Exploring the stochastic production frontier in the presence of outliers: a simulation study

Technical efficiency measures the performance of an observation unit in generating outputs effectively. The stochastic production frontier (SPF), which is a commonly used method for this purpose, determines how close a unit is to achieving maximum output based on its inputs. However, the outliers in the data can distort the accuracy of SPF models. To address this issue, various error distribution modifications like gamma, Student’s-t, Weibull and Rayleigh distributions have been proposed. However, there is limited research comparing these distributions in handling outliers. This study describes a simulation conducted to compare five SPF models: Normal-half Normal, Normal-Gamma, Normal-Weibull, Normal-Rayleigh, and Student’s-t-half Normal. Applying simulated data across nine scenarios with varying data amounts and outlier percentages, the findings demonstrate that the SPF Student’s t-half Normal model provides the most accurate prediction of technical efficiency. Using a heavy-tailed distribution, such as the Student's t distribution, for the disturbance component is more effective in handling outliers in the response variable than modifying the inefficiency of the component distribution.