Scale elasticity and technical efficiency measures in two-stage network production processes: an application to the insurance sector

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.