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The Optimal Use of Hospital Capacity in the Presence of Stochastic Demand and Output Heterogeneity

Hughes, D. (1997). The Optimal Use of Hospital Capacity in the Presence of Stochastic Demand and Output Heterogeneity. (Unpublished Doctoral thesis, City, University of London)


Hospitals provide a substantial proportion of the care services within health care systems: around 55% of total NHS expenditure is on hospital care. The majority of hospital care is undertaken on an inpatient basis requiring patients to be admitted to hospital. The range and type of admissions to hospitals, however, vary widely: Demand for care is heterogeneous. Hospitals, however, have limited space available to treat all the demands for care and excess demand is considered to be an endemic problem in the NHS revealed by the existence of long waiting lists.

Given the conflicting demands for care, hospitals must determine the mix of patients that they will treat given available capacity. As hospitals have limited capacity available to treat patients who demand services, choices must be made regarding the use of scarce resources in the face of these conflicting demands for available capacity. In addition hospitals face uncertain demand for some of their services, most notably those seeking emergency care. The clearest choice facing the hospital is whether to use available capacity to reduce waiting lists and treat elective cases, or keep capacity available to treat emergency cases should the need arise.

It is our intention to address the issue of how hospitals allocate capacity under conditions of demand uncertainty and output heterogeneity, in this thesis. In particular, we will consider whether hospitals appear to respond to the inherent trade off in a way that can be explained by economics in terms of the behaviour of a rational economic agent. In order to investigate this we will attempt to formulate an integrated approach to considering the behaviour of hospitals given the nature of the environment within which they operate.

The thesis provides a review of the current strands of literature within hospital economics that deals with issues related to capacity utilisation and identifies different strands in the literature. We also review empirical estimates of hospital costs; these identify the theoretical foundations of the empirical studies to date.

The thesis is then separated into theoretical and empirical chapters. The theoretical chapter constructs a formal model of hospital behaviour building on theoretical foundations, to enable the problem of hospital capacity allocation decisions to be viewed within standard economic theory. The basic model introduces output heterogeneity, separating output into two, planned and unplanned (elective and emergency). In this model we also consider a utility function including a wider social perspective. Uncertainty is then introduced into the model, allowing stochastic demand for one of the outputs. The impact of uncertainty is considered in a formal manner by drawing on current theoretical knowledge regarding the influence of demand uncertainty on the production responses of the firm. A mathematical approach is specified, which allows an optimal allocation of capacity to be identified. This highlights the empirical content necessary to identify a fully specified model of hospital allocation decisions.

The empirical section estimates a cost function that is consistent with the theoretical specification identified in the previous section, by adjusting for demand uncertainty and output heterogeneity. The implications for the estimation of a hospital cost function are then considered and, particularly, the implications for standard economic theory of cost analyses. A number of different estimation approaches are assessed. The Box-Cox model is the preferred approach and this performs well, most notably, the demand variable included to pick up the influence of demand uncertainty is both significant and of the correct hypothesised sign.

The final part of the thesis attempts to bring together a more fully specified empirical solution to the problem, by focusing on the social costs of turning emergency patients away and leaving elective patients on waiting lists. Two empirical elements are identified from the theoretical model as being important: The probability of turnaway, and the relationship between waiting lists and this probability. The probability of turnaway for each hospital for each month is estimated. A number of different estimation techniques were employed to estimate the latter including a Tobit, Heckman two-stage and Box-Cox analysis. Based on these estimates a fully specified empirical model allowed the calculation of the implied marginal social costs of turning an emergency patient away. These were estimated to be around £300, and the implied marginal social costs of placing a patient on the waiting list were estimated to be just over £1. These represent indicative values and are based on aggregate estimates across all hospitals, nonetheless, they provide the first estimates of this kind adjusting for demand uncertainty and including output heterogeneity.

Publication Type: Thesis (Doctoral)
Subjects: H Social Sciences > HB Economic Theory
H Social Sciences > HJ Public Finance
R Medicine > RA Public aspects of medicine > RA0421 Public health. Hygiene. Preventive Medicine
Departments: School of Policy & Global Affairs > Economics
School of Policy & Global Affairs > School of Policy & Global Affairs Doctoral Theses
Doctoral Theses
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