Measures of Productivity Change

  • Christopher J. O’DonnellEmail author


In this book, measures of productivity change are defined as measures of output quantity change divided by measures of input quantity change. Computing measures of output and input quantity change involves assigning numbers to baskets of outputs and inputs. The most distinguishing feature of this book is that it computes index numbers that are consistent with measurement theory. So please add the following to the end of this paragraph: Measurement theory says that so-called index numbers must be assigned in such a way that the relationships between the numbers mirror the relationships between the baskets. This chapter explains how to compute output and input quantity index numbers (and therefore productivity index numbers) that are consistent with measurement theory.


  1. Aczel J, Eichhorn W (1974) A note on additive indices. J Econ Theory 8(4):525–529Google Scholar
  2. Anik AR, Rahman S, Sarker J (2017) Agricultural productivity growth and the role of capital in South Asia (1980–2013). Sustainability 9(3):470Google Scholar
  3. Arjomandi A, Valadkhani A, O’Brien M (2014) Analysing banks’ intermediation and operational performance using the Hicks-Moorsteen TFP index: the case of Iran. Res Int Bus Finance 30:111–125Google Scholar
  4. Arjomandi A, Salleh MI, Mohammadzadeh A (2015) Measuring productivity change in higher education: an application of Hicks-Moorsteen total factor productivity index to Malaysian public universities. J Asia Pac Econ 20(4):630–643Google Scholar
  5. Arora H, Arora P (2013) Measuring and decomposing productivity change using Hicks-Moorsteen index numbers: evidence from Indian banks. Int J Prod Qual Manag 11(1):74–95Google Scholar
  6. Balk B (1998) Industrial price, quantity, and productivity indices: the micro-economic theory and an application. Kluwer Academic Publishers, BostonGoogle Scholar
  7. Balk B (2008) Price and quantity index numbers: models for measuring aggregate change and difference. Cambridge University Press, New YorkGoogle Scholar
  8. Balk B, Diewert W (2003) The Lowe consumer price index and its substitution bias. Department of Economics Discussion Paper 04-07, University of British ColombiaGoogle Scholar
  9. Ball V, Hallahan C, Nehring R (2004) Convergence of productivity: an analysis of the catch-up hypothesis within a panel of states. Am J Agric Econ 86(5):1315–1321Google Scholar
  10. Bao H (2014) Provincial total factor productivity in Vietnamese agriculture and its determinants. J Econ Dev 16(2):5–20Google Scholar
  11. Baráth L, Fertö I (2017) Productivity and convergence in European agriculture. J Agric Econ 68(1):228–248Google Scholar
  12. Beavis B, Dobbs I (1990) Optimization and stability theory for economic analysis. Cambridge University Press, CambridgeGoogle Scholar
  13. Bjurek H (1996) The Malmquist total factor productivity index. Scand J Econ 98(2):303–313Google Scholar
  14. Blancas F, Contreras I, Ramirez-Hurtado J (2013) Constructing a composite indicator with multiplicative aggregation under the objective of ranking alternatives. J Oper Res Soc 64(5):668–678Google Scholar
  15. Briec W, Kerstens K (2011) The Hicks-Moorsteen productivity index satisfies the determinateness axiom. Manch Sch 79(4):765–775Google Scholar
  16. Briec W, Kerstens K, Prior D, Van de Woestyne I (2018) Testing general and special Färe-Primont indices: a proposal for public and private sector synthetic indices of European regional expenditures and tourism. Eur J Oper Res (forthcoming)Google Scholar
  17. Carrington R, O’Donnell C, Rao D (2016) Australian university productivity growth and public funding revisited. Stud High Educ pp 1–22.,079.2016.1259,306
