Interval Network Malmquist Productivity Index for Examining Productivity Changes of Insurance Companies under Data Uncertainty: A Case Study

The insurance industry is one of the important financial institutions that has a significant place in the economic growth and development of the country. Given the industry's influential role in the financial markets, it is imperative to evaluate the performance and calculate changes in insurance companies' productivity over time. It is necessary to explain that the internal structure of insurance companies can be considered as a two-stage process involving marketing and investment. The purpose of the current study is to propose a novel approach to calculate the changes in insurance companies' productivity by considering their two-stage structure as well as the inherent uncertainties in the data. It should be noted that in order to propose of new interval network Malmquist Productivity Index, the network data envelopment analysis approach (NDEA), Malmquist productivity index (MPI), and interval programming are applied. The implementation of the proposed research approach is also evaluated using real data of 10 insurance companies in Iran. According to the obtained results, most of the companies have regressed from the first stage and marketing perspective, but in the second stage and from the investment perspective, the majority of companies have represented an acceptable improvement in their productivity.