Anarcho-capitalists argue that private governance institutions could profitably replace government and often appeal to medieval Iceland, which was governed privately. Conventional wisdom regards this as insane: medieval Iceland was poor, and every rich society has government. While that is true, every society in medieval Europe was poor by modern standards, and whether living standards would have been higher in medieval Iceland under government is an empirical question that has not been evaluated empirically. We provide such an evaluation by exploiting the fact that, in contrast to Iceland, other territories in medieval Europe were governed partly by government. We use historical data on human height, wages, and population growth to compare living standards across medieval European territories. Living standards in state-governed medieval Europe do not seem to have been higher than they were in Iceland. Anarcho-capitalists, it seems, are not insane.