  18. Caves D, Christensen L, Diewert W (1982a) The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica 50(6):1393–1414Google Scholar
  19. Caves D, Christensen L, Diewert W (1982b) Multilateral comparisons of output, input, and productivity using superlative index numbers. Econ J 92(365):73–86Google Scholar
  20. Chambers R, Färe R, Grosskopf S (1996) Productivity growth in APEC countries. Pac Econ Rev 1(3):181–190Google Scholar
  21. Cherchye L, Moesen W, Rogge N, van Puyenbroeck T (2007) An introduction to ‘benefit of the doubt’ composite indicators. Soc Indic Res 82(1):111–145Google Scholar
  22. Cherchye L, Moesen W, Rogge N, van Puyenbroeck T, Saisana M, Saltelli A, Liska R, Tarantola S (2008) Creating composite indicators with DEA and robustness analysis: the case of the Technology Achievement Index. J Oper Res Soc 59(2):239–251Google Scholar
  23. Coelli T, Rao D (2005) Total factor productivity growth in agriculture: a Malmquist index analysis of 93 countries, 1980–2000. Agric Econ 32(s1):115–134Google Scholar
  24. Coelli T, Rao D, O’Donnell C, Battese G (2005) An introduction to efficiency and productivity analysis, 2nd edn. Springer, New YorkGoogle Scholar
  25. Dakpo K, Desjeax Y, Latruffe L (2016) Productivity: indices of productivity using Data Envelopment Analysis (DEA). R Package Version 0.1.0,
  26. Daraio C, Simar L (2007) Advanced robust and nonparametric methods in efficiency analysis: methodology and applications. Springer, BerlinGoogle Scholar
  27. Deaza J, Gilles E, Vivas A (2016) Productivity measurements for South Korea and three countries of the Pacific Alliance: Colombia, Chile and Mexico, 2008–2012. Appl Econ Int Dev 16(2):75–92Google Scholar
  28. Despotis D (2005) A reassessment of the Human Development Index via data envelopment analysis. J Oper Res Soc 56(8):969–980Google Scholar
  29. Diewert W (1976) Exact and superlative index numbers. J Econ 4(2):115–145Google Scholar
  30. Diewert W (1992) Fisher ideal output, input, and productivity indexes revisited. J Prod Anal 3(3):211–248Google Scholar
  31. Diewert W, Fox K (2017) Decomposing productivity indexes into explanatory factors. Eur J Oper Res 256(1):275–291Google Scholar
  32. Drechsler L (1973) Weighting of index numbers in multilateral international comparisons. Rev Income Wealth 19(1):17–34Google Scholar
  33. Economic Inisights (2014) Economic benchmarking assessment of operating expenditure for NSW and Tasmanian electricity TNSPs. Report prepared by Denis Lawrence, Tim Coelli and John Kain for the Australian Energy RegulatorGoogle Scholar
  34. Elnasri A, Fox K (2017) The contribution of research and innovation to productivity. J Prod Anal 47(3):291–308Google Scholar
  35. Elteto O, Koves P (1964) On a problem of index number computation relating to international comparison. Statisztikai Szemle 42:507–518Google Scholar
  36. Färe R, Grosskopf S (1990) The Fisher ideal index and the indirect Malmquist productivity index: a comparison. New Zealand Econ Pap 24(1):66–72Google Scholar
  37. Färe R, Primont D (1995) Multi-output production and duality: theory and applications. Kluwer Academic Publishers, BostonGoogle Scholar
  38. Färe R, Grosskopf S, Lindgren B, Roos P (1992) Productivity changes in Swedish pharmacies 1980–1989: a non-parametric Malmquist approach. J Prod Anal 3:85–101Google Scholar
  39. Färe R, Grosskopf S, Norris M, Zhang Z (1994) Productivity growth, technical progress, and efficiency change in industrialized countries. Am Econ Rev 84(1):66–83Google Scholar
  40. Fisher I (1922) The making of index numbers. Houghton Mifflin, BostonGoogle Scholar
  41. Fissel B, Felthoven R, Kaperski S, O’Donnell C (2015) Decomposing productivity and efficiency changes in the Alaska head and gut factory trawl fleet. Mar Policy.
