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Biases in technical efficiency scores caused by intra-input aggregation: mathematical analysis and a DEA application using simulated data


  • Darold Barnum
  • John Gleason


In Data Envelopment Analysis (DEA) applications involving multiple inputs and outputs, inputs are aggregated into the total amounts of each type of input. For example, if input types 'labour' and 'capital' are used to produce multiple outputs, the total amount of labour used to produce all outputs is treated as one aggregated input and the total amount of capital as another. Resources are not disaggregated into input variables measuring the amount of labour used to produce the first output, the amount of labour used to produce the second output, the amount of labour used to produce the third output and so on, for both labour and capital. It is shown that such intra-input aggregation causes downward bias in reported technical efficiency scores, with variations in bias unrelated to true technical efficiency. Therefore, with few exceptions, any technical efficiency comparisons among DMUs are invalid. The presence of intra-input aggregation bias is demonstrated mathematically, simulation is used to exhibit its severity, and the exceptions that permit intra-input aggregation without causing bias are identified. It is concluded that, for multiple-input, multiple-output DEA applications, inputs must be disaggregated into the amounts used to produce each output in order to validly report technical efficiency, unless one of the exceptions is present.

Suggested Citation

  • Darold Barnum & John Gleason, 2006. "Biases in technical efficiency scores caused by intra-input aggregation: mathematical analysis and a DEA application using simulated data," Applied Economics, Taylor & Francis Journals, vol. 38(14), pages 1593-1603.
  • Handle: RePEc:taf:applec:v:38:y:2006:i:14:p:1593-1603
    DOI: 10.1080/00036840500405714

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    Cited by:

    1. Welch, Eric & Barnum, Darold, 2009. "Joint environmental and cost efficiency analysis of electricity generation," Ecological Economics, Elsevier, vol. 68(8-9), pages 2336-2343, June.
    2. Barnum, Darold T. & Karlaftis, Matthew G. & Tandon, Sonali, 2011. "Improving the efficiency of metropolitan area transit by joint analysis of its multiple providers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 1160-1176.
    3. Fatima S. Al Shamsi & Hassan Aly & Mohamed El-Bassiouni, 2009. "Measuring and explaining the efficiencies of the United Arab Emirates banking system," Applied Economics, Taylor & Francis Journals, vol. 41(27), pages 3505-3519.

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