Robust Maximum Likelihood Estimation of Stochastic Frontier Models

When analysing the efficiency of decision-making units, the robustness of efficiency scores to changes in the data is desirable, especially in the context of managerial or regulatory benchmarking. However, the robustness of maximum likelihood estimation of stochastic frontier models remains underexplored. We examine the behaviour of the influence function of the estimator in a stochastic frontier context, and derive some sufficient conditions for robust maximum likelihood estimation in terms of the properties of the marginal distributions of the error components and, in cases where they are dependent, the copula density. We find that the canonical distributional assumptions do not satisfy these conditions. The Student’s t noise distribution is found to have some particularly attractive properties which means it can be paired with a broad class of inefficiency distributions while still satisfying our conditions under independence. We show that parameter estimates and efficiency predictions from robust specifications are significantly less sensitive to contaminating observations than those from non-robust specifications.