Salnykov, Mykhaylo and Zelenyuk, Valentin (2005): On the Commensurability of Directional Distance Functions. Published in: Techinical Report of Statistical Institute of UCL (2005)

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Abstract
Shephard’s distance functions are widely used instruments for characterizing technology and for estimating efficiency in contemporary economic theory and practice. Recently, they have been generalized by the Luenberger shortage function, or ChambersChungFäre directional distance function. In this study, we explore a very important property of an economic measure known as commensurability or independence of units of measurement up to scalar transformation. Our study discovers both negative and positive results for this property in the context of the directional distance function, which in turn helps us narrow down the most critical issue for this function in practice—the choice of direction of measurement.
Item Type:  MPRA Paper 

Original Title:  On the Commensurability of Directional Distance Functions 
Language:  English 
Keywords:  Directional distance functions, commensurability, efficiency 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C43  Index Numbers and Aggregation D  Microeconomics > D2  Production and Organizations > D24  Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity 
Item ID:  7068 
Depositing User:  Mykhaylo Salnykov 
Date Deposited:  09. Feb 2008 10:24 
Last Modified:  12. Feb 2013 12:30 
References:  [1] G. Bol, On technical efficiency measures: a remark, J. Econ. Theory 38 (1986), 380385. [2] R.G. Chambers, Y. Chung, R. Färe, Benefit and distance function, J. Econ. Theory 70 (1996), 407419. [3] R.G. Chambers, Y. Chung, R. Färe, Profit, directional distance function and Nerlovian efficiency, J. Optimization Theory and Applications 98 (1998), 351364. [4] Y. Chung, R. Färe, S. Grosskopf, Productivity and undesirable outputs: a directional distance function approach, J. Environmental Management 51 (1997), 229240. [5] W. Eichhorn, J. Voeller, Theory of the price index, Fisher’s test approach and generalizations, Lectures Notes in Economics and Mathematical Systems, Vol. 140, SpringerVerlag, Berlin, 1976. [6] R. Färe, C.A.K. Lovell, Measuring the technical efficiency of production, J. Econ. Theory 19 (1978), 150162. [7] R. Färe, S. Grosskopf, Theory and application of directional distance functions J. Productiv. Anal. 13 (2000), 93103. [8] D.G. Luenberger, New optimality principles for economic efficiency and equilibrium, J. of Optimization Theory and Applications 75 (1992), 221264. [9] D.G. Luenberger, Optimality and the theory of value, J. Econ. Theory 63 (1994), 147169. [10] R.R. Russell, On the axiomatic approach to the measurement of technical efficiency, in: W. Eichhorn (Ed.), Measurement in Economics: Theory and Application of Economic Indices, PhysicaVerlag, Heidelberg, 1987, pp. 207217. [11] R.R. Russell, Continuity of measures of technical efficiency, J. Econ. Theory 51 (1990), 255267. [12] R.W. Shephard, Cost and Production Functions, Princeton Univ. Press, Princeton, NJ, 1953. [13] V. Zelenyuk, Essays in Efficiency and Productivity Analysis of Economic Systems, PhD thesis, Oregon State University, Corvallis, OR, 2002. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/7068 