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Exact tests on returns to scale and comparisons of production frontiers in nonparametric models

Anders Rønn-Nielsen (), Dorte Kronborg () and Mette Asmild ()
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Anders Rønn-Nielsen: Center for Statistics, Department of Finance, Copenhagen Business School
Dorte Kronborg: Center for Statistics, Department of Finance, Copenhagen Business School
Mette Asmild: Department of Food and Resource Economics, University of Copenhagen

No 2019/04, IFRO Working Paper from University of Copenhagen, Department of Food and Resource Economics

Abstract: When benchmarking production units by non-parametric methods like data envelopment analysis (DEA), an assumption has to be made about the returns to scale of the underlying technology. Moreover, it is often also relevant to compare the frontiers across samples of producers. Until now, no exact tests for examining returns to scale assumptions in DEA, or for test of equality of frontiers, have been available. The few existing tests are based on asymptotic theory relying on large sample sizes, whereas situations with relatively small samples are often encountered in practical applications. In this paper we propose three novel tests based on permutations. The tests are easily implementable from the algorithms provided, and give exact significance probabilities as they are not based on asymptotic properties. The first of the proposed tests is a test for the hypothesis of constant returns to scale in DEA. The others are tests for general frontier differences and whether the production possibility sets are, in fact, nested. The theoretical advantages of permutation tests are that they are appropriate for small samples and have the correct size. Simulation studies show that the proposed tests do, indeed, have the correct size and furthermore higher power than the existing alternative tests based on asymptotic theory.

Keywords: Data Envelopment Analysis (DEA); returns to scale; equality of production frontiers; exact tests; permutations (search for similar items in EconPapers)
JEL-codes: C12 C14 C44 C46 C61 D (search for similar items in EconPapers)
Pages: 23 pages
Date: 2019-05
New Economics Papers: this item is included in nep-ecm and nep-eff
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