IDEAS home Printed from https://ideas.repec.org/a/kap/jproda/v38y2012i3p255-272.html
   My bibliography  Save this article

An aggregate quantity framework for measuring and decomposing productivity change

Author

Abstract

Total factor productivity (TFP) can be defined as the ratio of an aggregate output to an aggregate input. This definition naturally leads to TFP indexes that can be expressed as the ratio of an output quantity index to an input quantity index. If the aggregator functions satisfy certain regularity properties then these TFP indexes are said to be multiplicatively complete. This paper formally defines what is meant by completeness and reveals that (1) the class of multiplicatively complete TFP indexes includes Laspeyres, Paasche, Fisher, Törnqvist and Hicks-Moorsteen indexes, (2) the popular Malmquist TFP index of Caves et al. (Econometrica 50(6):1393–1414, 1982a ) is incomplete, implying it cannot always be interpreted as a measure of productivity change, (3) all multiplicatively complete TFP indexes can be exhaustively decomposed into measures of technical change and efficiency change, and (4) the efficiency change component can be further decomposed into measures of technical, mix and scale efficiency change. Artificial data are used to illustrate the decomposition of Hicks-Moorsteen and Fisher TFP indexes. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • C. O’Donnell, 2012. "An aggregate quantity framework for measuring and decomposing productivity change," Journal of Productivity Analysis, Springer, vol. 38(3), pages 255-272, December.
  • Handle: RePEc:kap:jproda:v:38:y:2012:i:3:p:255-272
    DOI: 10.1007/s11123-012-0275-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11123-012-0275-1
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11123-012-0275-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. D. W. Jorgenson & Z. Griliches, 1967. "The Explanation of Productivity Change," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 34(3), pages 249-283.
    2. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960, September.
    3. C. Lovell, 2003. "The Decomposition of Malmquist Productivity Indexes," Journal of Productivity Analysis, Springer, vol. 20(3), pages 437-458, November.
    4. Robert G. Chambers & Rulon D. Pope, 1996. "Aggregate Productivity Measures," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(5), pages 1360-1365.
    5. repec:bla:scandj:v:98:y:1996:i:2:p:303-13 is not listed on IDEAS
    6. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, October.
    7. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    8. John R. Hicks, 1961. "The Measurement of Capital in Relation to the Measurement of Other Economic Aggregates," International Economic Association Series, in: D. C. Hague (ed.), The Theory of Capital, chapter 0, pages 18-31, Palgrave Macmillan.
    9. Bert Balk, 2001. "Scale Efficiency and Productivity Change," Journal of Productivity Analysis, Springer, vol. 15(3), pages 159-183, May.
    10. Ray, Subhash C & Mukherjee, Kankana, 1996. "Decomposition of the Fisher Ideal Index of Productivity: A Non-parametric Dual Analysis of US Airlines Data," Economic Journal, Royal Economic Society, vol. 106(439), pages 1659-1678, November.
    11. Richard H. Moorsteen, 1961. "On Measuring Productive Potential and Relative Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(3), pages 451-467.
    12. F. A. Lutz, 1961. "The Theory of Capital," International Economic Association Series, Palgrave Macmillan, number 978-1-349-08452-4 edited by D. C. Hague.
    13. Timo Kuosmanen & Timo Sipiläinen, 2009. "Exact decomposition of the Fisher ideal total factor productivity index," Journal of Productivity Analysis, Springer, vol. 31(3), pages 137-150, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vu, Quang & Tran, Tuyen Quang, 2021. "Government financial support and firm productivity in vietnam," Finance Research Letters, Elsevier, vol. 40(C).
    2. Aparicio, Juan & López-Torres, Laura & Santín, Daniel, 2018. "Economic crisis and public education. A productivity analysis using a Hicks-Moorsteen index," Economic Modelling, Elsevier, vol. 71(C), pages 34-44.
    3. Mocholi-Arce, Manuel & Sala-Garrido, Ramon & Molinos-Senante, Maria & Maziotis, Alexandros, 2021. "Water company productivity change: A disaggregated approach accounting for changes in inputs and outputs," Utilities Policy, Elsevier, vol. 70(C).
