Savings in the allocation of financial resources per health region in Portugal – Yes, we can. Ana Rita Borges

Between 9th January and 11th January of 2013, I had the opportunity to participate in the module “Challenges and Leadership in the Portuguese National Health System (NHS)” organized by Professor Pedro Pita Barros in partnership with ACSS (the Portuguese Central Administration of the NHS) for the Master students at Nova School of Business and Economics. As the name suggests, this module focused on the Portuguese NHS, covering topics such as its sustainability, efficiency and equity; the demand for health; waiting lists and the pharmaceutical market. Nonetheless, this was not just one theoretical module. Even though we were contextualized on the mentioned topics, with presentations at the faculty and the ACSS, the most striking feature of the module was the possibility to develop several group empirical projects on the Portuguese NHS, at request of the ACSS. These projects, which were quite appealing for the majority of the students, were presented to the ACSS in the end of the module. Their impressive and sometimes surprising results were quite successful, leaving the participants fully aware of the potential for collaboration between the academia and the healthcare sector.

In the scope of this module, my group[i] developed a project on the allocation of financial resources for hospital operations among the five Portuguese health regions, the so called ARS: North, Centre, Lisbon and Tagus Valley, Alentejo and Algarve. Essentially, our work aimed at answering three fundamental questions:

1.       How to create a model to access the determinants of the per capita hospital costs?

2.       What are the optimal per capita budgets of each ARS?

3.       Which are the ARS with potential for cost reduction?

Using data provided by the ACSS for the year of 2011 grouped by municipalities within each ARS, our first step was to clarify the variables involved in the estimation of the model. For convenience, these are summarized in the following table:

Dependent variables




Costs of admissions per capita


First component of total hospital costs per capita.

Costs of ambulatory per capita


Second component of total hospital costs per capita.

Total costs per capita


Sum of costs of admission per capita and costs of ambulatory per capita, i.e, cpc_total=cpc_adm+cpc_amb

Possible Independent Variables




Population density


Population per m2

Aging Index


Number of individuals aged above 65 years old per 100 individuals below 65 years old



The percentage of individuals with mandatory schooling within a municipality

Dependency Index


Ratio between the number of individuals below 14 years old or above 65 years old and the individuals between 14 and 65 years old

Per Capita Purchasing Power


Amount of goods that can be purchased with a unit of currency per person

Standardized Mortality


Ratio expressing the mortality rate with respect to the population in the municipality

Regional Dummies: North, Centre, Alentejo and Algarve

north, centre, alentejo and algarve

Correspond to 1 if the individual is from these regions; are 0 otherwise

Table 1. Variables used in the determination of the model

To approach the first question proposed, and thus identify the determinants of per capita costs, we ran OLS on three different model specifications (each considering a differing dimension of per capita costs as dependent variable) using Stata and found that the variables were jointly statistical significant at a 1% significance level, but not all of them were individually statistical significant, even considering a significance level of 5%. Through the command stepwise, we were able to identify the individually statistical significant variables at a 5% level in each of the three regressions, which were the actual determinants of per capita costs. These were different according to the per capita cost estimated, as shown below:

formula 1.1

formula 1.2formula 1.3

Having identifying the determinants of per capita costs in the three different areas considered, we had now the task of estimating the optimal per capita budgets of each ARS for hospital funding, using the regressors obtained before. However, OLS was not certainly the best method for estimating them. Since our goal was the estimation of the efficient cost frontier, we could not use a method that weighted all observations equally and was very sensitive to outliers. We needed a method whose output was the minimization of per capita costs, as the stochastic frontier model for cost estimation. Under this estimation method, the error term is divided into two components: the deterministic component (always positive, representing the inefficiency – spending more than desired to achieve a given level of output) and the idiosyncratic component (which could be positive or negative).

Still, even if we used the stochastic frontier model for cost estimation, we apparently had two forms of estimating the total costs per capita: directly or based on the sum of the estimated admissions and ambulatory costs per capita.  Nonetheless, the sum of the estimated admissions and ambulatory costs per capita could carry a certain degree of downward bias, since we would be aggregating two per capita costs which are efficient individually but might not be jointly. Therefore, direct estimation seemed the best form of estimating the optimal per capita budget per ARS, even though the estimation by the alternative method was important to access whether there were significant outliers in ambulatory and admissions’ costs, which happens if the estimations by the two different methods are significantly different. As such, we estimated the optimal per capita budgets per ARS using the two methods, but found that the difference was around 5% only. Given this, we still preferred to use directly the stochastic frontier model for the estimation of total per capita hospital costs, but could estimate the efficient per capita admissions and ambulatory costs as well (which I will not present in this article, for simplification).

With the model settled and apparently valid, we were then able to compare our estimations for the optimal per capita budgets for hospital funding per ARS with the observed ones. Since we found that all ARS had the potential to reduce per capita costs, it was possible to find the per capita savings per ARS as the difference between observed and estimated per capita hospital costs. Our results were the following:

graph1 (1)

Graph 1. Savings per capita across ARS

 As shown in this graph, the most inefficient ARS were the Centre, the North and the Algarve, with possible savings of 61,72€, 59,44€ and 50,09€, respectively. The most efficient ARS is Lisbon and Tagus Valley, where the per capita savings are considerably lower compared to the other ARS, of only 43,66€. Deepening this analysis, our group found that the most inefficient municipalities in the country were Covilhã, in the ARS Centre (with an estimated per capita saving of 242,98€); Sabrosa, in the ARS North (with an estimated per capita saving of 200,66€) and Fundão, in the ARS Centre (with an estimated per capita saving of 194,94€). On the other hand, the most efficient municipalities, all located in the ARS North, were Braga (with an excess of 93,91€ per capita); Póvoa do Lanhoso (with an excess of 62,18€ per capita) and Vizela (with an excess of 61,70€ per capita).

Even though these numbers may seem peaceful at a first glance, at an aggregated level they are not. Indeed, the savings from all ARS with per capita payments in hospital funding amounted to 534.046.908,74 €, quite an impressive value, specially because it represents 14,70% of the 3.632.835.733,96 € budget distributed across ARS in 2011, the year in analysis.

To conclude, even though the results obtained by my group during the module were merely indicative and should be refined in the future, there is no doubt that our simple model clearly captures the idea that per capita savings in hospital costs in all ARS across Portugal are possible, especially  in the Centre and in the North. Thus, I strongly suggest that new methods of allocation of financial resources per capita for hospital funding across ARS are implemented in the future, so that the distribution of funding across ARS is made evenly and more consistently with the different healthcare needs of the population.

[i] I would like to thank Sofia Oliveira (student in the Msc. Economics at Nova SBE, class 2012/2013) and Sofia Amaral (student in the Master in Economics at Nova SBE and the CEMS MIM Program 2012/2013) for their collaboration and invaluable work during the development of this empirical project. This article would have never been possible without them.

About the Author, Ana Rita Borges graduated in economics by Nova SBE and is currently attending the Master in Economics at the same school, with conclusion predicted for June 2013. Her fields of interest include: econometrics, microeconomics policy analysis, particularly in the sectors of labour market, health and energy.


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