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Economic elasticities of input substitution using data envelopment analysis

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  • Noah J Miller
  • Jason S Bergtold
  • Allen M Featherstone

Abstract

The use of elasticities of substitution between inputs is a standard method for addressing the effect of a change in the mix of inputs used for production from a technical or cost standpoint. Most estimation methods use parametric production or cost functions or frontiers to estimate these elasticities. A potentially useful nonparametric alternative is data envelopment analysis (DEA). The purpose of this paper is to derive elasticities of input substitution for both technical and cost frontiers using DEA, extending the use of this approach in the field of economics and associated fields. The paper provides derivations for both Hicksian (production and cost frontier) and Morishima (cost frontier) elasticities of input substitution, as well as a parsimonious method for estimating them using DEA. The derivations are presented using an agricultural example form Kansas, USA.

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  • Noah J Miller & Jason S Bergtold & Allen M Featherstone, 2019. "Economic elasticities of input substitution using data envelopment analysis," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-15, August.
    • Handle: RePEc:plo:pone00:0220478
    DOI: 10.1371/journal.pone.0220478
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    References listed on IDEAS

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    1. Charles Blackorby & R. Robert Russell, 1981. "The Morishima Elasticity of Substitution; Symmetry, Constancy, Separability, and its Relationship to the Hicks and Allen Elasticities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(1), pages 147-158.
    2. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    3. Ray,Subhash C., 2012. "Data Envelopment Analysis," Cambridge Books, Cambridge University Press, number 9781107405264, January.
    4. Bryon J. Parman & Allen M. Featherstone, 2019. "A comparison of parametric and nonparametric estimation methods for cost frontiers and economic measures," Journal of Applied Economics, Taylor & Francis Journals, vol. 22(1), pages 60-85, January.
    5. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    6. Subhash C. Ray, 1982. "A Translog Cost Function Analysis of U.S. Agriculture, 1939–77," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 64(3), pages 490-498.
    7. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2019. "A bootstrap approach for bandwidth selection in estimating conditional efficiency measures," European Journal of Operational Research, Elsevier, vol. 277(2), pages 784-797.
    8. 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.
    9. Alejandra Gonzalez-Mejia & David Styles & Paul Wilson & James Gibbons, 2018. "Metrics and methods for characterizing dairy farm intensification using farm survey data," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-18, May.
    10. Vigeant, Stéphane, 2016. "From partial derivatives of DEA frontiers to marginal products, marginal rates of substitution, and returns to scaleAuthor-Name: Ouellette, Pierre," European Journal of Operational Research, Elsevier, vol. 253(3), pages 880-887.
    11. Ravelojaona, Paola, 2019. "On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions," European Journal of Operational Research, Elsevier, vol. 272(2), pages 780-791.
    12. Victor V. Podinovski & Robert G. Chambers & Kazim Baris Atici & Iryna D. Deineko, 2016. "Marginal Values and Returns to Scale for Nonparametric Production Frontiers," Operations Research, INFORMS, vol. 64(1), pages 236-250, February.
    13. Thomas W. Hertel, 1989. "Negotiating Reductions in Agricultural Support: Implications of Technology and Factor Mobility," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 71(3), pages 559-573.
    14. 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.
    15. Daniel McFadden, 1963. "Constant Elasticity of Substitution Production Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(2), pages 73-83.
    16. Dan Rosen & Claire Schaffnit & Joseph Paradi, 1998. "Marginal Rates and Two-dimensional Level Curves in DEA," Journal of Productivity Analysis, Springer, vol. 9(3), pages 205-232, March.
    17. Levi Alan Russell & Michael R. Langemeier & Brian C. Briggeman, 2013. "The impact of liquidity and solvency on cost efficiency," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 73(3), pages 413-425, November.
    18. Magdalena Kapelko & Alfons Oude Lansink & Spiro E Stefanou, 2015. "Effect of Food Regulation on the Spanish Food Processing Industry: A Dynamic Productivity Analysis," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-16, June.
    19. Ahn, Taesik & Charnes, Abraham & Cooper, William W., 1988. "Efficiency characterizations in different DEA models," Socio-Economic Planning Sciences, Elsevier, vol. 22(6), pages 253-257.
    20. Ferrier, Gary D. & Lovell, C. A. Knox, 1990. "Measuring cost efficiency in banking : Econometric and linear programming evidence," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 229-245.
    21. 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.
    22. Podinovski, Victor V., 2019. "Direct estimation of marginal characteristics of nonparametric production frontiers in the presence of undesirable outputs," European Journal of Operational Research, Elsevier, vol. 279(1), pages 258-276.
    23. Hirofumi Uzawa, 1962. "Production Functions with Constant Elasticities of Substitution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 291-299.
    24. 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.
    25. Pierre Ouellette & Stephane Vigeant, 2016. "From partial derivatives of DEA frontiers to marginal products, marginal rates of substitution, and returns to scale," Post-Print hal-01533531, HAL.
    26. Nikki McCaffrey & Meera Agar & Janeane Harlum & Jonathon Karnon & David Currow & Simon Eckermann, 2015. "Better Informing Decision Making with Multiple Outcomes Cost-Effectiveness Analysis under Uncertainty in Cost-Disutility Space," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-19, March.
    27. Bryon J. Parman & Allen M. Featherstone & Brian K. Coffey, 2017. "Estimating product-specific and multiproduct economies of scale with data envelopment analysis," Agricultural Economics, International Association of Agricultural Economists, vol. 48(4), pages 523-533, July.
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