Risk aversion is traditionally defined as aversion to variance, but theoretical and empirical work suggest that higher moments of probability distributions, specifically skewness and kurtosis, also affect choice under risk. Unlike aversion to variance, where structural estimation of the utility function is common, higher order risk preferences are rarely estimated through structural models, primarily due to the lack of flexible and continuous higher order derivatives of common parametric functions. We propose a utility function derived from the Bézier curve, which is continuously differentiable for all derivatives, and allows us to structurally estimate risk aversion, prudence, and temperance. We demonstrate the value of estimating the intensity, not purely the sign, of higher order risk preferences using Bayesian econometric methods and experimental data that varies the mean, variance, skewness, and kurtosis of lotteries presented to subjects.