We investigated the macroeconomic determinants of neonatal, infant, and under-five mortalities in Bangladesh for the period 1991–2018 and discuss implications of the United Nations’ Sustainable Development Goal 3 (SDG 3) and Millennium Development Goal 4 (MDG 4) for developing countries. We used annual time series data and the econometric techniques of Fully Modified Ordinary Least Squares (FMOLS) and Dynamic Ordinary Least Squares (DOLS) regressions for analysis. Determinants most effective in combating neonatal, infant, and under-five mortalities include variables such as ‘protecting newborns against tetanus’, ‘increasing healthcare expenditure’, and ‘making sure births are attended by skilled healthcare staff’. Employing more healthcare workers and assuring more and improved healthcare provisions can further reduce the neonatal, infant, and under-five mortalities. Developing countries with similar macroeconomic profiles can achieve similar SDG 3 and MDG 4 outcomes by emulating the policies and strategies Bangladesh applied to reducing child mortalities over the last three decades.Supplementary InformationThe online version contains supplementary material available at 10.1057/s41271-023-00413-w.