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A system-of-equations two-stage DEA approach for explaining capacity utilization and technical efficiency

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Abstract

In this paper we develop a system-of-equations two-stage approach to explain the simultaneous effect of a number of contextual variables on technical efficiency and capacity utilization, which were derived using Johansen measure of capacity utilization and DEA. The model is applied to a sample of public hospitals in Greece and provides estimates of capacity utilization and optimal input usage. Our results indicate that the sample hospitals operated with excess capacity and by underutilizing doctors and nursing personnel. We also found some variation in capacity and variable input utilization across urban and non-urban hospitals. The results from the second stage SUR system of equations show that hospital size and location have a positive effect on hospital capacity utilization while the average length of stay a negative one.

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Notes

  1. Other approaches are the frontier separation approach and the all-in-one approach. For details see Thanassoulis et al. (2008, pp. 340–353).

  2. Prior to the technical inefficiency effect model (see Kumbhakar and Lovell 2000, Chap. 7 and the references therein), where estimation of technical efficiency and its determinants can be carried out simultaneously in one-stage, the two-stage approach was also used in stochastic frontier analysis. It has been criticized however as being an inconsistent and mis-specified formulation (see Wang and Schmidt 2002 for a detail discussion). On the other hand, notice that it is not possible to integrate the two-stage DEA into a one-stage model because it involves deterministic (first stage) and stochastic (second stage) components. We will like to thank an anonymous referee for making this point.

  3. Notice than none of previous studies analyzing capacity utilization in hospitals (e.g., Fare et al. 1989a; Magnussen and Mobley 1999; Valdmanis et al. 2004 and Ferrier et al. 2009) have used the second-stage DEA to explain factors that affect it. All the empirical studies in the subject are from the field of fisheries.

  4. We could have used a log-log specification but since some of the contextual variables are dummy variables the log-linear specification is more plausible.

  5. For two recent applications of the Banker and Natarajan (2008) approach see Banker et al. (2010a, 2010b).

  6. See Lovo (2011) for a recent application of McDonald (2009) approach to a single equation two-stage DEA model.

  7. This reasoning holds for capacity utilization rates, which also represent fractional data within the unit interval.

  8. Data are collected from National Statistical Service of Greece (1998, 2007).

  9. Simar and Wilson (2002) introduced an alternative test to examine the existence of returns to scale.

  10. The non-parametric rank-sum test statistic that follows approximately the standard normal distribution is defined as (Cooper et al. 2000): \(T=\frac{S-I_{1}(I_{1}+I_{2}+1)/2}{\sqrt{I_{1}I_{2}(I_{1}+I_{2}+1)/12}}\), where S being the sum of rankings corresponding to DEA estimates.

  11. Notice that the White (1980) test detected the presence of heteroscedasticity for all equations.

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  1. Centre for Planning and Economic Research, 11 Amerikis str., 10672, Athens, Greece

    Roxani Karagiannis

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  1. Roxani Karagiannis
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Correspondence to Roxani Karagiannis.

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Karagiannis, R. A system-of-equations two-stage DEA approach for explaining capacity utilization and technical efficiency. Ann Oper Res 227, 25–43 (2015). https://doi.org/10.1007/s10479-013-1367-7

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