How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies
We discuss how to properly decompose economic efficiency when the underlying technology is non-homothetic using alternative allocative and technical efficiency criteria. We first show that only under the production of one output and assuming the particular case of constant returns to scale homotheticity, we may claim that the standard radial models correctly measure pure technical efficiency. Otherwise, when non-homotheticity is assumed, we then show that these traditional estimations would measure an undetermined mix of technical and allocative efficiency. To restore a consistent measure of technical efficiency in the non-homothetic case we introduce a new methodology that takes as reference for the economic efficiency decomposition the preservation of the allocative efficiency of firms producing in the interior of the technology. This builds upon the so-called reversed approach recently introduced by Bogetoft et al. (2006) that allows estimating allocative efficiency without presuming that technical efficiency has been already accomplished. We illustrate our methodology within the Data Envelopment Analysis framework adopting the most simple nonhomothetic BCC model and a numerical example. We show that there are significant differences in the allocative and technical efficiency scores depending on the approach.
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- Sato, Ryuzo, 1977. "Homothetic and Non-Homothetic CES Production Functions," American Economic Review, American Economic Association, vol. 67(4), pages 559-569, September.
- Simar, Léopold & Vanhems, Anne & Wilson, Paul W., 2012. "Statistical inference for DEA estimators of directional distances," European Journal of Operational Research, Elsevier, vol. 220(3), pages 853-864.
- R. Färe & S. Grosskopf & G. Whittaker, 2013. "Directional output distance functions: endogenous directions based on exogenous normalization constraints," Journal of Productivity Analysis, Springer, vol. 40(3), pages 267-269, December.
- Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
- Jacobsen, S E, 1970. "Production Correspondences," Econometrica, Econometric Society, vol. 38(5), pages 754-771, September.
- Robert Chambers & Thomas Mitchell, 2001. "Homotheticity and Non-Radial Changes," Journal of Productivity Analysis, Springer, vol. 15(1), pages 31-39, January.
- Delis, Manthos D & Iosifidi, Maria & Tsionas, Efthymios, 2012.
"On the estimation of marginal cost,"
43514, University Library of Munich, Germany.
- Jose Zofio & Jesus Pastor & Juan Aparicio, 2013.
"The directional profit efficiency measure: on why profit inefficiency is either technical or allocative,"
Journal of Productivity Analysis,
Springer, vol. 40(3), pages 257-266, December.
- Zofío, José Luis & Pastor, Jesús & Aparicio, Juan, 2010. "The Directional Profit Efficiency Measure: On Why Profit Inefficiency is either Technical or Allocative," Working Papers in Economic Theory 2010/09, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
- Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
- Lee, Chia-Yen, 2014. "Meta-data envelopment analysis: Finding a direction towards marginal profit maximization," European Journal of Operational Research, Elsevier, vol. 237(1), pages 207-216.
- Bogetoft, Peter & Fare, Rolf, 1999.
"Allocative Efficiency of Technically Inefficient Production Units,"
Unit of Economics Working papers
24217, Royal Veterinary and Agricultural University, Food and Resource Economic Institute.
- Bogetoft, Peter & Fare, Rolf & Obel, Borge, 2006. "Allocative efficiency of technically inefficient production units," European Journal of Operational Research, Elsevier, vol. 168(2), pages 450-462, January.
- repec:spr:compst:v:60:y:2004:i:1:p:101-123 is not listed on IDEAS
- R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
- Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
- Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
- Kopp, Raymond J. & Diewert, W. Erwin, 1982. "The decomposition of frontier cost function deviations into measures of technical and allocative efficiency," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 319-331, August.
- Walter Briec & Philippe Gardères, 2004. "Generalized benefit functions and measurement of utility," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(1), pages 101-123, 09.
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