Comparing long-term care systems: A multi-dimensional, actor-centred typology

Like other fields of social policy, the organization of long-term care (LTC) varies temporally and geographically. The present article aims to advance the comparison of LTC systems worldwide by proposing a conceptual framework to analyse variation, putting a special focus on analysing the role of public and private actor types. In a precluding literature review of existing LTC typologies, we find that there are various promising classification approaches, but with an overwhelming concentration on European countries and often constructed in-transparently and superficially. Building on the concept of the care/welfare mix, we develop a multi-dimensional , actor-centred typology of LTC systems . In doing so, we employ the methodological procedure of theoretically constructing a typological attribute space . We argue that three dimensions , that is service provision, financing and regulation, are crucial for differentiating types. Further-more, we chose an actor-centred approach, asking who bears the main responsibility in each dimension. Five relevant types of corporate actors are distinguished: state, societal actors, private for-profit actors, private individual actors, and global actors. Finally, we present and discuss the resulting attribute space and further illustrated the typo-logy's use by exemplarily classifying three countries.


| INTRODUCTION
being of care recipients and their care providers; on the societal level, gender relations and the organisation of labour (markets) are deeply intertwined with care modalities (Daly, 2002). Moreover, the extent and kind of state involvement in LTC systems have direct implications, for instance, for access to (adequate) care and public finances (Colombo et al., 2011, p. 214). Analysing variation can therefore help to assess dis(advantages) of certain types of LTC systems and guide policies (Bettio & Verashchagina, 2012, p. 83). Furthermore, comparison of similarities and differences is also relevant for a more theoretical, comparative welfare perspective, as this helps to track change over time and identifysocietal, political and transnationalfactors that shape the organisation of LTC (Alber, 1995;Wendt, Frisina, & Rothgang, 2009).
Taking a step back from concrete empirical manifestations, this paper approaches the variance of LTC systems from a conceptual perspective. In doing so, we focus on a specific instrument widely used in the social sciences and comparative welfare studies in particular: typologies. These 'organized systems of types' (Collier, Laporte, & Seawright, 2012, p. 217) are useful in facilitating systematic comparison of complex social phenomena. For the field of (long-term) care, several classificationssome of them sketchy, some more elaboratehave been proposed and/or applied in the last three decades, offering important insights into country groupings and variation. However, many of them seem to lack clarity and/or are designed for a very limited geographical scope. To gain a better understanding of existing scholarship, we begin by conducting a literature review of extant LTC typologies in Section 2.
The remainder of the article presents a multi-dimensional, actor-centred typology for facilitating systematic, global comparisons of LTC systems. In doing so, we employ the methodological procedure of theoretically constructing a typological attribute space presented in Section 3 of the article. In Section 4, we proceed to discuss the choice of attributes as a basis for building the typology. While paying close attention to the peculiarities of LTC (e.g., relevance of informal care), we mainly build on scholarship on the care/welfare mix (e.g., Powell, 2007;Razavi, 2007;Sipilä, Anttonen, & Baldock, 2003), comparative research on healthcare systems (e.g., Wendt et al., 2009), and global social policy (e.g., Gough, 2001;Kaasch, Koch, & Martens, 2019). Subsequently, the typology's attribute space is presented and discussed. Finally, we provide an example on the typology's use for classifying empirical cases and conclude with a reflection on the framework's strengths and limitations.

| LITERATURE REVIEW: TYPOLOGIES IN THE STUDY OF LTC
A typology is a conceptual framework for sorting instances of a phenomenon according to (dis)similarities on various attributes into different groups. 1 Since the publication of Esping-Andersen's (1990) influential classification of welfare regimes three decades ago, typologies have become a widely used tool in the field of comparative welfare analysis (Arts & Gelissen, 2010;Van Kersbergen, 2013). While concrete classifications as well as the typological approach per se have attracted critique (see for example, Arts & Gelissen, 2010;Collier et al., 2012), well-constructed typologies can be a useful tool for particular research endeavours. They help to order and reduce empirical complexity, systematically assess diversity, detect patters, and facilitate theory development (Collier et al., 2012;Kluge, 1999;Van Kersbergen, 2013). We thus argue that the application of a typological framework is a helpful instrument for comparatively analysing the complex theoretical and empirical variety of LTC arrangements in different countries.
