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Measurement of Productivity Changes: Two Malmquist Index Approaches

Abstract

The adjacent Malmquist productivity index is compared to the more recently suggested base period Malmquist productivity index. The two index approaches are evaluated with respect to base period dependency, the circular test, and with respect to a set of additional classical index tests. In addition it is shown that the base period index is independent of base period if and only if the marginal rate of substitution of inputs is independent of time. Finally, the adjacent and the base period indexes are put through a Monte Carlo (bootstrap) test to see if they yield similar results when applied to a panel of Swedish pharmacy data.

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References

  • Balk, B. M. and R. Althin. (1996). “A New, Transitive Productivity Index.” The Journal of Productivity Analysis 7, 19–27.

    Google Scholar 

  • Berg, S. A., F. R. Førsund and E. S. Jansen. (1992). “Malmquist Indices of Productivity Growth during the Deregulation of Norwegian Banking, 1980–89.” Scandinavian Journal of Economics (Supplement), 211–228.

    Google Scholar 

  • Caves, D. W., L. R. Christensen and W. E. Diewert. (1982). “The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity.” Econometrica. 50(6), 1393–1414.

    Google Scholar 

  • Diewert, W. E. (1987). “Index Numbers.” In J. Eatwell, M. Milgate and P. Newman (eds.), The New Palgrave; A Dictionary of Economics. London: The Macmillan Press.

    Google Scholar 

  • Diewert, W. E. (1992). “Fisher Ideal Output, Input, and Productivity Indexes Revisited.” The Journal of Productivity Analysis 3, 211–248.

    Google Scholar 

  • Eichhorn, W. and J. Voeller. (1976). Theory of the Price Index. Berlin: Springer-Verlag.

    Google Scholar 

  • Efron, B. (1979). “Bootstrap Methods: Another Look at the Jackknife.” Annals of Statistics 7, 1–26.

    Google Scholar 

  • Farrell, M. J. (1957). “The Measurement of Productive Efficiency.” Journal of the Royal Statistical Society. Ser. A: 120, 253–281.

    Google Scholar 

  • Fisher, I. (1911). Purchasing Power of Money. New-York.

  • Fisher, I. (1922). The Making of Index Numbers: A Study of Their Varieties, Tests, and Reliability. Boston: Houghton Mifflin Company.

    Google Scholar 

  • Frisch, R. (1936). “Annual Survey of General Economic Theory: The Problem of Index Numbers.” Econometrica 4, 1–38.

    Google Scholar 

  • Färe, R., S. Grosskopf and C. A. K. Lovell. (1985). The Measurement of Efficiency of Production. Boston: Kluwer-Nijhoff Publishing.

    Google Scholar 

  • Färe, R. (1988). Fundamentals of Production Theory. Berlin: Springer-Verlag.

    Google Scholar 

  • Färe, R., S. Grosskopf, B. Lindgren and P. Roos. (1989). “Productivity Developments in Swedish Hospitals: A Malmquist Output Index Approach.” Discussion Paper 89-3, Department of Economics, Southern Illinois University, Carbondale. Forthcoming in A. Charnes, W. W. Cooper, A. Y. Lewin and L. M. Seiford (eds.), Kluwer Academic Publishers.

    Google Scholar 

  • Färe, R., S. Grosskopf, B. Lindgren and P. Roos. (1992). “Productivity Changes in Swedish Pharmacies 1980–1989: A Non-Parametric Approach.” The Journal of Productivity Analysis 3, 85–101.

    Google Scholar 

  • Färe, R. (1993). “The Malmquist Productivity Index and the Circular Test.” Mimeo, at CORE.

  • Hjalmarsson, L. (1991). “Teorier och metoder i forskning om produktivitet och effektivitet med tillämpningar på produktionen av tjänster.” In: Hur mäta produktivitet?. Expertrapport nr. 1 till produktivitetsdelegationen.

  • Malmquist, S. (1953). “Index Numbers and Indifference Surfaces.” Trabajos de Estatistica 4, 209–242.

    Google Scholar 

  • Manly, B. F. J. (1991). Randomization and Monte Carlo Methods in Biology. London: Chapman and Hall.

    Google Scholar 

  • Noreen, E. W. (1989). Computer Intensive Methods for Testing Hypotheses. New-York: John Wiley & Sons.

    Google Scholar 

  • Samuelson, P. A. and S. Swamy. (1974). “Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis.” The American Economic Review 66(4), 566–593.

    Google Scholar 

  • Shephard, R. W. (1953). Cost and Production Functions. Princeton: Princeton University Press.

    Google Scholar 

  • Shephard, R. W. (1970), Theory of Cost and Production Functions. Princeton: Princeton University Press.

    Google Scholar 

  • Törnqvist, L. (1936), “The Bank of Finland's Consumption Price Index.” Bank of Finland Monthly Bulletin 10, 1–8.

    Google Scholar 

  • Westergaard, H. (1890). Die Grundzüge der Theorie der Statistik. Jena: Gustav Fischer.

    Google Scholar 

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Althin, R. Measurement of Productivity Changes: Two Malmquist Index Approaches. Journal of Productivity Analysis 16, 107–128 (2001). https://doi.org/10.1023/A:1011682625976

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  • DOI: https://doi.org/10.1023/A:1011682625976

  • efficiency change
  • technical change
  • productivity change
  • circular test