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Origin and Evolution of Malmquist Productivity Index: Review of the Literature Cover

Origin and Evolution of Malmquist Productivity Index: Review of the Literature

Central European Economic Journal
Volume 12 (2025): Issue 59 (January 2025)
By:
Open Access
|Apr 2025

Figures & Tables

Figure 1.

MI under VRS
MI under VRS

Figure 2.

Measuring Various Efficiency With the MI
Measuring Various Efficiency With the MI

Figure 3.

The Different Nature of Variables and Data Used by the MI
The Different Nature of Variables and Data Used by the MI

Figure 4.

Various Developments and Modifications of MI
Various Developments and Modifications of MI

Figure 5.

MI Development and Modification Pathways
MI Development and Modification Pathways

Assumptions of the Review

Periods 1990–2025
Database Scopus, Web of Science Core Collection, Semantic Scholar, ResearchGate.com, Academia.com, Google Scholar, search engine Google
Inclusion criteria

  • - Papers (articles and chapters) which were written in English

  • - Publication presenting new (theoretical assumptions) modifications and developments of the MI based on DEA methodology

Exclusion criteria

  • - Technical reports, doctoral theses, conference presentations, unofficial documents, working papers – “grey literature”, books

  • - Application (empirical) articles that do not present new (theoretical assumptions) modifications and developments of the MI

Search term used (keywords)

  • (1): Malmquist index OR Malmquist Productivity Index OR Productivity Index

  • AND

  • (2): decomposition OR constant returns to scale OR variable returns to scale OR radial OR non-radial OR network OR two-stage OR dynamic OR window OR cost OR profit OR revenue OR allocation OR negative data OR undesirable outputs OR interval data OR fuzzy data OR non-discretionary variable OR boostrap OR stochastic OR double frontiers OR weights OR distance function

Definitions of Different Types of Efficiency (Apart From Technical Efficiency)

Name of efficiency Definition
Cost efficiency (CE) “The cost efficiency of a producer using input vector x to produce output vector y when input prices are w is measured by the ratio of minimum cost to actual cost”.
Allocative efficiency (AE) “The input allocative efficiency of a producer using input vector x to produce output vector y when input prices are w is measured by the ratio of cost efficiency to input technical efficiency”. AE=CE/TE “The output allocative efficiency of a producer producing output vector y with input vector x when output prices are p is measured by the ratio of revenue efficiency to output technical efficiency”. AE= RE/TE
Revenue efficiency (RE) “The revenue efficiency of a producer producing output vector y with input vector x when output prices are p is measured by the ratio of maximum revenue to actual revenue”.
Profit efficiency (PE) “The profit efficiency of a producer facing input prices w and output prices p is measured by the ratio of maximum profit to actual profit”.
DOI: https://doi.org/10.2478/ceej-2025-0007 | Journal eISSN: 2543-6821 | Journal ISSN: 2544-9001
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Language: English
Page range: 102 - 119
Published on: Apr 11, 2025
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 1 times per year
Keywords:
Malmquist index,
productivity,
productivity index,
review,
DEA
Related subjects:
Business and economics,
Political economics,
Economic theory, systems and structures,
Microeconomics,
Macroeconomics,
Economic policy

© 2025 Łukasz Brzezicki, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 License.

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