Sampling size and efficiency bias in data envelopment analysis

Abstract

Abstract. In Data Envelopment Analysis, when the number of decision making units is small, the numb e r o f u n i t s o f t h e d o m i n a n t or e cient set is relatively large and the average e ciency is generally high. The high average e ciency is the result of assuming that the units in the e cient set are 100% e cient. If this assumption is not valid, this results in an overestimation of the e ciencies, which will be larger for a smaller number of units. Samples of various sizes are used to nd the related bias in the e ciency estimation. The samples are drawn from a large scale application of DEA to bank branch e ciency. The e ects of di erent assumptions as to returns to scale and the number of inputs and outputs are investigated.

Trademarking activities and total factor productivity: Some evidence for British commercial banks using a metafrontier approach

“…One of the disadvantages of DEA is that it is sensitive to the size of the sample. Indeed, it has been argued that when the number of observations is small, the number of efficient units is large (Alirezaee et al, 1998). To avoid this problem, we first ensure that the number of observations is greater than the combined sum of inputs and outputs and then we check that the number of fully efficient observations is less than one third of the total observations in the sample (Manzoni and Islam, 2009).…”

Measuring efficiency of the banking industry before and after the recent financial crisis: some international evidence

“…Besides the selection of input and output variables, another important consideration in DEA is the number of DMUs needed to conduct the analysis since the accuracy of the estimation depends on this number. Alirezaee, Howland, and van de Panne (1998) found that for 3 inputs and 3 outputs and constant return to scale, a reasonably accurate estimation of efficiency is possible if the number of units is at least a few hundred and should be roughly double for variable return to scale. However, Dyson, Allen, Camanho, Podinovski, Sarrico and Shale (2001) argued that the number of units should be at least twice the product of the number of inputs and outputs.…”

“…The possible explanations of higher efficiency scores may be the selection of the sampled banks and/or input and output variables since DEA results are sensitive to the selection of inputs and outputs and the number of DMUs under consideration (Alirezaee et al, 1998;and Berg (2010). Since we chose the largest market-cap and the best performing banks from the sampled countries, necessarily we can expect higher efficiency scores.…”

Regional Differences in Measuring the Technical Efficiency of Rice Production in Vietnam: A Metafrontier Approach

“…Although DEA's advantage when compared to SFA is that DEA can deal with a small sample size (Coelli et al, 1998), many recent studies such as those by Alirezaee et al (1998), Zhang and Bartels (1998), Staat (2001, and Andor and Hesse (2011), have proved that sample size variations may lead to biased technical efficiency scores. Specifically, Alirezaee et al (1998) argued that when the number of decision-making units (DMU) is small, the number of dominant units or efficient sets will be relatively large and the average efficiency; therefore, generally high.…”

“…Although DEA's advantage when compared to SFA is that DEA can deal with a small sample size (Coelli et al, 1998), many recent studies such as those by Alirezaee et al (1998), Zhang and Bartels (1998), Staat (2001, and Andor and Hesse (2011), have proved that sample size variations may lead to biased technical efficiency scores. Specifically, Alirezaee et al (1998) argued that when the number of decision-making units (DMU) is small, the number of dominant units or efficient sets will be relatively large and the average efficiency; therefore, generally high. Furthermore, two important conditions need to be in place when using DEA, and these are sample size related, as follows: (1) the number of DMU should be greater than the combined number of inputs plus outputs (Cooper et al, 2000), and (2) the sample size is only acceptable if the number of fully efficient DMUs is no greater than one-third of the total number of DMUs in the sample (Manzoni & Islam, 2009).…”