In this paper we consider a novel stochastic frontier model with multi-output multi-input production technology that accommodates non-radial inefficiency in both inputs and outputs. These measures are also observation-specific. To identify them, we use (i) a system model consisting of the revenue and cost share equations derived from the profit function and (ii) distributional assumptions on the inefficiency components and the noise terms. The error vector of the system is shown to have a closed skew normal distribution that is used to derive the likelihood function. The ML estimator of the parameters is used to derive formulas for predicting output- and input-specific inefficiencies, which are also observation-specific. We showcase the working of our model by applying it to a farm level data with two inputs and two outputs from Norway.

在本文中，我们考虑了一种具有多输出多输入生产技术的新型随机前沿模型，该模型可同时适应输入和输出中的非径向效率低下的问题。这些措施也是特定于观察的。为了识别它们，我们使用（i）一个系统模型，该模型包括从利润函数得出的收入和成本份额方程式，以及（ii）对低效率成分和噪声项的分布假设。系统的误差向量显示为具有封闭的偏斜正态分布，用于导出似然函数。参数的ML估计器用于推导用于预测特定于输出和输入的低效率的公式，这些效率也是特定于观察的。我们通过将模型应用于来自挪威的两个输入和两个输出的农场级数据来展示我们模型的工作原理。