Multi-Dimensional Material Deprivation in the Visegrád Group: Zero-Inflated Beta Regression Modelling

Hanna Dudek and Wieslaw Szczesny


Poverty and social exclusion are complex multi-dimensional concepts. In economically advanced societies, they are often defined in terms of the inability to participate in mainstream society because they have insufficient resources. To identify these phenomena, we take various approaches, depending on the country or the purpose of the research. In the European Union (EU), we agreed on a set of indicators for monitoring poverty and social exclusion and enabling the assessment of progress in achieving the Europe 2020 Strategy targets. This indicates a shift in policy focus from one-dimensional income poverty to a multi-dimensional approach. To capture the complex nature of poverty and social exclusion in the Europe 2020 Strategy, we consider the material deprivation (MD) component in parallel with monetary poverty and exclusion from the labour market. MD in the EU conditions refers to a state of economic strain and durables defined as the enforced inability to pay unexpected expenses, afford a one- week annual holiday away from home, consume meals with meat, fish, or other sources of protein regularly, afford adequate heating of a dwelling, durable goods such a washing machine, colour television, telephone, or car and being in payment arrears (Eurostat Glossary, 2018).

Our chapter focuses on MD because analysing it has many benefits. First, it enables us to measure living standards directly by looking at the ‘enforced lack’ of ‘necessities’. The ‘enforced lack’ approach means that an item is counted as lacking if people cannot afford it - distinguishing between those who choose not to obtain a specific item and those forced to forgo it because they lack the necessary economic resources (Hallerod, 1995). Thus, the lack of items is not due to lifestyle preferences and choice but, rather, is the result of the enforced lack of items, i.e. things that people would like to possess (have access to) but cannot afford (Fusco et ah, 2013). Analysing MD not only provides a broad picture of living standards but also captures elements of persistent poverty because the lack of goods is usually associated with a prolonged shortage of resources (Calandrino, 2003). Moreover, an analysis of common items in the EU that captures the same aspect of deprivation enables comparability across countries (Guio, 2009).

Various approaches can be used to identify deprived households in a multi-dimensional framework (Alkire and Foster, 2011; Atkinson, 2003; Betti et al., 2015; Nasri and Belhadj, 2017; Panek, 2010; Pattanaik and Xu, 2018). The approaches most commonly used are the intersection and the union methods: the intersection method considers as deprived only those who experience a failure of functioning in every dimension, whereas the union method refers to those who are deprived at least in one dimension. However, although these approaches are intuitive and straightforward to apply, they can be ineffective at separating those who are deprived of those who are not (the non-deprived). In particular, the intersection method might consider households which evidently suffer substantial deprivation as non-deprived. In contrast, the union-based methodology might not be helpful in distinguishing and targeting the most seriously deprived (Alkire and Foster, 2011). Thus, the literature proposes the use of different intermediate approaches. In particular, the fuzzy-set approach builds on the idea of ambiguity in the identification of who is deprived. In this study, we use this approach because, like some other authors (i.e. Betti and Lemmi, 2013; Betti et al., 2015; Su et al., 2020; Wang and Wang, 2016), we think that MD should be considered a question of the degree of poverty, rather than a characteristic of households in a given population that is either present or absent. Moreover, in our opinion, the relative importance of deprivation items varies across households. Therefore, we use a system of weighting that captures the prevalence of specific deprivation items and the correlation between them. This approach, proposed by Betti and Verma (2008), is based on how common a given item is among all households in a given country and enables us to avoid double counting when the informational content of two different items partly overlaps. On the one hand, this method implies that forms of deprivation which affect only a small share of the country’s population are assigned a larger weight than those that are more common in the country. On the other hand, it assesses redundancy across deprivation indicators.

Our study is conducted at the household level with cross-sectional data from the European Union Statistics on Income and Living Conditions (EU-SILC) for 2017. The analysis is based on a standard set of nine MD items adopted by all EU countries and the European Commission. In our study, we examined correlates of the risk and intensity of MD in the Visegrad Group (V4) countries - the Czech Republic, Hungary, Poland and Slovakia. These Central European countries have a lot in common in terms of their history, culture and socio-economic status. They have successfully transformed from centrally planned to market economies and joined the EU at the same time in 2004. Thus, because of their numerous common characteristics, we analyse MD across households in the V4 countries.

