Journal of Productivity Analysis

, Volume 46, Issue 2–3, pp 109–119 | Cite as

Multi-directional productivity change: MEA-Malmquist

  • Mette AsmildEmail author
  • Tomas Baležentis
  • Jens Leth Hougaard


In this paper we introduce an extension of the Malmquist total factor productivity index, which utilizes the Multi-directional Efficiency Analysis approach. This enables variable-specific analysis of productivity change as well as its components (efficiency change and technical change). The new approach is illustrated and compared to the conventional Data Envelopment Analysis Malmquist approach by considering a empirical data set on Lithuanian family farms. The results highlight that important differences in variable-specific performance of the farms can be hidden when using the conventional (radial) Data Envelopment Analysis-based Malmquist index.


Total factor productivity Malmquist TFP index Multi-directional efficiency analysis Agricultural efficiency 

JEL classification

C430 C440 C610 Q100 Q120 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests.

Supplementary material

11123_2016_486_MOESM1_ESM.pdf (266 kb)
Supplementary Appendix


  1. Aparicio J, Pastor JT (2014) On how to properly calculate the Euclidean distance-based measure in DEA. Optimization 63(3):421–432CrossRefGoogle Scholar
  2. Aparicio J, Ruiz JL, Sirvent I (2007) Closest targets and minimum distance to the Pareto-efficient frontier in DEA. J Prod Anal 28(3):209–218CrossRefGoogle Scholar
  3. Asmild M, Baležentis T, Hougaard JL (2016) Multi-directional program efficiency: the case of Lithuanian family farms. J Prod Anal 45:23–33CrossRefGoogle Scholar
  4. Asmild M, Hougaard JL, Kronborg D, Kvist HK (2003) Measuring inefficiency via potential improvements. J Prod Anal 19(1):59–76CrossRefGoogle Scholar
  5. Asmild M, Matthews K (2012) Multi-directional efficiency analysis of efficiency patterns in Chinese banks 1997-2008. Eur J Oper Res 219:434–441CrossRefGoogle Scholar
  6. Asmild M, Tam F (2007) Estimating global frontier shifts and global Malmquist indices. J Prod Anal 27:137–148CrossRefGoogle Scholar
  7. Baek C, Lee JD (2009) The relevance of DEA benchmarking information and the least-distance measure. Math Comput Model 49(1):265–275CrossRefGoogle Scholar
  8. Balezentis T, De Witte K (2015) One-and multi-directional conditional efficiency measurement-efficiency in Lithuanian family farms. Eur J Oper Res 245:612–622CrossRefGoogle Scholar
  9. Balk B (2013) Industrial price, quantity, and productivity indices: The micro-economic theory and an application. Springer Science & Business Media New YorkGoogle Scholar
  10. Berg SA, Førsund FR, Jansen ES (1992) Malmquist indices of productivity growth during the deregulation of Norwegian banking, 1980-89. Scand J Econ 94:211–228CrossRefGoogle Scholar
  11. Bogetoft P, Hougaard JL (1999) Efficiency evaluations based on potential (non-proportional) improvements. J Prod Anal 12:233–247CrossRefGoogle Scholar
  12. Bogetoft P, Hougaard JL (2004) Super efficiency evaluations based on potential slack. Eur J Oper Res 152:14–21CrossRefGoogle Scholar
  13. Bojnec S, Latruffe L (2008) Measures of farm business efficiency. Ind Manage Data Syst 108:258–270CrossRefGoogle Scholar
  14. Briec W (1999) Hölder distance function and measurement of technical efficiency. J Prod Anal 11:111–131CrossRefGoogle Scholar
  15. Briec W, Kerstens K (2009) Infeasibilities in directional distance functions: with application to the determinateness of the Luenberger productivity indicator. J Optim Theory Appl 141:55–73CrossRefGoogle Scholar
  16. Chambers C, Miller A (2014) Inefficiency measurement. Am Econ J 6:79–92Google Scholar
  17. Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2(6):429–444CrossRefGoogle Scholar
  18. Chen Y (2003) A non-radial Malmquist productivity index with an illustrative application to Chinese major industries. Int J Prod Econ 83(1):27–35CrossRefGoogle Scholar
  19. Christensen F, Hougaard JL, Keiding H (1999) An axiomatic characterization of efficiency indices. Econ Lett 63:33–37CrossRefGoogle Scholar
  20. Chung YH, Färe R, Grosskopf S (1997) Productivity and undesirable outputs: a directional distance function approach. J Environ Manage 51:229–240CrossRefGoogle Scholar
  21. Coelli T (1998) A multi-stage methodology for the solution of orientated DEA models. Oper Res Lett 23(3):143–149CrossRefGoogle Scholar
  22. Coelli TJ, Rao DSP (2005) Total factor productivity growth in agriculture: a Malmquist index analysis of 93 countries, 1980–2000. Agric Econ 32(s1):115–134CrossRefGoogle Scholar
  23. Cooper WW, Park KS, Pastor JT (1999) RAM: a range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. J Prod Anal 11(1):5–42CrossRefGoogle Scholar
