Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator
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.
|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|
|Contact details of provider:|| Postal: 3, rue de la Digue, FR-59000 Lille|
Web page: http://www.ieseg.fr/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Jean-Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Wisconsin-Madison Agricultural and Applied Economics Staff Papers 422, Wisconsin-Madison Agricultural and Applied Economics Department.
- 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.
- Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
- 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.
- 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.
- 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.
- 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.
- 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.
- Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 751-765.
- Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-97, May.
- 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.
- Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
- 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.
- Fare, Rolf & Lyon, Vern, 1981. "The Determinateness Test and Economic Price Indices," Econometrica, Econometric Society, vol. 49(1), pages 209-13, January.
When requesting a correction, please mention this item's handle: RePEc:ies:wpaper:e200811. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Monika Marin)
If references are entirely missing, you can add them using this form.