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.
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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;
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- 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.
- 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.
- Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
- Robert G. Chambers, 2002. "Exact nonradial input, output, and productivity measurement," Economic Theory, Springer, vol. 20(4), pages 751-765.
- 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.
- 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.
- 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.
- Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
- 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 & Rulon D. Pope, 1996. "Aggregate Productivity Measures," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 78(5), pages 1360-1365.
- 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.
- 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.
- 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.
- 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.
- Briec, Walter & Kerstens, Kristiaan, 2009.
"The Luenberger productivity indicator: An economic specification leading to infeasibilities,"
Elsevier, vol. 26(3), pages 597-600, May.
- Walter Briec & Kristiaan Kerstens, 2008. "The Luenberger Productivity Indicator: An Economic Specifcation Leading to Infeasibilities," Working Papers 2008-ECO-09, 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.
- Walter Briec & Kristiaan Kerstens, 2009. "Portfolio Selection in Multidimensional General and Partial Moment Space," Working Papers 2009-ECO-08, IESEG School of Management.
- 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.
- 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.
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