IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v256y2017i3p1004-1014.html
   My bibliography  Save this article

Geometric mean quantity index numbers with Benefit-of-the-Doubt weights

Author

Listed:
  • Van Puyenbroeck, Tom
  • Rogge, Nicky

Abstract

Geometric mean index numbers are a multiplicative aggregation of (price or quantity) ratios with their importance exponents/weights derived from one or more observed budget shares. In the specific context of composite indicator construction, we propose to use the budget shares as naturally generated by the linear Benefit-of-the-Doubt model. This approach is directly inspired by the literature on index number theory. Our basic model is easily extended to provide transitive composite indicator orderings in a multilateral setting. Also, a multi-factor decomposition is proposed to explain the intertemporal evolution of a single entity. We illustrate our results with social inclusion data for the EU-countries.

Suggested Citation

  • Van Puyenbroeck, Tom & Rogge, Nicky, 2017. "Geometric mean quantity index numbers with Benefit-of-the-Doubt weights," European Journal of Operational Research, Elsevier, vol. 256(3), pages 1004-1014.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:3:p:1004-1014
    DOI: 10.1016/j.ejor.2016.07.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221716305938
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2016.07.038?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cooper, William W. & Ruiz, Jose L. & Sirvent, Inmaculada, 2007. "Choosing weights from alternative optimal solutions of dual multiplier models in DEA," European Journal of Operational Research, Elsevier, vol. 180(1), pages 443-458, July.
    2. Wang, Ying-Ming & Chin, Kwai-Sang, 2010. "Some alternative models for DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 128(1), pages 332-338, November.
    3. Athanassoglou, Stergios, 2015. "Revisiting Worst-case DEA for Composite Indicators," Climate Change and Sustainable Development 198712, Fondazione Eni Enrico Mattei (FEEM).
    4. Ebert, Udo & Welsch, Heinz, 2004. "Meaningful environmental indices: a social choice approach," Journal of Environmental Economics and Management, Elsevier, vol. 47(2), pages 270-283, March.
    5. Blancard, Stéphane & Hoarau, Jean-François, 2013. "A new sustainable human development indicator for small island developing states: A reappraisal from data envelopment analysis," Economic Modelling, Elsevier, vol. 30(C), pages 623-635.
    6. Hatefi, S.M. & Torabi, S.A., 2010. "A common weight MCDA-DEA approach to construct composite indicators," Ecological Economics, Elsevier, vol. 70(1), pages 114-120, November.
    7. Michela Nardo & Michaela Saisana & Andrea Saltelli & Stefano Tarantola & Anders Hoffman & Enrico Giovannini, 2005. "Handbook on Constructing Composite Indicators: Methodology and User Guide," OECD Statistics Working Papers 2005/3, OECD Publishing.
    8. P. Zhou & B. Ang & D. Zhou, 2010. "Weighting and Aggregation in Composite Indicator Construction: a Multiplicative Optimization Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 96(1), pages 169-181, March.
    9. B. Hollingsworth & P. Smith, 2003. "Use of ratios in data envelopment analysis," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 733-735.
    10. Balk,Bert M., 2012. "Price and Quantity Index Numbers," Cambridge Books, Cambridge University Press, number 9781107404960, September.
    11. Verschelde, Marijn & Rogge, Nicky, 2012. "An environment-adjusted evaluation of citizen satisfaction with local police effectiveness: Evidence from a conditional Data Envelopment Analysis approach," European Journal of Operational Research, Elsevier, vol. 223(1), pages 214-225.
    12. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    13. Francesca Giambona & Erasmo Vassallo, 2014. "Composite Indicator of Social Inclusion for European Countries," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 116(1), pages 269-293, March.
    14. Cherchye, Laurens & Knox Lovell, C.A. & Moesen, Wim & Van Puyenbroeck, Tom, 2007. "One market, one number? A composite indicator assessment of EU internal market dynamics," European Economic Review, Elsevier, vol. 51(3), pages 749-779, April.
    15. Cook, Wade D. & Zhu, Joe, 2007. "Within-group common weights in DEA: An analysis of power plant efficiency," European Journal of Operational Research, Elsevier, vol. 178(1), pages 207-216, April.
