Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator
AbstractThe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by IESEG School of Management in its series Working Papers with number 2008-ECO-11.
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
Directional distance function; Shortage function; Well-definedness; Infeasibility; Determinateness;
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.:
- Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
- 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.
- Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-97, May.
- Fare, Rolf & Lyon, Vern, 1981. "The Determinateness Test and Economic Price Indices," Econometrica, Econometric Society, vol. 49(1), pages 209-13, January.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
- 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.
- Kerstens, Kristiaan & Van de Woestyne, Ignace, 2009.
"Negative Data in DEA: A Simple Proportional Distance Function Approach,"
2009/04, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
- 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.
- Walter Briec & Kristiaan Kerstens, 2008.
"The Luenberger Productivity Indicator: An Economic Specifcation Leading to Infeasibilities,"
2008-ECO-09, IESEG School of Management.
- Briec, Walter & Kerstens, Kristiaan, 2009. "The Luenberger productivity indicator: An economic specification leading to infeasibilities," Economic Modelling, Elsevier, vol. 26(3), pages 597-600, May.
- 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.
- Walter Briec & Kristiaan Kerstens, 2009.
"Portfolio Selection in Multidimensional General and Partial Moment Space,"
2009-ECO-08, IESEG School of Management.
- Briec, Walter & Kerstens, Kristiaan, 2010. "Portfolio selection in multidimensional general and partial moment space," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 636-656, April.
- 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.
- 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.
- Kuosmanen, Timo & Kazemi Matin, Reza, 2011. "Duality of weakly disposable technology," Omega, Elsevier, vol. 39(5), pages 504-512, October.
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.