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