Spanish Economic Review

, Volume 8, Issue 2, pp 113–138 | Cite as

Return to Dollar, Generalized Distance Function and the Fisher Productivity Index

  • José L. Zofío
  • Angel M. Prieto
Regular Article


Exploring the duality between a return to dollar definition of profit and the generalized distance function we establish the relationship between the Laspeyres, Paasche and Fisher productivity indexes and their alternative Malmquist indexes counterparts. By proceeding this way, we propose a consistent decomposition of these productivity indexes into two mutually exclusive components. A technical component represented by the Malmquist index and an economical component which can be identified with the contribution that allocative criteria make to productivity change. With regard to the Fisher index, we indicate how researchers can further decompose the Malmquist technical component rendering explicit the sources of productivity change. We also show how the proposed model can be implemented by means of Data Envelopment Analysis techniques, and illustrate the empirical process with an example data set.


Generalized distance function Return to dollar Fisher and Malmquist productivity indexes 

JEL Classification

C43 C61 D24 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abramovitz M (1956) Resource and output trends in the United States Since 1870. National Bureau of Economic Research Occasional Paper, 52Google Scholar
  2. Althin R, Färe R, Grosskopf S (1996) Profitability and productivity change: an application to Swedish pharmacies. Ann Oper Res 66:219–233CrossRefGoogle Scholar
  3. Balk B (1998) Industrial price, quantity and productivity indexes: the microeconomic theory and an application. Kluwer, BostonGoogle Scholar
  4. Balk B (2001) Scale efficiency and productivity change. J Product Anal 15:153–183CrossRefGoogle Scholar
  5. Chambers R, Chung Y, Färe R (1998) Profit, directional distance functions and Nerlovian Efficiency. J Optim Theory Appl 95(2):351–364CrossRefGoogle Scholar
  6. Chavas J-P, Cox TM (1999) A generalized distance function and the analysis of production efficiency. Southern Econ J 66(2):295–318CrossRefGoogle Scholar
  7. Cooper W, Seiford L, Tone K (2000) Data envelopment analysis. a comprehensive text with models, applications, references and DEA-Software. Kluwer, BostonGoogle Scholar
  8. Diewert EW (1992) The measurement of productivity. Bull Econ Res 44(3):163–198CrossRefGoogle Scholar
  9. Diewert EW, Lawrence D (1999) Measuring New Zealand’s productivity, Treasury Working Paper 99/5, Scholar
  10. Färe R, Grosskopf S (2000) Notes on some inequalities in economics. Econ Theory 15(1):227–233CrossRefGoogle Scholar
  11. Färe R, Grosskopf S, Lindgren B, Roos P (1994). Productivity developments in Swedish hospitals: a Malmquist output approach. In: Charnes A, Cooper W, Lewin A, Seiford L (eds). Data envelopment analysis: theory, methodology and applications. Kluwer, DordrechtGoogle Scholar
  12. Färe R, Grosskopf S, Lovell CAK (1985) The measurement of efficiency of production. Kluwer, BostonGoogle Scholar
  13. Färe R, Grosskopf S, Zaim T (2002) Hyperbolic efficiency and return to dollar. Eur J Oper Res 136:671–679CrossRefGoogle Scholar
  14. Färe R, Primont D (1995) Multi-output production and duality: theory and applications. Kluwer, DordrechtGoogle Scholar
  15. Farrell M (1957) The measurement of productive efficiency. J R Stat Soc. A 120(3):253–281CrossRefGoogle Scholar
  16. Fisher I (1921) The best form of index number. J Am Stat Assoc 17:533–537Google Scholar
  17. Georgescu-Roegen N (1951). The aggregate linear production function and its application to von Newman’s economic model. In: Koopmans T (eds). Activity analysis of production and allocation. Wiley, New YorkGoogle Scholar
  18. Grifell-Tatjé E, Lovell CAK (1999) A generalized Malmquist productivity index. Trab Invest Oper Top 7(1):81–101Google Scholar
  19. Griliches Z (1987). Productivity: measurement problems. In: Eatwell J, Milgate M, Newman P (eds). The new Palgrave: a dictionary of economics. Palgrave Macmillan, New YorkGoogle Scholar
  20. Harberger AC (1998) A vision of the growth process. Am Econ Rev 88(1):1–32Google Scholar
  21. Laspeyres E (1871) Die Berechnung einer mittlerer Waarenpreissteigerung. Järbucher für Nationalokönomie und Statistik 16:296–314Google Scholar
  22. Lovell CAK (2003) The decomposition of Malmquist productivity indexes. J Prod Anal 20:437–438CrossRefGoogle Scholar
  23. Malmquist S (1953) Index numbers and indifference curves. Trabajos de Estadística 4(1):209–242Google Scholar
  24. McFadden D (1978) Cost, revenue, and profit functions. In: Fuss M, McFadden D (eds) Production economics: a dual approach to theory and applications. North-Holland, AmsterdamGoogle Scholar
  25. OECD (2001) Measuring productivity. Measurement of aggregate and industry level productivity growth. Organization for Economic Co-operation and Development, ParisGoogle Scholar
  26. Orea L (2002) Parametric decomposition of a generalized Malmquist productivity index. J Prod Anal 18:5–22CrossRefGoogle Scholar
  27. Paasche H (1874) Uber die Preisentwicklung der Letzen Jahre Nach den Hamburger Börsennotinrungen. Järbucher für Nationalokönomie und Stististik 23:168–178Google Scholar
  28. Ray S, Desli E (1997) Productivity growth, technical progress, and efficiency change in industrialized countries: comment. Am Econ Rev 87(5): 1.033–1.039Google Scholar
  29. Shephard R (1970) Theory of cost and production functions. Princeton University Press, New JerseyGoogle Scholar
  30. Törnqvist L (1936) The bank of finland’s consumer price index. Bank Finl Mon Bull 19:1–8Google Scholar
  31. Zofío JL, Lovell CAK (2001) Graph efficiency and productivity measures: an application to U.S. Agriculture. Appl Econ 33:1433–1442CrossRefGoogle Scholar
  32. Zofio JL (2001) Malmquist productivity index decompositions: a unifying framework. Departamento de Análisis Económico, Universidad Autónoma de Madrid (forthcoming in Appl Econ)Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Departamento de Análisis Económico: Teoría Económica e Historia EconómicaUniversidad Autónoma de MadridMadridSpain
  2. 2.Ministerio de Educación y CienciaC.S.I.C.SalamancaSpain

Personalised recommendations