Conical FDH Estimators of General Technologies, with Applications to Returns to Scale and Malmquist Productivity Indices

Alois Kneip, Leopold Simar and Paul Wilson
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Alois Kneip: Universität Bonn

No 2022024, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Nonparametric envelopment estimators are often used to estimate the attainable sets and its efficient boundary and to assess efficiency and changes in productivity. Kneip et al. (2015, 2016) provide asymptotic theory enabling inference about expected efficiency and testing constant versus variable returns to scale using these estimators, and Kneip et al. (2021) provide asymptotic results that can be used to make inference about expected changes in productivity measured by Malmquist indices. All of these results require convexity of the attainable set, but in a number of situations this assumption is questionable. Kneip et al. (2016) also provide a test of convexity versus non-convexity of a production set, and convexity is rejected in several recent studies. This paper extends the results mentioned above to allow for possibly nonconvex technologies. Properties of a nonparametric envelopment estimator of distance to the boundary of the cone spanned by a possibly non-convex attainable set are derived. These new results are then extended to make inference about geometric means of Malmquist indices and to test constant versus non-constant returns to scale when the production set is not convex.

Keywords: Non-convex production sets; FDH; hypothesis test; returns to scale; Malmquist index; productivity change (search for similar items in EconPapers)
JEL-codes: C12 C14 C18 (search for similar items in EconPapers)
Pages: 63
Date: 2022-08-01
New Economics Papers: this item is included in nep-ecm and nep-eff
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Citations: View citations in EconPapers (1)

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