Children living on a dollar a day—the international extreme poverty line—appear to have radically different chances of dying in childhood and being malnourished, depending on the country in which they live. In Kazakhstan, a child living on a dollar a day, has only a 10% risk of being underweight, while the risk facing a child living on a dollar a day in India is nearly 60%. The Kazakh child has a risk of less than 40 per 1000 of dying before his first birthday, while a child living on a dollar a day in Niger faces a risk of nearly 160 per 1000. Countries where mortality and malnutrition risks at a dollar a day are high are not typically those where there are large gaps in child survival and in malnutrition between the poor and better off. The two concepts of inequality and health risks at the poverty line are not only conceptually distinct—they are empirically distinct too. The large differences between countries in the risks of mortality and malnutrition in childhood beg the obvious question—what accounts for these differences? Some regression results presented in the paper suggest that these differences may be due to differences across countries in levels of per capita expenditure on the health sector. Regressions find that higher levels of per capita public spending on the health sector are associated with significantly lower levels of mortality and malnutrition amongst children living on a dollar a day.