The standard total factor productivity index and its decomposition

The Malmquist productivity index is one of the best known and most widely used measures in the economic literature to quantify and decompose changes in productivity of multi-input multi-output production processes over time. Two main approaches are used to calculate this index: the adjacent Malmquist index and the base period Malmquist index. No base period is required to calculate the adjacent Malmquist index, but it fails to comply with the circularity property. The base period Malmquist index uses the technology of a base period and is circular, but the base period choice is arbitrary. There is, therefore, a trade-off between the choice of one or another version of the Malmquist index. The aim of this paper is to introduce a new total factor productivity index that is simultaneously circular and does not need to resort to a base period or ad hoc reference. To this end, we propose a new multi-input multi-output reference production technology for use as a standard for measuring and decomposing total factor productivity changes. The standard production technology is conceptually attractive because its parameterization is versatile and adaptable to the evolution of a set of firms performing any multi-input multi-output production process. Additionally, the new approach can bring about a true total factor productivity index, which can be decomposed into an output change and an input change.