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Directional marginal productivity: a foundation of meta-data envelopment analysis

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  • Chia-Yen Lee

    (National Cheng Kung University)

Abstract

Differential characteristics of the production function represent elasticity measures and marginal rates of production technologies; in particular, marginal productivity (MP) plays an important role in economic theory and applications. This study provides a theoretical foundation of directional marginal productivity (DMP) supporting the meta-data envelopment analysis (meta-DEA) which measures the efficiency via marginal-profit-maximized orientation. In addition, the segmented marginal rate of technical substitution is developed based on DMP. In fact, DMP is developed to address finding the improving direction of the efficient firm on the frontier towards the marginal profit maximization. This approach, which emphasizes “planning” over “efficiency evaluation”, forms the basis for transforming a typical “ex-post” DEA into an “ex-ante” DEA study. Two case studies show that the DMP provides an explicit span of directions for productivity improvement via a trade-off between these distinct directions.

Suggested Citation

  • Chia-Yen Lee, 2017. "Directional marginal productivity: a foundation of meta-data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(5), pages 544-555, May.
    • Handle: RePEc:pal:jorsoc:v:68:y:2017:i:5:d:10.1057_s41274-016-0129-8
    DOI: 10.1057/s41274-016-0129-8
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    1. Banker, Rajiv D. & Thrall, R. M., 1992. "Estimation of returns to scale using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 62(1), pages 74-84, October.
    2. Fried, Harold O. & Lovell, C. A. Knox & Schmidt, Shelton S. (ed.), 2008. "The Measurement of Productive Efficiency and Productivity Growth," OUP Catalogue, Oxford University Press, number 9780195183528.
    3. V E Krivonozhko & O B Utkin & A V Volodin & I A Sablin & M Patrin, 2004. "Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1049-1058, October.
    4. R. Färe & S. Grosskopf & G. Whittaker, 2013. "Directional output distance functions: endogenous directions based on exogenous normalization constraints," Journal of Productivity Analysis, Springer, vol. 40(3), pages 267-269, December.
    5. Lee, Chia-Yen & Johnson, Andrew L., 2014. "Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments," European Journal of Operational Research, Elsevier, vol. 232(3), pages 537-548.
    6. Lee, Chia-Yen & Johnson, Andrew L. & Moreno-Centeno, Erick & Kuosmanen, Timo, 2013. "A more efficient algorithm for Convex Nonparametric Least Squares," European Journal of Operational Research, Elsevier, vol. 227(2), pages 391-400.
    7. Timo Kuosmanen, 2008. "Representation theorem for convex nonparametric least squares," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 308-325, July.
    8. Asmild, Mette & Paradi, Joseph C. & Reese, David N., 2006. "Theoretical perspectives of trade-off analysis using DEA," Omega, Elsevier, vol. 34(4), pages 337-343, August.
    9. F R Førsund & L Hjalmarsson, 2004. "Calculating scale elasticity in DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1023-1038, October.
    10. Lee, Chia-Yen, 2014. "Meta-data envelopment analysis: Finding a direction towards marginal profit maximization," European Journal of Operational Research, Elsevier, vol. 237(1), pages 207-216.
    11. Fare, Rolf & Grosskopf, Shawna & Kokkelenberg, Edward C, 1989. "Measuring Plant Capacity, Utilization and Technical Change: A Nonparametric Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 655-666, August.
    12. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    13. Hadjicostas, Petros & Soteriou, Andreas C., 2006. "One-sided elasticities and technical efficiency in multi-output production: A theoretical framework," European Journal of Operational Research, Elsevier, vol. 168(2), pages 425-449, January.
    14. José Zofío & Angel Prieto, 2006. "Return to Dollar, Generalized Distance Function and the Fisher Productivity Index," Spanish Economic Review, Springer;Spanish Economic Association, vol. 8(2), pages 113-138, June.
    15. Timo Kuosmanen, 2005. "Weak Disposability in Nonparametric Production Analysis with Undesirable Outputs," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1077-1082.
    16. Victor V. Podinovski & Finn R. Førsund, 2010. "Differential Characteristics of Efficient Frontiers in Data Envelopment Analysis," Operations Research, INFORMS, vol. 58(6), pages 1743-1754, December.
    17. Färe, Rolf & Grosskopf, Shawna & Pasurka, Carl A., 2007. "Environmental production functions and environmental directional distance functions," Energy, Elsevier, vol. 32(7), pages 1055-1066.
    18. Rolf Färe & Shawna Grosskopf, 2003. "Nonparametric Productivity Analysis with Undesirable Outputs: Comment," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 85(4), pages 1070-1074.
    19. Grosskopf, S. & Margaritis, D. & Valdmanis, V., 1995. "Estimating output substitutability of hospital services: A distance function approach," European Journal of Operational Research, Elsevier, vol. 80(3), pages 575-587, February.
    20. Timo Kuosmanen & Andrew L. Johnson, 2010. "Data Envelopment Analysis as Nonparametric Least-Squares Regression," Operations Research, INFORMS, vol. 58(1), pages 149-160, February.
    21. Fare, Rolf & Grosskopf, Shawna & Zaim, Osman, 2002. "Hyperbolic efficiency and return to the dollar," European Journal of Operational Research, Elsevier, vol. 136(3), pages 671-679, February.
    22. O. B. Olesen & N. C. Petersen, 1996. "Indicators of Ill-Conditioned Data Sets and Model Misspecification in Data Envelopment Analysis: An Extended Facet Approach," Management Science, INFORMS, vol. 42(2), pages 205-219, February.
    23. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    24. Fare, Rolf, et al, 1989. "Multilateral Productivity Comparisons When Some Outputs Are Undesirable: A Nonparametric Approach," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 90-98, February.
    25. W. Cooper & Dr. Park & Professor Ciurana, 2000. "Marginal Rates and Elasticities of Substitution with Additive Models in DEA," Journal of Productivity Analysis, Springer, vol. 13(2), pages 105-123, March.
    26. Bougnol, M.-L. & Dulá, J.H., 2009. "Anchor points in DEA," European Journal of Operational Research, Elsevier, vol. 192(2), pages 668-676, January.
    27. Ole Olesen & N. Petersen, 2003. "Identification and Use of Efficient Faces and Facets in DEA," Journal of Productivity Analysis, Springer, vol. 20(3), pages 323-360, November.
    28. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    29. Rajiv D. Banker & Richard C. Morey, 1986. "Efficiency Analysis for Exogenously Fixed Inputs and Outputs," Operations Research, INFORMS, vol. 34(4), pages 513-521, August.
    30. Mekaroonreung, Maethee & Johnson, Andrew L., 2012. "Estimating the shadow prices of SO2 and NOx for U.S. coal power plants: A convex nonparametric least squares approach," Energy Economics, Elsevier, vol. 34(3), pages 723-732.
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    2. Lee, Chia-Yen & Charles, Vincent, 2022. "A robust capacity expansion integrating the perspectives of marginal productivity and capacity regret," European Journal of Operational Research, Elsevier, vol. 296(2), pages 557-569.
    3. Lee, Chia-Yen & Wang, Ke, 2019. "Nash marginal abatement cost estimation of air pollutant emissions using the stochastic semi-nonparametric frontier," European Journal of Operational Research, Elsevier, vol. 273(1), pages 390-400.

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