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Aggregation and decomposition of Farrell efficiencies

Author

Listed:
  • Rolf Färe

    (Oregon State University
    Oregon State University
    University of Maryland)

  • Giannis Karagiannis

    (University of Macedonia)

Abstract

In paper we examine the conditions under which aggregate overall Farrell efficiency decomposes by both observation (i.e., firms) and source (i.e., technical and allocative efficiency) using the same set of aggregation weights. These conditions require firms to produce a single output with a homogenous of degree $$r > 0$$ r > 0 technology. Then, Farrell decomposition at the firm level is also preserved at the industry level.

Suggested Citation

  • Rolf Färe & Giannis Karagiannis, 2022. "Aggregation and decomposition of Farrell efficiencies," Operational Research, Springer, vol. 22(5), pages 5675-5683, November.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:5:d:10.1007_s12351-022-00721-1
    DOI: 10.1007/s12351-022-00721-1
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    References listed on IDEAS

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    1. Färe, Rolf & Karagiannis, Giannis, 2014. "A postscript on aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 233(3), pages 784-786.
    2. Juan Aparicio & José L. Zofío, 2017. "Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach," Journal of Productivity Analysis, Springer, vol. 48(2), pages 133-146, December.
    3. Aparicio, Juan & Pastor, Jesus T. & Zofio, Jose L., 2015. "How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies," European Journal of Operational Research, Elsevier, vol. 240(3), pages 882-891.
    4. Fare, Rolf & Zelenyuk, Valentin, 2003. "On aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 146(3), pages 615-620, May.
    5. Tone, Kaoru & Tsutsui, Miki, 2007. "Decomposition of cost efficiency and its application to Japanese-US electric utility comparisons," Socio-Economic Planning Sciences, Elsevier, vol. 41(2), pages 91-106, June.
    6. Walter Briec & Benoit Dervaux & Hervé Leleu, 2003. "Aggregation of Directional Distance Functions and Industrial Efficiency," Journal of Economics, Springer, vol. 79(3), pages 237-261, July.
    7. Rolf Fare & Valentin Zelenyuk, 2005. "On Farrell's Decomposition and Aggregation," International Journal of Business and Economics, School of Management Development, Feng Chia University, Taichung, Taiwan, vol. 4(2), pages 167-171, August.
    8. Portela, Maria Conceição A. Silva & Thanassoulis, Emmanuel, 2014. "Economic efficiency when prices are not fixed: disentangling quantity and price efficiency," Omega, Elsevier, vol. 47(C), pages 36-44.
    9. Camanho, A.S. & Dyson, R.G., 2008. "A generalisation of the Farrell cost efficiency measure applicable to non-fully competitive settings," Omega, Elsevier, vol. 36(1), pages 147-162, February.
    10. Färe, Rolf & Karagiannis, Giannis, 2017. "The denominator rule for share-weighting aggregation," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1175-1180.
    11. Jean-Philippe Boussemart & Walter Briec & Nicolas Peypoch & Christophe Tavéra, 2009. "α-Returns to scale and multi-output production technologies," Post-Print halshs-00418883, HAL.
    12. K Tone, 2002. "A strange case of the cost and allocative efficiencies in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(11), pages 1225-1231, November.
    13. Bogetoft, Peter & Fare, Rolf & Obel, Borge, 2006. "Allocative efficiency of technically inefficient production units," European Journal of Operational Research, Elsevier, vol. 168(2), pages 450-462, January.
    14. Leleu, Hervé & Briec, Walter, 2009. "A DEA estimation of a lower bound for firms' allocative efficiency without information on price data," International Journal of Production Economics, Elsevier, vol. 121(1), pages 203-211, September.
    15. Färe, Rolf & Karagiannis, Giannis, 2020. "On the denominator rule and a theorem by Janos Aczél," European Journal of Operational Research, Elsevier, vol. 282(1), pages 398-400.
    16. Viera Mendelová, 2021. "Decomposition of cost efficiency with adjustable prices: an application of data envelopment analysis," Operational Research, Springer, vol. 21(4), pages 2739-2770, December.
    17. W. Erwin Diewert, 2005. "Index Number Theory Using Differences Rather Than Ratios," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 311-360, January.
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