other reasons.

Incidentally, I've mailed the World Bank about this. Let's see if they get the time to reply.

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