Inference Procedures to Quantify the Efficiency–Equality Trade-Off in Health from Stated Preferences: A Case Study in Portugal



This article develops two inference procedures to calculate the inequality aversion and alpha parameters of a health-related social welfare function with constant elasticity (CES-HRSWF) using stated preferences. Based on the relative concept of inequality, a range of values were proposed for the trade-offs between improving total population health and reducing health inequalities.


A self-administered questionnaire was used to collect data from a sample of 422 college students in Portugal. Respondents faced three hypothetical allocation scenarios where they needed to decide between two health programmes that assign different health gains to two anonymous sub-groups of the population and to two sub-groups identified by socioeconomic class. Combinations of the median response to these three questions were used to estimate the parameters of the CES-HRSWF.


Findings suggest that the quantification of the efficiency–equality trade-off is not independent of the inference procedure used. Plausible values for the inequality aversion and for the alpha parameters were obtained ranging from 2.24 to 4.85 and from 0.5 to 0.58, respectively.


Respondents revealed some aversion to health inequality. However, the extent of this aversion seems to be sensitive to (1) the identification of the groups by occupation status, (2) the size of the health gain, and (3) the inference procedure used.

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Fig. 1


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    A reviewer cautioned that, in each version, the median responses to question 1 (Q1) and question 2 (Q2) may not be empirically correlated in the sense that they may belong to different respondents. While this behavioral hypothesis points to the development of different statistical analyses, we do not find this behavior in the current data. In fact, in version 4 (version 7) 78% (74%) of the 118 (129) participants whose response to Q1 was below or equal to the respective median response also responded below or equal to the median response to Q2 as identified in Table 2. Likewise, 79% (73%) of the 117 (130) participants whose response to Q2 was below or equal to the respective median response also responded below or equal to the median response to Q1 as identified in Table 2. This indicates a high degree of agreement between the ranking of respondents in Q1 and the ranking of respondents in Q2. Additional analysis (available upon request) confirms the statistical significance of this apparent agreement in each Version.


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Data Availability Statement

Authors can confirm that all relevant data are included in the article and/or its supplementary information files. The authors declare that (the/all other) data supporting the findings of this study are available within the article (and its supplementary information files).

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MP conceived and designed the study and drafted the first draft of the paper. AB analysed the data and reviewed and suggested the structure of the manuscript. All authors contributed critically to the revision of the manuscript for intellectual content and approved its submission for publication.

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Correspondence to Micaela Pinho.

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Micaela Pinho and Anabela Botelho disclose no receipt of any financial support for the research, authorship, and/or publication of this article.

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Micaela Pinho and Anabela Botelho declare they have no conflicts of interest.

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the Helsinki Declaration of 1975, as revised in 2000. Informed consent was obtained from all participants before being included in the study.

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Pinho, M., Botelho, A. Inference Procedures to Quantify the Efficiency–Equality Trade-Off in Health from Stated Preferences: A Case Study in Portugal. Appl Health Econ Health Policy 16, 503–513 (2018).

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