Convergence of European healthcare systems: a cluster analysis

* The author is grateful to two anonymous referees who have contributed to the quality of the final version of the paper.

¹ Hermann (2010); Taylor-Gooby, Leruth and Chung (2017), especially chapter 1; Pestieau and Lefebvre (2018), especially chapter 11.

² For a discussion see Bambra (2005b); Bergqvist, Yngwe and Lundberg (2013); Fosse (2011).

³ See, for example, Arts and Gelissen (2002); Ferragina and Seeleib-Kaiser (2011); Danforth (2014); Emmenegger et al. (2015); Saint-Arnaud and Bernard (2003); Taylor Brown and Ben Brik (2024).

⁴ See Rothgang (2021); for a recent review, Powell, Yörük and Bargu (2019).

⁵ See also Reibling, Ariaans and Wendt (2019).

⁶ See, for example, Fosse (2011) on health promotion policies. Similar challenges also arise with earlier classifications, such as Wilensky and Lebeaux (1965) residual-institutional distinction, later adopted by Pinker (1971) and Titmuss (1974). See Higgins (1981); Pierson (2006); Carreira Da Silva (2017).

⁷ Beta-convergence occurs when units with initially lower levels of a given indicator grow faster over time than those with higher levels; sigma-convergence refers to a reduction in dispersion across units.

⁸ The European Practice Assessment (EPA), introduced in the early 2000s, established a common framework for evaluating primary care performance across countries.

⁹ See Kringos et al. (2015); Gilardi, Füglister and Luyet (2009); Dubas-Jakóbczyk et al. (2020); Polin et al. (2021).

¹⁰ On Bismarck-type models, see Palier (2010).

¹¹ As recently argued by Lu (2024), when applied to longitudinal data, clustering seeks to group units of analysis (individuals, regions, countries, etc.) according to the patterns and trends characterizing their repeated measurements over time. Hierarchical clustering represents one methodological option capable of accommodating temporal trajectories, even in the presence of sparse or irregular observations (Zhou, Zhang and Tu, 2023). Applications of longitudinal clustering span multiple domains, including criminology, sociology, medicine, and ecology. Recent examples include the identification of subgroups exhibiting distinct cigarette-smoking patterns for the purpose of predicting health outcomes (Lee et al., 2016), as well as the characterization of adolescent substance-use trajectories and their association with leisure experience (Weybright et al., 2016). For a comparative assessment of methods for clustering longitudinal data, see Den Teuling, Pauws and van den Heuvel (2021).

¹² After z-scoring, the variance of each variable equals 1, which can be interpreted as a special case of weighting based on the reciprocal of the sample standard deviation. This implies that, under the z-score transformation, the influence (or weight) of a variable decreases as its variability increases.

¹³ To assess the temporal properties of the series across countries, correlograms were computed for each national time series. The analysis revealed significant autocorrelation in all cases, indicating that observations are not temporally independent but are influenced by their own past values. This evidence supports the use of a pooled data framework for the subsequent cluster analysis, as it enables the identification of cross-country similarities in underlying dynamic patterns while appropriately accounting for the serial dependence inherent in each series and, potentially, cross-correlation across countries.

¹⁴ Given two pairs of clusters with equally distant centroids, Ward’s linkage will preferentially merge the smaller pair, aiming to minimize the total within-cluster inertia (or error sum of squares) rather than the direct distance between clusters. This implies that Ward’s method is, in principle, less sensitive to noise and outliers, and it tends to produce compact, approximately spherical clusters of similar size and variance (see Everitt et al., 2011, Chapter 4; Kaufman and Rousseeuw, 1990).

¹⁵ See also Milligan and Cooper (1985).

¹⁶ For example, the Global Health Database provides very limited data even for European countries on key variables related to primary care and health quality indicators.

¹⁷ See also Burau and Blank (2006:65).

¹⁸ See Sowula et al. (2023) for Sweden and Germany.

