The link between the mortality and epidemiological transitions is used to identify the effect of the former on the fertility transition: a mortality transition that is not accompanied by improving morbidity causes slower demographic and economic change. In a model where children may die from infectious disease, childhood health affects human capital and noninfectious-disease-related adult mortality. When child mortality falls from lower prevalence, as it did in western Europe, labor productivity improves, fertility falls and the economy prospers. When it falls mainly from better cures, as it has in sub-Saharan Africa, survivors are less healthy and there is little economic growth. The model can quantitatively explain sub-Saharan Africa's experience. More generally it shows that the commonly used indicator, life expectancy at birth, is a poor predictor of population health and economic growth unless morbidity falls with mortality.