Several classifications of care regimes and/or policies have been brought forward since the 1990s. The influential pioneer publications on European care regimes like the classifications by Anttonen and Sipilä (1996) and Bettio and Plantenga (2004) have mostly taken a comprehensive (social) care perspective, including both childcare and eldercare arrangements. This approach has its merits and can be especially useful for a broad perspective and/or a gendered analysis of the welfare state. However, in many countries, the historical trajectories, extent of benefits and type of familialism of LTC and childcare differ (e.g., Leitner, 2003;Ochiai, 2009). Accordingly, the emerging policy field of LTC merits a separate analysis within its ownalbeit inspired by social and health care researchconceptual framework. Before we proceed to present our typological framework, the remainder of this section examines extant typologies to identify both the qualities and limits of existing scholarship. The review includes publications, which present a typology for grouping countries according to their LTC arrangements specifically, be it for the elderly and/or other segments of the population. 2 In total, this results in 17 LTC typologies fulfilling these criteria (see Table A1, Appendix).
Consequently, these classifications are driven by inductive logic, starting from empirical observations to arrive at 'real types'. Furthermore, three classifications (Burau, Theobald, & Blank, 2007, p. 55;MISSOC Secretariat, 2009, pp. 9-10;Rothgang, 2009, pp. 27-32) are based on theoretical considerations about the variance of LTC systems, employing deductive reasoning: they combine multiple existing classificatory and theoretical models to construct their framework. Meanwhile, remaining studies do not, to our knowledge, specify any procedures or methods.
The reviewed classifications use various criteria to distinguish system types. For an overview, we have grouped the criteria in Table 1 and attributed them, whenever possible, to overarching dimensions. Financing is the most popular topic, used by 11 classifications. Here, most studies focus either on financing schemes, that is, taxes versus social insurance contributions or on financing source, differentiating between private and public spending. However, no typology combines both criteria to differentiate multiple schemes/sources. Eight classifications are concerned with at least one aspect of regulation, mainly by looking at the extent of coverage and underlying entitlement criteria in the LTC system, but also at rules governing choice. Moving to the next dimension, seven typologies include at least one criterion, which is concerned with the provision of LTC. While most typologies look at the amount of (in)formal LTC services provided, Timonen (2005, p. 32) employs a more complex criterion, distinguishing three providing actor typesstate, family, and private sector. Finally, there are six typologies, which address aspects of integrationor fragmentationof LTC systems with two foci: The coordination of different LTC schemes within a country and the integration of the LTC system with other social protection schemes.
The number of classified cases per typology varies from five (Timonen, 2005) to 31 (MISSOC Secretariat, 2009) countries. Two typologies (Bettio & Verashchagina, 2012;Colombo et al., 2011) provide typical examples instead of classifying a whole sample of cases. The 15 remaining studies assign 225 cases in total to types, covering 36 different countries; of which Sweden and Germany feature most prominently (see Table A2, Appendix). Regarding regional coverage, existing classifications focus overwhelmingly on high-income countries and the European continent in particular, with more than 95 per cent of all cases belonging to this region. 3 Within Europe, 75 times Northern and 67 times Western European countries were classified, while there has also been considerable, but less focus on the Southern (42 times) and Eastern European (31 times) sub-regions.