    16. L Cherchye & W Moesen & N Rogge & T Van Puyenbroeck & M Saisana & A Saltelli & R Liska & S Tarantola, 2008. "Creating composite indicators with DEA and robustness analysis: the case of the Technology Achievement Index," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(2), pages 239-251, February.
    17. R. Allen & A. Athanassopoulos & R.G. Dyson & E. Thanassoulis, 1997. "Weights restrictions and value judgements in Data Envelopment Analysis: Evolution, development and future directions," Annals of Operations Research, Springer, vol. 73(0), pages 13-34, October.
    18. Cristina Bernini & Andrea Guizzardi & Giovanni Angelini, 2013. "DEA-Like Model and Common Weights Approach for the Construction of a Subjective Community Well-Being Indicator," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 114(2), pages 405-424, November.
    19. Robert J. Hill, 1997. "A Taxonomy Of Multilateral Methods For Making International Comparisons Of Prices And Quantities," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 43(1), pages 49-69, March.
    20. Verschelde, Marijn & Rogge, Nicky, 2012. "An environment-adjusted evaluation of local police e ectiveness: evidence from a conditional Data Envelopment Analysis approach," Working Papers 2012/09, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    21. Laurens Cherchye & Wim Moesen & Tom Van Puyenbroeck, 2004. "Legitimately Diverse, yet Comparable: On Synthesizing Social Inclusion Performance in the EU," Journal of Common Market Studies, Wiley Blackwell, vol. 42(5), pages 919-955, December.
    22. Zanella, Andreia & Camanho, Ana S. & Dias, Teresa G., 2015. "Undesirable outputs and weighting schemes in composite indicators based on data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 245(2), pages 517-530.
    23. Chris Tofallis, 2014. "On constructing a composite indicator with multiplicative aggregation and the avoidance of zero weights in DEA," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(5), pages 791-792, May.
    24. Roll, Y & Golany, B., 1993. "Alternate methods of treating factor weights in DEA," Omega, Elsevier, vol. 21(1), pages 99-109, January.
    25. Wade D. Cook & Joe Zhu, 2015. "DEA Cross Efficiency," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 2, pages 23-43, Springer.
    26. Ravallion, Martin, 2012. "Troubling tradeoffs in the Human Development Index," Journal of Development Economics, Elsevier, vol. 99(2), pages 201-209.
    27. Rogge, Nicky, 2012. "Undesirable specialization in the construction of composite policy indicators: The Environmental Performance Index," Working Papers 2012/08, Hogeschool-Universiteit Brussel, Faculteit Economie en Management.
    28. Laurens Cherchye & Willem Moesen & Nicky Rogge & Tom Puyenbroeck, 2007. "An Introduction to ‘Benefit of the Doubt’ Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 82(1), pages 111-145, May.
    29. Sinuany-Stern, Zilla & Friedman, Lea, 1998. "DEA and the discriminant analysis of ratios for ranking units," European Journal of Operational Research, Elsevier, vol. 111(3), pages 470-478, December.
    30. Liang, Liang & Wu, Jie & Cook, Wade D. & Zhu, Joe, 2008. "Alternative secondary goals in DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 113(2), pages 1025-1030, June.
    31. Amado, Carla A.F. & São José, José M.S. & Santos, Sérgio P., 2016. "Measuring active ageing: A Data Envelopment Analysis approach," European Journal of Operational Research, Elsevier, vol. 255(1), pages 207-223.
    32. Karagiannis, Giannis & Knox Lovell, C.A., 2016. "Productivity measurement in radial DEA models with a single constant input," European Journal of Operational Research, Elsevier, vol. 251(1), pages 323-328.
    33. Ozren Despić & Mladen Despić & Joseph Paradi, 2007. "DEA-R: ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications," Journal of Productivity Analysis, Springer, vol. 28(1), pages 33-44, October.
    34. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
    35. Ali Emrouznejad & Emilyn Cabanda, 2010. "An aggregate measure of financial ratios using a multiplicative DEA model," International Journal of Financial Services Management, Inderscience Enterprises Ltd, vol. 4(2), pages 114-126.
    36. Fusco, Elisa, 2015. "Enhancing non-compensatory composite indicators: A directional proposal," European Journal of Operational Research, Elsevier, vol. 242(2), pages 620-630.
