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2021 | OriginalPaper | Chapter

Individual Efficient Frontiers in Performance Analysis

Authors : Markku Kallio, Merja Halme

Published in: Advances in Efficiency and Productivity Analysis

Publisher: Springer International Publishing

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Abstract

We propose a new approach for performance comparisons with a goal similar to the DEA or efficiency analysis based on stochastic frontiers. Our approach accounts for varying environmental factors and human resources among the units under consideration by assuming individual production possibility sets (PPS). In a partial equilibrium framework we assume that the observed netputs represent an equilibrium. Thus, each DMU is efficient with respect to its individual PPS. The netputs and estimated prices common for all units reveal characteristics of the individual PPSs and assess the units’ relative performance. To obtain such prices from scarce data we assume that the observed netput vectors represent a random sample of netput vectors. We use prices which render the realizations of individual profits or returns of the DMUs most likely. We compare the DEA based efficiency rankings with our performance rankings. Strong rank correlation is observed between the two. The discriminatory power of our ranking is superior to conventional DEA methods.

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Footnotes
1
If prices of some products or services are not observable in the market, we interpret the prices resulting from rational expectations equilibrium.
 
2
In this case we expect that the likelihood for x≱0 and y≱0 is small.
 
3
For integer k ≥ 1, k!! is the product of positive integers up to k with the same parity as k, and 0!!=(-1)!!=1.
 
4
For VEA this additional requirement under CRS leads to infeasibility.
 
5
Note that in Fig. 3 the REA and RPA scores are positively correlated whereas in Fig. 3 the VEA and VPA scores have negative correlation because high VEA score means poor performance.
 