Overall, existing classifications provide valuable insights into the empirical variations of LTC arrangements, most notably in Europe. Furthermore, they have advanced comparative LTC research by presenting and discussing multiple conceptual approaches and criteria on how to compare LTC systems/policies cross-nationally in a meaningful way. However, our review shows that extant typological LTC research suffers from several limitations, primarily when considering their methodological basis: to a large extent, the classifications display a lack of transparency T A B L E 1 Criteria used in 15 extant LTC typologies, sorted by dimension
regarding the specification of criteria and/or underlying procedure/methods. The more quantitatively oriented typologies (especially Damiani et al., 2011;Hal askov a et al., 2017;Kraus et al., 2010) are an exception here. However, they carry other (methodological) limitations: due to the inherently inductive approach toward classification, theses typologies cannot simply be extended to other countries or regions (De Carvalho, Schmid, & Fischer, 2020). This is particularly problematic given that cases concentrate strongly on Europe. Furthermore, while typologies capture many important aspects of LTC arrangements/schemes, most typologies seem to select the criteria rather arbitrarily without clear theoretical considerations of how to differentiate among types. What is more, the inclusion of information on more than two LTC system dimensions is considered only in few cases. Bearing these issues in mind, in the remainder of the paper, we proceed to develop a novel typology that aims to overcome some of the identified limitations. Before we present our criteria and types, the next sections outline our methodological approach.

| METHOD OF TYPOLOGY CONSTRUCTION
To identify relevant criteria for our typology, we start from theoretical considerations about (the variance of) LTC systems. As empirically driven, inductive typologies are highly time-and space-dependent (Kluge, 1999, p. 60), we see a deductive approach as better suited to keep the framework functional for diverse research objectives, facilitating the analysis of (newly emerging) LTC systems in different regions and time periods. Our choice of attributes, as well as their concrete specifications are discussed in Section 4. Subsequently, the typology is built by establishing a typological attribute space, which is an instrument well suited for developing a typology in a systematic, transparent and reproducible way (Kluge, 1999, p. 109). The concept of the attribute space is based on the definition of types as a combination of attributes (Lazarsfeld, 1937, p. 120). Consequently, each typology can be depicted as a matrix, where cell types are identified using a unique combination of attributes/variables (Collier et al., 2012). However, when following such a rigorous combination logic, the resulting number of types easily becomes large. Here, the 'typological operation' of reduction comes in as a second step, which aims at the elimination or merger of particular attribute (value) combinations (Lazarsfeld, 1937). Different forms of reduction have been distinguished in the literature, for instance, functional reductions, which eliminate unlikely or implausible types and pragmatic reductions, which delete/ combine irrelevant combinations in line with the research question (e.g., Kluge, 1999, pp. 101-103;Lazarsfeld, 1937, pp. 128-129). To keep our framework widely usable, we do not implement any fixed reduction steps but discuss several possibilities when presenting the attribute space.

| A CONCEPTUAL FRAMEWORK FOR COMPARING LTC SYSTEMS
The framework presented in the following is intended to facilitate comparison of LTC systems. Similar to Seeleib-Kaiser's (2002, pp. 751-752) notion of 'welfare systems', a LTC system can be defined as the sum of societal arrangements dealing specifically with LTC as an area of social protection. Consequently, the typology is most suitable for classifying LTC arrangements of whole countries. Moreover, with minor constraints, the framework can also be used to compare specific LTC systems under public responsibility, such as the LTC insurance scheme in Israel, the Medicaid programme in the United States or the Eldershield scheme of Singapore, which make up only one part of the overall LTC arrangements of the respective countries.
LTC systems of any kind can be broken down into several dimensions. An analysis of these individual attributes is crucial to gain a differentiated picture of any social policy field (e.g., Powell, 2007;Seeleib-Kaiser, 2008), in particular if they involve services delivery as is the case of LTC (Alber, 1995;Rothgang et al., 2010). So far, we often find unidimensional characterisations of LTC systems such as 'social insurance system' or 'public model' (see e.g., Table A1, Appendix). While these labels can be helpful by putting essential properties into a nutshell, they easily obscure which component of a system is societal or public. For instance, do the systems based on financing from social insurance contributions exhibit similar traits also regarding their provision or regulatory structure? This question can only be disentangled using a multi-dimensional framework that captures greater heterogeneity and complexity. Indeed, as research on healthcare systems has shown, most countries do not fit into any of the 'pure' state, societal or private types (Böhm, Schmid, Götze, Landwehr, & Rothgang, 2013).
