Polluting technologies can be represented using output distance functions. A common approach to estimating such functions is to factor out one of the outputs and estimate the resulting equation using well-known stochastic frontier estimation methods, including maximum likelihood. A problem with this approach is that the outputs that are not factored out may be correlated with the error term, leading to biased and inconsistent estimates. This paper addresses the problem in a Bayesian framework. The methodology is applied to data on U.S. electric utilities. Results include estimates of technical inefficiencies and the shadow price of a pollutant.