Fuzzy and Multi-Dimensional Measures of the Degree of Social Exclusion Risk: Evidence of Social Exclusion of the Population Aged 50+ in Poland

Tomasz Panek and Jan Zwierzchowski

Introduction

Social exclusion is a subject that attracts great interest in the social, economic and political sciences. As a concept, social exclusion is complex and multi-faceted and can be defined in various ways. It is generally understood as a process in which individuals or social groups are hindered from full participation in substantial areas of the social, cultural, economic and political life of the society in which they live (Silver, 1994, 1995). This non-participation is a result of factors that are outside individual control. The various dimensions of social exclusion often reinforce one another and consequently lead to even deeper marginalisation of individuals. Based on a comprehensive literature review, Levitas (2006) adopted the following definition of social exclusion:

“Social exclusion is a complex and multi-dimensional process. It involves the lack or denial of resources, rights, goods and services, and the inability to participate in the normal relationships and activities, available to the majority of people in a society, whether in economic, social, cultural or political arenas. It affects both the quality of life of individuals and the equity and cohesion of society as a whole.”

Social exclusion has a negative impact on the quality of human capital, limits activity, entrepreneurship and innovation and generates higher cost for the state. Hence, the goal of inclusive social policies is to counteract the threat of social exclusion. Combating social exclusion is one of the main objects of the social policy by the European Union (EU) and its member states (Maastricht Treaty). In 1989, the European Council and EU social affairs ministers adopted a resolution for combating social exclusion that outlines the different forms and shapes of social exclusion and declares it a major problem for many social groups (Commission of the European Communities, 1990). That same year, the Treaty of Amsterdam was adopted, which listed ‘combating social exclusion’ as one of the EU Community’s objectives. A reduction in poverty and social exclusion are fundamental parts of the Lisbon Strategy. In 2010 the Council of Europe enacted policies aimed at achieving the five major goals in the Europe 2020 Strategy - one of which is to promote social inclusion (Copeland and Daly, 2012).

Because of the progressive ageing of European society, the fight against the social exclusion of older people has become an increasing challenge in EU member countries. In order to develop an environment in which people can live well into old age, we need to monitor the threat of social exclusion among the elderly and explore the factors which determine it. The main objective of this chapter is to construct a tool to help realise these goals. We propose a new methodology to measure the degree of social exclusion risk using a fuzzy multi-dimensional approach.

Social Exclusion as Capability Deprivation

The capability approach was developed and refined by Amartya Sen, after his Tanner lecture in 1979 (Sen, 1980), to describe how the well-being of an individual should be measured (Sen, 1982, 1985, 1987, 1999, 2000, 2010). It has been synthesised and applied practically by various authors in a variety of fields (Alkire, 2002; Robeyns, 2003, 2005; Kuklys, 2005; Comim, Qizilbash and Alkire, 2008; Schokkaert, 2009; Basu and Lopez- Calva, 2011; Schlosberg, 2012; Lorgelly et al., 2015; Slabbert, 2018). This concept is based on the assumption that commodities are not crucial for achieving a high quality of life. Rather, it is their properties that enable the achievement of the desired lifestyle by individuals. Not all capabilities are generated from goods or services (Robeyns, 2005). For example, being a respected member of a community only requires the respectful behaviour of other community members. According to Nussbaum and Sen (1992, p. 27) a person’s capability to live a good life can be defined:

“in terms of the capability to achieve valuable functionings ... where functionings represent parts of the state of a person - in particular the various things that he or she manages to do or be in leading a life. Capability reflects the alternative combinations of functionings the person can achieve, and from which he or she can choose one collection.”

In other words, capabilities refer to effective potential for realising goals and fulfilling expectations, whereas functioning, which represents the ‘beings and doings’ of a person, refer to realised goals and fulfilled expectations.

Figure 12.1 illustrates the relationship between commodities, capabilities and functioning, using the key concepts of the capability approach.

We use three sets of conversion factors - personal, social and environmental - to transform commodities into capabilities (Sen, 1992; Robeyns, 2005): personal conversion factors (personal characteristics, e.g. metabolism,

Relationship between commodities, capabilities and functioning in the capability approach. Source

Figure 12.1 Relationship between commodities, capabilities and functioning in the capability approach. Source: Adapted from Robeyns (2005).

physical condition, intelligence and gender), which influence the type and degree of capabilities that a person can create with commodities; social conversion factors from the society in which one lives (the characteristics of social settings, social institutions and power structures, e.g. social norms, public policies, social hierarchies, rule of law, political rights); and environmental conversion factors from the physical or built environment in which a person lives (environmental characteristics, e.g. climate, infrastructure, institutions and public goods). The functioning achieved is the result of personal choices in selecting from among the capabilities available and subject to personal preferences, social pressure and other decision-making mechanisms. Moreover, they are constrained by personal, social and environmental characteristics (Robeyns, 2005; Crocker, 2008).