While dimensions can be broken down in terms of many different conceptual foci (cf. Alber, 1995;Jenson, 1997), for the purposes of typology-building, the researcher is faced with limiting her focus to a single set of attribute values suitable for capturing the most amount of relevant information or else risking over-complexity. In the present study, we employ an actor-centred approach 4 to define attribute values, as we are especially interested in capturing the role of the state vis-à-vis other important actors. In general, actors can be conceived of at different aggregation levels, from a monolithic understanding of nations to individuals (Becker, Shriwise, & Schmitt, 2020). For studying LTC systems, the meso-level perspective with a focus on (quasi) corporate actors (Coleman, 1990) seems most fruitful. While corporate actors are formally organised groups with centralised means for collective action, also 'quasi groups' of people or organisations that share certain attributes and (re)act similarly can be regarded as such (Mayntz & Scharpf, 1995a). For instance, informal caregivers, who do not typically collectivise but occupy a similar role in the LTC system, can be treated as a quasi-corporate actor.
The analysis of the question who does what in organizing and supplying social protection is a key concern of welfare studies, as actor typessuch as the state, the commercial sector or familyand associated (inter)action mechanismssuch as hierarchy, market, or reciprocityhave implications for societal (power) structures, (re)distribution processes, and welfare outcomes. Regarding the latter, the role of different actors in social policy can influence, for instance, the degree of (de)familiarisation (Leitner, 2003), stratification, and (de)commodification (Esping-Andersen, 1990). Similarly, a focus on the 'who question' has been emphasised as particularly useful for the analysis of social services and care (e.g., Jenson, 1997;Razavi, 2007;Sipilä et al., 2003). However, out of the reviewed typologies, only one (Timonen, 2005) explicitly focuses on actors. Given the widely acknowledged analytical value of the actor framework, we argue that we can tease out more from this approach for systematic comparison of LTC systems, especially if combined with multiple dimensions. Therefore, in the remainder of this section, we discuss the choice of dimensions and actors for our typology.

| Dimensions
Service provision, financing and regulation are three dimensions which have frequently been proposed and used for the analysis of welfare studies in general (e.g., Powell, 2007;Seeleib-Kaiser, 2008), healthcare systems (Wendt et al., 2009) and also LTC (e.g., Alber, 1995;Burau et al., 2007). However, in practice, often only one or two of the dimensions are actually employed (see review section). We argue that all three are important constitutive elements of any LTC system, predestining them for laying the foundation of our typology. First, the provision of care is the elementary function that constitutes the ultimate rational of any LTC system. Provision refers to the actual task of caring, which can consist of more medically related tasks such as administering medicines, hygiene, household-related tasks such as washing or cooking as well as strengthening societal participation and providing emotional support.
Second, financing can be considered a 'second basic function' (Rothgang et al., 2010), as the input of resources is necessary for 'producing' LTC. However, it is important to note that in contrast to healthcare systems, financing does not only unfold explicitly by monetarily remunerating the provision of LTC services (and aids), but is often only implicitly present. The latter is the case with informal, unpaid care provision, where financing is present in the sense of time-resources used, which can also be measured in foregone earnings (WHO, 2015, p. 131).
Third, a LTC system isdirectly or indirectlysubject to regulation, that is the 'intervention in the behavior or activities of individual and/or corporate actors' (Koop & Lodge, 2017, p. 97). Contrary to the provision and financing dimension, regulatory activity is not directly involved in the 'production' of LTC. However, regulatory interventions influence and modify the production structure, crucially shaping the system (Mayntz & Scharpf, 1995b, pp. 16-19).