    4. Laurenceson, James & O'Donnell, Christopher, 2014. "New estimates and a decomposition of provincial productivity change in China," China Economic Review, Elsevier, vol. 30(C), pages 86-97.
    5. Aparicio, Juan & Ortiz, Lidia & Santín, Daniel, 2021. "Comparing group performance over time through the Luenberger productivity indicator: An application to school ownership in European countries," European Journal of Operational Research, Elsevier, vol. 294(2), pages 651-672.
    6. Rosenkranz, Lydia & Seintsch, Björn & Dieter, Matthias, 2015. "Decomposition analysis of changes in value added. A case study of the sawmilling and wood processing industry in Germany," Forest Policy and Economics, Elsevier, vol. 54(C), pages 36-50.
    7. See, Kok Fong & Ma, Zhanxin, 2018. "Does non-revenue water affect Malaysia's water services industry productivity?," Utilities Policy, Elsevier, vol. 54(C), pages 125-131.
    8. Afsharian, Mohsen & Ahn, Heinz & Harms, Sören Guntram, 2019. "Performance comparison of management groups under centralised management," European Journal of Operational Research, Elsevier, vol. 278(3), pages 845-854.
    9. Liu, Hongwei & Wu, Jie & Chu, Junfei, 2019. "Environmental efficiency and technological progress of transportation industry-based on large scale data," Technological Forecasting and Social Change, Elsevier, vol. 144(C), pages 475-482.
    10. Tang, Liwei & He, Gang, 2021. "How to improve total factor energy efficiency? An empirical analysis of the Yangtze River economic belt of China," Energy, Elsevier, vol. 235(C).
    11. Karagiannis, Giannis & Knox Lovell, C.A., 2016. "Productivity measurement in radial DEA models with a single constant input," European Journal of Operational Research, Elsevier, vol. 251(1), pages 323-328.
    12. Walker, Nathan L. & Styles, David & Williams, A. Prysor, 2023. "Water sector resilience in the United Kingdom and Ireland: The COVID-19 challenge," Utilities Policy, Elsevier, vol. 82(C).
    13. Ipatova, Irina, 2015. "The dynamics of total factor productivity and its components: Russian plastic production," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 21-40.
    14. See, Kok Fong & Li, Fei, 2015. "Total factor productivity analysis of the UK airport industry: A Hicks-Moorsteen index method," Journal of Air Transport Management, Elsevier, vol. 43(C), pages 1-10.
    15. Tran, Trung & Thanh, Hai Trinh & Van Le, Dao & Phuong, Thao Trinh Thi & Lan, Phuong Nguyen, 2022. "Does government financial support decrease the inefficiency of public universities? A decomposition approach," Finance Research Letters, Elsevier, vol. 47(PA).
    16. Grifell-Tatjé, E. & Lovell, C.A.K., 2021. "Dual productivity analysis: A Konüs/Shephard approach," European Journal of Operational Research, Elsevier, vol. 289(1), pages 328-337.
    17. Hiep, Tran Duc & Trung, Bui Hoang & Van Chien, Le, 2022. "Quantifying productivity gains from foreign direct investment: The mediating role of provincial institutional quality," Finance Research Letters, Elsevier, vol. 49(C).
    18. Neves Bezerra de Melo, Felipe Luiz & Sampaio, Raquel Menezes Bezerra & Sampaio, Luciano Menezes Bezerra, 2018. "Efficiency, productivity gains, and the size of Brazilian supermarkets," International Journal of Production Economics, Elsevier, vol. 197(C), pages 99-111.
    19. Miao, Zhuang & Baležentis, Tomas & Shao, Shuai & Chang, Dongfeng, 2019. "Energy use, industrial soot and vehicle exhaust pollution—China's regional air pollution recognition, performance decomposition and governance," Energy Economics, Elsevier, vol. 83(C), pages 501-514.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Diogo Cunha Ferreira & Rui Cunha Marques, 2016. "Malmquist and Hicks–Moorsteen Productivity Indexes for Clusters Performance Evaluation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1015-1053, September.
    2. C.J. O'Donnell, 2011. "The Sources of Productivity Change in the Manufacturing Sectors of the U.S. Economy," CEPA Working Papers Series WP072011, School of Economics, University of Queensland, Australia.