In the context of analysing inequality, people must have equal opportunity to function in the way they prefer (Sen, 1982). Only then are they free to determine their capabilities, i.e. potential ways of functioning, and to maximise their quality of life in accordance with them. Moreover, the effective freedom ‘to be and to do’ is essential for assessing capabilities.

In Sen’s capability approach, social exclusion can be understood as the inability to achieve preferred functioning (Sen, 2000). A limited choice of capabilities can lead to deprivation and, in extremis, social exclusion. Thus, the process of social exclusion leads to a state of social exclusion, which can be interpreted as the deprivation of some important functioning (Poggi, 2007).

Operationalisation of the Measurement of Social Exclusion Risk in the Capabilities Approach

Despite several important advances concerning the measurement of social exclusion (e.g. Chakravarty and D’Ambrosio, 2006), there is still ongoing debate about the best analytical approach for understanding its nature and effects. The main unifying theme in the literature is that social exclusion is a multi-dimensional phenomenon.

The multi-dimensional evaluation of social exclusion under the capability approach requires consideration of several different dimensions corresponding to the relevant parts of life. Moreover, measuring social exclusion requires the determination of the social exclusion indicators in each dimension (basic indicators), the aggregation of basic indicators within dimensions, and finally the aggregation of dimension indicators into a proxy indicator for overall social exclusion. The choice of domains and basic indicators depends on both the natural complexity underlying the concept of social exclusion (criterion of reference validity) and the potential for its application in empirical assessments (criterion of usefulness).

Sen (2010, p. 148) advocated measuring latent capability, which reflects the scope of freedom, rather than observed functioning, for the purpose of assessing the quality of life. The idea is that policymakers should not attempt to design and constrain people’s lives in order to optimise the value of abstract indices. They should strive to provide the population with a broad set of potential standards of living from which to choose and leave the optimisation process to individuals.

Following Sen’s concept of freedom, we propose to assess social exclusion by estimating values (scores) corresponding to their latent capabilities, rather than focusing solely on observable indicators. In this way, we allow individuals to demonstrate their latent capabilities through various observable phenomena in different local settings. Therefore, we take into account the differences in individual resources, potential and preferences, as well as cultural diversity between EU member countries. That enables us to conduct a comparative empirical analysis.

In order to measure social exclusion within the framework of the capabilities approach, we apply a multi-indicator and multiple causes model (MIMIC), which is a particular version of the structural equation model (SEM) (Bollen, 1989; Brown and Moore, 2012). The MIMIC model was formulated by Hauser and Goldberger (1971) and then popularised by Joreskog and Goldberger (1975), who presented its detailed assumptions as a special version of the SEM. Krishnakumor and Ballon (2008) considered the SEM approach the most suitable tool for estimating latent capabilities. This model allows an explanation of an individual’s deprivation status and not only describe it but also assesses the impact of external determinants (individual personal, social and environmental characteristics) on latent capabilities.

The measurement of social exclusion under a MIMIC model is as follows (Krishnakumar, 2007; Krishnakumor and Ballon, 2008). The freedom of individual choice in each capability domain is represented by an unobservable latent indicator, which can be estimated based on two sets of observable indicators. First, the reflective part of the model is constructed using a set of selected basic indicators of social exclusion (signs of social exclusion). These variables can be interpreted as achieved functioning, which potentially reflects capability deprivation. The formative part of the model is constructed based on individual personal, social and environmental exogenous characteristics, which are interpreted as conversion factors that strengthen or weaken capabilities and influence the transformation of available resources into achieved functioning.

The starting point for building the MIMIC model is to define social exclusion domains as well as corresponding signs and determinants. We begin our analysis of social exclusion using the MIMIC model by defining the relationships between unobservable indicators (capabilities) and observable indicators (signs and determinants of social exclusion). The model of these relationships is presented in the form of a path diagram in Figure 12.2.

