IDEAS home Printed from https://ideas.repec.org/p/aeg/report/2018-02.html
   My bibliography  Save this paper

A Bootstrap Approach for Bandwidth Selection in Estimating Conditional Efficiency Measures

Author

Listed:
  • Luiza Badin

    (Department of Applied Mathematics, Bucharest University of Economic Studies and Gh. Mihoc-C. Iacob Institute)

  • Cinzia Daraio

    (Department of Computer, Control and Management Engineering Antonio Ruberti (DIAG), University of Rome La Sapienza, Rome, Italy)

  • Léopold Simar

    (Institut de Statistique, Biostatistique et de Sciences Actuarielles, Universite´ Catholique de Louvain, Louvain-la-Neuve, Belgium)

Abstract

Conditional efficiency measures are needed when the production process does not depend only on the inputs and outputs, but may be influenced by external factors and/or environmental variables (Z). They are estimated by means of a nonparametric estimator of the conditional distribution function of the inputs and outputs, conditionally on values of Z. For doing this, smoothing procedures and smoothing parameters, the bandwidths, are involved. So far, Least Squares Cross Validation (LSCV) methods have been used, which have been proven to provide bandwidths with optimal rates for estimating conditional distributions. In efficiency analysis, the main interest is in the estimation of the conditional efficiency score, which typically depends on the boundary of the support of the distribution and not on the full conditional distribution. In this paper, we show indeed that the rate for the bandwidths which is optimal for estimating conditional distributions, may not be optimal for the estimation of the efficiency scores. We propose hence a new approach based on the bootstrap which overcomes these difficulties. We analyze and compare, through Monte Carlo simulations, the performances of LSCV techniques with our bootstrap approach in ï¬ nite samples. As expected, our bootstrap approach shows generally better performances and is more robust to the various Monte Carlo scenarios analyzed. We provide in an Appendix the Matlab code performing our experiments.

Suggested Citation

  • Luiza Badin & Cinzia Daraio & Léopold Simar, 2018. "A Bootstrap Approach for Bandwidth Selection in Estimating Conditional Efficiency Measures," DIAG Technical Reports 2018-02, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    • Handle: RePEc:aeg:report:2018-02
    as

