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Estimating DEA technical and allocative inefficiency using aggregate cost or revenue data

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Abstract

In this paper, we address the question of Data Envelopment Analysis (DEA) evaluation of efficiency when aggregate cost or revenue data must be used. We show that the DEA technical inefficiency measure using total revenues as the single output variable or total costs as the single input variable equals the aggregate technical and allocative inefficiency. We employ this result to estimate allocative inefficiency and construct statistical tests of the null hypothesis of no allocative inefficiency analogous to those of the null hypothesis of no scale inefficiency. We illustrate our method using revenue and personnel data for the top U.S. public accounting firms over 1995–1998. Our empirical results indicate the existence of statistically significant allocative inefficiency in the public accounting industry.

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Notes

  1. For each observation, at least one output y rj and one input x ij are assumed to be strictly positive with a positive price.

  2. While we present our theoretical analysis in the context of aggregate revenues, analogous results obtain also for the case of aggregate costs.

  3. The data generating process comprises the generation of the input vector X j , the direction vector representing the relative mix of outputs, and the scalar \({\theta _j^B }\) that determines the distance traversed by the observed output vector Y j along the direction vector representing the relative output mix.

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Authors and Affiliations

  1. Fox School of Business, Temple University, Philadelphia, PA, 19122, USA

    Rajiv D. Banker

  2. Whitman School of Management, Syracuse University, Syracuse, NY, 13244, USA

    Hsihui Chang

  3. School of Management, University of Texas at Dallas, Richardson, TX, 75083, USA

    Ram Natarajan

Authors
  1. Rajiv D. Banker
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  2. Hsihui Chang
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  3. Ram Natarajan
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Correspondence to Hsihui Chang.

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Banker, R.D., Chang, H. & Natarajan, R. Estimating DEA technical and allocative inefficiency using aggregate cost or revenue data. J Prod Anal 27, 115–121 (2007). https://doi.org/10.1007/s11123-006-0027-1

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  • DOI: https://doi.org/10.1007/s11123-006-0027-1

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