While regulation is often mainly associated with the state (Koop & Lodge, 2017), regulation also comes in other forms, for instance, through societal norms, international organisations or market mechanisms (Braithwaite, Makkai, & Braithwaite, 2007, pp. 8-10). It is this comprehensive understanding of multiple actor types as potential regulators that we follow. 5 Regarding its contents, the regulatory dimension is also comparably broad, comprising, among other aspects, regulation of entitlement criteria, care recipient's choice of provider, or remuneration modalities (cf. Wendt et al., 2009; Table 1). Arguably, this complexity necessitates a careful operationalisation when empirically comparing regulatory arrangements, which the present paper can only marginally touch upon. The next section continues to define attribute values to be subsumed within the three dimensions.

| Actors
A widely used distinction in welfare studies is the ideal-typical dichotomy of public/state versus private/market actor types (e.g., Esping-Andersen, 1990, pp. 79-82;Seeleib-Kaiser, 2008). However, especially since the 1990s, research on gender, care and welfare (e.g., Leitner, 2003;Lewis, 1992) and literature on the 'welfare mix' (Evers, 1995;Johnson, 1999) have stressed the importance of the household/family and the third/voluntary sector, respectively, as other private and public actor types beyond the state and profit-based entities. Consequently, a fourfold set of actors, which has aptly been characterised as a welfare or care 'diamond' (Pijl, 1994;Razavi, 2007), has previously been proposed for the analysis of (long-term) care (Burau et al., 2007;Lyon & Glucksmann, 2008;Ochiai, 2009;Sipilä et al., 2003). It is this care diamond that we take as a point of departure for choosing (quasi) corporate actors for our typology.
First, with a view to collectively organised social protection for LTC, we naturally include the state as an actor type. 'State' is an umbrella term for the set of public institutions making up the political-administrative system of a country (Johnson, 1999, pp. 30-31). Importantly, it has to be noted that LTC policy is not only a responsibility of the central state but is often organised and/or delivered on the regional or local level as well, such as, for instance, by provinces in Canada (Béland & Marier, 2020) or municipalities in Latvia (Rajevska, 2018). Therefore, it has to be considered how to deal with the variety of levels in the conceptualisation of the state. Keeping the above-mentioned risk of over-complexity in mind, as the analysis of multi-level governance in LTC is already highly complex (see for example, Theobald & Ozanne, 2016), we chose to employ a broad conception of the state including all state levelscentral, regional or local institutionsinto a single category. The state can assume responsibility in all three dimensions: In publicly introduced LTC systems, care can be delivered and regulated by state agencies and financed by taxes. While globally many LTC systems exist in which single dimensions are state-led, one particularly well known example of the state-dominated system across all three dimensions is Sweden (Theobald & Ozanne, 2016;Timonen, 2005).
Besides the state, there is a second, non-governmental public actor assuming responsibility for LTC, which has, among others, been denoted as the third, intermediary, non-profit, or civil society sector. To express its community/ society embeddedness and collective self-organisation, we employ the term societal actor (cf. Wendt et al., 2009), which encompasses organisations that are neither governmental nor profit-maximising, but formal and self-governing (Johnson, 1999, pp. 147-148). In many countries, societal actors such as mutual aid associations, charitable or religious organisations have long-standing traditions in organizing and supplying LTC (Alber, 1995;Razavi, 2007, p. 21).
Today, they are also important providers, both in states with and without comprehensive public LTC systems, for instance in Portugal (OECD, 2011) and South Africa (Lloyd-Sherlock, 2019). Besides these organisations, which can also finance (e.g., through donations) and (self-)regulate, there is also another important kind of societal actor present in the latter two dimensions: Social insurance (SI) bodies. As non-governmental, self-governing institutions, they collect contributions from their memberstoday often all formal employees and employers in a countryto financially mitigate the risk of LTC, while regulatory power, for instance for setting contribution rates, can lay with the SI itself or the state. While SI is not (yet) that widespread in LTC, there are several prominent examples such as Germany, Japan and South Korea (Joshua, 2017).