    37. Mariano, Enzo Barberio & Sobreiro, Vinicius Amorim & Rebelatto, Daisy Aparecida do Nascimento, 2015. "Human development and data envelopment analysis: A structured literature review," Omega, Elsevier, vol. 54(C), pages 33-49.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rogge, Nicky, 2018. "Composite indicators as generalized benefit-of-the-doubt weighted averages," European Journal of Operational Research, Elsevier, vol. 267(1), pages 381-392.
    2. Salvatore Greco & Alessio Ishizaka & Menelaos Tasiou & Gianpiero Torrisi, 2019. "On the Methodological Framework of Composite Indices: A Review of the Issues of Weighting, Aggregation, and Robustness," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(1), pages 61-94, January.
    3. Rogge, Nicky & De Jaeger, Simon & Lavigne, Carolien, 2017. "Waste Performance of NUTS 2-regions in the EU: A Conditional Directional Distance Benefit-of-the-Doubt Model," Ecological Economics, Elsevier, vol. 139(C), pages 19-32.
    4. Verbunt, Pim & Rogge, Nicky, 2018. "Geometric composite indicators with compromise Benefit-of-the-Doubt weights," European Journal of Operational Research, Elsevier, vol. 264(1), pages 388-401.
    5. Milica Maricic & Jose A. Egea & Veljko Jeremic, 2019. "A Hybrid Enhanced Scatter Search—Composite I-Distance Indicator (eSS-CIDI) Optimization Approach for Determining Weights Within Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 144(2), pages 497-537, July.
    6. Nicky Rogge & Ilse Nijverseel, 2019. "Quality of Life in the European Union: A Multidimensional Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(2), pages 765-789, January.
    7. Amado, Carla A.F. & São José, José M.S. & Santos, Sérgio P., 2016. "Measuring active ageing: A Data Envelopment Analysis approach," European Journal of Operational Research, Elsevier, vol. 255(1), pages 207-223.
    8. Fusco, Elisa & Vidoli, Francesco & Sahoo, Biresh K., 2018. "Spatial heterogeneity in composite indicator: A methodological proposal," Omega, Elsevier, vol. 77(C), pages 1-14.
    9. Stergios Athanassoglou, 2016. "Revisiting Worst-Case DEA for Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 128(3), pages 1259-1272, September.
    10. Zanella, Andreia & Camanho, Ana S. & Dias, Teresa G., 2015. "Undesirable outputs and weighting schemes in composite indicators based on data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 245(2), pages 517-530.
    11. Athanassoglou, Stergios, 2015. "Revisiting Worst-case DEA for Composite Indicators," Climate Change and Sustainable Development 198712, Fondazione Eni Enrico Mattei (FEEM).
    12. Hatefi, S.M. & Torabi, S.A., 2010. "A common weight MCDA-DEA approach to construct composite indicators," Ecological Economics, Elsevier, vol. 70(1), pages 114-120, November.
    13. Panagiotis Ravanos & Giannis Karagiannis, 2021. "A VEA Benefit-of-the-Doubt Model for the HDI," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 155(1), pages 27-46, May.
    14. Nicky Rogge & Emilia Konttinen, 2018. "Social Inclusion in the EU Since the Enlargement: Progress or Regress?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 135(2), pages 563-584, January.
    15. Giménez, Víctor & Thieme, Claudio & Prior, Diego & Tortosa-Ausina, Emili, 2022. "Evaluation and determinants of preschool effectiveness in Chile," Socio-Economic Planning Sciences, Elsevier, vol. 81(C).
    16. Diogo Ferraz & Enzo B. Mariano & Daisy Rebelatto & Dominik Hartmann, 2020. "Linking Human Development and the Financial Responsibility of Regions: Combined Index Proposals Using Methods from Data Envelopment Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 150(2), pages 439-478, July.
    17. Fusco, Elisa & Maggi, Bernardo & Rizzuto, Livia, 2022. "Alternative indicators for the evaluation of renewables in Europe: An efficiency approach," Renewable Energy, Elsevier, vol. 190(C), pages 48-65.
    18. M. M. Segovia-González & I. Contreras, 2023. "A Composite Indicator to Compare the Performance of Male and Female Students in Educational Systems," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 165(1), pages 181-212, January.
    19. Fusco, Elisa, 2015. "Enhancing non-compensatory composite indicators: A directional proposal," European Journal of Operational Research, Elsevier, vol. 242(2), pages 620-630.
    20. Francesco Vidoli & Elisa Fusco & Claudio Mazziotta, 2015. "Non-compensability in Composite Indicators: A Robust Directional Frontier Method," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 122(3), pages 635-652, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:256:y:2017:i:3:p:1004-1014. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.