The consistent biennial Malmquist productivity change index and ranking using the cross validation method

Narges Soltani () and Zijiang Yang
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Narges Soltani: York University
Zijiang Yang: York University

OR Spectrum: Quantitative Approaches in Management, 2025, vol. 47, issue 3, No 10, 1047-1069

Abstract: Abstract Measuring productivity changes is an important subject in evaluating time-series data using Data Envelopment Analysis (DEA). In this paper, we introduce the consistent biennial Malmquist Productivity Index (MPI) as an index for measuring the productivity change. It has one more advantage in addition to all favorable properties of the previous MPIs. It is calculated based on a single supporting hyperplane that does not change over the time for a unit. Since MPIs are used as a criterion to compare a unit with itself but not with other units, the hyperplane is chosen such that it is the best comparison base for the unit under evaluation over the time and it is not common among all units. For the cases that decision makers are interested to use MPIs as a criterion for ranking, we adjust the proposed index using the cross validation method such that it considers not only the results of self-evaluations, but also the results of peer-evaluations. We use a combination of principle component analysis and DEA as an aggregation function in the cross validation method. The proposed procedure to calculate the productivity changes and rank units is applied to the data set of eighteen Canadian power companies and the results are compared with the results of the conventional biennial MPI. We observe some cases with a reverse change in their productivity when we consider the common base for comparison over time.

Keywords: Data envelopment analysis; Biennial Malmquist productivity index; Common weight; Consistency; Ranking; Principal component analysis (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00291-025-00811-4

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