Income Distribution and Infant Mortality Fantasy

Robert Waldmann

Tilman Tacke and I wrote this manuscript looking at income inequality and infant mortality (I’ve discussed it here before).

I am going to indulge myself describing the paper I wanted to write but couldn’t because the data didn’t cooperate (gave essentially no empirical support for my pet theory). After the jump, my pet hypothesis:

The surprising stylized fact is that the correlation between inequality and infant mortality is very strong — too strong to be explained just by the obvious assumption that the probability of an infant death is convex in family income.

In fact, it seems that even given the incomes of the non rich, in countries where the rich are richer, more babies die.

This empirical result actually comes and goes in the data, but it was noted in the early 90s and there is a large literature on it. Also it’s back in recent data.

There are many many possible explanations. The one I like is
the life styles of the rich and famous hypothesis, or the bad role model hypothesis.

The idea is that non rich people enjoy having consumption profiles which are similar to those of the rich. This is similar as in “similar triangles” less of all goods and services but in the same proportions. That is, the idea is that non rich people consume luxuries because they enjoy pretending they are rich.

Formally this corresponds to maximizing an ordinary utility function u(c_i) plus one that penalized the difference between the proportions of different goods consumed and that of the role model — the glamorous rich and famous people v(c_i,c_rich).

Now the second part of the utility function will cause choices which don’t maximize the first (obviously if you are maximizing the sum of 2 functions you don’t max either one).

The rich and famous might like being like themselves but that doesn’t change their consumption (if you are maximizing the sum of a function and a constant you are maximizing the function).

Now consider 2 countries. The non rich have the exact same income in both but the rich have different income. If the rich are very rich, their consumption is very different from that which would maximize u(c_i) for the non rich. This means that the v term pulls choices further from u maximizing and u(c_i) is lower.

If the rich are just a little bit richer than the non rich, the choices of the rich are close to maximizing u(c_i) so the v term has little effect on choices and u(c_i) is higher. If the rich are richer, that part of welfare of the non rich which does not depend on enjoying pretending they are rich is lower. That part of welfare u() will be the one related to measurable things like health.

Well that was pointless (my hope is that it is inimitable style of doing pointless math without any mathematical notation).

The example — breast feeding. In micro data from poor countries, breast feeding has a strong negative association with the risk of infant mortality (risk of death as low as one third of that of bottle fed babies). Clearly the key issue is mixing formula with unsafe drinking water. However, another issue is that poor people can’t always afford enough formula to keep their babies healthy. So to conserve it they over dilute it and the babies are malnourished, or the fill the bottle with something cheap but not as healthy as formula. Here deaths are due to buying too little of a luxury rather than none at all.

Now imagine that the relatively rich can afford formula in 2 countries but in A they have to scrimp and save and in B the cost is no problem. In B more of the relatively rich will bottle feed. This is a reasonable choice (hey I have spent many many hours holding a bottle full of formula oh and more drinking formula from a bottle but don’t blame the formula). However it is a dangerous example for the non rich.

So the story is that the association can be explained if one includes the proportion of mothers who breast feed in the regression. The data say You Lose.