Cost functions are nonconvex in the outputs when the technology is nonconvex: convexification is not harmless

Kristiaan Kerstens and Ignace van de Woestyne

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Abstract: This contribution focuses on testing the empirical impact of the convexity assumption in estimating costs using nonparametric specifications of technology and cost functions. Apart from reviewing the scant available evidence, the empirical results based on two publicly available data sets reveal the effect of the convexity axiom on cost function estimates: cost estimates based on convex technologies turn out to be on average between 21% and 38% lower than those computed on nonconvex technologies. These differences are statistically significant when comparing kernel densities and can be illustrated using sections of the cost function estimates along some output dimension. Finally, also the characterization of returns to scale and economies of scale using production and cost functions for individual units yields conflicting results for between 19% and 31% of individual observations. The theoretical known potential impact as well as these empirical results should make us reconsider convexity in empirical production analysis: clearly, convexity is not harmless.

Keywords: Data envelopment analysis; Economics; Technology; Cost analysis (search for similar items in EconPapers)
Date: 2021-06-18
New Economics Papers: this item is included in nep-eff
Note: View the original document on HAL open archive server: https://hal.science/hal-03274911
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Citations: View citations in EconPapers (9)

Published in Annals of Operations Research, 2021, 305, pp.81-106. ⟨10.1007/s10479-021-04069-1⟩

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Journal Article: Cost functions are nonconvex in the outputs when the technology is nonconvex: convexification is not harmless (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03274911

DOI: 10.1007/s10479-021-04069-1

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