Random variation in output may lead to serious bias in cost function estimates. Despite the availability of simple, consistent instrumental variable estimators to deal with this problem, most empirical studies appear to have ignored this errors-in-variables problem, or dealt with it in an ad hoc manner. In this note, an instrumental variable approach is suggested, and applied to the estimation of cost-output relationships for a sample of irrigated citrus farms. Ordinary least squares was found to result in a statistically significant bias. Although this bias did not alter the economic interpretation of the results for the sample used, the bias is likely to be more serious for samples with greater chance variation in output. Thus, it is argued that all cost function studies should explicitly deal with this problem.