The “wrong skewness” problem in stochastic frontier models: A new approach
针对随机前沿模型中残差偏度方向与模型预期相反导致效率估计失效的问题，提出通过推广无效率项分布来修正模型，使数据即使出现“错误偏度”也能得到合理的效率估计，并通过模拟和美国纺织业数据验证了方法的有效性。
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 nondegenerate efficiency measures. We discuss the statistical properties of the model, and we discuss a test for the symmetry of the error term (no inefficiency). We provide a simulation study to show that our model delivers estimators of efficiency with smaller bias 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 technical efficiencies well below the frontier while the classical one estimates no inefficiency in those years.