Formally, the MIMIC model equations take the following form:

where

yk is a vector of observable endogenous indicators representing the signs of social exclusion in the &th domain;

t]k is a vector of latent endogenous indicators representing latent capabilities in the kth domain;

Ayi_ is a vector of factor loadings of endogenous indicators inserted into the measurement equations, i.e. relationships between observable signs of social exclusion and latent capabilities in the &th domain; sk is a vector of random errors in the kxh domain;

fk is a vector of the coefficients of latent capabilities related to observable signs of social exclusion in the kth domain, defining the pattern of structural relations;

xk is a vector of observable exogenous structural indicators representing the personal, social and environmental determinants of capabilities in the kxh domain; and

Ck is a vector of random errors representing unknown omitted signs of social exclusion in the kxh domain.

MIMIC model of individual domains of social exclusion using the capability approach

Figure 12.2 MIMIC model of individual domains of social exclusion using the capability approach

The first system of equations forms the measurement model (12.1). It describes the relationships between unobservable capabilities and their observable indicators (signs). The second system of equations describes the structural sub-model (12.2), which determines the impact of observable individual personal, social and environmental characteristics in the formation of unobservable capabilities.

The main purpose of the MIMIC analysis is an estimation of the value of latent capabilities at the individual level, which will be used in further empirical analysis as proxies for the estimation of the DSER. However, the model also allows us to assess the adequacy of the postulated theoretical model, which links the observable exogenous causes and endogenous indicators of social exclusion through latent, unobservable capabilities.

In the next step, we aggregate the resulting estimated latent capabilities into a single indicator representing overall social exclusion using classical factor analysis.

Construction of Indicators of the DSER Using a Fuzzy-Set Approach

Fuzzy-set theory (Zadeh, 1965) was used in the context of social exclusion by Cerioli and Zani (1990), who proposed the construction of indicators of the degree of poverty with survey data. That approach was further developed in a number of applications (Lemmi and Betti, 2006; Betti and Lemmi, 2013). It avoids a simplifying division of the population into groups based on whether people are socially excluded in relation to a particular threshold value. Using fuzzy-set theory, social exclusion is defined as a matter of degree of membership in the sub-set of those who are socially excluded. In addition to those who are or are not socially excluded, a set of those who feel at risk of social exclusion with varying levels of risk can be identified.

We transform both the estimated values of latent capabilities deprivation for each domain of social exclusion and the overall aggregated score of social exclusion using fuzzy-set theory.

Recent studies are dominated by a relative approach, in which all people are characterised by the degree to which one is a member of the relevant set in the range (0,1). The major drawback of this approach is that it makes assessment of the DSER totally dependent on the degree of inequality in the distribution of the exclusion risk indicator, not by the actual DSER. To avoid this shortcoming, we define the membership function using the fuzzy and absolute (FA) multi-dimensional approach (Cerioli and Zani, 1990; Panek, 2006, 2011). This approach is feasible for estimating the DSER, as the threshold values of the membership function can be defined in a natural way, because we treat individuals with the lowest values of all those signs as not being socially and those with the highest values as socially excluded.

We define the function of membership in a group of those who are socially excluded in the /zth dimension for the zth individual as follows:

where:

xkj is the DSER indicator’s empirical value for the zth individual and &th domain;

xjj, is the DSER indicator’s lower threshold value in the /zth domain; and xk is the DSER indicator’s upper threshold value in the /zth domain.

In the proposed approach, established normative thresholds x‘ and x“ are used to determine whether people are experiencing social exclusion. Those whose value of membership functions is below the lower threshold are not considered socially excluded. Similarly, those whose value of membership functions is above the upper threshold are considered socially excluded. However, when the empirical value of the membership function is between the threshold values, the DSER is proportional to the relative distance of the indicator’s value to the lower threshold.

For each domain, the lower threshold value x‘was calculated using the distribution of estimated values of the membership function among those who were not socially excluded based on the observed signs of exclusion. The 90th percentile of this distribution was adopted as the minimum threshold. The maximum threshold value x" was defined in a similar way; however, this time we considered only individuals who were socially excluded based on the empirical basic indicators of social exclusion in any given domain. In this distribution, the threshold value was the 10th percentile.

This solution was adopted to provide the method with a certain degree of robustness to outliers in the data. The estimated values of the relevant social exclusion risk indicators are dependent not only on the signs of exclusion but also on the determinants of social exclusion. Among individuals who are socially excluded based on all the basic signs, the lowest values of the membership function are estimated for those who have the most favourable value of social exclusion determinants. In some extreme cases, the value of the membership function may be lower than it is for people who have no signs of exclusion but have an unfavourable value of social exclusion determinants.

In the final step, the values of the membership function with respect to the aggregated, overall social exclusion were calculated using the following equation:

where

xt is the empirical value of the DSER indicator for the ith individual;

is the lower threshold value of the DSER indicator; and x" is the upper threshold value of the DSER indicator.