Turning now away from the public actor spectrum, two types of 'private' actors are to be introduced: First, there are what we term private for-profit actors, that is, commercial-oriented enterprises or single persons selling care services and making use of market mechanisms as a mode of exchange. As in other fields of social policy, for-profit actors can appear in provision and financing, for instance, by operating nursing homes, delivering assistance to a care recipient at home or offering LTC insurance policies. In contrast to SI or tax financing, such private insurance plans do not engage in on societal redistribution but make use of mechanism such as prepayment and risk pooling to safeguard insured individuals against the financial risk of LTC dependency (Colombo et al., 2011). Private for-profit actors can also (self-)regulate their activities as providers and financing agenciesas the rise of managed care in the US has demonstrated. Alternatively, they may be subject to external rules set by public actors, such as in the Eldershield programme in Singapore (Le Corre, 2012).
Second, in a different understanding of 'private' as a personal space that is, as opposed to a public space, not (openly) accessible or visible (Starr, 1989, pp. 16-17), we introduce the type of private individual actors. This actor type, which is often also denoted as 'family' or 'household' (see e.g., Lyon & Glucksmann, 2008;Pijl, 1994;Razavi, 2007), is characterised by (previously) existing social relations with the care recipient, comprising the provision of LTC by relatives, friends and neighbours (Timonen, 2009;WHO, 2015, pp. 129-130). When employing the common analyticalalbeit far from clear-cutdistinction of formal vs. informal care, private individual actors are the group situated most in the less regulated informal spectrum, generally characterised by an absence of formal training, contracts and remuneration (Kraus et al., 2010;Timonen, 2009). Naturally, private individual actors are also a relevant actor type in the financing dimension. This is especially the case for LTC arrangements with a high share of informal care provision where the (implicit) cost is born by the care recipient's household and, potentially, other family members or even other persons from the care recipient's social network (WHO, 2015, p. 131). If there are direct monetary transactions involved, for instance, for remunerating a care worker continuously or purchasing respite care, this type of financing can be referred to as household out-of-pocket expenditure (OOP). A certain share of OOP is also common in countries with public LTC systems, such as the Netherlands or South Korea (Colombo et al., 2011, p. 238). Furthermore, if there are no external standards set for informal care provision as is, due to its private and personalised nature, often the case, private individual actors also (self-)regulate their relationship and modalities of care provision and financing.
While the distinction of private for-profit and individual actors as defined above seems evident at first sight, it poses some challenges when delineating the groups in the provision and regulation dimension. Regarding the former, it becomes necessary to carefully consider the 'placement' of (migrant) domestic care workers, who constitute an important phenomenon in LTC provision in different world regions (e.g., Bettio & Verashchagina, 2012;King-Dejardin, 2019;Michel & Peng, 2012). On the one hand, domestic workers can sustain familialistic forms of care provision (Michel & Peng, 2012) and, especially when living with the care recipient in the same household as so-called 'live-ins', show 'striking resemblance to informal caregivers' (Timonen, 2009, p. 310). On the other hand, they operate in the care market, establishing contractual relationships with care recipients (or alternatively their families or intermediaries) and offering services in return for payment (monetary and/or in-kind like accommodation; see e.g., King-Dejardin, 2019; Lyon & Glucksmann, 2008;Simonazzi, 2009). Thus, despite their shared traits with private individual actors, they rather qualify as one form of for-profit actors together with the more formalised (self-) employees and small and large provider organisations situated in this category.
