Wednesday, July 07, 2010

Inequality and health: the non-causal link

Reading the recent post on The Spirit Level book book by Wilkinson & Pickett set me thinking about some old results that may be relevant. To recall, the basic claim is that the average of one variable (health) depends on the inequality of another (income). Forget the dreaded word endogeneity for the moment and recall an even nastier one: non-linearity.
There are a series of results in aggregation theory that basically show that when you aggregate a non-linear relationship that the correct specification includes a measure of inequality - which will be a Theil entropy index to be precise. In other words even if there is absolutely no causal relationship between the outcome and inequality one should include a measure of inequality of one's independent variable on the right hand side. If the underlying relationship is concave then the inequality term enters with a negative coefficient, if it is convex it has a positive coefficient.
So say individual health is a concave function of individual income then when we estimate a model of aggregate health as a function of aggregate income then we expect inequality of income to enter negatively. While this does not rule out that there is also a causal relationship, nonetheless I believe this may go some way to explaining Wilkinson & Pickett's result.

See, in increasing order of difficulty:
N Heerink, A Mulatu, E Bulte Ecological Economics, 2001, 38, 359-367
M Ravallion Economics Letters 1998, 61, 73-77
R Blundell, P Pashardes, G Weber, American Economic Review 1993, 83(3), 570-597

7 comments:

David Madden said...

You are right, Kevin. This particular link between health and income inequality has been labelled the "statistical artefact" by Hugh Gravelle (I think) and is also referred to by Angus Deaton in a number of his articles on this issue. What Deaton (and others) have tried to do is to come up with a convincing link between income inequality and health outcomes apart from this statistical artefact. My reading of the literature is that so far they have met with only limited success. But as I have said elsewhere, the jury is still out on this question.

Kevin Denny said...

Nice to know I am in good company. Actually, calling it "non-causal" as I did is a bit misleading: there is an effect but its a very different mechanism. So where W&P argue that inequality affects individual health & therefore the mean, with this route it has no individual effect but still affects the mean.
So the argument is that if you take a few thousand from such rich guy like Denis O'Brien (or a few million in the case of Adam Clayton) he's not going to notice and so if you give it to some homeless people you will increase the health of the poor by more than you diminish that of the rich, given concavity.
So its just boring old diminishing returns. But it still provides an argument for reducing inequality to improve health. So thats not really just a statistical artifact or is this different from the aggregation argument?

David Madden said...

Yes, the statistical artefact argument does imply that redistribution of the sort you describe should increase overall health. What Deaton and others have also tried to do is to see if there is any pathway whereby say an increase in inequality could lead to a deterioration in someone's health (holding their income constant) and this is where they run into problems. Its also worth pointing out that W&P suggests that inequality plays a role in a lot of other "social pathologies" like crime etc

Mark McG said...

The authors were in Dublin around this time last year, and were interviewed on Vincent Browne (where else?). Hard evidence is difficult to come by, however I think the Whitehall studies are pretty compelling in showing a link between health and social status/stress e.g. this paper. Probably deserves a separate post.

I was at their presentation, and of course they “prove” nothing, but I personally find that the descriptive stats present an important challenge to social scientists. They are very consistent; you can pick pretty much whatever indicator you like, infant mortality, obesity, teenage pregnancy etc. And more unequal societies are not more innovative. Some examples from here. At least they were using Stata.

Kevin Denny said...

Mark, my understanding of those papers is that they are saying thats its stressful for you if you are at the bottom of the pile so the health of i depends on rank of i, say. Thats not too controversial.
Whereas the W&P argument is, as I understand it, that individual health is affected by characteristics of the distribution of health so the health of i is affected by the variance, say. So, in that case, lets say my income and Liam's income become more different then this would be bad for your health. Thats quite a different proposition. One thats hard to rationalize too.

Mark McG said...

Are they not making the argument that your health depends on the variance of income because stress levels are higher (given any particular income, and the Whitehall studies show this holds even in well off cohorts), the greater the distance between you and the individuals above you in the distribution

Kevin Denny said...

I'd need to read those papers more closely. But one would need to distinguish between the variation between my income & others and the pure variance.
So in the example I gave, why would an increase in the variance between my income & Liam's stress you out ? (You don't have to answer that btw).
One might also think that these stress effects are asymmetric: I'm stressed because certain people are paid more than me. That certain others are paid less than me doesn't bother me unduly. Frankly, I can see an upside. Variance is neutral between up and down, of course.
So without really having read the literature, I am inclined to think this is quite a 'mare of a problem to get to grips with.