Ranking Invariant DEA Based Efficiency Measures

38 Pages Posted: 20 Mar 2021 Last revised: 5 May 2021

See all articles by Jafar Sadeghi

Jafar Sadeghi

University of Western Ontario - Richard Ivey School of Business

Mehmet A. Begen

Ivey Business School, University of Western Ontario

Fredrik Odegaard

Ivey Business School, Western University

Date Written: April 28, 2021

Abstract

Public service spending is an important issue with great economic, social and political ramifications. Consequently, correct measurements with respect to productivity evaluation of such expenditures is of paramount significance. Motivated by evaluating public services from a non-parametric production efficiency perspective and the computational irregularities this may entail, we present refined bounds for the crucial non-Archimedean infinitesimal ({\it aka} epsilon). In non-parametric efficiency models the epsilon plays a key role as a multiplication factor to the sum of input and output slacks in the objective function, equivalently, it is used as a lower bound for the input and output weights in productivity multiplier models. Selecting a value for epsilon is non-trivial since: it has to be sufficiently small to guarantee the envelopment model is bounded (or the multiplier model feasible) yet large enough to provide managerial insight and not cause computational problems; is highly context specific, depending on the input and output metrics; sensitive to underlying assumptions with respect to constant or variable returns-to-scale; and may lead to drastically different relative efficiency rankings. To guarantee the relative ranking of the evaluated units remain consistent we provide two bounds for the epsilon. The first,{\it positive efficiency guarantee}, ensures the obtained efficiency measures are positive and well-defined, and the second, {\it ranking invariance guarantee}, is a refinement such that the relative efficiency rankings are provably consistent. We illustrate our bounds and their implications using data from twelve public healthcare centers.

Keywords: Data Envelopment Analysis; Production Efficiency Measures; Public Productivity; Unique Efficiency Ranking; Non-Archimedean.

Suggested Citation

Sadeghi, Jafar and Begen, Mehmet A. and Odegaard, Fredrik, Ranking Invariant DEA Based Efficiency Measures (April 28, 2021). Available at SSRN: https://ssrn.com/abstract=3785715 or http://dx.doi.org/10.2139/ssrn.3785715

Jafar Sadeghi

University of Western Ontario - Richard Ivey School of Business ( email )

1255 Western Road
London, N6G 0N1
Canada

Mehmet A. Begen (Contact Author)

Ivey Business School, University of Western Ontario ( email )

1255 Western Road
London, Ontario N6G 0N1
Canada

HOME PAGE: http://www.ivey.uwo.ca/faculty/MBegen

Fredrik Odegaard

Ivey Business School, Western University ( email )

Ivey Business School
1255 Western Road
London, Ontario N6G 0N1
Canada

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