¹⁹ Means-tested and non-means-tested cash and in-kind benefits are included under the category of health expenditure, as they represent either a direct monetary transfer or a direct form of public spending. To some extent, they also constitute an element of health coverage. However, both in-kind and cash components of the welfare state are classified within the same category, as part of a broader definition of collective resources. See, for example, Lundberg et al. (2015).

²⁰ See Polin et al. (2021) for a description of health reforms in 2018-2019.

²¹ See, for example, Musgrove (2023).

²² See, for example, De Simone, Gaeta and Ercolano (2012).

²³ A principal component analysis (PCA) was also performed to identify core characteristics of the health system. Although detailed results are not reported in the text, the analysis suggests that each variable has a significant loading (either higher or lower than ±0.3) on at least one component, and that each component can be meaningfully interpreted in terms of healthcare characteristics. If every variable has at least one significant loading on some component, it contributes to the variance (or correlation structure) of the data within the PCA subspace. This reduces the risk of including completely “noisy” or irrelevant variables. It also implies that clustering performance is less affected by the presence of less influential variables, as long as they are not entirely “silent” – i.e., they contribute with a significant loading somewhere (see, for example, Giuliani and Vici, 2024). Nevertheless, the presence of many “weak” variables – even if minimally contributing – can still introduce noise, increase model complexity, and reduce the stability or interpretability of the clusters. To avoid arbitrary variable selection, especially given the constraints posed by limited data availability, all variables were retained in the subsequent cluster analysis.

²⁴ Joumard, André and Nicq (2010). OECD (2025b) also provides a cluster analysis, identifying seven distinct clusters that include European countries. However, the analysis is not limited to European countries, encompassing other OECD member states.

²⁵ The optimal number of clusters is determined using both the pseudo-F and pseudo-T-squared statistics from the Duda-Hart rule. In general, higher pseudo-F values indicate greater separation between clusters, suggesting a more distinct clustering structure. Conversely, lower pseudo-T-squared values imply greater within-cluster homogeneity. Thus, the optimal number of clusters reflects a balance between cluster separation and internal cohesion.

²⁶ This result is consistent with a recent study by OECD (2025b), which – addressing three key policy areas in the health domain – shows that there is no indication that any one group of health systems would systematically outperform another. See also Wendt (2009); Böhm et al. (2013). As argued by Giaimo and Manow (1999) and Reibling (2010), despite their formal differences, systems often converge functionally in response to shared policy pressures.

²⁷ Castles and Obinger (2008); Kuitto (2016). For a different perspective, see Filipovic and Dobrotic (2022 :199).

²⁸ See Lamping and Rüb (2004) for the definition of a “recombinant welfare system” in the case of pensions.

²⁹ Polin et al. (2021); Dubas-Jakóbczyk et al. (2020). The argument was also anticipated by Ruggles and O’Higgins (1987).

³⁰ Sláintecare is a cross-party, ten-year plan launched in Ireland in 2017 to create a universal, single-tier health and social care system. The plan aims to provide equitable access to care based on need rather than ability to pay, focusing on population health, integrated primary and community care, and reforms to entitlements, funding, and implementation. Key goals include shifting care to the community, expanding workforce capacity, and increasing public investment to deliver integrated, person-centred services for all Irish residents. See Burke et al. (2018); Thomas et al. (2021).

³¹ Note that Witt et al. (2018) use average linkage clustering, while Movahed (2023) employs a k-means method.

³² It is also worth noting that this shortage in Cluster 1 reflects a broader EU-wide issue. As reported by OECD (2024), the EU faces a health workforce deficit, with an estimated shortage of 1.2 million doctors, nurses, and midwives as of 2022. This shortage stems from multiple factors: demographic ageing affecting both patients and the health workforce, combined with difficult working conditions that contribute to staff burnout and retention challenges.

³³ Note that these indicators are not strictly comparable with the other data, as the number of countries for which data are available is smaller than in the general case.

³⁴ See also Rothgang et al. (2010:247).

³⁵ For a different perspective, see Goodin and Le Grand (1987).