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Measuring efficiency of Tunisian schools in the presence of quasi-fixed inputs: A bootstrap data envelopment analysis approach


  • Essid, Hédi
  • Ouellette, Pierre
  • Vigeant, Stéphane


The objective of this paper is to measure the efficiency of high schools in Tunisia. We use a statistical Data Envelopment Analysis (DEA)-bootstrap approach with quasi-fixed inputs to estimate the precision of our measure. To do so, we developed a statistical model serving as the foundation of the Data Generation Process (DGP). The DGP is constructed such that we can implement both smooth homogeneous and heterogeneous bootstrap methods. Bootstrap simulations were used to estimate and correct the bias, and to construct confidence intervals for the efficiency measures. The simulation results show that the efficiency measures are subject to sampling variations. The adjusted measure reveals that high schools with residence services would have to give up less than 12.1 percent of their resources on average to be efficient.

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  • Essid, Hédi & Ouellette, Pierre & Vigeant, Stéphane, 2007. "Measuring efficiency of Tunisian schools in the presence of quasi-fixed inputs: A bootstrap data envelopment analysis approach," MPRA Paper 14415, University Library of Munich, Germany, revised 2009.
  • Handle: RePEc:pra:mprapa:14415

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    References listed on IDEAS

    1. Leopold Simar & Paul Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 779-802.
    2. Léopold Simar & Paul Wilson, 2000. "Statistical Inference in Nonparametric Frontier Models: The State of the Art," Journal of Productivity Analysis, Springer, vol. 13(1), pages 49-78, January.
    3. Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
    4. Ouellette, Pierre & Vierstraete, Valerie, 2004. "Technological change and efficiency in the presence of quasi-fixed inputs: A DEA application to the hospital sector," European Journal of Operational Research, Elsevier, vol. 154(3), pages 755-763, May.
    5. 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.
    6. Silva Portela, Maria Conceicao A. & Thanassoulis, Emmanuel, 2001. "Decomposing school and school-type efficiency," European Journal of Operational Research, Elsevier, vol. 132(2), pages 357-373, July.
    7. Hanushek, Eric A, 1986. "The Economics of Schooling: Production and Efficiency in Public Schools," Journal of Economic Literature, American Economic Association, vol. 24(3), pages 1141-1177, September.
    8. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    9. Johnes, Jill, 2006. "Data envelopment analysis and its application to the measurement of efficiency in higher education," Economics of Education Review, Elsevier, vol. 25(3), pages 273-288, June.
    10. Muniz, M. A., 2002. "Separating managerial inefficiency and external conditions in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 143(3), pages 625-643, December.
    11. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
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    Cited by:

    1. Kristof de Witte & Laura López-Torres, 2015. "Efficiency in Education. A Review of Literature and a Way Forward," Working Papers 1501, Departament Empresa, Universitat Autònoma de Barcelona, revised Apr 2015.
    2. Lee, Boon L. & Worthington, Andrew C., 2014. "Technical efficiency of mainstream airlines and low-cost carriers: New evidence using bootstrap data envelopment analysis truncated regression," Journal of Air Transport Management, Elsevier, vol. 38(C), pages 15-20.
    3. repec:eee:soceps:v:61:y:2018:i:c:p:29-36 is not listed on IDEAS
    4. Johnes, Jill, 2015. "Operational Research in education," European Journal of Operational Research, Elsevier, vol. 243(3), pages 683-696.
    5. Boon Lee & Andrew Worthington, 2011. "Operational performance of low-cost carriers and international airlines: New evidence using a bootstrap truncated regression," School of Economics and Finance Discussion Papers and Working Papers Series 271, School of Economics and Finance, Queensland University of Technology.
    6. Hédi Essid & Pierre Ouellette & Stéphane Vigeant, 2013. "Small is not that beautiful after all: measuring the scale efficiency of Tunisian high schools using a DEA-bootstrap method," Applied Economics, Taylor & Francis Journals, vol. 45(9), pages 1109-1120, March.
    7. Giuseppe Di Giacomo & Aline Pennisi, 2015. "Assessing Primary and Lower Secondary School Efficiency Within Northern, Central and Southern Italy," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 1(2), pages 287-311, July.
    8. Yang, Jun & Zhang, Tengfei & Sheng, Pengfei & Shackman, Joshua D., 2016. "Carbon dioxide emissions and interregional economic convergence in China," Economic Modelling, Elsevier, vol. 52(PB), pages 672-680.
    9. José Manuel Cordero & Cristina Polo & Daniel Santín & Gabriela Sicilia, 2016. "Monte-Carlo Comparison of Conditional Nonparametric Methods and Traditional Approaches to Include Exogenous Variables," Pacific Economic Review, Wiley Blackwell, vol. 21(4), pages 483-497, October.

    More about this item


    Educational economics; Efficiency; Productivity; Data Envelopment Analysis; Bootstrap; Quasi-fixed inputs;

    JEL classification:

    • D2 - Microeconomics - - Production and Organizations
    • I2 - Health, Education, and Welfare - - Education


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