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Do market share and efficiency matter for each other? An application of the zero-sum gains data envelopment analysis

  • Theoretical Paper
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Journal of the Operational Research Society

Abstract

Current studies that use traditional data envelopment analysis (DEA) neglect the 100% market share restriction. This study adopts zero-sum gains data envelopment analysis to measure the efficiency scores of securities firms (SFs) and indicates that the traditional DEA model underestimates the efficiency scores of inefficient SFs. This research analyses 266 integrated securities firms in Taiwan from 2001 to 2005 and employs three inputs (fixed assets, financial capital, and general expenses) and a single output (market share). The foreign-affiliated ownership of SFs positively affects the efficiency scores. The two-stage least squares procedure confirms that the market share and efficiency score simultaneously reinforce each other.

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Acknowledgements

The authors are grateful to an anonymous referee and a joint editor of this journal for their constructive comments, which have led to substantial improvements in this paper. Partial financial support from Taiwan's National Science Council (NSC96-2415-H-009-002-MY2) is gratefully acknowledged.

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Authors and Affiliations

  1. National Chiao Tung University, Taipei City, Taiwan

    J-L Hu & C-Y Fang

  2. China University of Technology, Taipei City, Taiwan

    C-Y Fang

Authors
  1. J-L Hu
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  2. C-Y Fang
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Correspondence to J-L Hu.

Appendices

Appendix A. A simple numerical example

To illustrate the equal reduction strategy and proportional strategy pointed out by Lins et al (2003), we derive our new measure of output reduction by providing a simple example involving observations for 10 DMUs with their market share y i in Table A1.

Step 1::

Assume that DMU 1 tries to achieve an efficiency score of 100 via market share maximization from 25 to 43%. DMU 1 gains an 18% market share, indicating that the other DMU j (j≠1) loses a market share of y i (φ iR −1)=18%.

Step 2::

Replace the output (y j ) of each DMU j (j≠1) based on the original output minus the equal output reduction following the equation: y j −((y i (φ iR −1))/(N−1)). ((y i (φ iR −1))/(N−1))=18%/(10−1)=2%. Then calculate y je =y j −((y i (φ iR −1))/(N−1)) for each j in Table A1.

Step 3::

The fourth column of Table A1 shows that the equal output reduction strategy is inappropriate because of the negative market share value (y 10e =−0.5%) in DMU 10 after applying this measurement.

Step 4::

The proportional output reduction calculations are shown in the last column of Table A1 via

for DMU j(j≠1). When

When

The proportional output reduction strategy avoids the drawback of the equal output reduction, and becomes the model that we apply.

Table a1 An illustrative example
Full size table

Appendix B

In Table B1 are the efficiency scores using the BCC-DEA and ZSG-DEA models for the SFs in Taiwan during the period 2001–2005.

Table a2 Efficiency scores (θ i ) of BCC-DEA and ZSG-DEA models for the SFs in Taiwan during 2001–2005
Full size table

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Hu, JL., Fang, CY. Do market share and efficiency matter for each other? An application of the zero-sum gains data envelopment analysis. J Oper Res Soc 61, 647–657 (2010). https://doi.org/10.1057/jors.2009.11

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