The economic theory of producer behavior requires certain conditions to hold in order for a functional form to be representative of a production technology. Agricultural production studies are usually conducted using classical econometrics that do not allow for the imposition of curvature conditions in flexible functional forms. Therefore, some conditions required by economic theory do not hold globally in estimation. Some studies report the proportion of the sample for which curvature conditions do not hold, and the reader is warned about the unknown distorting effects that those data points might have on their final results.Bayesian methods allow for the imposition of first- and second-order restrictions in the estimation of flexible functional forms. We estimate a flexible representation of the US agricultural production technology using Bayesian econometrics under alternative sets of restrictions, and elaborate on the effects of the restrictions on the pdfs of the parameter estimates.