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Testing the convexity hypothesis in nonparametric cost functions

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  • Kerstens, Kristiaan
  • Zhao, Shirong

Abstract

We develop statistical tests to formally test the convexity axiom for cost functions by extending a recently developed statistical tests in nonparametric models of production. The tests are applied to a panel of US electric power generation plants and strong evidence against convexity is found for most years in the resulting cost functions. Our results suggest that empirical researchers need to be more cautious about the often implicit embedding of the convexity assumption for the cost functions.

Suggested Citation

  • Kerstens, Kristiaan & Zhao, Shirong, 2025. "Testing the convexity hypothesis in nonparametric cost functions," Economics Letters, Elsevier, vol. 247(C).
    • Handle: RePEc:eee:ecolet:v:247:y:2025:i:c:s0165176525000333
    DOI: 10.1016/j.econlet.2025.112196
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    References listed on IDEAS

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    1. Alois Kneip & Léopold Simar & Paul W. Wilson, 2016. "Testing Hypotheses in Nonparametric Models of Production," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 435-456, July.
    2. Léopold Simar & Paul W. Wilson, 2020. "Hypothesis testing in nonparametric models of production using multiple sample splits," Journal of Productivity Analysis, Springer, vol. 53(3), pages 287-303, June.
    3. Subhash C. Ray, 2022. "Data Envelopment Analysis: A Nonparametric Method of Production Analysis," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 10, pages 409-470, Springer.
    4. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2022. "Nonconvexity in Production and Cost Functions: An Exploratory and Selective Review," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 18, pages 721-754, Springer.
    5. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2015. "When Bias Kills The Variance: Central Limit Theorems For Dea And Fdh Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 31(2), pages 394-422, April.
    6. Kristiaan Kerstens & Ignace Van de Woestyne, 2021. "Cost functions are nonconvex in the outputs when the technology is nonconvex: convexification is not harmless," Annals of Operations Research, Springer, vol. 305(1), pages 81-106, October.
    7. Balaguer-Coll, Maria Teresa & Prior, Diego & Tortosa-Ausina, Emili, 2007. "On the determinants of local government performance: A two-stage nonparametric approach," European Economic Review, Elsevier, vol. 51(2), pages 425-451, February.
    8. Simar, Léopold & Wilson, Paul W., 2020. "Technical, allocative and overall efficiency: Estimation and inference," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1164-1176.
    9. Subal C. Kumbhakar & Efthymios G. Tsionas, 2011. "Stochastic error specification in primal and dual production systems," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 270-297, March.
    10. M. J. Farrell, 1959. "The Convexity Assumption in the Theory of Competitive Markets," Journal of Political Economy, University of Chicago Press, vol. 67(4), pages 377-377.
    11. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2022. "Conical FDH Estimators of General Technologies, with Applications to Returns to Scale and Malmquist Productivity Indices," LIDAM Discussion Papers ISBA 2022024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    More about this item

    Keywords

    Convexity; Cost function; Convex technology; Nonconvex technology;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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