Georgiadis, Georgios , and José Pineda, and Francisco Rodríguez (2010). "Has the Preston Curve Broken Down?" United Nations Development Programme, Human Development Reports Research Paper 2010/32 United Nations Development Programme pp. 1-55

Three apparently contradictory stylized facts characterize the relationship between per capita incomes and life expectancy: (i) the existence of a strong correlation between the level of life expectancy and the level of per capita income, (ii) the absence of a significant correlation between changes in per capita income and changes in life expectancy, and (iii) the persistence of twin peaks in the distribution of life expectancy, despite their progressive disappearance from the income data. This paper seeks to reconcile these apparently contradictory findings. We argue that a data generating process in which there is a relationship between income and life expectancy for high levels of development but not for low ones can explain these stylized facts, while models that apply a uniform relationship to all countries cannot. We also argue that the slope of the relationship between income and life expectancy is significantly overestimated by standard cross-sectional estimates, with the true slope being much lower for some countries and not statistically significantly different from zero for others. Lastly, we provide evidence from an error-correction model showing that the elasticity of life expectancy to incomes has been declining both for countries at high and low levels of development. We suggest that these results can be interpreted as showing that income matters only for countries that are close enough to the world health technological frontier.