Abstract
The paper focuses on the possibilities for a cost efficiency (CE) decomposition using data envelopment analysis (DEA) models in situations when input prices are not identical among decision making units (DMUs). To date, several approaches dealing with the CE decomposition under conditions of non-competitive markets with adjustable input prices have been developed in the DEA literature. This paper summarizes four main DEA models for CE decomposition in situations where DMUs are not price takers and compares them with the newly developed approach for CE decomposition in which the individual efficiency components are consistent with their traditional definitions. Based on the decomposition of the actual total cost of DMUs on the minimum total cost and the potential cost savings due to input inefficiencies, the CE measure is disentangled into Pareto-Koopmans efficiency component, price efficiency component and allocative efficiency component. To highlight the main differences between the new and the existing CE models a simple illustrative example is given. The applicability of the measures developed is illustrated in the context of the analysis of bus transport undertaking performance.
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References
Aparicio J, Borras F, Pastor JT, Vidal F (2013) Accounting for slacks to measure and decompose revenue efficiency in the Spanish designation of origin wines with DEA. Eur J Oper Res 231:443–451
Aparicio J, Borras F, Pastor JT, Vidal F (2015) Measuring and decomposing firm’s revenue and cost efficiency: the Russell measures revisited. Int J Prod Econ 165:19–28
Asbullah MA, Jaafar A (2010) A new approach to estimate the mix efficiency in data envelopment analysis. Appl Math Sci 4:2135–2143
Banker RD, Charnes A, Cooper WW (1984) Some models for estimating technical scale inefficiencies in data envelopment analysis. Manag Sci 30:1078–1092
Barnum DT, Gleason JM (2011) Measuring efficiency under fixed proportion technologies. J Prod Anal 35:243–262
Besstremyannaya G (2013) The impact of Japanese hospital financing reform on hospital efficiency: a difference-in-difference approach. Jpn Econ Rev 64:337–362
Briec W (1998) Hölder distance function and measurement of technical efficiency. J Prod Anal 11:111–131
Camanho AS, Dyson RG (2008) A generalisation of the Farrell cost efficiency measure applicable to non-fully competitive settings. Omega Int J Manag Sci 36:147–162
Chambers RG, Chung Y, Färe R (1996) Benefit and distance functions. J Econ Theory 70:407–419
Chambers RG, Chung Y, Färe R (1998) Profit, directional distance functions, and Nerlovian efficiency. J Optim Theory App 98:351–364
Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2:429–444
Chavas JP, Cox TM (1999) A generalized distance function and the analysis of production efficiency. South Econ J 66:295–318
Cooper WW, Seiford LM, Tone K (2007) Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software, 2nd edn. Springer, New York
Coupet J (2018) Exploring the link between government funding and efficiency in nonprofit colleges. Nonprofit Manag Lead 29:65–81
Debreu G (1951) The coefficient of resource utilization. Econometrica 19:273–292
Dong Y, Hamilton R, Tippett M (2014) Cost efficiency of the Chinese banking sector: a comparison of stochastic frontier analysis and data envelopment analysis. Econ Model 36:298–308
Färe R, Grosskopf S (2000) Theory and application of directional distance functions. J Prod Anal 13:93–103
Färe R, Grosskopf S (2003) New directions: efficiency and productivity. Kluwer, Dordrecht
Färe R, Grosskopf S, Lovell CAK (1985) The measurement of efficiency of production. Kluwer, Dordrecht
Färe R, Grosskopf S, Zelenyuk V (2007) Finding common ground: efficiency indices. In: Färe R, Grosskopf S, Primont D (eds) Aggregation, efficiency, and measurement. Springer, Boston, pp 83–96
Färe R, Fukuyama H, Grosskopf S, Zelenyuk V (2016) Cost decompositions and the efficient subset. Omega Int J Manag Sci 62:123–130
Farrell MJ (1957) The measurement of productive efficiency. J R Stat Soc A Stat 120:253–281. https://doi.org/10.2307/2343100
Fried HO, Lovell CAK, Schmidt SS (2008) The measurement of productive efficiency and productivity growth. Oxford University Press, New York
Koopmans TC (1951) An analysis of production as an efficient combination of activities. In: Koopmans TC (ed) Activity analysis of production and allocation. Wiley, New York, pp 33–97
Pančurová D, Lyocsa S (2013) Determinants of commercial banks’ efficiency: evidence from 11 CEE countries. Finance Uver 63:152–179
Portela MCAS (2014) Value and quantity data in economic and technical efficiency measurement. Econ Lett 124:108–112
Portela MCAS, Thanassoulis E (2014) Economic efficiency when prices are not fixed: disentangling quantity and price efficiency. Omega Int J Manag Sci 47:36–44
Ray S, Chen L, Mukherjee K (2008) Input price variation across locations and a generalised measure of cost efficiency. Int J Prod Econ 116:208–218
Roháčová V (2011) Cost efficiency of selected transport companies in the Czech Republic—an application of data envelopment analysis. Ekon Rev Cent Eur Rev Econ Issues 14:175–182. https://doi.org/10.7327/cerei.2011.09.03(in Slovak)
Shephard RW (1953) Cost and production functions. Princeton University Press, New Jersey
Thanassoulis E, Portela MCAS, Graveney M (2012) Estimating the scope for savings in referrals and drug prescription costs in the General Practice units of a UK Primary Care Trust. Eur J Oper Res 221:432–444
Thanassoulis E, Sotiros D, Koronakos G, Despotis D (2018) Assessing the cost-effectiveness of university academic recruitment and promotion policies. Eur J Oper Res 264:742–755
Tone K (1998) On mix efficiency in DEA, vol 1. The Operations Research Society of Japan, pp 14–15. http://ci.nii.ac.jp/naid/110003478327/en. Accessed 6 April 2016
Tone K (2002) A strange case of the cost and allocative efficiencies in DEA. J Oper Res Soc 53:1225–1231
Tone K, Tsutsui M (2007) Decomposition of cost efficiency and its application to Japan-US electric utility comparisons. Socio Econ Plan Sci 41:91–106
Yu MM, Chang YC, Chen LH (2016) Measurement of airlines’ capacity utilization and cost gap: evidence from low-cost carriers. J Air Transp Manag 53:186–198
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The support of the grant scheme VEGA (1/0843/18 Methodological aspects of DEA application on efficiency assessment of production units) is gladly acknowledged.
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Mendelová, V. Decomposition of cost efficiency with adjustable prices: an application of data envelopment analysis. Oper Res Int J 21, 2739–2770 (2021). https://doi.org/10.1007/s12351-019-00525-w
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DOI: https://doi.org/10.1007/s12351-019-00525-w