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Measures of Efficiency

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Productivity and Efficiency Analysis

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Abstract

Measures of efficiency can be viewed as ex post measures of how well firm managers have solved different optimisation problems. For example, measures of output-oriented technical efficiency can be viewed as measures of how well managers have maximised outputs when inputs and output mixes have been predetermined. Similarly, measures of profit efficiency can be viewed as measures of how well managers have maximised profits when inputs and outputs have been chosen freely. This chapter discusses various output-, input-, revenue-, cost-, profit- and productivity-oriented measures of efficiency. Except where explicitly stated otherwise, all measures of efficiency defined in this chapter take values in the closed unit interval. A firm manager is said to have been fully efficient by some measure if and only if that measure takes the value one.

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Notes

  1. 1.

    As \(\tau \rightarrow 1\), \(\sigma \rightarrow -\infty \). By a limiting argument originally due to Hardy et al. (1934, pp. 13, 15) , \(\lim _{\sigma \rightarrow -\infty }\left( \sum _n \gamma _n^\sigma a_n^{1-\sigma }\right) ^{1/(1-\sigma )}=\max \{a_1/\gamma _1,\dots ,a_N/\gamma _N\}\).

  2. 2.

    Equation (5.15) can be viewed as a special case of (5.14) corresponding to \(\partial p(q_{it},d_{it})/\partial q_{it}=0\).

  3. 3.

    Equation (5.20) can be viewed as a special case of (5.19) corresponding to \(\partial w(x_{it},s_{it})/\partial x_{it}=0\).

  4. 4.

    Equation (5.27) can be viewed as a special case of (5.26) corresponding to \(\partial p(q_{it},d_{it})/\partial q_{it}=0\) and \(\partial w(x_{it},s_{it})/\partial x_{it}=0\).

  5. 5.

    The ‘group-k’ distance function in O’Donnell et al. (2008) is not necessarily a technology-specific distance function. It could, for example, be a period-and-environment-specific distance function.

References

  • Balk B (1998) Industrial price, quantity, and productivity indices: the micro-economic theory and an application. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

  • Banker R, Maindiratta A (1988) Nonparametric analysis of technical and allocative efficiencies in production. Econometrica 56(6):1315–1332

    Article  Google Scholar 

  • Banker R, Charnes A, Cooper W (1984) Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manage Sci 30(9):1078–1092

    Article  Google Scholar 

  • Battese G, Rao DSP (2002) Technology gap, efficiency, and a stochastic metafrontier function. Int J Bus Econ 1(2):87–93

    Google Scholar 

  • Chambers R, Chung Y, Färe R (1998) Profit, directional distance functions, and Nerlovian efficiency. J Optim Theory Appl 98(2):351–364

    Article  Google Scholar 

  • Charnes A, Cooper W, Rhodes E (1981) Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through. Manage Sci 27(6):668–697

    Article  Google Scholar 

  • Debreu G (1951) The coefficient of resource utilization. Econometrica 19(3):273–292

    Article  Google Scholar 

  • Dervaux B, Kerstens K, Vanden Eeckaut P (1998) Radial and nonradial static efficiency decompositions: a focus on congestion measurement. Transp Res Part B: Methodol 32(5):299–312

    Article  Google Scholar 

  • Färe R (1975) Efficiency and the production function Zeitschrift für Nationalökonomie. J Econ 35(3–4):317–324

    Article  Google Scholar 

  • Färe R, Grosskopf S (1997) Profit efficiency, farrell decompositions and the mahler inequality. Econ Lett 57(3):283–287

    Article  Google Scholar 

  • Färe R, Lovell C (1978) Measuring the technical efficiency of production. J Econ Theory 19(August):150–162

    Article  Google Scholar 

  • Färe R, Primont D (1995) Multi-output production and duality: theory and applications. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

  • Färe R, Grosskopf S, Lovell C (1985) The measurement of efficiency of production. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

  • Farrell M (1957) The measurement of productive efficiency. J R Stat Soc, Series A (General) 120(3):253–290

    Article  Google Scholar 

  • Hardy G, Littlewood J, Polya G (1934) Inequalities. Cambridge University Press, Cambridge

    Google Scholar 

  • O’Donnell C (2010) Measuring and decomposing agricultural productivity and profitability change. Aust J Agric Resour Econ 54(4):527–560

    Article  Google Scholar 

  • O’Donnell C (2012) Nonparametric estimates of the components of productivity and profitability change in U.S. agriculture. Am J Agric Econ 94(4):873–890

    Article  Google Scholar 

  • O’Donnell C (2016) Using information about technologies, markets and firm behaviour to decompose a proper productivity index. J Econometrics 190(2):328–340

    Article  Google Scholar 

  • O’Donnell C, Nguyen K (2013) An econometric approach to estimating support prices and measures of productivity change in public hospitals. J Prod Anal 40(3):323–335

    Article  Google Scholar 

  • O’Donnell C, Rao D, Battese G (2008) Metafrontier frameworks for the study of firm-level efficiencies and technology ratios. Empirical Econ 34(2):231–255

    Article  Google Scholar 

  • O’Donnell C, Fallah-Fini S, Triantis K (2017) Measuring and analysing productivity change in a metafrontier framework. J Prod Anal 47(2):117–128

    Article  Google Scholar 

  • Panzar J, Willig R (1981) Economies of scope. Am Econ Rev 72(1):268–272

    Google Scholar 

  • Portela M, Thanassoulis E (2007) Developing a decomposable measure of profit efficiency using DEA. J Oper Res Soc 58(4):481–490

    Article  Google Scholar 

  • Russell R, Schworm W (2009) Axiomatic foundations of efficiency measurement on data-generated technologies. J Prod Anal 31(2):77–86

    Article  Google Scholar 

  • Russell R, Schworm W (2011) Properties of inefficiency indexes on \({<}\)input, output\({>}\) space. J Prod Anal 36(2):143–156

    Google Scholar 

  • Zhang N, Zhou P, Choi Y (2013) Energy efficiency, CO\(_2\) emission performance and technology gaps in fossil fuel electricity generation in Korea: a meta-frontier non-radial directional distance function analysis. Energy Policy 56(May):653–662

    Google Scholar 

  • Zieschang K (1984) An extended farrell technical efficiency measure. J Econ Theory 33(2):387–396

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Queensland, Brisbane, QLD, Australia

    Christopher J. O’Donnell

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  1. Christopher J. O’Donnell
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Correspondence to Christopher J. O’Donnell .

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O’Donnell, C.J. (2018). Measures of Efficiency. In: Productivity and Efficiency Analysis. Springer, Singapore. https://doi.org/10.1007/978-981-13-2984-5_5

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  • DOI: https://doi.org/10.1007/978-981-13-2984-5_5

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