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Stochastic frontier models are widely used to measure, e.g., technical efficiencies of firms. The classical stochastic frontier model often suffers from the empirical artefact that the residuals of the production function may have a positive skewness, whereas a negative one is expected under the model, which leads to estimated full efficiencies of all firms. We propose a new approach to the problem by generalizing the distribution used for the inefficiency variable. This generalized stochastic frontier model allows the sample data to have the wrong skewness while estimating well-defined and non-degenerate efficiency measures. We discuss the properties of the model and its maximum likelihood estimator, and provide a simulation study to show that our model delivers estimators of efficiency with smaller mean squared error than those of the classical model even if the population skewness has the correct sign. Finally, we apply the model to data of the U.S. textile industry for 1958-2005, and show that for a number of years our model suggests efficiencies well below the frontier, while the classical one estimates no inefficiency in those years.
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Hafner, C., Manner, H., & Simar, L. (2013). The “wrong skewness” problem in stochastic frontier models: A new approach (ISBA Discussion Paper 2013/46). https://hdl.handle.net/2078.5/200452