The hinging hyperplanes: An alternative nonparametric representation of a production function

O. B. Olesen*, J. Ruggiero

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


In this paper we propose hinging hyperplanes (HHs) as a flexible nonparametric representation of a concave or an S-shaped production function. We derive the HHs using expressions with focus on the distinction between hinge location and the bending along each hinge. We argue that the HHs approximation can be estimated using a fixed endogenous determined partitioning of the input space. Assuming a homothetic production function allows us to separate the S-shape scaling law and the underlying core function. We propose an estimation procedure where two HHs function approximations of the core function and the scaling law are estimated simultaneously. A closed form expression of the inverse of the piecewise linear inverse scaling law is proposed and proved. We stress the known result that the HHs formulation is equivalent to the Canonical Piecewise-Linear representation of a piecewise linear function and exploit the result that the HHs formulations for the core function and for the scaling law provide global representations of all piecewise linear functional forms. A simulation study evaluates the performance of the proposed estimation procedure of an S-shaped production function.

Original languageEnglish
JournalEuropean Journal of Operational Research
Issue number1
Pages (from-to)254-266
Publication statusPublished - Jan 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier B.V.


  • Canonical piecewise linear Representation
  • Data envelopment analysis
  • Fixed endogenous partitioning of the input space
  • Hinge functions
  • S-shaped nonparametric frontier estimation


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