It is intuitive that decision-makers might have attitudes towards uncertainty just as they might have attitudes towards risk. However, it is only recently that this intuitive notion has been formalized and axiomatically characterized. We estimate the extent of uncertainty aversion in a manner that is parsimonious and consistent with theory. We demonstrate that one can jointly estimate attitudes towards uncertainty, attitudes towards risk, and subjective probabilities in a rigorous manner. Our structural econometric model constructively demonstrates the theoretical claims that it is possible to define uncertainty aversion in an empirically tractable manner. Our results show that attitudes towards risk and uncertainty can be different, qualitatively and quantitatively, and that allowing for these differences can have significant effects on inferences about subjective probabilities.