A toolbox for calculating and decomposing Total Factor Productivity indices

• Published in: Computers & operations research 2020-03, Vol.115, p.104853, Article 104853
• Main Authors: Balk, Bert M., Barbero, Javier, Zofío, José L.
• Format: Article
• Language: English
• Subjects: Data envelopment analysis; Decomposition; Fisher; Malmquist; Mathematical analysis; Moorsteen–Bjurek; Operations research; Productivity; Total factor productivity; Törnqvist
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2019.104853

•TFP toolbox is a new set of functions to calculate the main Total Factor Productivity indices.•Quantity only indices (Malmquist and Moorsteen-Bjurek) as well as price-based indices (Fisher and Trnqvist) can be calculated and decomposed.•The toolbox relies on Data Envelopment Analysis mathematical programming techniques to calculate the different indices.•The paper describes both the underlying theory and illustrates the use of the toolbox with USDA publicly available data.•All supplemental material (including code and data) is available at www.tfptoolbox.com for editing and replicability. Total Factor Productivity Toolbox is a new set of functions to calculate the main Total Factor Productivity (TFP) indices and their decompositions, based on Shephard’s distance functions, and using Data Envelopment Analysis (DEA) programming techniques. The package includes code for the standard Malmquist, Moorsteen–Bjurek, price-weighted and share-weighted TFP indices, allowing for the choice of orientation (input or output), reference period (base, comparison, geometric mean), returns to scale (variable or constant), and specific decompositions (aggregate, or identifying scale effects, as well as input and output mix effects). Classic definitions of TFP corresponding to the Laspeyres, Paasche, Fisher, or Törnqvist formulas can also be calculated as particular cases. This paper describes the methodology and implementation of the productivity functions in MATLAB. We compare the results corresponding to the different definitions by studying productivity trends in the US agriculture at the individual state level.