In this study, effects of public and private health expenditures on life expectancy at birth and infant mortality are analysed on a global scale with 195 countries in the years 1995-2014. The global data set is divided into country categories according to growth in life expectancy, decrease in infant mortality rate, and level of gross national income per capita. Some new dynamic panel model estimators, argued to be more efficient with high persistence series and predetermination compared to popular but complex GMM estimators, show that public health expenditures are generally more health-promoting than private expenditures. However, the health effects are not as great as primary education effects. Although the new estimators provide some new and valuable information on health expenditure effects on life expectancy and infant mortality on a global scale, they do not show desired robustness.