Technical inefficiencies in stochastic frontier models can be thought of as non-negative parameters. Since, however, their number along with other parameters exceeds the sample size, an adaptive LASSO estimator is a reasonable way to overcome the problem, especially in view of the oracle properties of the estimator under broad conditions. It is shown that the adaptive LASSO estimator can be thought of as the posterior mean of a usual stochastic frontier model with a special prior that benchmarks inefficiencies on known quantities. We take these quantities from DEA scores to obtain technical inefficiencies having oracle properties. The LASSO parameters can be estimated routinely in the Bayesian context without the need for cross-validation. In an application to a data set of large U.S. banks we find that adaptive LASSO outperforms significantly traditional stochastic frontier models.