Do Efficiency Scores Depend on Input Mix?

A Statistical Test and Empirical Illustration

Mette Asmild, Jens Leth Hougaard, Dorte Kronborg

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper we examine the possibility of using the standard Kruskal-Wallis (KW) rank test in order to evaluate whether the distribution of efficiency scores resulting from Data Envelopment Analysis (DEA) is independent of the input (or output) mix of the observations. Since the DEA frontier is estimated, many standard assumptions for evaluating the KW test statistic are violated. Therefore, we propose to explore its statistical properties by the use of simulation studies. The simulations are performed conditional on the observed input mixes. The method, unlike existing approaches in the literature, is also applicable when comparing distributions of efficiency scores in more than two groups and does not rely on bootstrapping of, or questionable distributional assumptions about, the efficiency scores. The approach is illustrated using an empirical case of demolition projects. Since the assumption of mix independence is rejected the implication is that it, for example, is impossible to determine whether machine intensive project are more or less efficient than labor intensive projects.
Original languageEnglish
JournalAnnals of Operations Research
Volume211
Issue number1
Pages (from-to)37-48
Number of pages12
ISSN0254-5330
DOIs
Publication statusPublished - Dec 2013

Cite this

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title = "Do Efficiency Scores Depend on Input Mix?: A Statistical Test and Empirical Illustration",
abstract = "In this paper we examine the possibility of using the standard Kruskal-Wallis (KW) rank test in order to evaluate whether the distribution of efficiency scores resulting from Data Envelopment Analysis (DEA) is independent of the input (or output) mix of the observations. Since the DEA frontier is estimated, many standard assumptions for evaluating the KW test statistic are violated. Therefore, we propose to explore its statistical properties by the use of simulation studies. The simulations are performed conditional on the observed input mixes. The method, unlike existing approaches in the literature, is also applicable when comparing distributions of efficiency scores in more than two groups and does not rely on bootstrapping of, or questionable distributional assumptions about, the efficiency scores. The approach is illustrated using an empirical case of demolition projects. Since the assumption of mix independence is rejected the implication is that it, for example, is impossible to determine whether machine intensive project are more or less efficient than labor intensive projects.",
keywords = "Data envelopment analysis (DEA), Homogeneous efficiencies, Mix independence, Kruskal-Wallis test, Ranking",
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Do Efficiency Scores Depend on Input Mix? A Statistical Test and Empirical Illustration. / Asmild, Mette; Hougaard, Jens Leth; Kronborg, Dorte.

In: Annals of Operations Research, Vol. 211, No. 1, 12.2013, p. 37-48.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Do Efficiency Scores Depend on Input Mix?

T2 - A Statistical Test and Empirical Illustration

AU - Asmild, Mette

AU - Hougaard, Jens Leth

AU - Kronborg, Dorte

PY - 2013/12

Y1 - 2013/12

N2 - In this paper we examine the possibility of using the standard Kruskal-Wallis (KW) rank test in order to evaluate whether the distribution of efficiency scores resulting from Data Envelopment Analysis (DEA) is independent of the input (or output) mix of the observations. Since the DEA frontier is estimated, many standard assumptions for evaluating the KW test statistic are violated. Therefore, we propose to explore its statistical properties by the use of simulation studies. The simulations are performed conditional on the observed input mixes. The method, unlike existing approaches in the literature, is also applicable when comparing distributions of efficiency scores in more than two groups and does not rely on bootstrapping of, or questionable distributional assumptions about, the efficiency scores. The approach is illustrated using an empirical case of demolition projects. Since the assumption of mix independence is rejected the implication is that it, for example, is impossible to determine whether machine intensive project are more or less efficient than labor intensive projects.

AB - In this paper we examine the possibility of using the standard Kruskal-Wallis (KW) rank test in order to evaluate whether the distribution of efficiency scores resulting from Data Envelopment Analysis (DEA) is independent of the input (or output) mix of the observations. Since the DEA frontier is estimated, many standard assumptions for evaluating the KW test statistic are violated. Therefore, we propose to explore its statistical properties by the use of simulation studies. The simulations are performed conditional on the observed input mixes. The method, unlike existing approaches in the literature, is also applicable when comparing distributions of efficiency scores in more than two groups and does not rely on bootstrapping of, or questionable distributional assumptions about, the efficiency scores. The approach is illustrated using an empirical case of demolition projects. Since the assumption of mix independence is rejected the implication is that it, for example, is impossible to determine whether machine intensive project are more or less efficient than labor intensive projects.

KW - Data envelopment analysis (DEA)

KW - Homogeneous efficiencies

KW - Mix independence

KW - Kruskal-Wallis test

KW - Ranking

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JO - Annals of Operations Research

JF - Annals of Operations Research

SN - 0254-5330

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