Measuring utility is at the heart of microeconomics and has important applications in many areas of economics. Here we present a new experimental method to elicit utility functions and associated measures of (higher order) risk preferences. The method we propose builds on a non-parametric estimation technique called P-spline regression in order to obtain continuous and differentiable estimations of utility functions from any mapping of experimental income to utility levels. Using this method we can compute well-known theoretically derived measures of the intensities of risk aversion, prudence and temperance. We apply this method to study precautionary saving with a sample of poor households in Bogota: Leland (1968) suggests that under risky income prudent individuals increase savings as a precautionary measure. We obtain results comparable to those of earlier studies with respect to the classification of individuals as prudent or imprudent. In addition, our results strongly support the theoretical prediction that income risk leads to increases in savings for prudent individuals. An accompanying laboratory experiment validates our method: We find significant relations to other methods, and are able to replicate our finding with respect to precautionary saving.