In performance analysis with tools such as data envelopment analysis, calculations of scale properties of the frontier points are studied using both qualitative and quantitative approaches. When the production process is a bit complicated, the calculation needs to be modified. Most existing studies are focused on a single-stage production process under the constant or variable returns to scale specification. However, some processes have two-stage structures, and, in such processes, the concepts of scale elasticity and returns to scale are inextricably related to the conditions of the stages of production. Thus, an evaluation of efficiency, scale elasticity, and returns to scale is sensitive to stages. In this study, we introduced a procedure to calculate technical efficiency and scale elasticity in a two-stage parallel-series production system. Then, our proposed technical efficiency and scale elasticity programs are applied to real data on 20 insurance companies in Iran. After applying our estimations to a real-world insurance industry, we found that, (i) overall, the total inputs of insurers in the life insurance sector should be reduced by 9%. Moreover, the inputs of nonlife insurers should be reduced by 50%. The final output in the investment sector must be increased by 48%. (ii) There are inefficiencies among all insurers in the investment sector, and to improve technical efficiency, the income from investments should be increased significantly. (iii) Finally, the efficiency and elasticity characterizations of insurers are directly subject to stages.

中文翻译：

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两阶段网络生产过程中的规模弹性和技术效率措施：在保险业的应用

在使用数据包络分析等工具进行性能分析时，使用定性和定量方法研究前沿点尺度属性的计算。当生产过程有点复杂时，需要修改计算。大多数现有研究都集中在恒定或可变规模收益规范下的单阶段生产过程。然而，有些过程具有两阶段结构，在这种过程中，规模弹性和规模报酬的概念与生产阶段的条件有着密不可分的关系。因此，效率、规模弹性和规模回报的评估对阶段很敏感。在本研究中，我们介绍了计算两阶段并串联生产系统中的技术效率和规模弹性的程序。然后，我们提出的技术效率和规模弹性计划应用于伊朗 20 家保险公司的真实数据。将我们的估计应用于现实世界的保险行业后，我们发现，(i)总体而言，保险公司在寿险行业的总投入应减少9%。此外，非寿险公司的投入应减少50%。投资部门的最终产出必须增加48%。（二）各保险公司在投资领域均存在效率低下的问题，要提高技术效率，应大幅提高投资收益。(iii) 最后，保险公司的效率和弹性特征直接受阶段影响。