The lower and upper threshold levels x' and x“ are defined as estimated latent factor values for people whose calculated DSER in all five domains was considered to be 0 and 1, respectively. In this way, only these people in each domain are and are not considered socially excluded, respectively. All the others are characterised by a varying level of the DSER, represented by a value in the range (0,1), where higher values represent a higher DSER.

Comparative Analysis of the DSER for the Population Aged 50+ in Selected European Countries in 2017

Data Source

The empirical analyses in this chapter are based on data from the Survey of Health Aging and Retirement in Europe (SHARE)1, containing international research on the European population aged 50 and over (Maker and Borsch-Supan, 2017). The eighth wave of this panel study was performed in 2017, with detailed interviews conducted with randomly drawn people aged 50 and over as well as their partners, regardless of age (Bethmann, Bergmann and Scherpenzeel, 2019). The results obtained are generalised with appropriate weighting at the national level (De Luca and Rosetti, 2018; Bethmann, Bergmann and Scherpenzeel, 2019).

The main unit of analysis was a person (the respondents or their partners). In situations where partial indicators (signs of social exclusion) apply not to persons but their households, people were assigned the value of an indicator that applied to their household.

Scope and Assumptions of the Analysis

The assessment of the DSER for Poland was carried out by voivodship. The analysis of the DSER considered the following domains of social exclusion: material conditions, economic and social activity, health and education. In addition, the DSER for all domains together was assessed. The list of domains in the analysis came from the range of data available in the SHARE study. To measure the DSER, the signs of exclusion were determined for individual areas (partial indicators, Table 12.4). All signs of social exclusion were defined as drivers: the higher the value of any given indicator, the higher the degree of exclusion. Moreover, the selected determinants of social exclusion are presented in Table 12.5 in the Appendix.

The income category used in the study was the average monthly net equivalent income in 2017. The net equivalent income was calculated by dividing disposable household income with the scale of OECD (Organisation for Economic Co-operation and Development)-modified equivalents.

Estimation of the MIMIC Model

For each domain, a MIMIC model was constructed, and its parameters were estimated. The parameters for measuring the sub-model were estimated using the maximum likelihood method with missing values using Stata 15. We began the construction of each model by defining all the signs of social exclusion for a given domain. Then, we added possible determinants one at a time, controlling for the statistical significance of the estimated parameters and overall model fit. Table 12.1 presents the estimated results and the composition of the final models.

The model fit was assessed using three measures (Hu and Bentler, 1999): NNFI, CFI and RMSEA. The NNFI and CFI measures have values in the range [0,1], where higher values indicate better fit, and values of at least 0.95 demonstrated very good fit. By contrast, for RMSEA, the lower the value, the better the model fit; values below 0.08 show an acceptable model fit.

In all the models, RMSEA and CFI met the required criteria (Table 12.6 in the Appendix). Given the complexity of the model and the richness of the underlined theoretical concepts, the models show an overall good fit.

Finally, the classical factor analysis model was proposed. It aggregates the values of the estimated group indicators of the DSER, which resulted from the five MIMIC models for each dimension of social exclusion. The purpose of the factor analysis is not only to assess the degree of overall social exclusion risk but also to determine how much each single dimension accounts for, i.e. the weight of each social exclusion domain as a share of the overall social exclusion risk determination. The models used to measure the degree of the risk of social exclusion in each domain and for all the domains are illustrated in Table 12.1.

DSER of the Population Aged 50+

The estimated DSER for every individual takes a value in the range [0,1], where 0 indicates no risk of social exclusion and 1 indicates a person who is socially excluded. These estimated values for individuals were aggregated for countries using appropriate survey weights. Therefore, values for countries should be interpreted as the average degree of risk of social exclusion in any given area for individuals aged 50 and over.