As regards private actor regulation, (self-)regulation of both private for-profit and private individual actors is, as outlined above, plausible and a necessary category to capture LTC systems without central or binding regulation by third parties. However, it should be noted that compared to more direct and pronounced regulatory competences, as exerted by the public types of actors, the possibility of private actors to intervene into the LTC system remains limited. Moreover, a differentiation between for-profit and individual private regulation remains theoretically as well as empirically ambiguous. Consequently, instead of differentiating two forms of private actor types as in provision and financing, we use the superordinate category of private actors in the regulatory dimension.
In line with the care diamond approach, so far, we have discussed four types of actors for our typological attribute space: State, societal actors, private for-profit actors, private individual actors. However, as pointed out by Gough (2001), the four actor-types do not only represent domestic actors, but the welfare mix also needs to be conceptualised supra-nationally (see Figure 1). Accordingly, the non-domestic actor group is equally heterogeneous as that of domestic actors, taking on forms such as international organizations (IOs in the Global South (e.g., Kaasch et al., 2019;Kaasch & Martens, 2015). While supra-and international actors do not play a large role in the policy field of LTC so far, many IOs are increasingly becoming active in this field (see e.g., Colombo et al., 2011;Esquivel, 2017;WHO, 2015). Therefore, it is important to consider global actors with their distinct rationales when constructing a comprehensive typology applicable to future system contexts. Already, there are some examples of INGOs and foreign states' international cooperation agencies involved in LTC provision and financing in Southeast Asian countries (Loichinger & Pothisiri, 2018). To keep the typological attribute as concise as possible, we subsume all forms of public (i.e., state or societal related), non-domestic organisations, such as foreign states, United Nations' agencies, regional organisations or INGOs like HelpAge International, under the corporate actor group termed 'global actors' (see Figure 1)

| The universe of LTC system types
So far, we have outlined three typological dimensionsprovision, financing and regulationplus five sets of actors as attribute values. As argued above, we include all five actor types in the provision and financing dimension, while the regulation dimension contains four actor types with a combined private actor category. Consequently, the attribute space displayed in Figure 2 consists of four times five times five, resulting in 100 types, of which five are pure types consisting of one actor type only. However, when taking a closer look at the combinations, it becomes clear that many of them will probably not occur at all in empirical reality or are irrelevant when studying certain cases/regions. Therefore, as outlined in the methods section, attributes, attribute values and cells can be merged flexibly depending on the aim and objects of research to reduce the attribute space. In general, some combinations seem to be quite implausible when considering the power relations of actor types, in particular of the state. For instance, it is difficult to imagine that private actors dominate in regulating and financing LTC while the state provides care (cf. Böhm et al., 2013). Furthermore, while it is reasonable to assume, as trends in population ageing in the Global South continue to intensify in the coming years, that global actors may indeed take on a stronger role in LTC, when using the typology to analyse historical LTC arrangement in the Global North, it is unlikely that the global actors' category will be of much relevance. While these theoretical exercises can be useful, at this point we refrain from definitely reducing the attribute space, as, first, we aim to offer a framework applicable to different periods and regions, and second, a reduction based on empirical classification results can later more easily point to the relevant types than theoretical considerations about their plausibility. Still, to display our initial considerations about the relevance of types discussed above, we have marked types, which can tentatively be regraded as unlikely and/or implausible in Figure 2.

