Applied decompositions of Malmquist, cost Malmquist, and allocation Malmquist indices by considering changes in cost efficiency and technology

So far, various decompositions of the Malmquist productivity growth index have been presented. Although factors such as efficiency, scale, and technology have already been examined, there is no factor measures productivity growth from a financial perspective by covering costs. The purpose of this article is to show the impact of cost efficiency changes as an important component on the productivity growth indices. This article evaluates the rate of productivity growth in the cost space and decomposes the Malmquist productivity growth index into components of cost efficiency and allocative efficiency. Then a similar Decomposition for the cost Malmquist index, and the allocation Malmquist index based on changes in cost efficiency and price effect is obtained. In the following, we obtain the relation between the Malmquist index, the Cost Malmquist index, and the allocation Malmquist index with changes in technology and cost efficiency. Then we model, and calculate the parsing factors of Malmquist indices related to decision-making units using data envelopment analysis and input distance functions. Finally, the data obtained from a real case study are modeled and compared the results of previous Malmquist indices with the new Malmquist indices and the preference of new decompositions has been analyzed.