Dimension

Variable

Coefficient Std. Err. z

P > z

95% Confidence Interval

Material conditions

Structural part

Economic activity status

-0.051

0.010

-5.33

0

-0.070

-0.032

Health self-assessment

0.161

0.013

12.55

0

0.136

0.186

Place of residence

0.085

0.010

8.3

0

0.065

0.105

Sex

0.028

0.009

3.1

0.002

0.010

0.046

Measurement part

Monetary poverty

Material conditions

1.000 (constrained)

Constant

0.085 0.018

4.79

0

0.050

0.120

Material deprivation

Material conditions

0.749

0.054

13.82

0

0.643

0.855

Constant

0.005

0.015

0.36

0.72

-0.024

0.034

Income self-assessment

Material conditions

1.310

0.090

14.62

0

1.134

1.485

Constant

0.357

0.013

26.51

0

0.331

0.384

Health

Structural part

Age

0.231

0.012

19.99

0

0.208

0.253

Education

-0.105

0.015

-7.16

0

-0.134

-0.076

Sex

0.013

0.010

1.27

0.205

-0.007

0.034

Measurement part

Health self-assessment

Health

1.000 (constrained)

Constant

0.390 0.014

28.6

0

0.363

0.417

Health limitations

Health

1.269

0.029

44.22

0

1.213

1.326

Constant

0.310

0.015

20.4

0

0.280

0.340

Long-term health problems

Health

0.970

0.023

42.61

0

0.925

1.014

Constant

0.337

0.014

24.48

0

0.310

0.364

(Continued)

Dimension

Variable

Coefficient Std. Err. z

P> z

95% Confidence Interval

Education

Structural part

Age

0.146

0.022

6.49

0

0.102

0.190

Family's financial situation

0.025

0.014

1.75

0.08

-0.003

0.052

Father's education

-0.188

0.052

-3.61

0

-0.290

-0.086

Number of books at home

-0.259

0.020

-12.94

0

-0.298

-0.219

Place of residence

0.100

0.015

6.85

0

0.071

0.128

Sex

0.051

0.012

4.12

0

0.027

0.075

Measurement part

Educational attainment

Education

1 (constrained)

Constant

-0.137

0.027

-4.97

0

-0.190

-0.083

Lifelong learning

Education

0.483

0.027

17.59

0

0.429

0.537

Constant

0.097

0.017

5.7S

О

0.064

0.130

Economic and social activity

Structural part

Age

-0.026

0.004

0

-0.034

-0.017

Education

-0.071

0.009

0

-0.089

-0.053

Health limitations

-0.033

0.005

0

-0.043

-0.023

Health self-assessment

0.037

0.006

0

0.025

0.048

Measurement part

Voluntary activity

Economic and social activity

1 (constrained)

Constant

0.197

0.009

22.97

0

0.180

0.214

Political Activity

Economic and social activity

0.934

0.204

4.58

0

0.535

1.333

Constant

-0.050

0.017

-2.99

0.003

-0.083

-0.017

Clubs activity

Economic and social activity

1.142

0.142

8.03

0

0.863

1.421

Constant

0.348

0.009

39.45

0

0.331

0.365

Economic activity

Economic and social activity

3.273

0.403

8.11

0

2.483

4.064

Constant

-0.114

0.017

-6.69

0

-0.148

-0.081

Source: Author’s analysis based on SHARE data.

Material Living Conditions

In 2017, in the voivodships, the DSER in the domain of material living conditions was the lowest among all the domains of social exclusion. The highest DSER in this area by far is observed in Lubelskie (Table 12.2), followed by Podkarpackie and Opolskie (the function of the degree of membership in the group of those excluded had a value of 0.460, 0.438 and

Table 12.2 DSER of the population aged 50+ in Poland by voivodship in 2017

Voivodsbips

Values of the function of belonging to the socially excluded set

overall

social

exclusion

material

living

conditions

economic activity and social

health

education

todzkie

  • 0.631
  • (0.014)
  • 0.317
  • (0.021)
  • 0.739
  • (0.013)
  • 0.495
  • (0.032)
  • 0.745
  • (0.015)

Mazowieckie

  • 0.636
  • (0.012)
  • 0.384
  • (0.020)
  • 0.725
  • (0.010)
  • 0.479
  • (0.029)
  • 0.745
  • (0.011)

Malopolskie

  • 0.647
  • (0.019)
  • 0.400
  • (0.032)
  • 0.742
  • (0.015)
  • 0.496
  • (0.042)
  • 0.742
  • (0.017)

Slqskie

  • 0.593
  • (0.011)
  • 0.274
  • (0.020)
  • 0.718
  • (0.011)
  • 0.441
  • (0.028)
  • 0.694
  • (0.011)

Lubelskie

  • 0.677
  • (0.015)
  • 0.460
  • (0.024)
  • 0.766
  • (0.015)
  • 0.522
  • (0.035)
  • 0.762
  • (0.015)

Podkarpackie

  • 0.672
  • (0.014)
  • 0.438
  • (0.027)
  • 0.744
  • (0.013)
  • 0.429
  • (0.039)
  • 0.831
  • (0.013)

Swif tokrzys kie

  • 0.660
  • (0.015)
  • 0.377
  • (0.026)
  • 0.754
  • (0.013)
  • 0.514
  • (0.036)
  • 0.778
  • (0.017)

Podlaskie

  • 0.623
  • (0.019)
  • 0.315
  • (0.030)
  • 0.722
  • (0.019)
  • 0.399
  • (0.041)
  • 0.783
  • (0.019)

Wielkopolskie

  • 0.636
  • (0.013)
  • 0.320
  • (0.022)
  • 0.749
  • (0.011)
  • 0.486
  • (0.032)
  • 0.751
  • (0.013)

Zachodniopomorskie

  • 0.613
  • (0.015)
  • 0.294
  • (0.024)
  • 0.737
  • (0.013)
  • 0.489
  • (0.032)
  • 0.703
  • (0.016)

Lubuskie

  • 0.618
  • (0.016)
  • 0.306
  • (0.028)
  • 0.73
  • (0.016)
  • 0.481
  • (0.038)
  • 0.726
  • (0.015)

Dolnoslqskie

  • 0.618
  • (0.013)
  • 0.299
  • (0.022)
  • 0.739
  • (0.012)
  • 0.474
  • (0.032)
  • 0.720
  • (0.013)

Opolskie

  • 0.657
  • (0.024)
  • 0.422
  • (0.037)
  • 0.739
  • (0.020)
  • 0.470
  • (0.055)
  • 0.777
  • (0.022)

Kujaws ko-pomorskie

  • 0.631
  • (0.020)
  • 0.361
  • (0.030)
  • 0.734
  • (0.017)
  • 0.496
  • (0.041)
  • 0.724
  • (0.019)

Warmins ko-mazurskie

  • 0.605
  • (0.016)
  • 0.344
  • (0.026)
  • 0.696
  • (0.015)
  • 0.398
  • (0.038)
  • 0.739
  • (0.016)

Pomorskie

  • 0.602
  • (0.016)
  • 0.328
  • (0.026)
  • 0.705
  • (0.015)
  • 0.443
  • (0.037)
  • 0.708
  • (0.019)

Poland

  • 0.628
  • (0.004)
  • 0.341
  • (0.006)
  • 0.732
  • (0.003)
  • 0.471
  • (0.009)
  • 0.739
  • (0.004)

Source: Author’s analysis based on SHARE data.

0.422, respectively) and the lowest was in Slqskie, Zachodniopomorskie and Dolnoslqskie (average value of the membership function equals 0.274, 0.294 and 0.299, respectively).

Economic and Social Activity

In 2017 the DSER by voivodship was higher in economic and social activity than in other areas of social exclusion. These relatively high values reflect the fact that the majority of people in the population aged 50 and over are retired or economically inactive for other reasons. The DSER was the highest in Lubelskie and Swi^tokrzyskie (with a membership function value of 0.766 and 0.754, respectively) and the lowest in Warminsko-Mazurskie and Pomorskie (value of the membership function of 0.696 and 0.705, respectively).

Health

The variations between the voivodships in the area of health were relatively high in 2017. Lubelskie and Swiytokrzyskie (0.522 and 0.514, respectively) had the highest value of the function of membership in the group of those who are socially excluded. The degree of exclusion risk was the lowest in Warminsko-Mazurskie and Podlaskie (the membership function was 0.398 and 0.399, respectively).

Education

Differences between voivodships were relatively high regarding exclusion in the domain of education as well as health. Opolskie is the most affected voivodship by the degree of social exclusion risk in this domain in 2017 (average value of the function of membership in the socially excluded group of 0.055). The DSER in this area was the lowest in Slqskie and Mazowieckie (average value of the membership function of 0.028 and 0.029, respectively).

Overall Social Exclusion

Lubelskie, Podkarpackie and £wi?tokrzyskie have the highest DSER for the population aged 50 and over in 2017. The membership function had a value of 0.721, 0.708 and 0.708, respectively. The lowest DSER was in Warminsko-Mazurskie, Pomorskie and Slqskie (with an average membership function value of 0.651 and 0.656, respectively).

Symptoms and Determinants of Social Exclusion

Material Living Conditions

The DSER in the domain of material conditions (latent variable) is most strongly reflected by changes in the self-assessment of the household’s income situation by the respondent, followed by changes in monetary poverty.

A low level of health self-assessment had the strongest impact on the increasing DSER in the area of material conditions. Moreover, the DSER is significantly higher for individuals living in rural areas and in small towns. In addition, reduction of this risk is influenced by people who worked in the previous week.

Economic and Social Activity

The increase in the DSER in the domain of economic and social activity is accompanied primarily by a decrease in economic activity. At the same time, the decrease in the degree of this risk is significantly and positively reflected by club activity, voluntary activity and political activity. The DSER in this domain increases significantly with a low level of education and of health self-assessment.

Health

The DSER in the area of health is most strongly reflected in the occurrence of health problems that limit paid work and health self-assessment, and the least, although significantly, by health self-assessment and by long-term or chronic health problems. The degree of exclusion risk in the health domain is significantly influenced by age. This degree of risk is also statistically significantly higher for persons with lower educational attainment.

Education

The increase in the DSER in the domain of education is accompanied by low educational attainment and, to a lesser extent, by non-participation in education. The reduction in the degree of exclusion risk in the area of education is mainly affected by having a large home library in childhood and by the father’s level of higher education. At the same time, the factors that give rise to the DSER in this domain are an increase in the age of the person, being a woman and living in rural areas or small towns.

Overall Social Exclusion

The overall DSER was estimated by aggregating the values of four social exclusion domains using classical factor analysis (Table 12.3). The first factor explained over 60% of the common variance of the five dimensions of the DSER. Therefore, social exclusion risk proved to be rather unidimensional.

Factor loadings for the first factor were the highest in economic and social activity. All factor loadings were higher than 0.7, meaning that overall social exclusion represented by the first factor is highly correlated with common variance of all four dimensions. Moreover, economic and social activity have the lowest uniqueness. The uniqueness of the remaining three dimensions equalled almost 50%, meaning that almost half the variation in these domains is not shared with other domains.

Table 12.3 Factor analysis

Factors

Eigenvalue

Proportion of common variance

Factor1

2.432

60.8%

Factor!

0.736

18.4%

Factor3

0.616

15.4%

Factor4

0.215

5.4%

Variable

Factor loadings

Uniqueness

Material conditions

0.72

48.4%

Health

0.74

45.2%

Education

0.73

47.1%

Economic and social activity

0.92

16.2%

Source: Author’s analysis based on SHARE data.

Conclusions

The measurement and monitoring of the risk of social exclusion for the elderly is crucial for the designers of inclusive social policies. The potential for exploring which factors determine social exclusion in its distinct dimensions is of great significance. We propose a tool that is tailored for the effective achievement of these goals. Our fuzzy multi-dimensional approach based on Sen’s capability approach provides a framework for explaining the deprivation status of individuals. Under the proposed MIMIC model, the capability set of individuals is considered as a latent indicator, observed through a vector of the signs of social exclusion (deprived functioning) and influenced by external determinants (personal, social and environmental characteristics). As a result of estimation of a vector of latent indicators (factor scores), we measure the social exclusion status of individuals in its different dimensions. Next, we measure the degree of overall social exclusion risk by aggregating these scores across social exclusion domains and construct a model of these indices incorporating fuzzy-set theory.

We use this methodology to conduct a comparative analysis of the DSER of the population aged 50 and over in Poland by voivodship in 2017. In addition, we assess the impact of external determinants that strengthen or weaken the risk of social exclusion. The highest DSER among older people was recorded in voivodships with very low GDP per capita, i.e. in Lubelskie, Podkarpackie and Swiftokrzyskie. The average DSER in the domain of education and economic and social activity is the higher in the voivodships studied than in other areas with social exclusion.

As shown in the results of our empirical analysis, combating social exclusion requires the individualisation of policies and programmes for each voivodship, as the levels of DSER vary significantly. Moreover, as the DSER in each of the domains is determined by different underlying factors and has a significant level of unique variance, the relevant policies should be designed specifically in order to address different dimensions of social exclusion.

Appendix

Table 12.4 Symptoms of social exclusion

Domains

Variables

Description of indicators and corresponding SHARE variables

1. Material living conditions

1.1. Monetary poverty

A binary indicator for a person who is a member of a household with an equivalent net income, in an average month in a year, lower than the poverty line in a given country; poverty line - 60% of the median distribution of equivalent net income [hh 17]

1.2. Material deprivation

Number of signs of material deprivation from the list:

  • • inability to cover unexpected expenses from one’s own resources (co206);
  • • inability to afford to purchase meat, poultry, fish, or vegetarian equivalents every other day [br028 and ЬгОЗЗ];
  • • inability to afford to heat one’s home

[co209];

• arrears related to rent, mortgage, or other

housing [ho010,ho022];

• declining to seek medical care for financial

reasons [rh026dl, rh050dl, rh782, rh783].