  24. European Commission (2014) FADN public database.
  25. Farrell MJ (1957) The measurement of technical efficiency. J R Stat Soc 120(3):253–281. Series A, GeneralGoogle Scholar
  26. Frei FX, Harker PT (1999) Projections onto efficient frontiers: theoretical and computational extensions to DEA. J Prod Anal 11(3):275–300CrossRefGoogle Scholar
  27. Fukuyama H, Masaki H, Sekitani K, Shi J (2014) Distance optimization approach to ratio-form efficiency measures in data envelopment analysis. J Prod Anal 42:175–186CrossRefGoogle Scholar
  28. Färe R, Grosskopf S, Lindgren B, Roos P (1992) Productivity changes in Swedish pharamacies 1980–1989: a non-parametric Malmquist approach. In: Gulledge TT, Lovell CAK (eds) International Applications of Productivity and Efficiency Analysis. Springer, The NetherlandsGoogle Scholar
  29. Färe R, Grosskopf S, Margaritis D (2008) Efficiency and productivity: Malmquist and more. In: Fried HO, Lovell CAK, Schmidt SS (eds.) The Measurement of Productive Efficiency and Productivity Growth. Oxford University Press, New YorkGoogle Scholar
  30. Färe R, Grosskopf S, Norris M (1997) Productivity growth, technical progress, and efficiency change in industrialized countries: reply. Am Econ Rev 87(5):1040–1044Google Scholar
  31. Färe R, Grosskopf S, Norris M, Zhang Z (1994) Productivity growth, technical progress, and efficiency change in industrialized countries. Am Econ Rev 84:66–83Google Scholar
  32. Färe R, Knox Lovell CA (1978) Measuring the technical efficiency of production. J Econ Theory 19(1):150–162CrossRefGoogle Scholar
  33. Hougaard JL, Keiding H (1998) On the functional form of an efficiency index. J Prod Anal 9(2):103–111CrossRefGoogle Scholar
  34. Kapelko M, Lansink AO (2017) Dynamic multi-directional inefficiency analysis of European dairy manufacturing firms. Eur J Oper Res 257(1):338–344Google Scholar
  35. Kimura S, Le Thi C (2013) Cross country analysis of farm economic performance, OECD Food, Agriculture and Fisheries Papers, No. 60, OECD Publishing. doi:  10.1787/5k46ds9ljxkj-en
  36. Lithuanian Institute of Agrarian Economics (2012) Ukiu veiklos rezultatai (UADT tyrimo duomenys) 2011 [FADN survey results 2011]. Lietuvos agrarines ekonomikos institutas, Vilnius, Lithuania, ISSN 2029-1221Google Scholar
  37. Ministry of Agriculture of the Republic of Lithuania (2007) Rural Development Programme for Lithuania 2007–2013. 19 September 2007.
  38. Odeck J (2006) Identifying traffic safety best practice: an application of DEA and Malmquist indices. Omega 34(1):28–40CrossRefGoogle Scholar
  39. Pastor JT, Asmild M, Lovell CAK (2011) The Biennial Malmquist Productivity Change Index, Socio-Economic Planning. Science 45:10–15Google Scholar
  40. Pastor JT, Lovell CAK (2005) A global Malmquist productivity index. Econ Lett 88(2):266–271CrossRefGoogle Scholar
  41. Pastor JT, Ruiz JL, Sirvent I (1999) An enhanced DEA Russell graph efficiency measure. Eur J Oper Res 115(3):596–607CrossRefGoogle Scholar
  42. Portela MCAS, Borges PC, Thanassoulis E (2003) Finding closest targets in non-oriented DEA models: the case of convex and non-convex technologies. J Prod Anal 19(2–3):251–269CrossRefGoogle Scholar
  43. Portela MCAS, Thanassoulis E (2006) Malmquist indexes using a geometric distance function (GDF). Application to a sample of Portuguese bank branches. J Prod Anal 25(1–2):25–41CrossRefGoogle Scholar
  44. Ray SC, Desli E (1997) Productivity growth, technical progress, and efficiency change in industrialized countries: comment. Am Econ Rev 87(5):1033–1039Google Scholar
  45. Ray SC, Ghose A (2014) Production efficiency in Indian agriculture: an assessment of the post green revolution years. Omega 44:58–69CrossRefGoogle Scholar
  46. Russell RR (1990) Continuity of measures of technical efficiency. J Econ Theory 51:255–267CrossRefGoogle Scholar
  47. Russell RR, Schworm W (2009) Axiomatic foundation of efficiency measurement on data-generated technologies. J Prod Meas 31:77–86Google Scholar
  48. Russell RR, Schworm W (2011) Properties of efficiency measures on input, output space. J Prod Anal 36:143–156CrossRefGoogle Scholar
  49. Tone K (2001) A slacks-based measure of efficiency in data envelopment analysis. Eur J Oper Res 130(3):498–509CrossRefGoogle Scholar
  50. Wang K, Wei YM, Zhang X (2013) Energy and emissions efficiency patterns of Chinese regions: a multi-directional efficiency analysis. Appl Energy 104:105–116CrossRefGoogle Scholar
  51. Zieschang KD (1984) An extended Farrell technical efficiency index. J Econ Theory 33:387–396CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.IFRO, University of CopenhagenFrederiksbergDenmark
  2. 2.Lithuanian Institute of Agrarian EconomicsVilniusLithuania

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