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Measuring performance in the presence of stochastic demand for hospital services: an analysis of Belgian general care hospitals

Abstract

Since demand for hospital services is subject to substantial variability, the relationship between uncertain demand, excess capacity, hospital costs and performance should be investigated thoroughly. In this paper a waiting time indicator to proxy hospital standby capacity is incorporated into a multi-product translog cost function for Belgian general care hospitals. The indicator is derived from queuing theory and improves on the conventionally used (inverse of the) occupancy rate. The multi-product stochastic frontier specification allows calculation of cost elasticities and marginal cost of seven hospital departments, as well as the degree of economies of scale and scope and enables identification of differences in efficiency.

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Notes

  1. If this assumption is left, calculation of the typical queuing indicators becomes very complicated and it is often not possible to derive exact closed form expressions.

  2. The typical queuing term “utilisation rate” is equal to the “occupancy rate” which was used in the sections describing hospital cost function studies that accounted for uncertain demand.

  3. Unfortunately we don’t have data on the number of beds per department.

  4. Using L’Hôpital’s rule: \({\mathop {\lim }\limits_{\lambda _B \to 0} \frac{y_i^{\lambda _B} -1}{\lambda _B }=\ln y_i }\)

  5. National Institute for Sickness and Invalidity Insurance.

  6. Under this system inefficient hospitals have their budget decreased.

  7. 82 specialised hospitals (mostly psychiatric) were not included in this analyses. Because of their nature they often only provide one specific treatment (output) which makes it almost impossible to compare them with general care hospitals.

  8. Because of the long history of involvement of the Catholic Church in the provision of health care, the majority of hospital care is provided by state-subsidised, not-for-profit (catholic) private initiative, i.e. most private hospitals are owned by religious charitable orders. The public and the private (not-for-profit) sectors operate in the same market and receive more or less comparable levels of resources.

  9. A model including input prices and using cost share equations generated poor results.

  10. It is also possible to specify own starting values.

  11. Unfortunately, more detailed variables such as a casemix indicator were not available.

  12. HHI is calculated as the sum of the squared local market shares (measured in number of beds).

  13. These indicators are on the level of the town in which the hospital is located and were obtained from ECODATA, FOD Economie, K.M.O., Middenstand &Energie.

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Acknowledgments

The author would like to thank Diana De Graeve, Walter Nonneman, Wilfied Pauwels and two anonymous referees of this journal for their useful comments on ealier versions of this paper. I also wish to thank the Belgian Federal Ministry of Social Affairs, Public Health and the Environment for providing the data for this study. However, the author is the sole responsible for the empirical analysis and conclusions presented here.

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Correspondence to Mike Smet.

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Smet, M. Measuring performance in the presence of stochastic demand for hospital services: an analysis of Belgian general care hospitals. J Prod Anal 27, 13–29 (2007). https://doi.org/10.1007/s11123-006-0021-7

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Keywords

  • Hospital costs
  • Stochastic demand
  • Efficiency
  • Productivity
  • Stochastic frontier analysis
  • Econometrics
  • Queuing theory
  • Multi-product cost function

JEL Classifications

  • C01
  • C13
  • C21
  • D24
  • H51
  • l11
  • l12