Demand uncertainty and hospital costs: an application to Portuguese public hospitals

Abstract

In this paper, we evaluate the effect of demand uncertainty on hospital costs. Since hospital managers want to minimize the probability of not having enough capacity to satisfy demand, and since demand is uncertain, hospitals have to build excess capacity and incur the associated costs. Using panel data comprising information for 43 Portuguese public hospitals for the period 2007–2009, we estimate a translog cost function that relates total variable costs to the usual variables (outputs, the price of inputs, some of the hospitals’ organizational characteristics) and an additional term measuring the excess capacity related to the uncertainty of demand. Demand uncertainty is measured as the difference between actual and projected demand for emergency services. Our results indicate that the cost function term associated with the uncertainty of demand is significant, which means that cost functions that do not include this type of term may be misspecified. For most of our sample, hospitals that face higher demand uncertainty have higher excess capacity and higher costs. Furthermore, we identify economies of scale in hospital costs, at least for smaller hospitals, suggesting that a policy of merging smaller hospitals would contribute to reducing hospital costs.

Appendices

Appendix 1: Information on the data

In this paper, we used data on all Portuguese public hospitals included in the National Health Service network, with an emergency care service. Table 4 provides a list of the hospitals considered.

Table 4 Hospitals in the sample

Emergency services in Portuguese NHS hospitals are of three types: basic, medical-surgical and polyvalent. Polyvalent emergency services are those that receive the most complex patients. Basic emergency services receive only patients with simple cases. Medical-surgical emergency services are at an intermediate level, receiving cases with some complexity, but referring the most complex ones to polyvalent emergency services.

Some of the hospitals in the sample are integrated into Local Health Units (ULS)—organizational structures of primary care health centers and hospitals under the same management. Since the publicly available data refer to the ULS as a whole, and this study is applied exclusively to hospitals, data for hospitals included in ULS were estimated. The estimation is based on the weight of human resources used in the hospital in total ULS human resources, which is a good proxy given the importance of personnel cost on the operating costs of health care institutions.

The cost, input and output data were obtained from the Base de Dados de Elementos Analíticos, a database with analytical accounting data for Portuguese NHS hospitals provided by the ACSS—Administração Central do Sistema de Saúde, IP, available at http://www.acss.min-saude.pt/bdea/ [29], and from the Recursos e Produção do SNS, the statistical reports of the NHS resources and production published by Direção-Geral de Saúde, available at http://www.dgs.pt/ [30–32]. The monthly data on the number of emergency episodes for each hospital were provided directly to the authors by ACSS. Table 5 provides a list of all variables used.

Table 5 List of variables used in the paper

For estimation of the cost function, the nominal current costs were transformed into real values for 2006 using the GDP deflator provided by INE—National Statistics Institute and Bank of Portugal. The dependent variable “annual total variable cost” (TVC) was measured in thousand of 2006 €. For the variable AMB—the number of ambulatory surgeries—we followed Cowing and Holtmann [28] and replaced the zero values with 0.1, a constant close to zero, given the inability of the translog function to handle null values for output categories. The variable average length of stay for in-patient admissions (ALOS) is the ratio of total number of inpatient days and total number of discharged patients. It is an output variable, since a hospital may produce more health care, increasing the number of admissions or raising the average length of stay [13].

The dummy variables capture the differences in the complexity of cases treated in each hospital. Remember that polyvalent emergency services (DUP) are those that receive the most complex patients, and that medical-surgical emergency services (DMC) are at an intermediate level, referring the most complex cases to polyvalent emergency services, but receiving cases more complex than basic emergency services (the default option on the dummy variables). On the other hand, teaching hospitals with a polyvalent emergency service treat more complex cases, and thus are likely to have higher costs per patient, than other hospitals with other types of emergency departments and no teaching.

Appendix 2: Additional results and tests

Estimation of Eq. (1)

The individual results of the estimation of expected demand using Eq. (1) for each hospital, are presented in Table 6.

Table 6 Emergency demand estimation for each hospital

Specification tests

Several specifications and estimation methods were used to estimate the cost function, and the appropriate tests allowed us to conclude that the most adequate specification was the translog cost model, estimated with random effects. The fixed effects method may not be used in this case because the model includes dummy variables. However, estimations of the model without dummy variables were performed and Lagrange multiplier (LM) and Hausman tests allowed us to conclude that the most appropriate estimation method is the random effects method, even if dummy variables were not used.

LM has the null hypothesis the estimation by OLS against the alternative hypothesis of variable effects. The rejection of the null hypothesis leads us to consider the existence of unobservable individual effects. Therefore we use the Hausman test in order to analyze whether the estimation should use random effects (null hypothesis) or fixed effects (alternative hypothesis). The non-rejection of the null hypothesis led us to conclude that the random effects must be considered.

The tests also allowed us to conclude that the dummy variables are jointly significant. The results of these tests are presented in Table 7.

Table 7 Tests for different estimation methods

We compared the results of the translog cost model with the results of the Cobb Douglas model, and tested for the significance of the terms that distinguish both specifications (the cross and squared terms). The results show (see Table 8) that there is statistical evidence to reject the null hypothesis, meaning therefore that a translog model is the adequate specification for the cost function.

Table 8 Test of the specification of the cost function

Impact of main variables on costs

The effect of explanatory variables (except dummies) on hospital costs may not be inferred directly, but the elasticity of costs to each of these explanatory variables presented in Table 9 allows for an evaluation of that effect.

Table 9 Elasticity of costs of each variable

Table 10 displays the impact of X1 on costs, considering hospital size.

Table 10 Elasticity of costs to X1

Estimation of Eq. (5)

The results of the estimation of Eq. (5)—the relationship between demand uncertainty and hospital size, measured by number of beds (BEDS)—are presented in Table 11.

Table 11 Relationship between demand uncertainty and hospital size, measured by number of beds (BEDS)

Tests for the hypothesis of joint production and input/output separability

Table 12 presents the results of the tests for the hypothesis of joint production and input/output separability. The results show the interaction terms between outputs are significant, which indicates that hospital outputs are not produced separately.

Table 12 Joint production and input/output separability

Regarding the input/output separability, the test shows the interaction terms between input and output are statistically significant, meaning that hospital costs depend on input and outputs mixes.

Simulation of three hypothetical mergers

We simulated the effect of three hypothetical mergers on hospitals costs (see Table 13).

Table 13 Estimation of the effect on hospitals costs of three hypothetical mergers

The simulations show that mergers that involve small or medium hospitals would result in a reduction in X1, i.e., the creation of a larger hospital would reduce demand uncertainty and the excess capacity associated with it. However, in the case of the merger of smaller hospitals, the reduction of X1 causes an increase in costs, but in the merger of medium-sized hospitals, the reduction of X1 decreases hospital costs. For large hospitals, excess capacity due to demand uncertainty increases with the merger and so do costs. The results also show that small hospitals exhibit economies of scale, but the merger of medium and large hospitals is associated with diseconomies of scale.