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Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator

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Author Info

  • Walter Briec

    ()
    (University of Perpignan, LAMPS)

  • Kristiaan Kerstens

    (CNRS-LEM (UMR 8179), IESEG School of Management)

Abstract

The purpose of this contribution is to highlight an underexplored property of the directional distance function, a recently introduced generalization of the Shephard distance function. It diagnoses in detail the economic conditions under which infeasibilities may occur for the case of directional distance functions and explores whether there exist any solutions that remedy the problem in an economically meaningful way. This discussion is linked to determinateness as a property in index theory and illustrated by analyzing the Luenberger total factor productivity indicator, based upon directional distance functions. This indicator turns out to be impossible to compute under certain weak conditions. A fortiori, the same problems can also occur for less general productivity indicators and indexes.

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File URL: http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=103380412_2008-ECO-11_Briec_Kerstens.pdf
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Bibliographic Info

Paper provided by IESEG School of Management in its series Working Papers with number 2008-ECO-11.

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Length: 48 pages
Date of creation: Sep 2008
Date of revision:
Publication status: Published in Journal of Optimization Theory and Applications,April 2009, 14(1), pp. 55-73
Handle: RePEc:ies:wpaper:e200811

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Related research

Keywords: Directional distance function; Shortage function; Well-definedness; Infeasibility; Determinateness;

References

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  1. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  2. Fare, Rolf & Shawna Grosskopf & Mary Norris & Zhongyang Zhang, 1994. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries," American Economic Review, American Economic Association, vol. 84(1), pages 66-83, March.
  3. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-97, May.
  4. Mukherjee, Kankana & Ray, Subhash C. & Miller, Stephen M., 2001. "Productivity growth in large US commercial banks: The initial post-deregulation experience," Journal of Banking & Finance, Elsevier, vol. 25(5), pages 913-939, May.
  5. Edward Jaenicke, 2000. "Testing for Intermediate Outputs in Dynamic DEA Models: Accounting for Soil Capital in Rotational Crop Production and Productivity Measures," Journal of Productivity Analysis, Springer, vol. 14(3), pages 247-266, November.
  6. Samuelson, Paul A & Swamy, S, 1974. "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, American Economic Association, vol. 64(4), pages 566-93, September.
  7. 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.
  8. Banker, Rajiv D & Maindiratta, Ajay, 1988. "Nonparametric Analysis of Technical and Allocative Efficiencies in Production," Econometrica, Econometric Society, vol. 56(6), pages 1315-32, November.
  9. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
  10. Fare, Rolf & Lyon, Vern, 1981. "The Determinateness Test and Economic Price Indices," Econometrica, Econometric Society, vol. 49(1), pages 209-13, January.
  11. Atkinson, Scott E & Cornwell, Christopher & Honerkamp, Olaf, 2003. "Measuring and Decomposing Productivity Change: Stochastic Distance Function Estimation versus Data Envelopment Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 284-94, April.
  12. Jean-Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Southern Economic Journal, Southern Economic Association, vol. 66(2), pages 294-318, October.
  13. Ouellette, Pierre & Vierstraete, Valerie, 2004. "Technological change and efficiency in the presence of quasi-fixed inputs: A DEA application to the hospital sector," European Journal of Operational Research, Elsevier, vol. 154(3), pages 755-763, May.
  14. Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer, vol. 20(4), pages 751-765.
  15. 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 1659-78, November.
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Citations

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Cited by:
  1. Walter Briec & Kristiaan Kerstens, 2008. "The Luenberger Productivity Indicator: An Economic Specifcation Leading to Infeasibilities," Working Papers 2008-ECO-09, IESEG School of Management.
  2. Färe, Rolf & Grosskopf, Shawna & Lundgren, Tommy & Marklund, Per-Olov & Zhou, Wenchao, 2012. "Productivity: Should We Include Bads?," CERE Working Papers 2012:13, CERE - the Center for Environmental and Resource Economics.
  3. Walter Briec & Kristiaan Kerstens, 2009. "Portfolio Selection in Multidimensional General and Partial Moment Space," Working Papers 2009-ECO-08, IESEG School of Management.
  4. Mondelaers, Koen & Kuosmanen, Timo & Van Passel, Steven & Buysse, Jeroen & Lauwers, Ludwig H. & Van Huylenbroeck, Guido, 2011. "Sustainable Efficiency Of Firms When New Sustainability Targets Are Introduced," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114633, European Association of Agricultural Economists.
  5. Kuosmanen, Timo & Kazemi Matin, Reza, 2011. "Duality of weakly disposable technology," Omega, Elsevier, vol. 39(5), pages 504-512, October.
  6. Kristiaan Kerstens & Ignace Van de Woestyne, 2009. "Negative Data in DEA: A Simple Proportional Distance Function Approach," Working Papers 2009-ECO-03, IESEG School of Management.
  7. Epure, Mircea & Kerstens, Kristiaan & Prior, Diego, 2011. "Technology-based total factor productivity and benchmarking: New proposals and an application," Omega, Elsevier, vol. 39(6), pages 608-619, December.

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