    3. Pastor, Jesus T. & Lovell, C.A. Knox & Aparicio, Juan, 2020. "Defining a new graph inefficiency measure for the proportional directional distance function and introducing a new Malmquist productivity index," European Journal of Operational Research, Elsevier, vol. 281(1), pages 222-230.
    4. Valentin Zelenyuk, 2023. "Productivity analysis: roots, foundations, trends and perspectives," Journal of Productivity Analysis, Springer, vol. 60(3), pages 229-247, December.
    5. Aparicio, Juan & López-Torres, Laura & Santín, Daniel, 2018. "Economic crisis and public education. A productivity analysis using a Hicks-Moorsteen index," Economic Modelling, Elsevier, vol. 71(C), pages 34-44.
    6. Diewert, W. Erwin & Fox, Kevin J., 2017. "Decomposing productivity indexes into explanatory factors," European Journal of Operational Research, Elsevier, vol. 256(1), pages 275-291.
    7. Christopher J. O'Donnell, 2010. "Measuring and decomposing agricultural productivity and profitability change ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 54(4), pages 527-560, October.
    8. W. Erwin Diewert & Kevin J. Fox, 2014. "Decomposing Bjurek Productivity Indexes into Explanatory Factors," Discussion Papers 2014-33, School of Economics, The University of New South Wales.
    9. Aparicio, Juan & Ortiz, Lidia & Santín, Daniel, 2021. "Comparing group performance over time through the Luenberger productivity indicator: An application to school ownership in European countries," European Journal of Operational Research, Elsevier, vol. 294(2), pages 651-672.
    10. Rolf Färe & Valentin Zelenyuk, 2020. "POn Fisher Aggregation of Multi-factor Productivity Indexes," CEPA Working Papers Series WP082020, School of Economics, University of Queensland, Australia.
    11. Rolf Färe & Valentin Zelenyuk, 2021. "On aggregation of multi-factor productivity indexes," Journal of Productivity Analysis, Springer, vol. 55(2), pages 107-133, April.
    12. Feng, Guohua & Serletis, Apostolos, 2010. "A primal Divisia technical change index based on the output distance function," Journal of Econometrics, Elsevier, vol. 159(2), pages 320-330, December.
    13. W. Diewert & Alice Nakamura, 2003. "Index Number Concepts, Measures and Decompositions of Productivity Growth," Journal of Productivity Analysis, Springer, vol. 19(2), pages 127-159, April.
    14. W. Diewert & Kevin Fox, 2010. "Malmquist and Törnqvist productivity indexes: returns to scale and technical progress with imperfect competition," Journal of Economics, Springer, vol. 101(1), pages 73-95, September.
    15. Grifell-Tatjé, E. & Lovell, C.A.K., 2021. "Dual productivity analysis: A Konüs/Shephard approach," European Journal of Operational Research, Elsevier, vol. 289(1), pages 328-337.
    16. Balk, B.M. & Zofío, J.L., 2018. "The Many Decompositions of Total Factor Productivity Change," ERIM Report Series Research in Management ERS-2018-003-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    17. Mad Ithnin Salleh & Shariffah Nur Illiana Syed Ismail & Nurul Fadly Habidin & Nor Azrin Md Latip, 2016. "Efficiency and Productivity Changes of the Malaysian Community Colleges," International Journal of Academic Research in Business and Social Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Business and Social Sciences, vol. 6(12), pages 407-424, December.
    18. Lippe Peter von der & Diewert W. Erwin, 2010. "Introduction to the Special Issue on Index Number Theory and Price Statistics," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 230(6), pages 660-672, December.
    19. Pontus Mattsson & Jonas Månsson & Christian Andersson & Fredrik Bonander, 2018. "A bootstrapped Malmquist index applied to Swedish district courts," European Journal of Law and Economics, Springer, vol. 46(1), pages 109-139, August.
    20. Andrew Maredza & Sylvanus Ikhide, 2013. "The Impact of the Global Financial Crisis on Efficiency and Productivity of the Banking System in South Africa," Working Papers 328, Economic Research Southern Africa.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jproda:v:38:y:2012:i:3:p:255-272. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.