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 Stu-dent'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 in-dependence. We show that parameter estimates and efficiency predictions from robust specifications are significantly less sensitive to contaminating observations than those from non-robust specifications.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

The robustness of efficiency scores in decision-making units is important in managerial or regulatory benchmarking. However, the robustness of maximum likelihood estimation of stochastic frontier models has not been thoroughly explored. This study examines the influence function of the estimator in a stochastic frontier context and derives sufficient conditions for robust maximum likelihood estimation based on the properties of error component distributions and copula density. It is found that the canonical distributional assumptions do not satisfy these conditions. The Student's t noise distribution shows attractive properties and can be paired with a broad range of inefficiency distributions while satisfying the conditions under independence. The parameter estimates and efficiency predictions from robust specifications are less sensitive to contaminating observations compared to non-robust specifications.