A reverse directional distance function to reconcile between competing efficiency goals: an application to Indian manufacturing


In analysis of technical efficiency in production, either the maximum proportional increase in all outputs or a minimal proportional scaling down of all inputs is generally selected as the criterion. In the recent literature, the directional distance function combines the two objectives by increasing outputs and reducing inputs simultaneously to the extent possible. This paper introduces a reverse directional distance function as one possible approach to resolve the conflict between incompatible goals through a minimal adjustment applicable to both of the two objectives. In our empirical analysis we apply the proposed method to Indian manufacturing where increasing the output and conserving energy use are both highly important objectives. A comparison of the feasible targets obtained through the conventional and the reverse directional distance functions yields an estimated tradeoff between output increase and CO2 reduction (due to energy conservation) along the frontier.

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Fig. 2


  1. 1.

    There may, of course, be multiple bundles all of which are optimal.

  2. 2.

    India Energy Outlook, World Energy Outlook Special Report, International Energy Agency (2015).

  3. 3.

    See Ebinger (2016) for a discussion of the challenges involved in India’s industrialization and climate change goals.

  4. 4.

    Note that a unit of energy saved is more than a unit of energy produced because it avoids the loss that typically occurs in the transmission and distribution process.

  5. 5.

    Aparicio et al. (2013) page 157, Eqs. (17), (18) describe this as a ‘modified directional distance function’.

  6. 6.

    If \( (1 - \theta^{*} ) > (\varphi^{*} - 1),\,\kappa > 1 \) and the projection based on the Reverse DDF will show a greater degree of input saving compared to the conventional DDF. The opposite would be true if \( (1 - \theta^{*} ) < (\varphi^{*} - 1). \)

  7. 7.

    The data are reported by accounting year which runs from April 1st to March 31st. Thus, the year 2013-14 refers to the period April 1, 2013 to March 31, 2014.

  8. 8.

    For the output measure, the gross value of manufacturing production was deflated by the wholesale price index for manufactured products. For the inputs, the value of fixed capital was deflated by the wholesale price index of machinery and machine tools. The expenditure on fuels was deflated by the wholesale price index for fuel and power. Similarly, the expenditure on materials was deflated by the wholesale price index for non-food primary articles.

  9. 9.

    The state of Andhra Pradesh lost its size advantage after the bifurcation of the state.

  10. 10.

    Note that the reported numbers in the tables are rounded off. Therefore, the values reported in Table 6 may not be exactly what is obtained from the figures reported in Table 5.

  11. 11.

    Authors’ calculation based on Annual Survey of Industries Table 6A for 2013–2014. Values were deflated using 2004–2005 prices.

  12. 12.

    See Hong and Slatick (1994).


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Correspondence to Subhash C. Ray.

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Ray, S.C., Mukherjee, K. A reverse directional distance function to reconcile between competing efficiency goals: an application to Indian manufacturing. Ind. Econ. Rev. 52, 103–126 (2017). https://doi.org/10.1007/s41775-017-0005-8

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  • Data envelopment analysis
  • Minimax solution
  • Output growth
  • Energy saving

JEL Classification

  • C61
  • D24
  • L60