    Download full text from publisher

    File URL: https://wwwold.dis.uniroma1.it/~bibdis/RePEc/aeg/report/2018-02.pdf
    File Function: First version, 2018
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.
    2. Simar, Léopold & Vanhems, Anne & Van Keilegom, Ingrid, 2016. "Unobserved heterogeneity and endogeneity in nonparametric frontier estimation," Journal of Econometrics, Elsevier, vol. 190(2), pages 360-373.
    3. Halkos, George E. & Tzeremes, Nickolaos G., 2011. "A conditional nonparametric analysis for measuring the efficiency of regional public healthcare delivery: An application to Greek prefectures," Health Policy, Elsevier, vol. 103(1), pages 73-82.
    4. Matousek, Roman & Tzeremes, Nickolaos G., 2016. "CEO compensation and bank efficiency: An application of conditional nonparametric frontiers," European Journal of Operational Research, Elsevier, vol. 251(1), pages 264-273.
    5. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
    6. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non‐parametric, two‐stage models of production," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 170-191, June.
    7. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2012. "How to measure the impact of environmental factors in a nonparametric production model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 818-833.
    8. Léopold Simar & Paul Wilson, 2011. "Two-stage DEA: caveat emptor," Journal of Productivity Analysis, Springer, vol. 36(2), pages 205-218, October.
    9. Minviel, Jean Joseph & De Witte, Kristof, 2017. "The influence of public subsidies on farm technical efficiency: A robust conditional nonparametric approach," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1112-1120.
    10. D’Alfonso, Tiziana & Daraio, Cinzia & Nastasi, Alberto, 2015. "Competition and efficiency in the Italian airport system: new insights from a conditional nonparametric frontier analysis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 80(C), pages 20-38.
    11. José Manuel Cordero & Daniel Santín & Rosa Simancas, 2017. "Assessing European primary school performance through a conditional nonparametric model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(4), pages 364-376, April.
    12. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    13. Serra, Teresa & Oude Lansink, Alfons, 2014. "Measuring the impacts of production risk on technical efficiency: A state-contingent conditional order-m approach," European Journal of Operational Research, Elsevier, vol. 239(1), pages 237-242.
    14. Tzeremes, Nickolaos G., 2015. "Efficiency dynamics in Indian banking: A conditional directional distance approach," European Journal of Operational Research, Elsevier, vol. 240(3), pages 807-818.
    15. Wilson, Paul W., 2018. "Dimension reduction in nonparametric models of production," European Journal of Operational Research, Elsevier, vol. 267(1), pages 349-367.
    16. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
    17. Daraio, Cinzia & Bonaccorsi, Andrea & Simar, Léopold, 2015. "Rankings and university performance: A conditional multidimensional approach," European Journal of Operational Research, Elsevier, vol. 244(3), pages 918-930.
    18. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2008. "Local likelihood estimation of truncated regression and its partial derivatives: Theory and application," Journal of Econometrics, Elsevier, vol. 146(1), pages 185-198, September.
    19. Camilla Mastromarco & Léopold Simar, 2015. "Effect of FDI and Time on Catching Up: New Insights from a Conditional Nonparametric Frontier Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 826-847, August.
    20. Simar, Léopold & Wilson, Paul W., 2013. "Estimation and Inference in Nonparametric Frontier Models: Recent Developments and Perspectives," Foundations and Trends(R) in Econometrics, now publishers, vol. 5(3–4), pages 183-337, June.
    21. Yauheniya Varabyova & Carl Rudolf Blankart & Aleksandra Torbica & Jonas Schreyögg, 2017. "Comparing the Efficiency of Hospitals in Italy and Germany: Nonparametric Conditional Approach Based on Partial Frontier," Health Care Management Science, Springer, vol. 20(3), pages 379-394, September.
    22. Sofia KOURTESI & Panos FOUSEKIS & Apostolos POLYMEROS, 2012. "Conditional Efficiency Estimation With Environmental Variables: Evidence From Greek Cereal Farms," Scientific Bulletin - Economic Sciences, University of Pitesti, vol. 11(1), pages 43-52.
    23. Haelermans, Carla & De Witte, Kristof, 2012. "The role of innovations in secondary school performance – Evidence from a conditional efficiency model," European Journal of Operational Research, Elsevier, vol. 223(2), pages 541-549.
    24. Cordero, José Manuel & Pedraja-Chaparro, Francisco & Pisaflores, Elsa C. & Polo, Cristina, 2016. "Efficiency assessment of Portuguese municipalities using a conditional nonparametric approach," MPRA Paper 70674, University Library of Munich, Germany.
    25. Witte, Kristof De & Geys, Benny, 2011. "Evaluating efficient public good provision: Theory and evidence from a generalised conditional efficiency model for public libraries," Journal of Urban Economics, Elsevier, vol. 69(3), pages 319-327, May.
    26. Cordero, José Manuel & Alonso-Morán, Edurne & Nuño-Solinis, Roberto & Orueta, Juan F. & Arce, Regina Sauto, 2015. "Efficiency assessment of primary care providers: A conditional nonparametric approach," European Journal of Operational Research, Elsevier, vol. 240(1), pages 235-244.