  42. Fox K, Grafton Q, Kirkley J, Squires D (2003) Property rights in a fishery: regulatory change and firm performance. J Environ Econ Manage 46(1):156–177Google Scholar
  43. Grifell-Tatjé E, Lovell C (1995) A note on the Malmquist productivity index. Econ Lett 47:169–175Google Scholar
  44. Hicks J (1961) Measurement of capital in relation to the measurement of other economic aggregates. Macmillan, LondonGoogle Scholar
  45. Hill P (2008) Lowe indices. In: Paper presented at the 2008 World Congress on national accounts and economic performance measures for nations, Washington, DCGoogle Scholar
  46. Hill R, Griffiths W, Lim G (2011) Principles of econometrics, 4th edn. Wiley, HobokenGoogle Scholar
  47. Hosch W (ed) (2011) The britannica guide to numbers and measurement, 1st edn. Britannica Educational Publishing, ChicagoGoogle Scholar
  48. IMF (2004) Producer price index manual: theory and practice. published for the ILO, IMF, OECD, UNECE and World Bank by the International Monetary Fund, Washington, DCGoogle Scholar
  49. Islam N, Xayavong V, Kingwell R (2014) Broadacre farm productivity and profitability in South-Western Australia. Aust J Agric Resour Econ 58(2):147–170Google Scholar
  50. Kerstens K, Van de Woestyne I (2014) Comparing the Malmquist and Hicks-Moorsteen productivity indices: Exploring the impact of unbalanced versus balanced panel data. Eur J Oper Res 233:749–758Google Scholar
  51. Khan F, Salim R, Bloch H (2015) Nonparametric estimates of productivity and efficiency change in Australian broadacre agriculture. Aust J Agric Resour Econ 59(3):393–411Google Scholar
  52. Khan F, Salim R, Bloch H, Islam N (2017) The public R&D and productivity growth in Australia’s broadacre agriculture: Is there a link? Aust J Agric Resour Econ 61(2):285–303Google Scholar
  53. Kuosmanen T, Sipiläinen T (2009) Exact decomposition of the Fisher ideal total factor productivity index. J Prod Anal 31(3):137–150Google Scholar
  54. Laurenceson J, O’Donnell CJ (2014) New estimates and a decomposition of provincial productivity change in China. China Econ Rev 30:86–97Google Scholar
  55. Lawrence D, Diewert W, Fox K (2006) The contributions of productivity, price changes and firm size to profitability. J Prod Anal 26(1):1–13Google Scholar
  56. Mahlberg B, Obersteiner M (2001) Remeasuring the HDI by data envelopment analysis. Interim Report IR-01-069, International Institute for Applied Systems Analysis (IIASA), Laxenburg, AustriaGoogle Scholar
  57. Maniadakis N, Thanassoulis E (2004) A cost Malmquist productivity index. Eur J Oper Res 154(2):396–409Google Scholar
  58. Melyn W, Moesen W (1991) Towards a synthetic indicator of macroeconomic performance: unequal weighting when limited information is available. Public Economics Research Paper 17, CES, KU LeuvenGoogle Scholar
  59. Mizobuchi H (2017) Productivity indexes under Hicks neutral technical change. J Prod Anal 48:63–68Google Scholar
  60. Moorsteen R (1961) On measuring productive potential and relative efficiency. Q J Econ 75(3):151–167Google Scholar
  61. Mugera A, Langemeier M, Ojede A (2016) Contributions of productivity and relative price change to farm-level profitability change. Am J Agric Econ 98(4):1210–1229Google Scholar
  62. O’Donnell C (2010a) DPIN version 1.0: A program for decomposing productivity index numbers. Centre for Efficiency and Productivity Analysis Working Papers WP01/2010, University of QueenslandGoogle Scholar
  63. O’Donnell C (2010b) Measuring and decomposing agricultural productivity and profitability change. Aust J Agric Resour Econ 54(4):527–560Google Scholar
