The Many Decompositions of Total Factor Productivity Change

Total factor productivity change, here defined as output quantity change divided by input quantity change, is the combined result of (technical) efficiency change, technological change, a scale effect, and input and output mix effects. Sometimes allocative efficiency change is supposed to also play a role. Given a certain functional form for the productivity index, the problem is how to decompose such an index into factors corresponding to these five or six components. A basic insight offered in the present paper is that meaningful decompositions of productivity indices can only be obtained for indices which are transitive in the main variables. Using a unified approach, we obtain decompositions for Malmquist, Moorsteen-Bjurek, price-weighted, and share-weighted productivity indices. A unique feature of this paper is that all the decompositions are applied to the same dataset of a real-life panel of decision-making units so that the extent of the differences between the various decompositions can be judged