Matt Berkley
Sent: 10 August 2000
Subject: Growth and survival

Dear Mark

I've seen your new paper on growth and the poor, and was relieved that someone has raised the possibility that income figures look better if the poorest die off.

This seems plausible to me, but maybe more plausible is that the figures look better if non-productive people die.

I wonder what you think of the following.

On the first point, Jonathan Morduch at Princeton has suggested to me that deaths of the poorest households may not have a statistically significant effect on the income figure for the poorest quintile. If he is right, why is this? I would have thought for the same reason that the average income in the quintile isn't far from the top income: if you're very far below the top you drop out of the figures, because the consumption level isn't enough to sustain life.

On the second point, It looks to me as though the biggest influence on per capita income figures is the proportion of non-productive members of households - largely children. One reason why per capita income figures go up can be that fertility rates have gone down (this might be due to growth among the poor, national growth, or something else). Per capita incomes in China have gone up - there aren't many children.

In a simple model, let's say children don't generate income and adults each generate $2. If you have 50 children and 50 adults, per capita income is $1. If you have 48 children and 52 adults, it's $1.04.

If we make this into a model of the bottom quintile, I think what happens is this: for each 2 children who die, their places are taken at the top of the quintile by 1 adult and 1 child. You end up with 49 children and 51 adults: $1.02 per person. 4% of existing children die and you get a 2% rise in per capita income. For each percentage change in child death rates you get half a percentage point change in per capita income.

Survival rates of under-fives can be only 75% in a vulnerable group. A 1% variation around this figure would make a significant difference to the growth figures - if 0.5% of per capita income is attributable to higher child deaths than in another country or at another time, this is a serious problem for the idea that growth is good for the poor.

In fact, to end up with 1% of existing children dying (the ones who've survived till now), you would only need to see a smaller increase in the total child mortality rate (all those who were born, including those who've already died).

There are obviously other factors: for example, over time, the poorest people may produce more children replacing the dead ones.

It would seem sensible to compare countries' national and bottom-quintile growth rates along with 1) fertility rates; 2) ratios of productive to non-productive members of households; and 3) death rates among non-productive members of households (under-fives would be a good start).

In practice there are more children than adults - so many that more than 50% of all deaths in the global poorest quintile are of people under 15, even though the death rate for people in this age group is 21% *. A small percentage increase in their death rate results in a large number of children dying.

I do wonder how in a situation where a high numbers of children die, there could be more debate about the effects of growth on fertility rates and survival rather than on tiny changes in income.

* Davidson R. Gwatkin and Michel Guillot, The Burden of Disease Among the Global Poor, 1999

Matt Berkley