We propose estimation of a stochastic production frontier model within a Bayesian framework to obtain the posterior distribution of single-input-oriented technical efficiency at the firm level. The proposed method is applicable to the estimation of environmental efficiency of agricultural production when the technology interaction with the environment is modeled via public inputs such as soil quality and environmental conditions. All computations are carried out using Markov chain Monte Carlo methods. We illustrate the approach by applying it to production data from Ukrainian collective farms.