    27. Jeong, Seok-Oh & Simar, Léopold, 2006. "Linearly interpolated FDH efficiency score for nonconvex frontiers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2141-2161, November.
    28. Tom Broekel & Charlotte Schlump, 2009. "The importance of R&D subsidies and technological infrastructure for regional innovation performance - A conditional efficiency approach," Papers in Evolutionary Economic Geography (PEEG) 0921, Utrecht University, Department of Human Geography and Spatial Planning, Group Economic Geography, revised Nov 2009.
    29. George E. Halkos & Shunsuke Managi, 2017. "Measuring the Effect of Economic Growth on Countries’ Environmental Efficiency: A Conditional Directional Distance Function Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 68(3), pages 753-775, November.
    30. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non‐parametric, two‐stage models of production," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 170-191, June.
    31. Luiza Bădin & Cinzia Daraio & Léopold Simar, 2014. "Explaining inefficiency in nonparametric production models: the state of the art," Annals of Operations Research, Springer, vol. 214(1), pages 5-30, March.
    32. Badin, Luiza & Daraio, Cinzia & Simar, Léopold, 2010. "Optimal bandwidth selection for conditional efficiency measures: A data-driven approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 633-640, March.
    33. Andrea Filippetti & Antonio Peyrache, 2015. "Labour Productivity and Technology Gap in European Regions: A Conditional Frontier Approach," Regional Studies, Taylor & Francis Journals, vol. 49(4), pages 532-554, April.
    34. Yauheniya Varabyova & Carl Rudolf Blankart & Jonas Schreyögg, 2017. "Using nonparametric conditional approach to integrate quality into efficiency analysis: empirical evidence from cardiology departments," Health Care Management Science, Springer, vol. 20(4), pages 565-576, December.
    35. George Halkos & Nickolaos Tzeremes, 2014. "Measuring the effect of Kyoto protocol agreement on countries’ environmental efficiency in CO 2 emissions: an application of conditional full frontiers," Journal of Productivity Analysis, Springer, vol. 41(3), pages 367-382, June.
    36. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions," European Journal of Operational Research, Elsevier, vol. 227(1), pages 182-189.
    37. Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, vol. 24(1), pages 93-121, September.
    38. Tom Broekel, 2012. "Collaboration Intensity and Regional Innovation Efficiency in Germany—A Conditional Efficiency Approach," Industry and Innovation, Taylor & Francis Journals, vol. 19(2), pages 155-179, February.
    39. Cinzia Daraio & Léopold Simar, 2007. "Conditional nonparametric frontier models for convex and nonconvex technologies: a unifying approach," Journal of Productivity Analysis, Springer, vol. 28(1), pages 13-32, October.
    40. 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.
    41. Michael Zschille, 2015. "Consolidating the water industry: an analysis of the potential gains from horizontal integration in a conditional efficiency framework," Journal of Productivity Analysis, Springer, vol. 44(1), pages 97-114, August.
    42. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    43. Jose M. Cordero & Francisco Pedraja-Chaparro & Elsa C. Pisaflores & Cristina Polo, 2017. "Efficiency assessment of Portuguese municipalities using a conditional nonparametric approach," Journal of Productivity Analysis, Springer, vol. 48(1), pages 1-24, August.
    44. Seok-Oh Jeong & Byeong Park & Léopold Simar, 2010. "Nonparametric conditional efficiency measures: asymptotic properties," Annals of Operations Research, Springer, vol. 173(1), pages 105-122, January.
    45. Zschille, Michael, 2015. "Consolidating the Water Industry: an Analysis of the Potential Gains from Horizontal Integration in a Conditional Efficiency Framework," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 44(1), pages 97-114.
    46. Dyson, R. G. & Allen, R. & Camanho, A. S. & Podinovski, V. V. & Sarrico, C. S. & Shale, E. A., 2001. "Pitfalls and protocols in DEA," European Journal of Operational Research, Elsevier, vol. 132(2), pages 245-259, July.
    47. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(6), pages 855-877, December.
    48. Daraio, Cinzia & Simar, Leopold, 2006. "A robust nonparametric approach to evaluate and explain the performance of mutual funds," European Journal of Operational Research, Elsevier, vol. 175(1), pages 516-542, November.
    49. 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.
    50. George E. Halkos & Nickolaos G. Tzeremes, 2013. "Modelling the effect of national culture on countries' innovation performances: A conditional full frontier approach," International Review of Applied Economics, Taylor & Francis Journals, vol. 27(5), pages 656-678, September.
    51. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    52. Baležentis, Tomas & De Witte, Kristof, 2015. "One- and multi-directional conditional efficiency measurement – Efficiency in Lithuanian family farms," European Journal of Operational Research, Elsevier, vol. 245(2), pages 612-622.
    53. George Halkos & Nickolaos Tzeremes, 2013. "National culture and eco-efficiency: an application of conditional partial nonparametric frontiers," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 15(4), pages 423-441, October.
