The Many Decompositions of Total Factor Productivity Change

150 Pages Posted: 2 May 2018 Last revised: 24 Sep 2019

See all articles by Bert M. Balk

Bert M. Balk

RSM Erasmus University

José L. Zofío

Universidad Autónoma de Madrid; Erasmus Research Institute of Management (ERIM)

Date Written: April 4, 2018


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.

Keywords: Total Factor Productivity, Index, Decomposition, Malmquist, Moorsteen, Bjurek, Fisher, Törnqvist

JEL Classification: C43, D24, D61

Suggested Citation

Balk, Bert M. and Zofío, Jose L., The Many Decompositions of Total Factor Productivity Change (April 4, 2018). ERIM Report Series Paper, Available at SSRN: or

Bert M. Balk (Contact Author)

RSM Erasmus University ( email )

Burg Oudlaan 50
Rotterdam, 3062 PA


Jose L. Zofío

Universidad Autónoma de Madrid ( email )

Francisco Tomás y Valiente, 5
Madrid, Madrid 28049
914972406 (Phone)

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics