Walls of glass. Measuring deprivation in social participation

This paper proposes a measure for deprivation in social participation, an important but so far neglected dimension of human well-being. Operationalisation and empirical implementation of the measure are conceptually guided by the capability approach. Essentially, the paper argues that deprivation in social participation can be convincingly established by drawing on extensive non-participation in customary social activities. In doing so, the present paper synthesizes philosophical considerations, axiomatic research on poverty and deprivation, and previous empirical research on social exclusion and subjective well-being. An application using high-quality German survey data supports the measure’s validity. Specifically, the results suggest, as theoretically expected, that the proposed measure is systematically different from related concepts like material deprivation and income poverty. Moreover, regression techniques reveal deprivation in social participation to reduce life satisfaction substantially, quantitatively similar to unemployment. Finally, the validity of the measure and the question of preference vs. deprivation are discussed.


Introduction
Social participation has attracted scholarly attention for a long time and still figures prominently in many disciplines, like sociology, economics, or psychology. Moreover, it also matters in political and practical affairs. For instance, the Universal Declaration of Human Rights of the United Nations endorses the right to freely 'participate in the cultural life of the community' (Art. 27. I). The principal relevance of social connections and relatedness for human well-being is undisputed. Indeed, recent efforts to improve the measurement of human well-being unequivocally demand measurement of 'social connections' in one form or another (see, e.g., the reports of Atkinson et al. 2002;Stiglitz et al. 2009;OECD 2011). However, these surveys also document that there is little consensus on how to ideally measure achievements or deprivation in social participation, partly because of conceptual ambiguities. While the aforementioned reports all highlight the need for more research, they also agree that proxy-measures, like formal membership in associations and political processes, voter turn-out, or charitable giving are inappropriate indicators. Instead, social activities and meeting friends are frequently enumerated indicators. Additionally, a large array of further indicators is usually listed, which relate, however, to different concepts (which is freely admitted). These include social capital (trust and reciprocity), social support, social networks, the number of close friends, workplace engagement, or religious engagement. After all, social connections frequently serve as an umbrella term for phenomena and concepts, which still demand clarification and more rigorous research.
In addition to this, more difficulties arise on the empirical side. First, social participation is an abstract activity, which manifests in a plethora of concrete social activities. These concrete social activities, moreover, vary markedly-inter alia with time, culture, or age. In fact, social participation is an inherently relational concept, meaning that it refers to a specific society at a given point of time (e.g., Sen 1983). To appropriately address these issues, conceptually and empirically, is essential for any exercise in measuring deprivation in social participation (DSP). Finally, Stiglitz et al. (2009) also note that aggregation is not trivial, which also applies to a rather narrow concept of social participation in the sense of social activities. Thus, despite its importance, a grounded approach to measure social participation is still lacking, partly due to conceptual intricacies, partly due to empirical diversity, and partly due to methodological challenges. To close this gap is the aim of the present paper.
This paper uses the capability approach to guide the conceptualisation and measurement of deprivation in social participation. 1 According to the capability approach, human well-being is a constitutively multidimensional construct, where social participation is one among other so-called functionings (the doings and beings a person has reason to value, e.g., Sen 1985Sen , 1992. The paper argues that adopting a capability perspective entails several implications that not only sharpen the contrast to related concepts like social capital but also facilitate operationalisation and measurement. Broadly speaking, the present paper proposes to rely on a wide set of specific social activities and to assert a deprivation if an individual is not performing any of these activities. Technically, a dual-cutoff counting approach is applied, which draws on dichotomised variables indicating whether or not a certain set of activities is performed, in combination with an intersection approach to aggregate across activities (Atkinson 2003;Alkire and Foster 2011).
The empirical part of this paper explores an implementation based on a dual-indicator approach using German data and, in particular, investigates the links to related concepts. The results show that income poverty, material deprivation, and deprivation in social par-ticipation to a large extent identify different people as deprived. Using standard fixed effects regression techniques to analyse potential determinants provides conclusive findings. Importantly, the results also document that deprivation in social participation is associated with a considerable loss in life satisfaction, indeed, quantitatively similar to unemployment (e.g., Clark and Oswald 1994;Winkelmann and Winkelmann 1998). 2 Overall the empirical analyses support the validity of the measures and encourage the construction of social indicators along the suggested lines.
The suggested approach offers several advantages. First, the measure captures low achievements, i.e. outcomes. Consequently, the measure is sensitive to different mechanisms causing deprivation, like insufficient income, the denial of rights, stigmatisation, or any combination thereof (e.g., Mood and Jonsson 2016;Kunze and Suppa 2017). 3 The empirical findings also suggest responsiveness to policy interventions. Additionally, the conceptual integration entails implications for both operationalisation and measurement, which prove useful to guide empirical exercises. For instance, social activities and the relational nature of social participation are placed at the heart of both conceptualisation and measurement. In contrast, social activities often play only an ancillary role in previous work. The research following Townsend (1979), for instance, seeks to measure relative deprivation through the 'absence or inadequacy of those diets, amenities, standards, services and activities which are common or customary in society ' [p. 915, emphasis added]. 4 For research on social exclusion, Levitas (2006, p. 154) observes that the social aspects and consequences have so far received rather little attention. 5 More fundamentally, this literature is still plagued by severe difficulties in providing clear definitions-in particular with regard to closely related concepts like poverty (e.g., Room 1999;Levitas 2006). 6 Unlike, these lines of research which extensively rely on information from the resource space, i.e. goods, services, or income, the present approach seeks (i) to shift identification of deprivation into the functioning space, and (ii) confines the measurement to one specific functioning.
Another advantage follows from borrowing methods from axiomatic research on multidimensional poverty measurement as it facilitates the understanding of the measure's behaviour and, moreover, allows to select methods which actually have been designed to work with ordinal indicator information (e.g., Alkire and Foster 2011;Bossert et al. 2013). In return, the present paper introduces a new concept into this line of research, which does require multidimensional measurement techniques, but conceptually demands a large number of complementary indicators combined with an intersection approach. In contrast, Dotter and Klasen (2014) recommend for poverty measurement to adopt a union-approach in combination with only a few selected indicators. Furthermore, a concern figuring prominently in research on poverty and deprivation is the question whether low achievements 2 Previous research on social activities and life satisfaction either relies on cross-sectional data or only examines specific social activities, or both (Kahneman and Krueger 2006;Winkelmann 2009). 3 Accordingly, the present approach also goes beyond a purely right-based or purely skill-based approach. 4 On this line of research, see in particular (Mack and Lansley 1985;Gordon and Pantazis 1997), but also the more recent work on material deprivation (e.g., Nolan and Whelan 2010;Whelan and Maitre 2010). 5 Measurement exercises in social exclusion usually distinguish four dimensions: exclusion from the labour market, from public or private service provision, from consumption, and from 'social interactions' in one form or another. Empirical applications include (Burchardt 2000(Burchardt , 2002b but also Gordon et al. (2000). Social relations are measured at times by social activities, the extent of social support (practical or emotional), and the number of friends. Membership in civic organisations has also been suggested (e.g., (Robinson and Oppenheim 1998)). 6 On the value-added of the research on social exclusion see, e.g., Atkinson 1998;Room 1999;Sen 2000). are actually caused by preferences rather than constraints (e.g., Mack and Lansley 1985;Piachaud 1987;Sen 1992;McKay 2004). However, both the design of the proposed measure and the presented empirical evidence support an interpretation as deprivation.
Finally, having well-defined measures for social participation and its deprivation is important for several reasons. First, it allows promising research into links to related concepts like social networks or social capital-links in which economists have recently become more interested (e.g., Bauernschuster et al. 2014;Satyanath et al. 2017). Indeed, a main criticism levelled against research on social capital is that distinct concepts are mixed (e.g., Portes 1998;Durlauf 2002). The present paper locates social participation outside of, but in relation to, social capital. Second, previous studies in applied research on multidimensional poverty in fact identified social connectedness as a missing dimension (e.g., Alkire 2007;Zavaleta 2007a). The present paper adds novel and grounded indicators to this line of research. The relation to relevant concepts like social networks, social capital, or social isolation is briefly discussed.
Moreover, operationalizing deprivation in social participation is also important for research on the capability approach. Indeed, the entire approach as such has been criticised for providing too few measurable functionings (let alone capabilities) to be useful at all (e.g., Comim 2008). Additionally, the present paper seizes on the social contingency and relational nature of social participation, i.e. on what (Sen 2002b, p. 85) calls 'socially dependent individual capabilities'. Therefore, the present paper also paves the way for an empirical analysis, of what, e.g., Evans (2002) and Ibrahim (2006) called 'collective capabilities', i.e. capabilities that can only be reached through collective actions. See, however, also Robeyns (2017) on this. Finally, an accurate and sound measure for deprivation in social participation is also much-needed for both policy purposes and well-being measurement, more generally. Unlike achievements in health or education, social participation is severely under-researched. In the absence of grounded deprivation indicators, previous studies only examined single activities or an average level of activity.
The remainder of this paper is structured as follows: Section 2 introduces the conceptual underpinnings, Section 3 outlines the operationalisation, Section 4 presents the empirical results, whereas Section 5 offers a discussion, and Section 6 some concluding remarks.

Conceptual integration of social participation
The capability approach posits that human well-being is constitutively multidimensional. 7 Dimensions are called functionings, meaning the doings and beings that a person has reason to value; for instance being well-nourished, being well-sheltered, being healthy, or being happy. One such functioning often enumerated is participating in social life. In addition to considering achievement in a single functioning, the capability approach also underlines the importance of the freedom to do so, which leads to the concept of an individual's capability: the set of all functionings the individual can actually choose from. Poverty is then conceived of as capability deprivation, implying not only severe shortfalls in achievements in one or several functionings but also that it was impossible to choose higher achievements, i.e. better achievements were not in the capability set in the first place. The capability approach claims that intrinsic importance can only be assigned to elements in the functioning space, i.e. functionings or capabilities. Howsoever important goods, income, and other resources are as a means to achieve functionings, they are of instrumental relevance only. More formally, the resources-functionings link is often described as follows (e.g., Sen 1985) where x i is a vector of goods and services (i.e. resources) that are transformed into functionings by a conversion function f (·), which is governed by conversion factors z • , which can vary with environment, society, and individual. For the present case it is instructive to focus on one coordinate of the functioning vector b i , say general social participation, denoted as SP i and, moreover, to explicitly introduce a vector of time-consuming activities a i . An individual's social participation can then be described as where a i like x i is a choice variable, subject to a time constraint (e.g., a ij = 1), and SP i is non-decreasing in both arguments. While some activities in a i are social, like visiting friends, others are not, like house production. The capability of an individual can then be written as the set of all actually available functioning vectors, given the amount of resources (where X i is set of commodity vectors the individual is entitled to): Customary social activities always refer to a specific community c at time t, i.e. a i ∈ A ct , which clearly exposes the relational nature of social participation. Since an individual can achieve social participation through often quite diverse, concrete social activities, it seems appropriate to view these social activities in a i as substitutes, i.e. alternative ways to achieve SP i . For the present purpose social participation, a valued doing, is best conceived of as an abstract activity that is performed in an immediate social context in which individuals relate and connect to each other and share an experience. 9 Consequently, deprivation in social participation is then also located in the functioning space and established if an individual achieves less than a normatively set, critical threshold, SP : Observing an individual achieving b * i ∈ B ≡ {b i |SP i ≥ SP } is sufficient to declare her as non-deprived. Capability deprivation with respect to social participation, however, not only requires SP * i < SP , but in fact b * i ∈ S ≡ {Q i ∩ B = ∅}, meaning that no functioningvector with an undeprived level of social participation was feasible. This requirement rules out low achievements due to preference (e.g., for religious beliefs). While empirically challenging, a thorough implementation of this condition is in practice often not necessary, see Section 5.2.

Selected features and implications
While the capability approach does entail several implications, it does not provide definite instructions for every single exercise. One reason is that the capability approach (in its gen-eral version) is 'open-ended', i.e. allows very different exercises to be carried out within its framework (e.g., measuring poverty or theorising justice), see Robeyns (2017, p. 29). Moreover, the capability approach is 'underspecified ' (e.g., Robeyns 2006;Robeyns 2017) in that it not only allows, but in fact requires additional elements before becoming effective, which are often provided by the particular research question or the country-specific context (e.g., choosing the dimensions, see, e.g, Alkire 2008). Thus further considerations are gradually added, in particular in Sections 2.3 and 3.
Defining social participation within a capability framework entails several features and implications central for the present study. 10 First, functionings and capabilities are of intrinsic relevance, i.e. objects of valuation (e.g., Sen 1992, p. 43) whereas resources (including means and income) are not. Moreover, deprivation in social participation is located in the functioning space, too. Importantly, the intrinsic relevance of functionings does not preclude instrumental relevance for other achievements (e.g., Sen 1999b, ch. 2). Social participation may, for instance, be helpful for other outcomes, like finding a good job. Additionally, since functionings are of intrinsic relevance for human well-being, they do not require additional justification. Consequently, if an individual is believed to be deprived in social participation, this is already reason enough for public policy to be concerned with this low achievement. In particular, there is no need to adduce an associated low income or low life satisfaction, even though this may provide valuable insights as to why someone is deprived in social participation.
Second, the dichotomy between concrete forms of social activities and the more abstract human functioning of social participation proves useful in several respects. Evidently, concrete forms of social activities vary substantially across time and among cultures, but also within societies, e.g, with socio-demographic characteristics. As highlighted by Eq. 2, different behavioural patterns and customs may however result in similar levels of social participation. Thus, the present conceptualisation allows for heterogeneity in the specific forms, or means of social participation, while emphasising the more abstract activity of social participation to be the same. Moreover, this dichotomy clearly exposes the relational nature of social participation, i.e. its contingency upon community and time-a key challenge for cross-country comparisons. For instance, since social activities vary with countries and activities vary in price, a relatively low income can translate into (absolute) deprivation in social participation in one country if most social activities there are costly, but it does not necessarily do so in others (e.g., Sen 1983).
Third, functionings are outcome variables, i.e. realised achievements. 11 Therefore, shortfalls may be caused by very diverse mechanisms. Low income is one explanation, particularly important in countries where most social activities are organised through markets. In fact, Mood and Jonsson (2016) present some evidence in support of this channel. However, Eq. 2 allows for other mechanisms as well, which may operate through a conversion factor or through a further constrained individual activity set. 12 Both ways effectively prevent individuals from achieving higher social participation-irrespective of their resources, e.g., due to racist or sexist legal or social norms. Likewise, the accessibility of public places and facilities can fairly direct affect the achievement in social participation, e.g., of 10 See also Klasen (2001) who enumerates similar aspects to be relevant for analysing the role of education in the social exclusion of children, which is, however, an entirely different exercise. 11 For the contrast of achievement, the freedom to achieve, and means to achievement see, e.g., Sen 1992, ch. 2). 12 Formally, one could state a i ∈ A ict ⊆ A ct . wheelchair users. Social norms may, however, also operate in more subtle or unconscious ways, e.g., through stigmatisation, which may induce behavioural responses (e.g., Kunze and Suppa 2017). 13 An outcome-based measurement allows these mechanisms to be more carefully investigated.
Given the initial reference to the right to participate in social life, one may wonder how capability and rights-based perspectives differ from each other (see, e.g., Sen 2004Sen , 2005 for more details). First of all, a rights-based perspective is consistent with the present approach to the extent it is only concerned with the right to participate in social life. However, a rights-based approach does not imply the focus on the functioning space, rather it could equally well emphasise the right to access the means necessary for social participation. Consequently, severe failures to achieve social participation may go undetected if the rights to access the means are not violated, but actual achievements are prevented through other mechanisms (e.g., discriminatory practices or bad health). Conversely, while the capability concept is well-prepared to reflect the opportunity aspect of freedom, a rights-based approach, allows to highlight the process aspect of freedom as well (see, e.g., Sen (1993Sen ( , 2002a) for this distinction). As Sen (2005, p. 163) put it "the two concepts-human rights and capabilities-go well with each other, so long as we do not try to subsume either entirely within the other."

Aggregation
In the present case, three types of aggregation can be distinguished, which are briefly addressed in sequence. First, there is no categorical answer to how many deprivation indicators should be used. Naturally, this depends on the concrete research question or measurement exercise. While a stronger aggregation into say one deprivation indicator condenses information, it may also prevent a more nuanced picture of deprivation. If the objective is to document more complex phenomena, a dual-or multi-indicator approach is advisable. In fact, a prominent issue in the social exclusion literature is the question of whether social exclusion refers to individuals or to entire neighbourhoods and communities (e.g., Barnes 2002;Lupton and Power 2002). Even though these studies address local service provision, this question also points to an important phenomenon of social participation in poor or deprived neighbourhoods(like 'ghettos' or 'banlieus'). While their residents may not participate in customary activities of the wider society under consideration, they may well participate in local social activities and share experiences with friends, enjoy meeting with peers, and provide and receive social support. The empirical part of this paper illustrates a dual-indicator approach: while one indicator captures activities with friends, peers, and family, another indicator captures participation in the most common activities of the society. Alternatively, using two dedicated indicators could also be argued to capture different qualities of social participation.
A second question is how to aggregate across concrete social activities to identify individuals deprived in social participation, which essentially corresponds to the identification step in poverty and deprivation analysis (Sen 1976). As outlined in Section 2.1, DSP is located in the functioning space and concrete social activities serve as substitutes to avoid such a deprivation. This paper adopts a conservative approach in setting the deprivation cutoff SP and requires an individual not to perform any of the concrete social activities. Intuitively, this indicator for DSP seeks to ensure that social participation is not achieved through any of an ideally wide range of concrete social activities. Indeed, axiomatic research on measuring multidimensional poverty offers a well-known framework for addressing such problems. One procedure is to apply a so-called intersection-approach (Atkinson 2003) to binary variables indicating whether or not a specific activity is performed, which is in fact a special case of the dual-cutoff counting approach (Alkire and Foster 2011). More formally, a social activity j is considered to be performed if more than a critical amount of time, a j , is spent on it. 14 An overall social activity count can then be expressed as ac i = 1(a ij > a j ), whereas deprivation in social participation is asserted if none of the social activities are carried out, i.e.
( 5 ) Note that adopting an intersection approach does not require to specify particular weighting scheme (beyond the indicator selection) and in fact, even the summation in Eq. 5 is not necessary, see Appendix A for more details. Moreover, this approach allows numerous refinements and modifications, whose exploration is however beyond the scope of this paper. In fact, the most suitable method may vary with the exact goal of the exercise (e.g., devising one comprehensive or a small set of complementary social indicators, studying deprivation in social participation alone or in the context of multidimensional poverty, etc.) and the data available. 15 A third question is how to aggregate across individuals, which again depends on the purpose of the concrete exercise. When needed, the empirical illustration adopts a simple headcount ratio for expositional convenience, not as an implication of the capability approach.
Indeed, the share of people who meet their friends or relatives less than monthly is already considered as a core indicator of the German reports on poverty and wealth (e.g., Bundesregierung 2013, p. 476). Note that being a member of the Alkire-Foster class of measures, the proposed measure satisfies the same axioms, see Appendix A for more details.

Related concepts
Section 2.1 suggests to understand social participation as an abstract activity that is performed in an immediate social context. This section briefly sketches how social participation connects with related concepts. These explanations are meant to be suggestive not definitive, as establishing the precise relationship goes well beyond the scope of this paper. The important aspect here is however that, by their nature, fundamentally distinct concepts are involved-and there is good reason to keep them separate, both conceptually and empirically. Only then an accurate operationalisation of the respective concepts can be made that finally allows a careful empirical analysis.
14 Activity-specific cutoffs provide a degree of freedom in their specification to account for potentially different qualities or types of activities and to allow the inclusion of ordinal data. Note that in contrast to the literature on multidimensional poverty measurement, non-activity indicators do not immediately signal deprivation, which is why the a j do not represent deprivation cutoffs. More generally, because concrete activities are substitutes for achievements in social participation, indicators of non-activity are highly complementary for asserting deprivation in social participation. 15 Modifications may include different activity cutoffs a j or overall activity count cutoffs (which is implicitly assumed ac i = 0 in Eq. 5). Refined methods could also explicitly exploit the quasi-count data nature of the social activities. Moreover, having detailed time-use survey data would permit entirely different methods, e.g., an aggregate achievement approach (Maasoumi and Lugo 2008).
Social networks connect individuals and have been studied from different perspectives (e.g., Ioannides and Loury 2004;Jackson 2011;Wrzus et al. 2013). Social participation may alter both the size and quality of social networks, whereas social networks, in turn, may shape the scope for social participation. While social networks as such escape any reasonable normative assessment, they provide the basis for other important concepts. While the different benefits from social networks were found to play an important role for the poor across the globe (Narayan et al. 2000), research in this field is still plagued by severe conceptual vagueness and overlap.
It can, for instance, be argued that affiliation, which provides a sense of belonging and identity is an important functioning as well. Indeed, Nussbaum (2001) considers affiliation as one out of ten key functionings. However, she also subsumes various forms of social interactions, the social basis of self-respect, and non-humiliation under this umbrella. Clearly affiliation is closely related to social participation: socializing may result in important shared experiences and ultimately create a sense of belonging and affiliation, but not necessarily so. 16 Conversely, affiliation may continue to live on even if concrete social participation with peers or family came to an end, e.g., due to migration. While social participation was previously described as an activity, affiliation is probably best conceived of as a state or condition, for which an individual's social network is a key factor. Whether and how exactly affiliation is relevant for a specific analysis depends on the specific research question at hand. A promising approach, e.g., for multidimensional poverty measurement, might be to complement indicators of deprivation in social participation with separate deprivedof-affiliation indicators. Being deprived in both aspects may then be understood as social isolation. Indeed, Zavaleta et al. (2017b) suggest frequencies of social contact (among other items) to measure social isolation.
A similar argument can be made for social support, which is often partitioned into emotional and practical support. Its importance is emphasised in the social exclusion literature (Gordon et al. 2000), and the OECD (2011) suggests related indicators to measure social connections. While social support may represent a benefit arising from social relations, it may however also be viewed (i) to reflect affiliation or (ii) to contain aspects that actually refer to other functionings. 17 Specifically, economic and social security matter in and of themselves for human well-being (Wolff and de-Shalit 2007;Stiglitz et al. 2009), and social support may provide services that could alternatively also be obtained through, e.g., insurance markets.
Social capital is another prominent concept that received lots of academic and public attention. Seminal sociological works have emphasised the thoroughgoing instrumental nature of social capital as a resource and its utilisation by individual members of a group (Bourdieu 1986). Subsequently, social capital was extended to be a feature of communities, in particular by political scientists (Putnam 1995), but also by economists (e.g., Knack and Keefer 1997). For the present analysis it seems sufficient to conceive of social capital as stock, which resides in the totality of the individual social networks. Social participation, by contrast, can then also be thought of as an investment activity that helps to build social capital (Glaeser et al. 2002). Note however that the view presented in this paper challenges the approach of measuring human well-being using social capital indicators, e.g., using the 'trust' or 'fairness' questions, as suggested in Stiglitz et al. (2009) andOECD (2011). Neither does social capital reflect social particpation in any direct way, nor is the intrinsic relevance of social capital obvious. Instead, most of the benefits arising from social capital seem to be of instrumental importance for other economic outcomes (e.g., lower crime rates or finding a job). More importantly, social capital is not an unambiguously desirable outcome, as already pointed out by Portes (1998) and more recently demonstrated by Satyanath et al. (2017).

Data and social activities
This paper uses data from the German Socio-Economic Panel (SOEP) to illustrate an operationalisation of deprivation in social participation. The SOEP is a high-quality panel data set, which started in 1984 and provides detailed information on different domains of life. 18 The empirical analysis is based on respondents aged 18-75.
Social participation is understood as an abstract activity which can manifest itself in many different forms. First, note that this rules out related, but conceptually different indicators, including items on material deprivation or social support. Instead, the present paper suggests to mount the operationalisation on a comprehensive set of common activities and the frequency with which they are performed. Table 1 contains the social activities used for the present study along with the exact wording of the questions. Responses to these questions are usually recorded on 4-point scale (weekly, monthly, less than monthly, never). These items as such are not new and, in fact, are well established. They have been collected in the SOEP since the mid-1980s (though with some modifications over time), but are also included in many other surveys (e.g., PSE, HILDA). Moreover, recommendations about how to measure social connections frequently include direct indicators like these (Stiglitz et al. 2009). Figure B.1 in the appendix shows the frequency distributions of the single social activities.
One question that is not easy to answer is to what extent the sum of these activities actually covers all the social activities of the respondents (unless a more comprehensive time-use survey is also available). For the present analysis, it is of particular importance whether some common social activity is not covered at all. What can be said, however, is that in 2011, for instance, 68% of the respondents do at least one activity on a weekly basis, whereas around 88% do, at minimum, one activity either on a weekly or on a monthly basis (data not shown). While this evidence, of course, does not preclude further improvements in coverage, it does suggest that many important activities are already covered.

Deprivation indicators
The present operationalisation relies on two separate deprivation indicators in order to allow more complex social deprivation patterns to be reflected as well. The first indicator is meant to capture deprivation from more intimate or private forms of social participation, which are often particularly faithful and sincere, and are frequently also characterised by high mutual expectations. This first indicator of deprivation in social participation, denoted In contrast, the second indicator seeks to reveal non-participation in the wider public, often also taking place with rather casual acquaintances and in the customary social activities of the society. While activities in this group may well generate a sense of belonging through shared experience, they often remain interpersonally shallow and non-binding. Ideally, this second deprivation in social participation indicator, DSP 2, would rely on all remaining activities enumerated in Table 1. However, for two activities, sports and arts, it is not entirely clear to what extent they are actually performed in a social context, because, e.g., solo activities like jogging are also quite common. Therefore, the subsequent analysis employs two variants of the second deprivation indicator, one without sports and arts activities (DSP 2A) and one including both activities (DSP 2B). Both DSP 2 indicators signal a deprivation if all included activities are 'never' performed. Technically, this threshold is a lower bound and is therefore the least contestable. Robustness checks in Tables B.1 and B.2, moreover, indicate similar findings for the threshold 'less often.' Since the social activity questions are not asked on a yearly basis and, moreover, not all questions are always asked simultaneously, the indicators can only be calculated for selected years. 19 It is important to note that setting a deprivation cutoff like 'never participating in any activity' is a normative decision, which is inevitably part of the analysis of poverty and deprivation. The capability approach is distinctly aware of this issue and requires such normative decisions be clearly exposed (e.g., Sen 1999b, p. 75). Moreover, public debate should contribute to a decision like this as well, and it certainly is not the scientist on his or her own who needs only to apply the 'right' method. That said, a natural starting point to set a deprivation cutoff is, e.g., the most conservative approach, which requires all activities to be performed 'never.' The final cutoff may however not only be modified through public debate (e.g., Sen 1999b, ch. 6 or Sen 1999a), but also depends on the concrete exercise at hand (e.g., a long-run comparison over time, a cross-country comparison, or a multidimensional poverty analysis). As usual with potentially critical decisions in empirical analysis, the robustness of key results should be routinely checked.
The subsequent section compares deprivation in social participation measures with income poverty and material deprivation. The income poverty measure is based on the monthly net household income and is adjusted using the modified OECD-equivalence scale, and deflated using a consumer price index with 2011 being the base year. 20 The poverty line is set using the official threshold, i.e. 60% of the median income. Additionally, a material deprivation index is compiled, whose items are however only occasionally collected in the SOEP. 21 Moreover, the material deprivation index adopts the concept of 'enforced lack' (Mack and Lansley 1985), i.e. a deprivation is only assigned if non-consumption of an item is reported to be for 'financial reasons.' Technically, a dual-cutoff counting approach (Alkire and Foster 2011) with equal weights is adopted. By no means is this the only way to compile such an index, but it comprises important special cases and is a well-documented and understood method. For k ∈ [26%, 54%] (which represent percentages of the maximum possible deprivations) interesting and useful headcount ratios emerge, as DSP and poverty rates then are of similar magnitude, which facilitates the concurrence analysis (see also Finally, Fig. 1 provides a first idea on incidences of the different poverty and deprivation measures. A first observation is that deprivation in more private or intimate activities, according to DSP 1, is with 5% less widespread than deprivation in more public and common activities, whether measured using DSP 2A (11%) or DSP 2B (8%). 22 The official income poverty measure, which uses 60% of median income as the cutoff implies a poverty rate of 14%, whereas applying stricter cutoffs, i.e. 50% or 40% sharply reduces the headcount ratio to 8% and to 3%. Likewise the material deprivation index finds 14% are deprived at a cutoff of 27% of all possible deprivations, which also decreases substantially for stricter cutoffs (k = 36%, 45%) to 9% and 4.5% respectively. 20 The analysis uses the generated variables provided by the SOEP group, which entail some data cleaning and consistency checks. 21 Specifically, the index draws on the following questions: the household has a colour television; the household has a telephone; the household has internet access; the household has a car; the flat is located in a building that is in good condition; the building is located in a good neighbourhood; I have put some money aside for emergencies; I take a vacation away from home for at least one week every year; I invite friends over for dinner at least once a month; I eat a hot meal with meat, fish, or poultry at least every other day; furniture that is worn out but can still be used is replaced by new furniture. The index is calculated for 2005, 2007, and 2011, where all the previous items are collected simultaneously. 22 To observe a higher headcount ratio for the deprivation measure that does not include sports and arts (DSP 2A) is not surprising since DSP 2B is more demanding in the sense that it additionally requires that there is never participation in arts and sports.  Table 2 contains socio-economic characteristics by deprivation status for all DSP -indicator variables. Two observations are salient: First, each socio-economic variable relates in the same way to each DSP indicator. Unemployed persons, for instance, are excessively represented in each deprivation indicator. These differences are, for most variables, more pronounced in terms of DSP 2-indicators than in terms of DSP 1 indicators, suggesting the more intimate and private social activities to be less subject to socio-economic factors. Importantly, this finding also holds for income, income poverty, and the (uncensored) material deprivation count. Average equivalence income, for instance, is approximately one third lower for DSP 2-deprived individuals.

Descriptive analyses
A second important observation is that the age-group dummies suggest a lifecycle pattern, as deprivation in social participation is more common among older persons.Specifically, individuals aged 45 and below are less frequently deprived, whereas individuals aged 46 and above are more frequently deprived. In fact, the difference in the population shares between deprived and non-deprived increases with age (irrespective of the deprivation indicator). Naturally, conclusions based on a descriptive analysis like this must be treated with caution, since confounding factors may well drive some of the findings.

Concurrence analyses of deprivations
An instructive exercise for analysing deprivation indicators is to examine to what extent the different measures agree on the individuals deemed deprived. Table 3(a) shows estimates of  Table 3 is a numerical representation of Venn diagrams in which one parameter (the poverty cutoff) is varied. Table 3(a) reveals a remarkably large population share to be only income poor and the overlap with social deprivation to be rather small. Specifically, around 11% of the population are income poor (at the 60% cutoff) but not deprived according to the activity index. In contrast, the population share that is income poor and deprived according to the DSP 2-indicators is only 2.9-3.4% and according to the DSP 1-indicator less than 1.3%. Moreover, applying a stricter income-poverty cutoff may give reason to expect a higher concurrence. However, Table 3 reveals that while shares for income-only poor and both poor and deprived decrease with a stricter cutoff, the previous result does not change substantially. In fact, the share of individuals who are both income poor and deprived in social participation relative to all income poor remains a fairly constant 20-24% (for the DSP 1 indicator this share is around 9-10%). Table 3b performs the same exercise for the material deprivation index. The observed pattern turns out to be quite similar, since most materially deprived persons are not deprived in social participation (at least 66%), i.e. at most a third of materially deprived persons are also deprived in social participation. This finding holds independently of the chosen poverty cutoff for both DSP indicators and is even more pronounced for the DP S2 indicators. Conversely, there is also a significant share of the population who are only deprived in social participation: 3-8% depending on measure and cutoff. Table 4 turns to the overlap of the DSP indicators and reveals that the more complex situation of not participating in customary activities, but spending time with friends or neighbours seems in fact to be quite common. Specifically, 74.6% (= 0.0595 0.0595+0.0203 ) of those persons who are deprived according to the DSP 2B indicator are not deprived of more private and intimate relations (DSP 1). In absolute terms 5.95% of the population are deprived of the common social life but not of social relations in general, and about 2% report alarmingly low social participation as they are deprived according to both DSP indicators. On the other hand, around about 60% who are deprived in DSP 1 are not deprived according to DSP 2B. Note that qualitatively similar results emerge, when using alternative thresholds for non-performance of an activity (see Table B.1).
In sum, the previously presented evidence suggests, first, that in some cases low income and material deprivation seem to translate into DSP, but also that other mechanisms seem to result in DSP-beyond a lack of resources. Accordingly, DSP measures that exclusively rely on resources would only identify a subset of DSP. Moreover, DSP is not only conceptually but also empirically distinct from income poverty and material deprivation: the large extent to which different people are identified as deprived supports this conclusion. Finally, the overlap of DSP indicators shows that both indicators capture related-but distinct and nonredundant-aspects of social participation.

Regression analyses
Using conventional regressions techniques, this section explores determinants of social activities and deprivation in social participation, as well as the the link between deprivation in social participation indicators and life satisfaction. Results are best viewed as conditional correlations, rather than causal effects, which are sufficient for assessing the validity of the proposed measures. All models are estimated using linear fixed effects and include control variables for regions and years, as well as a constant. Tables 5 and 6 contain the results for single activities and the deprivation indicators. In general, results are in line with intuition, but some findings are of particular interest.
First, income, modelled as log-income to allow for a decreasing marginal effect, affects most activities as expected. Specifically, income increases the activities labelled 'cinema', 'culture', 'socialise', and 'sports', but not 'attending church', 'volunteer work', or 'helping out friends and neighbours'. These single effects of income also converge into a significantly lower chance of being deprived in social participation. Unlike income, unemployment   increases some activities, but decreases others, whereas there is clear-cut influence on either deprivation indicator. 23 The presence of children decreases almost all activities, except volunteer activities and attending church, which are expanded. Together, these effects tend to result in deprivation in DSP 1 and DSP 2. Offsetting effects in different activities may drive the latter finding too, which then again may simply reflect changing behavioural patterns due to changed life conditions. Finally, comparing the broader pattern of DSP 1 and DSP 2 reveals the lifecycle pattern observed earlier for the DSP 2 indicators is largely replaced by a stronger dependence on socio-economic factors. Public participation activities, therefore, seem to be driven more by socio-economic characteristics and events (children, employment, or health), whereas engaging in intimate social relations seem to follow a more genuine lifecycle pattern.
By now, overall life satisfaction is a widely accepted measure of subjective well-being. Since social participation is a valued functioning, deprivation in social participation is expected to reduce life satisfaction sharply. Note that for higher levels of participation one may expect smaller or even negative effects on life satisfaction. Since deprivation indicators  by nature focus on critically low achievements, increases should however unambiguously increase life satisfaction. To this end a conventional linear life satisfaction model is estimated, which controls for fixed effects and the usual socio-economic variables. Table 7 contains the results. First, as expected, both DSP indicators reduce life satisfaction significantly. Moreover, the DSP 1 indicator seems to have the more detrimental effect (the DSP 2 coefficients amount to approximately 70% of the DSP 1 coefficients). Second, the combined effect of DSP indicators results in psychological distress similar to that of unemployment, thereby documenting their economic significance. Third, the effects associated with the DSP indicators hardly vary after adding important potentially related control variables such as income and employment status. While a more careful analysis of the causal impact is left for future research, this finding already suggests the effect of the DSP indicators to be rather independent from income and unemployment, which is also supported by the concurrence analysis in the case of income poverty. Finally, robustness checks with alternative cutoffs for non-performance suggest qualitatively similar findings, see Table B.2 and quantitatively coefficients change in the expected direction, e.g., restricting the DSP 1 indicator to 'never' meeting one's friends reduces life satisfaction even stronger.

Validity of indicators
Evaluating the validity of a measure looks into whether the proposed measure accurately reflects what it is supposed to. 24 A vital precondition is a sufficiently definite construct to be measured. DSP seeks to identify critically low levels in social participation and is established if an individual is observed not to participate in any of the enumerated concrete social activities (see Section 2). Indeed, the construct's elements (i.e. social activities) contrast with both non-social activities (like house production) and other aspects related to social networks (e.g., a sense of belonging). Additionally, the construct of DSP itself is also clearly distinguished from, and yet related to, income poverty and material deprivation (both of which are located in the resource space). Finally, DSP is a relational concept in the sense that it refers to the society an individual is actually living in. First one may ask whether all aspects of the theoretical construct are captured (sometimes called 'content validity'). In this respect, the validity of the suggested measures crucially hinges upon whether all social activities relevant for the society under study are really captured. Only then can simultaneous non-participation in all activities be confidently interpreted as DSP. If, however, important activities were disregarded, the indicators would systematically overlook a customary way to achieve social participation and therefore erroneously report deprivation. As noted above, about 88% of the individuals participated in at least one of the activities at least monthly, which is already indicative of considerable coverage. However, complementary research may deliberately assess social participation patterns and suggest refinements in terms of the most common activities. Notes: Data from SOEP v32.1 (waves 2001, 2005, 2007, 2009, 2011, 2015). The dependent variable is life satisfaction, recorded on a 10-point scale. All models are estimated using linear fixed effects and models (2) and (3)  A second question is whether the measures under study empirically relate to adjacent concepts as theoretically expected (sometimes called 'construct validity'). In this regard, the concurrence analysis demonstrates that DSP is neither equal to income poverty nor to material deprivation ('discriminant validity'), which is backed by the conceptual considerations. Nonetheless these concepts are, however, also theoretically related as income and goods or services are often important means for achieving social participation. As theoretically expected, the regression analyses find low income and material deprivation to be positively associated with DSP. Hence the conditional correlations from regression analyses lend further support to this nexus. Moreover, life-cycle patterns of social participation prove consistent with previous research on life-cycle pattern of social networks. Importantly, as theoretically expected, DSP also results in a significant loss of life satisfaction, which can be interpreted as predictive or concurrent validity.
Finally, note that both indicators aim to measure complementary aspects of DSP, namely private and intimate versus wider public participation. This feature is also supported by the results, as the DSP 2 indicator seems to be systematically more closely tied to socioeconomic factors and life-course developments. Additionally, the concurrence analysis also points to distinct and non-redundant aspects of social participation that are captured. In sum, the previous considerations justify confidence in the validity of the proposed measures.

Preference or deprivation?
A notorious intricacy in the measurement of poverty and deprivation is that an observed outcome, even though adverse, could also represent a preference and not a severe deprivation. A similar objection can also be raised for single social activities like, e.g., frequently attending the opera or the theatre. 25 In view of this concern, the suggested approach widens the informational basis of deprivation assessment (as ideally all customary activities are considered), and, in fact, allows different preferences for means to achieve social participation (as concrete social activities are considered to be substitutes). Effectively, the present approach seeks to lift the identification of deprivation from the resource space into the functioning space, where, according to the capability approach, normative assessments can take place. 26 While the principle concern about freely chosen low achievements does not vanish, it seems however less detrimental to deprivation measurement. Choosing specific activities (say going to the opera versus going to the stadium) certainly is subject to preferences. Achieving the functioning itself is less so, as it is an object of valuation-an end in itself and not the specific means to achieve it. Valuation is best viewed as a reflective activity that may go well beyond the current circumstances. This means that not choosing a certain functioning does not imply its non-valuation, since choice, like desire, involves "considerations of 'feasibility' and of 'practical possibility"' (e.g., Sen 1985, p. 15). Importantly, there is a large body of empirical evidence suggesting that across the world essentially the same functionings are valued (see, e.g., the overview in Alkire 2008). Moreover, the capability approach does indeed entail a universal claim regarding the valuation of functionings and capabilities (e.g., for the freedom aspect of the capability see Sen 1999b, pp.244-246).
Indeed, some empirical applications of deprivation indicators work convincingly well without relying on any counterfactual information (i.e. the availability of a non-chosen functioning vector). The application of malnutrition indicators illustrates this point very clearly: its force rests partly on the fact that most people do value being well-nourished and therefore seek to achieve it, and partly on the cogency of the deprivation cutoff. Even though, strictly speaking, discriminating between a fasting and starving person (assuming similar nutritional achievements) requires knowledge about the different underlying capability sets (see Section 2.1). Likewise, falling short of a 'good' or 'decent' level of social participation is one thing, falling short of any is another. Thus lifting the identification of deprivation in social participation from the resource space into the functioning space, when complemented by a cogent deprivation cutoff, seems to attenuate the 'preference concern' for low social participation. Additionally, the presented life satisfaction analysis precisely indicates 25 To distinguish preference and deprivation in the "consensual approach" to poverty, Mack and Lansley (1985) propose relying on the so-called 'enforced lack' question; for critiques see, e.g., Piachaud (1987) and McKay (2004). See, e.g., Burchardt and LeGrand (2002a) for a related approach. Moreover, e.g., Platt (2009) found that individuals do indeed have different patterns of social participation. 26 The degree to which this is successful essentially hinges upon the validity of the measurement; in particular whether all relevant activities are covered. In fact, since the activities are given empirically, it can be seen as the task of the researcher to process this information and reformulate it in the functioning space in such a way that, in the course of a public debate, a normative assessment can be reached. that DSP does hurt and therefore empirically supports the interpretation of DSP as deprivation. 27 While occasional deliberately chosen low achievements cannot be entirely ruled out, in many instances the acuteness of a deprivation gives point to such a measure.
Note that a discussion of additional aspects can be found in the working paper version of this manuscript including the role of unobserved heterogeneity, the feasibility of crosscountry comparisons, and the indicators' suitability as a social indicator. For instance, the proposed deprivation indicators are argued to fulfil common requirements (e.g., Atkinson et al. 2002, pp.20-23), i.e. they (i) measure outcomes, (ii) identify the essence of a problem, (iii) have a clear and accepted interpretation, (iv) an acceptable burden for respondents, and are (v) responsive to policy interventions.

Concluding remarks
Why should one measure deprivation in social participation and embark on its in-depth analysis? First, there is already a broad consensus that social participation is an important activity. Indeed, this paper emphasises that social participation is not only of instrumental relevance but also intrinsically important. Consequently, social participation can be conceived of as a constituent, but so far neglected dimension of human well-being. Second, particularly with its focus on deprivation in social participation, the measurement reveals a normative force, and its analysis emerges as imperative. Specifically, improvements in respective social indicators, like a simple deprivation rate for instance, can be expected to be widely met with approval. Achievements in health or education are already routinely examined, and low achievements in these dimensions are already often a concern for policymaker-whether coupled with other deprivations or not, and irrespective the reason. Additionally, the present paper also provides evidence that deprivation in social participation is highly relevant for subjective well-being, meaning that people do suffer from this deprivation.
Third, the present paper argues that DSP is relatively straightforward to operationalise, drawing on established survey instruments. While identifying relevant customary activities is essentially an empirical question, collecting information on these activities and processing it such that it can be interpreted as a functioning achievement are more technical challenges. Setting the deprivation cutoff is, finally, a normative question, requiring, among other things, a public debate. In sum, the presented evidence suggests that measurement of deprivation in social participation is both feasible and valid. Fourth, the conceptual integration and chosen level of abstraction offers a coherent and compact underlying construct. Together with a feasible measurement this significantly facilitates an empirical analysis with related concepts like material deprivation, monetary poverty, social capital, or social cohesion. For instance, the link with labour market participation or health impairments can be subjected to empirical scrutiny, rather than being stipulated in the course of measurement.
Fifth, indicators like the suggested DSP are intrinsically important outcome variables, where both design and complementary evidence support the interpretation as deprivation rather than preference. Thus DSP indicators not only immediately reflect the essence of the problem and have normative force, they also directly document that barriers which prevent individuals from social participation do exist. This is vital because some problems, which are more difficult to grasp in the first place, like the now-famous glass ceiling for professional achievements of women, only receive attention after being corroborated by a substantial body of empirical evidence. Otherwise, problems like these tend to be ignored or even denied-by policymakers and academics alike. Exposing these walls of glass, which prevent individuals' social participation, may involve rather diverse and possibly subtle mechanisms. Relevant mechanisms may range from deliberate discrimination, by law or by skin colour, to the debarring effect of prices, to more subtle channels like shying away to avoid stigmatisation. Therefore, a careful analysis becomes even more important to provide grounded advice for policymakers. Future research may probe and refine the coverage of customary activities and the accuracy of the response scale of the employed survey items using time-use modules, the experience sampling method, or the day reconstruction method. Additionally, future research is also needed to explore the role of virtual social activities for deprivation measurement and to examine both the determinants and the persistence of deprivation in social participation. Moreover, measures for different countries are to be devised and applied in order to investigate the possibility of cross-country comparisons. Finally, the performance of DSP measures may also be explored in analyses of social exclusion and multidimensional poverty.