    54. Guerrini, Andrea & Romano, Giulia & Mancuso, Fabrizio & Carosi, Laura, 2016. "Identifying the performance drivers of wastewater treatment plants through conditional order-m efficiency analysis," Utilities Policy, Elsevier, vol. 42(C), pages 20-31.
    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. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2020. "Fast and efficient computation of directional distance estimators," Annals of Operations Research, Springer, vol. 288(2), pages 805-835, May.
    2. Polemis, Michael L. & Tzeremes, Nickolaos G., 2019. "Competitive conditions and sectors’ productive efficiency: A conditional non-parametric frontier analysis," European Journal of Operational Research, Elsevier, vol. 276(3), pages 1104-1118.
    3. Jose M. Cordero & Cristina Polo & Daniel Santín, 2020. "Assessment of new methods for incorporating contextual variables into efficiency measures: a Monte Carlo simulation," Operational Research, Springer, vol. 20(4), pages 2245-2265, December.
    4. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2019. "Quality and its impact on efficiency," LIDAM Discussion Papers ISBA 2019004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Michael L. Polemis & Thanasis Stengos & Nickolaos G. Tzeremes, 2020. "Modeling the effect of competition on US manufacturing sectors’ efficiency: an order-m frontier analysis," Journal of Productivity Analysis, Springer, vol. 54(1), pages 27-41, August.
    6. Nickolaos G. Tzeremes, 2019. "Technological change, technological catch-up and export orientation: evidence from Latin American Countries," Journal of Productivity Analysis, Springer, vol. 52(1), pages 85-100, December.
    7. López-Torres, Laura & Johnes, Jill & Elliott, Caroline & Polo, Cristina, 2021. "The effects of competition and collaboration on efficiency in the UK independent school sector," Economic Modelling, Elsevier, vol. 96(C), pages 40-53.
    8. Cordero Ferrera, Jose Manuel & Alonso Morán, Edurne & Nuño Solís, Roberto & Orueta, Juan F. & Souto Arce, Regina, 2013. "Efficiency assessment of primary care providers: A conditional nonparametric approach," MPRA Paper 51926, University Library of Munich, Germany.
    9. Daraio, Cinzia & Simar, Léopold & Wilson, Paul W., 2021. "Quality as a latent heterogeneity factor in the efficiency of universities," Economic Modelling, Elsevier, vol. 99(C).
    10. Luiza Bădin & Cinzia Daraio & Léopold Simar, 2014. "Explaining inefficiency in nonparametric production models: the state of the art," Annals of Operations Research, Springer, vol. 214(1), pages 5-30, March.
    11. Guangshun Qiao & Zhan-ao Wang, 2021. "Vertical integration vs. specialization: a nonparametric conditional efficiency estimate for the global semiconductor industry," Journal of Productivity Analysis, Springer, vol. 56(2), pages 139-150, December.
    12. Fusco, Elisa & Vidoli, Francesco & Sahoo, Biresh K., 2018. "Spatial heterogeneity in composite indicator: A methodological proposal," Omega, Elsevier, vol. 77(C), pages 1-14.
    13. Cordero, Jose M. & Polo, Cristina & Santín, Daniel & Simancas, Rosa, 2018. "Efficiency measurement and cross-country differences among schools: A robust conditional nonparametric analysis," Economic Modelling, Elsevier, vol. 74(C), pages 45-60.
    14. Broadstock, David C. & Matousek, Roman & Meyer, Martin & Tzeremes, Nickolaos G., 2020. "Does corporate social responsibility impact firms' innovation capacity? The indirect link between environmental & social governance implementation and innovation performance," Journal of Business Research, Elsevier, vol. 119(C), pages 99-110.
    15. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    16. Camilla Mastromarco & Lenka Stastna & Jana Votapkova, 2019. "Efficiency of hospitals in the Czech Republic: Conditional efficiency approach," Journal of Productivity Analysis, Springer, vol. 51(1), pages 73-89, February.
    17. Cordero, José Manuel & Alonso-Morán, Edurne & Nuño-Solinis, Roberto & Orueta, Juan F. & Arce, Regina Sauto, 2015. "Efficiency assessment of primary care providers: A conditional nonparametric approach," European Journal of Operational Research, Elsevier, vol. 240(1), pages 235-244.
    18. Jose M. Cordero & Francisco Pedraja-Chaparro & Elsa C. Pisaflores & Cristina Polo, 2017. "Efficiency assessment of Portuguese municipalities using a conditional nonparametric approach," Journal of Productivity Analysis, Springer, vol. 48(1), pages 1-24, August.
    19. Minviel, Jean Joseph & De Witte, Kristof, 2017. "The influence of public subsidies on farm technical efficiency: A robust conditional nonparametric approach," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1112-1120.
    20. Baležentis, Tomas & De Witte, Kristof, 2015. "One- and multi-directional conditional efficiency measurement – Efficiency in Lithuanian family farms," European Journal of Operational Research, Elsevier, vol. 245(2), pages 612-622.

    More about this item

    Keywords

    Data Envelopment Analysis (DEA)/Free Disposal Hull (FDH); Conditional Efficiency ; Bandwidth ; Bootstrap ; Monte Carlo;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:aeg:report:2018-02. 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: Antonietta Angelica Zucconi (email available below). General contact details of provider: https://edirc.repec.org/data/dirosit.html .

    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.