| CLASSIFYING REAL-WORLD EXAMPLES
How can the above-presented typological framework be applied to the comparison of empirical manifestations of LTC systems? While a detailed discussion of operationalisation and cases is beyond the scope of this paper, this F I G U R E 2 Typological attribute space matrix. Remark: Bold highlighted types are pure types with one dominant actor only; grey highlighted types are presumably unlikely/implausible. Source: Own illustration section aims to briefly illustrate the use of the typology. In doing so, we take a look at three widely known cases of social LTC insurance (LTCI) systems, namely, Germany, Japan and South Korea and, based on empirical information on these cases, attribute their respective systems to the typesthat is, cells in Figure 2 which they most closely conform to. 7 As the name indicates, one would expect a large role for societal actors within all three countries' LTC arrangements. In Germany and South Korea, societal actors indeed prevail in the regulation dimension, while the Japanese LTCI system is governed by the state, with municipalities acting as the insurers. Regarding financing, comparative health statistics indicate that all three systems are predominantly funded by means of social insurance schemes (OECD, 2020). In care provision, multiple domestic actors are involved in all three countries. In South Korea, private for-profit actors are clearly at the top in both home and residential care settings, while in Japan, societal actors are slightly leading before private for-profit actors. In contrast to both other countries, the main LTCI benefit in Germany chosen by care recipients are unregulated cash payments. Even though some cash benefit recipients (or their families) also employ migrant care workers, the overwhelming majority of them relies on care provision by private individual actors, leading to a relative majority of this actor group in the provision dimension (see Table A3). 8 Consequently, all three cases fall into different cells: Germany belongs to the Societal-Societal-Private Individual Type, South Korea to the Societal-Societal-Private For-Profit Type, while Japan State-Societal-Societal Type (see Table 2). This differentiated analysis thus shows, first, that no system falls into the Societal Pure Type, and, second, that dominant actors in social insurance systems vary considerably in the provision and regulation dimension. While a larger number of classified cases would be necessary to identify the empirically most prevalent types and cluster of countries, the classification of three cases aims to illustrate how the framework can be employed for systematically showing variance (and similarity) of cases.

| CONCLUSIONS
This article has outlined a multi-dimensional, actor-centred typology to facilitate comparative analysis of countries' LTC systems, both in the sense of public schemes and complete LTC arrangements. In doing so, we have identified three constitutive dimensions of LTC systems and discussed severalboth public and private, domestic and globalactor types, which can assume responsibility in LTC provision, financing and regulation. With the resulting framework, we hope to offer an instrument for systematically and comprehensively comparing empirical instances of LTC systems by way of attributing them to the types and consequently identifying country groupings.
The typological framework proposed has several advantages. First, it identifies precisely where responsibility is assumed and by whom across the dimensions of the LTC system. This allows one to capture arrangements accurately while operating with aggregated and clearly defined categories, which is paramount for comparative work. This could be seen in the previous section with an illustration of variations existing in three social LTCI countries. Second, by discussing and exemplifying a broad universe of actor types, the typological framework facilitates research on a variety of diverse cases, both with and without (comprehensive) public LTC system, in the Global South and North. Consequently, the typology is suitable for (re-)classifying LTC arrangements in Europe, newly emerged public schemes such as in Uruguay or Taiwan, as well as within-country shifts in actor-mixes over time.
T A B L E 2 Dominant actors by dimension in the current German, Japanese and South Korean public LTC systems Source: Own compilation, details and sources see Table A3, Appendix.
However, the framework also suffers from several limitations. First, while the actor-centred approach provides information about societal responsibilities, power structures and (inter)action logics, it is not well suited to capture other important aspects of LTC systems. This is especially the case for the content of the regulation dimension when studying public schemes, that is, questions about coverage and generosity, but also as regards LTC provision settings, such as the differentiation between home-based or residential care. Second, the choice and aggregation of actor types is debatable.
For instance, for analysing certain cases such as Scandinavian LTC reforms of the last decades, the differentiation between the central state level and municipalities as two distinct actors could highlight important changes, which are obscured by using a combined category. Furthermore, while there are good reasons to include domestic care workers in the category of private for-profit actors, it certainly poses difficulties if the focus is on analysing care regimes, which differ exactly in the regard of their use of more formalised for-profit provision versus highly informal (migrant) live-in care arrangements. As an inflated number of actor types increases the number of combinations exponentially, we decided against a differentiation in both cases. However, we encourage researchers using the framework to flexibly combine and disaggregate actors in light of their specific research question. The transparent construction of the typological attribute space should be beneficial in this regard, as steps can be traced and adapted by others.