Literature
go back to reference Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30, 1078–1092.CrossRef Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30, 1078–1092.CrossRef
go back to reference Banker, R. D., & Natarajan, R. (2008). Evaluating contextual variables affecting productivity using data envelopment analysis. Operations Research, 56, 48–58.CrossRef Banker, R. D., & Natarajan, R. (2008). Evaluating contextual variables affecting productivity using data envelopment analysis. Operations Research, 56, 48–58.CrossRef
go back to reference Chambers, R. G., Chung, Y., & Färe, R. (1998). Profit, directional distance functions, and Nerlovian efficiency. Journal of Optimization Theory and Applications, 98, 351–364.CrossRef Chambers, R. G., Chung, Y., & Färe, R. (1998). Profit, directional distance functions, and Nerlovian efficiency. Journal of Optimization Theory and Applications, 98, 351–364.CrossRef
go back to reference Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.CrossRef Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.CrossRef
go back to reference Deb, K., Anand, A., & Joshi, D. (2002). A computationally efficient evolutionary algorithm for real-parameter optimization. Journal of Evolutionary Computation, 10(4), 371–395.CrossRef Deb, K., Anand, A., & Joshi, D. (2002). A computationally efficient evolutionary algorithm for real-parameter optimization. Journal of Evolutionary Computation, 10(4), 371–395.CrossRef
go back to reference Eskelinen, J., Halme, M., & Kallio, M. (2014). Bank branch sales evaluation using extended value efficiency analysis. European Journal of Operational Research, 232, 654–663.CrossRef Eskelinen, J., Halme, M., & Kallio, M. (2014). Bank branch sales evaluation using extended value efficiency analysis. European Journal of Operational Research, 232, 654–663.CrossRef
go back to reference Fourer, R., Gay, D., & Kernighan, B.W. (2003). AMPL, a modeling language for mathematical programming (2nd ed.). Pacific Grove: Brooks/Cole Thomson Learning. Fourer, R., Gay, D., & Kernighan, B.W. (2003). AMPL, a modeling language for mathematical programming (2nd ed.). Pacific Grove: Brooks/Cole Thomson Learning.
go back to reference Fried, H. O., Lovell, C. A. K., Schmidt, S. S., & Yaisawarng, S. (2002). Accounting for environmental effects and statistical noise in data envelopment analysis. Journal of Productivity Analysis, 17, 157–174.CrossRef Fried, H. O., Lovell, C. A. K., Schmidt, S. S., & Yaisawarng, S. (2002). Accounting for environmental effects and statistical noise in data envelopment analysis. Journal of Productivity Analysis, 17, 157–174.CrossRef
go back to reference Halme, M., Joro, T., Korhonen, P., Salo, S., & Wallenius, J. (1999). A value efficiency approach to incorporating preference information in data envelopment analysis. Management Science, 45(1), 103–115.CrossRef Halme, M., Joro, T., Korhonen, P., Salo, S., & Wallenius, J. (1999). A value efficiency approach to incorporating preference information in data envelopment analysis. Management Science, 45(1), 103–115.CrossRef
go back to reference Halme, M., & Korhonen, P. (2000). Restricting weights in value efficiency analysis. European Journal of Operational Research, 126, 175–188.CrossRef Halme, M., & Korhonen, P. (2000). Restricting weights in value efficiency analysis. European Journal of Operational Research, 126, 175–188.CrossRef
go back to reference Kallio, A. M. I., & Kallio, M. J. (2002). Nonparametric models for evaluating economic efficiency and imperfect competition. Journal of Productivity Analysis, 18, 171–189.CrossRef Kallio, A. M. I., & Kallio, M. J. (2002). Nonparametric models for evaluating economic efficiency and imperfect competition. Journal of Productivity Analysis, 18, 171–189.CrossRef
go back to reference Kneip, A., Simar, L., & Wilson, P. W. (2016). Testing hypotheses in nonparametric models of production. Journal of Business & Economic Statistics, 34(3), 435–456.CrossRef Kneip, A., Simar, L., & Wilson, P. W. (2016). Testing hypotheses in nonparametric models of production. Journal of Business & Economic Statistics, 34(3), 435–456.CrossRef
go back to reference Korhonen, P., Soismaa, M., & Siljamäki, A. (2002). On the use of value efficiency analysis and some further developments. Journal of Productivity Analysis, 17, 49–65.CrossRef Korhonen, P., Soismaa, M., & Siljamäki, A. (2002). On the use of value efficiency analysis and some further developments. Journal of Productivity Analysis, 17, 49–65.CrossRef
go back to reference Kumbhakar, S. C., & Lovell, C. A. K. (2000). Stochastic frontier analysis. Cambridge: Cambridge University Press.CrossRef Kumbhakar, S. C., & Lovell, C. A. K. (2000). Stochastic frontier analysis. Cambridge: Cambridge University Press.CrossRef
go back to reference Kumbhakar, S. C., Wang, H.-J., & Horncastle, A. (2015). A practitioner’s guide to stochastic frontier analysis using stata. Cambridge: Cambridge University Press.CrossRef Kumbhakar, S. C., Wang, H.-J., & Horncastle, A. (2015). A practitioner’s guide to stochastic frontier analysis using stata. Cambridge: Cambridge University Press.CrossRef
go back to reference Kuosmanen, T. (2012). Stochastic semi-nonparametric frontier estimation of electricity distribution networks: Application of the StoNED method in the Finnish regulatory model. Energy Economics, 34(6), 2189–2199.CrossRef Kuosmanen, T. (2012). Stochastic semi-nonparametric frontier estimation of electricity distribution networks: Application of the StoNED method in the Finnish regulatory model. Energy Economics, 34(6), 2189–2199.CrossRef
go back to reference Kuosmanen, T., Kortelainen, M., Sipiläinen, T., & Cherchye, L. (2010). Firm and industry level profit efficiency analysis using absolute and uniform shadow prices. European Journal of Operational Research, 202, 584–594.CrossRef Kuosmanen, T., Kortelainen, M., Sipiläinen, T., & Cherchye, L. (2010). Firm and industry level profit efficiency analysis using absolute and uniform shadow prices. European Journal of Operational Research, 202, 584–594.CrossRef
go back to reference Murtagh, B., & Saunders, M. (1978). Large-scale linearly constrained optimization. Mathematical Programming, 14, 41–72.CrossRef Murtagh, B., & Saunders, M. (1978). Large-scale linearly constrained optimization. Mathematical Programming, 14, 41–72.CrossRef
go back to reference Nerlove, K. (1965). Estimation and identification of Cobb-Douglas production functions. Chicago: Rand Mcnally. Nerlove, K. (1965). Estimation and identification of Cobb-Douglas production functions. Chicago: Rand Mcnally.
go back to reference Pedjara-Chaparro, F., Salinas-Jimenez, J., & Smith, P. (1997). On the role of weight restrictions in data envelopment analysis. European Journal of Operational Research, 8, 215–230. Pedjara-Chaparro, F., Salinas-Jimenez, J., & Smith, P. (1997). On the role of weight restrictions in data envelopment analysis. European Journal of Operational Research, 8, 215–230.
go back to reference Ramalho, E. A., Ramalho, J. J. S., & Henriques, P. D. (2010). Fractional regression models for second stage DEA efficiency analyses. Journal of Productivity Analysis, 34, 239–255.CrossRef Ramalho, E. A., Ramalho, J. J. S., & Henriques, P. D. (2010). Fractional regression models for second stage DEA efficiency analyses. Journal of Productivity Analysis, 34, 239–255.CrossRef
go back to reference Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, 27(3), 832–837.CrossRef Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics, 27(3), 832–837.CrossRef
go back to reference Ruggiero, J. (1998). Non-discretionary inputs in data envelopment analysis. European Journal of Operational Research, 111(3), 461–469.CrossRef Ruggiero, J. (1998). Non-discretionary inputs in data envelopment analysis. European Journal of Operational Research, 111(3), 461–469.CrossRef
go back to reference Silverman, B. W. (1998). Density estimation for statistics and data analysis. Boca Raton: Chapman & Hall. Silverman, B. W. (1998). Density estimation for statistics and data analysis. Boca Raton: Chapman & Hall.
Metadata
Title
Individual Efficient Frontiers in Performance Analysis
Authors
Markku Kallio
Merja Halme
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-47106-4_9