Generalised commensurability properties of efficiency measures: Implications for productivity indicators

Walter Briec, Audrey Dumas, Kristiaan Kerstens and Agathe Stenger

European Journal of Operational Research, 2022, vol. 303, issue 3, 1481-1492

Abstract: We analyse the role of new weak and strong commensurability conditions on efficiency measures and especially on productivity measurement. If strong commensurability fails, then a productivity index (indicator) may exhibit a homogeneity bias yielding inconsistent and contradictory results. In particular, we show that the Luenberger productivity indicator is sensitive to proportional changes in the input-output quantities, while the Malmquist productivity index is not affected by such changes. This is due to the homogeneity degree of the directional distance function under constant returns to scale. In particular, the directional distance function only satisfies the weak commensurability axiom in general. However, if the directional distance function is a diagonally homogeneous function of the technology, then the directional distance function satisfies strong commensurability. This explains why the direction of an arithmetic mean of the observed data works well. Numerical examples and an empirical illustration are proposed. Under a translation homothetic technology, the Luenberger productivity indicator is not affected by any additive directional transformation of the observations.

Keywords: Malmquist and Luenberger productivity; Directional and proportional distance function; Weak and strong commensurability (search for similar items in EconPapers)
JEL-codes: C43 C67 D24 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Working Paper: Generalised Commensurability Properties of Efficiency Measures: Implications for Productivity Indicators (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:303:y:2022:i:3:p:1481-1492

DOI: 10.1016/j.ejor.2022.03.037

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