1.3. Income self-assessment

Self-assessment of the ability to make ends meet [co007].

2. Economic and social activity

2.1. Economic activity

The indicator includes the following aspects of economic activity:

  • 1. being employed or self-employed [ep005]
  • 2. being unemployed or retired [ep005]
  • 3. long-term unemployed [epOOS, epl28]
  • 4. economically inactive [ep005]

2.2. Voluntary activity

How often one engaged in voluntary/charity work during the past 12 months [ac036_l].

2.3. Political activity

How often one has taken part in a political/ community-related organisation during the

2.4. Clubs activity

past 12 months [ac036_7|.

How often one has gone to a sport/social/ other kind of club during the past 12 months [ac036_5]

3. Health

3.1. Health

self-assessment

Health self-assessment [ph003].

3.2. Health limitations

Problems in carrying out activities due to health conditions |ph005].

3.3. Long-term health problems

Chronic or long-term physical problems |ph004].

4. Education

4.1. Educational attainment

Primary education or less [dnOlO],

4.2. Lifelong learning

Participation in an educational course or training [ac035_d4].

196 T. Panek and J. Zwierzcboivski

Table 12.5 Determinants of social exclusion

Determinants

Description

1. Economic activity status

0 = the person did not work in the past four weeks; 1 = the person did paid work in the past four weeks [ep002]

2. Age

Age in years and squared age in years |age2017]

3. Sex

1 = female; 0 = male [gender]

4. Place of residence

1 = Big cities; 2 = Suburbs of big cities; 3 = Big towns; 4 = Small towns; 5 = Rural areas [areabldgi]

5. Health

self-assessment

1 = Excellent; 2 = Very good; 3 = Good; 4 = Fair; 5 = Poor [ph003]

6. Health limitations

1 = lack of health problems limiting daily activities; 2 = occurrence of long-term health problems moderately limiting daily activities; 3 = occurrence of long-term health problems severely limiting dailv activities [ph0051

7. Education

Respondent’s highest level of education attained. 1 = ISCED code 8; 2 = ISCED codes 5, 6, and 7; 3 = ISCED code 4; 4 = ISCED code 3; 5 = ISCED code 2; 6 = ISCED code 1 and no education [isced2011_r]

8. Family’s financial conditions in childhood

Family was well off financially; about average; or poor: 1 = well off; 2 = above average; 3 = poor [cc733]

9. Number of books at home in childhood

Number of books when age 10 [cc008]

10. Father’s education

Father of respondent: ISCED-11 coding of education [isced201 l_f]

Table 12.6 Goodness-of-fit measures of MIMIC models

Goodness-of-fit

measures

Values of goodness-of-fit measures

Material

living

conditions

Economic and social activity

Health

Education

Social

relations

RMSEA

0.036

0.068

0.046

0.045

0.051

CFI

0.962

0.952

0.964

0.916

0.956

NNFI

0.932

0.914

0.913

0.791

0.923

Source: Author’s analysis based on SHARE data.

Note

1 This chapter uses data from SHARE Waves 1,2, 3,4, 5, 6 and 7 (DOIs: 10.6103/ SHARE.wl.700, 10.6103/SHARE.w2.700, 10.6103/SHARE.w3.700, 10.6103/ SHARE.w4.700, 10.6103/SHARE.w5.700, 10.6103/SHARE.w6.700, 10.6103/ SHARE.w7.700), see Borsch-Supan et.al. (2013) for methodological details.

The SHARE data collection has been funded by the European Commission through FP5 (QLK6-CT-2001-00360), FP6 (SHARE-13: RII-CT-2006-062193,

COMPARE: CIT5-CT-2005-028857, SHARELIFE: CIT4-CT-2006-028812), FP7 (SHARE-PREP: GA №211909, SHARE-LEAP: GA №227822, SHARE M4: GA №261982) and Horizon 2020 (SHARE-DEV3: GA №676536, SERISS: GA №654221) and by DG Employment, Social Affairs & Inclusion. Additional funding from the German Ministry of Education and Research, the Max Planck Society for the Advancement of Science, the U.S. National Institute on Aging (U01_AG09740- 13S2, P01_AG005842, P01_AG08291, P30_AG12815, R21_AG025169, Y1-AG- 4553-01, IAG_BSR06-11, OGHA_04-064, HHSN271201300071C), and from various national funding sources is gratefully acknowledged (see www.share-pro- ject.org). The SHARE data collection for Poland and the research presented in this paper have been со-funded from the European Social Fund under the Operational Program Knowledge Education Development.

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