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A Monte Carlo study on multiple output stochastic frontiers: a comparison of two approaches

机译：蒙特卡洛研究多个输出随机前沿：两种方法的比较

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In the estimation of multiple output technologies in a primal approach, the main question is how to handle the multiple outputs. Often, an output distance function is used, where the classical approach is to exploit its homogeneity property by selecting one output quantity as the dependent variable, dividing all other output quantities by the selected output quantity, and using these ratios as regressors (OD). Another approach is the stochastic ray production frontier (SR), which transforms the output quantities into their Euclidean distance as the dependent variable and their polar coordinates as directional components as regressors. A number of studies have compared these specifications using real world data and have found significant differences in the inefficiency estimates. However, in order to get to the bottom of these differences, we apply a Monte-Carlo simulation. We test the robustness of both specifications for the case of a Translog output distance function with respect to different common statistical problems as well as problems arising as a consequence of zero values in the output quantities. Although our results show clear reactions to some statistical misspecifications, on average none of the approaches is clearly superior. However, considerable differences are found between the estimates at single replications. Taking average efficiencies from both approaches gives clearly better efficiency estimates than taking just the OD or the SR. In the case of zero values in the output quantities, the SR clearly outperforms the OD with observations with zero output quantities omitted and the OD with zero values replaced by a small positive number.
机译：在用原始方法估算多种输出技术时，主要问题是如何处理多种输出。通常，使用输出距离函数，其中经典方法是通过选择一个输出量作为因变量，将所有其他输出量除以选定的输出量，然后将这些比率用作回归变量（OD）来利用其同质性。另一种方法是随机射线产生边界（SR），它将输出量转换为它们的欧几里德距离作为因变量，并将其极坐标作为方向分量作为回归变量。许多研究已经使用现实世界的数据对这些规范进行了比较，并发现效率低下的估算值存在显着差异。但是，为了弄清这些差异的深处，我们应用了蒙特卡洛模拟。对于不同的常见统计问题以及由于输出量为零而导致的问题，我们针对Translog输出距离函数的情况测试了这两种规范的鲁棒性。尽管我们的结果显示出对某些统计错误规格的明确反应，但平均而言，这些方法均未明显优于其他方法。但是，在单次复制的估计之间发现了相当大的差异。与仅采用OD或SR相比，两种方法均获得平均效率显然可以提供更好的效率估算。在输出量为零的情况下，SR明显优于OD，而忽略了输出量为零的观测值，而零值的OD被小的正数代替。

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