  64. O’Donnell C (2012a) An aggregate quantity framework for measuring and decomposing productivity change. J Prod Anal 38(3):255–272Google Scholar
  65. O’Donnell C (2012b) Alternative indexes for multiple comparisons of quantities and prices. Centre for Efficiency and Productivity Analysis Working Papers WP05/2012 (Version 21 May 2013), University of QueenslandGoogle Scholar
  66. O’Donnell C (2012c) Nonparametric estimates of the components of productivity and profitability change in U.S. agriculture. Am J Agric Econ 94(4):873–890Google Scholar
  67. O’Donnell C (2013) Econometric estimates of productivity and efficiency change in the Australian northern prawn fishery. In: Mamula A, Walden J (eds) Proceedings of the National Marine Fisheries Service Workshop, U.S. Department of Commerce National Oceanic and Atmospheric AdministrationGoogle Scholar
  68. O’Donnell C (2014) Econometric estimation of distance functions and associated measures of productivity and efficiency change. J Prod Anal 41(2):187–200Google Scholar
  69. O’Donnell C (2016) Using information about technologies, markets and firm behaviour to decompose a proper productivity index. J Econ 190(2):328–340Google Scholar
  70. O’Donnell C, Nguyen K (2013) An econometric approach to estimating support prices and measures of productivity change in public hospitals. J Prod Anal 40(3):323–335Google Scholar
  71. Pan M, Walden J (2015) Measuring productivity in a shared stock fishery: a case study of the Hawaii longline fishery. Mar Policy 62:302–308Google Scholar
  72. Rahman S (2007) Regional productivity and convergence in Bangladesh agriculture. J Dev Areas 41(1):221–236Google Scholar
  73. Ray S, Mukherjee K (1996) Decomposition of the Fisher ideal index of productivity: a non-parametric dual analysis of US airlines data. Econ J 106(439):1659–1678Google Scholar
  74. Samuelson P, Swamy S (1974) Invariant economic index numbers and canonical duality: survey and synthesis. Am Econ Rev 64(4):566–593Google Scholar
  75. Sarle W (1997) Measurement theory: frequently asked questions.
  76. See K, Coelli T (2013) Estimating and decomposing productivity growth of the electricity generation industry in Malaysia: a stochastic frontier analysis. Energy Policy 62(207–214)Google Scholar
  77. See K, Li F (2015) Total factor productivity analysis of the UK airport industry: a Hicks-Moorsteen index method. J Air Transp Manag 43(March):1–10Google Scholar
  78. Sheng Y, Mullen J, Zhao S (2011) A turning point in agricultural productivity: consideration of the causes. Research Report 11.4, Australian Bureau of Agricultural and Resource Economics and SciencesGoogle Scholar
  79. Silva Portela M, Thanassoulis E (2006) Malmquist indexes using a geometric distance function (GDF). Application to a sample of Portuguese bank branches. J Prod Anal 25(1):25–41Google Scholar
  80. Suhariyanto K, Thirtle C (2001) Asian agricultural productivity and convergence. J Agric Econ 52(3):96–110Google Scholar
  81. Szulc B (1964) Indices for multi-regional comparisons. Prezeglad Statystyczny (Stat Rev) 3:239–254Google Scholar
  82. Tal E (2016) Measurement in science. In: Zalta EN (ed) The Stanford encyclopedia of philosophy, winter, 2016th edn. Stanford University, Metaphysics Research LabGoogle Scholar
  83. Tozer P, Villano R (2013) Decomposing productivity and efficiency among Western Australian grain producers. J Agric Resour Econ 38(3):312–326Google Scholar
  84. Worthington A, Lee B (2008) Efficiency, technology and productivity change in Australian universities, 1998–2003. Econ Educ Rev 27(3):285–298Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.University of QueenslandBrisbaneAustralia

Personalised recommendations