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From partial derivatives of DEA frontiers to marginal products, marginal rates of substitution, and returns to scaleAuthor-Name: Ouellette, Pierre

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  • Vigeant, Stéphane

Abstract

The characterization of a technology, from an economic point of view, often uses the first derivatives of either the transformation or the production function. In a parametric setting, these quantities are readily available as they can be easily deduced from the first derivatives of the specified function. In the standard framework of data envelopment analysis (DEA) models these quantities are not so easily obtained. The difficulty resides in the fact that marginal changes of inputs and outputs might affect the position of the frontier itself while the calculation of first derivatives for economic purposes assumes that the frontier is held constant. We develop here a procedure to recover first derivatives of transformation functions in DEA models and we show how we can evacuate the problem of the (marginal) shift of the frontier. We show how the knowledge of the first derivatives of the frontier estimated by DEA can be used to deduce and compute marginal products, marginal rates of substitution, and returns to scale for each decision making unit (DMU) in the sample.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:253:y:2016:i:3:p:880-887
    DOI: 10.1016/j.ejor.2016.02.036
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    References listed on IDEAS

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    1. Ouellette, Pierre & Quesnel, Jean-Patrice & Vigeant, Stéphane, 2012. "Measuring returns to scale in DEA models when the firm is regulated," European Journal of Operational Research, Elsevier, vol. 220(2), pages 571-576.
    2. Kneip, Alois & Park, Byeong U. & Simar, Léopold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(6), pages 783-793, December.
    3. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    4. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    5. 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.
    6. 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.
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    Cited by:

    1. Lin, Winston T. & Chen, Yueh H. & Hung, TingShu, 2019. "A partial adjustment valuation approach with stochastic and dynamic speeds of partial adjustment to measuring and evaluating the business value of information technology," European Journal of Operational Research, Elsevier, vol. 272(2), pages 766-779.

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