We know that richer people live longer: but is it because they are richer?

A standard part of the story here in this sceptered isle is that there is a causal relationship between economic inequality and health and lifespan inequality. Michael Marmot has been telling us this for decades now. That there is a correlation between wealth and lifespan is obviously true: but what's the causality? 

What we'd really like to do is look at people who have randomly gained wealth and see whether it has changed either health or lifespan. And just to be inclusive about this we'd like to look at the children of those this happens to. Fortunately the spread of lottery systems around the world gives us some number of people who have randomly become wealthy.

Via Marginal Revolution, the result? 

We use administrative data on Swedish lottery players to estimate the causal impact of substantial wealth shocks on players’ own health and their children’s health and developmental outcomes. Our estimation sample is large, virtually free of attrition, and allows us to control for the factors conditional on which the prizes were randomly assigned. In adults, we find no evidence that wealth impacts mortality or health care utilization, with the possible exception of a small reduction in the consumption of mental health drugs. Our estimates allow us to rule out effects on 10-year mortality one sixth as large as the cross-sectional wealth-mortality gradient. In our intergenerational analyses, we find that wealth increases children’s health care utilization in the years following the lottery and may also reduce obesity risk. The effects on most other child outcomes, including drug consumption, scholastic performance, and skills, can usually be bounded to a tight interval around zero. Overall, our findings suggest that in affluent countries with extensive social safety nets, causal effects of wealth are not a major source of the wealth-mortality gradients, nor of the observed relationships between child developmental outcomes and household income.

Doesn't seem to be the money itself, does it? And thus is won't be economic redistribution which solves the point either, will it?