Abstract
The paper gives a brief review of the nonparametric approach to efficiency measurement or Data Envelopment Analysis as it is known in the operations research literature. Inequalities are derived between the efficiency measures when different assumptions are made on the technology sets or on the behavior of managers. Of particular interest is the derivation of a Le Chatelier Principle for measures of allocative inefficiency. Finally, the various inequalities are illustrated using some Canadian data, which is also used to compare DEA methods for measuring the relative efficiency of production units with more traditional index number methods.
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References
Afriat, S.N., “Efficiency Estimation of Production Function”, International Economic Review 13 (1972), 568–598.
Balk, B.M., Industrial Price, Quantity and Productivity Indices, Norweii MA: Kluwer Academic Publishers, 1998.
Charnes, A. and W.W. Cooper, “Preface to Topics in Data Envelopment Analysis”, Annals of Operations Research 2 (1985), 59–94.
Charnes, A., W.W. Cooper and E. Rhodes, “Measuring the Efficiency of Decision Making Units”, European Journal of Operational Research 2 (1978), 429–444.
Coelli, T., D.S. Prasada Rao and G. Battese, An Introduction to Efficiency and Productivity Analysis, Boston: Kluwer Academic Publishers, 1997.
Debreu, G., “The Coefficient of Resource Utilization”, Econometrica 19 (1951), 273–292.
Diewert, W.E., “Functional Forms for Profit and Transformation Functions”, Journal of Economic Theory 6 (1973), 284–316.
Diewert, W.E., “Applications of Duality Theory,” pp. 106–171 in M.D. Intriligator and D.A. Kendrick (ed.), Frontiers of Quantitative Economics, Vol. II, Amsterdam: North-Holland, 1974.
Diewert, W.E., “Superlative Index Numbers and Consistency in Aggregation”, Econometrica 46 (1978), 883–900.
Diewert, W.E., “Capital and the Theory of Productivity Measurement”, The American Economic Review 70 (1980), 260–267.
Diewert, W.E., “The Theory of Total Factor Productivity Measurement in Regulated Industries”, pp. 17–44 in Productivity Measurement in Regulated Industries, Tom Cowing and R. Stephenson (eds.), New York: Academic Press, 1981.
Diewert, W.E., “The Measurement of Productivity”, Bulletin of Economic Research 44 (1992), 163–198.
Diewert, W.E. (2005), Chapter 4: Notes on the Construction of a Data Set for an O.E.CD. Country, Lecture notes for Economics 594, Department of Economics, University of British Columbia, Vancouver, Canada, V6T 1Z1. May 2005. http://www.econ.ubc.ca/diewert/594ehmpg.htm
Diewert, W.E. and A.O. Nakamura, “Index Number Concepts, Measures and Decompositions of Productivity Growth”, Journal of Productivity Analysis 19 (2003), 127–159.
Diewert, W.E. and C. Parkan, “Linear Programming Tests of Regularity Conditions for Production Functions,” pp. 131–158 in Quantitative Studies on Production and Prices, W. Bichhorn, R. Henn, K. Neumann and RW. Shephard (eds.), Vienna: Physica Verlag, 1983.
Diewert, W.E. and T.J. Wales, “Flexible Functional Forms and Global Curvature Conditions”, Econometrica 55 (1987), 43–68.
Diewert, W.E. and T.J. Wales, “A Normalized Quadratic Semiflexible Functional Form”, Journal of Econometrics 37 (1988), 327–342.
Diewert, W.E. and T.J. Wales, “Quadratic Spline Models for Producer’s Supply and Demand Functions”, International Economic Review 33 (1992), 705–722.
Färe, R. and C.A.K. Lovell. “Measuring the Technical Efficiency of Production”, Journal of Economic Theory 19 (1978), 150–162.
Färe, R., S. Grosskopf and C.A.K. Lovell, The Measurement of Efficiency of Production, Boston: Kluwer-Nijhoff, 1985.
Farrell, M.J., “The Measurement of Production Efficiency”, Journal of the Royal Statistical Society, Series A, 120 (1957), 253–278.
Farrell, M.J. and M. Fieldhouse, “Estimating Efficient Production Functions under Increasing Returns to Scale”, Journal of the Royal Statistical Society, Series A, 125 (1962), 252–267.
Fisher, I., The Making of Index Numbers, Houghton-Mifflin, Boston. 1922.
Fox, K.J., “Specification of Functional Form and the Estimation of Technical Progress”, Applied Economics 28 (1996), 947–956.
Fox, K.J. (ed.), Efficiency in the Public Sector, Boston: Kluwer Academic Publishers, 2002.
Hanoch, G. and M. Rothschild, “Testing the Assumptions of Production Theory: A Nonparametric Approach”, Journal of Political Economy 80 (1972), 256–275.
Hoffman, A.J., “Discussion of Mr. Farrell’s Paper”, Journal of the Royal Statistical Society, Series A, 120 (1957), 284.
Mendoza, M.N.F., Essays in Production Theory: Efficiency Measurement and Comparative Statistics, Ph.D. Theses. University of British Columbia, Vancouver, Canada, 1989.
Nunamaker, T.R., “Using Data Envelopment Analysis to Measure the Efficiency of Non-profit Organisations: A Critical Evaluation”, Managerial and Decision Economics 6 (1985), 58–60.
Samuelson, P.A., Foundations of Economic Analysis, Cambridge, MA: harvard University Press, 1947.
Varian, H.R., “The Nonparametric Approach to Production Analysis”, Econometrica 52 (1984), 579–597.
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Diewert, W.E., Mendoza, M.N.F. (2007). The Le Chatelier Principle in Data Envelopment Analysis. In: Färe, R., Grosskopf, S., Primont, D. (eds) Aggregation, Efficiency, and Measurement. Studies in Productivity and Efficiency. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-47677-3_4
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DOI: https://doi.org/10.1007/978-0-387-47677-3_4
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