Regardless of the vast wealth that oil can bring to a country, it can be regularly observed that oil rich countries underperform in terms of economic and social outcomes compared to their oil poor counterparts. Actually, this pattern was observed so often that it was termed the ‘resource curse’. The political resource curse predicts that an abundance of natural resources leads to inefficient public policies, due to corruption and rent-seeking. This paper contributes to the discussion by applying Stochastic Frontier Analysis (SFA) to determine whether oil rents drive inefficiency in public policies, focusing on the health care sector. The SFA estimated simultaneously a production function for health outputs and the determinants of inefficiency in production. Using a sample of 119 countries covering the period 2000 to 2015, unexpectedly high oil revenues are shown to increase inefficiency. Oil rents hindered countries in reaching their potential life expectancy. Exploiting exogenous variation in the international oil price revealed that causality runs from oil rents to inefficiency and these results are robust to different model specifications - including different production functions and mean inefficiency determinants - the exclusion of oil price maker, time lags of the effect and different definition of price shocks. The effect varied with institutions, sex and age; while the effect was more pronounced in democracies, women and children were also affected more than adult men. Transparency and inequality are potential mechanisms that explain how oil rents leads to inefficiency in the health care sector. Hence, policy implications for democratic oil rich countries could be to invest the oil dividends into poverty reducing policies to battle inequality and reform institutions to increase transparency.