In the first step of our study, we used the fuzzy-set approach to construct a deprivation score, which is a composite indicator aggregating all nine MD items. Thus, for each household we obtained a score in the range [0,1], in which 0 means that a household is unambiguously non-deprived, and

1 means that a household is definitely deprived, while all intermediate values indicate partial deprivation. In the second step, to identify the correlates of MD, we conducted a regression analysis. The data analysed indicate the need to use a zero-inflated beta regression model. The application of this model in the analysis of household socio-economic conditions is relatively new, so our chapter contributes to the literature in this field.

In our study, we assumed that a score of zero on the MD scale is different from a score of at least one. Therefore, to test this hypothesis, we applied a zero-inflated beta regression model. We also hypothesised that MD profiles have significant country-specific heterogeneity. To test this hypothesis, we checked the statistical significance of country dummy variables in the model. Thus, the first goal of our chapter was to examine the methodological issues related to modelling MD. The second goal was to identify which households have a higher risk and greater intensity of MD.

The chapter contributes to the literature by providing the first econometric evidence of the factors that affect household MD in the V4 countries using a fuzzy multi-dimensional approach. Moreover, it investigates the differences between the risk and the intensity of the extent to which both indicators are subject to the same determinants. Thus, it aims to fill a gap in the literature regarding multi-dimensional MD in the V4 countries.

Literature Review

The literature on MD has expanded considerably in recent years. Important contributions in this field include Townsend (1979), Mack and Lansley (1985), Mayer and Jencks (1989), Hallerod (1995) and Nolan and Whelan (1996). Supported by these papers, the measurement of MD has been commonly used to capture the multi-dimensional character of poverty and social exclusion in developed countries. Specifically, the relevance of MD indicators in the EU has grown substantially since 2010 as a result of the adoption of the Europe 2020 Strategy on smart, sustainable, and inclusive growth (Guio et al., 2016). Currently, the set of social indicators in the EU include deprivation indicators that combine nine material and social items. They are used by all EU member states and the European Commission to monitor progress in the fight against poverty and social exclusion in individual countries and the EU (Fusco et ah, 2013; Guio, 2018).

Most studies on MD in the EU specify a particular threshold to distinguish between the deprived and the non-deprived. They mainly apply logit or probit models in which the binary variable usually takes a value of 1 if MD occurs and 0 otherwise. Examples of such research include Nelson (2012), Israel (2016) and Saltkjel (2018). In contrast, studies that consider the intensity of MD include Barcena-Martin et ah (2014), Busetta et ah (2016) and Bediik (2018) - the first two of which use composite indicators that aggregate the nine deprivation items. Nonetheless, the main differences concern the scope of data and the applied models. Specifically, to model the intensity of MD in the EU, Barcena-Martin et al. (2014) applied a multi-level linear model. They showed that differences in MD across the EU can be explained from both the individual- and country-level perspectives. Busetta et al. (2016) examine the risk and intensity of MD among foreigners in Italy using a zero-inflated beta regression model, which investigates the depth of MD, and a logit regression model on to the probability of not experiencing any MD. Like Barcena-Martin et al. (2014), Bediik (2018) uses a two-part model but focuses on the number of deprivation items using zero-inflated count models. The results confirm that individuals with zero deprivation items have significantly different profiles to those who experience deprivation of at least one item (Bediik, 2018).

To some extent, these three papers have been an inspiration to us. However, unlike Bediik (2018) but in line with Barcena-Martin et al. (2014) and Busetta et al. (2016), we weighted the number of deprivation items, using a more complex weighting scheme than these last two papers. At the same time, like Bediik (2018) and Busetta et al. (2016), we employed a more sophisticated econometric methodology than Barcena-Martin et al. (2014). In our study, we modelled the risk and intensity of household MD in the V4 countries with a two-part model that simultaneously estimates both issues.


The measurement of MD has been on the EU agenda regularly since at least 2010. Based on EU-SILC survey data, it focuses on enforced deprivation, including the inability to: (1) keep one’s home adequately warm, (2) eat a meal with meat, chicken, fish, or a protein equivalent every two days, (3) go on a weeklong annual holiday away from home, (4) pay unexpected expenses, (5) pay the rent, mortgage and utility bills, (6) afford to have a television, (7) afford to own a washing machine, (8) afford to have a car, and (9) afford to own a telephone. The first five items are considered ‘economic strain’ and the last four items ‘durable goods’. Our study uses a set of nine binary indicators for these items. Our calculations are based on cross- sectional data for 2017 encompassing 8,701 households in Czechia, 8,142 in Hungary, 5,602 in Slovakia and 13,057 in Poland.

Table 10.1 shows the share of households which did not experience any deprivation. We computed results for the sample and estimated results for

Table 10.1 Percentages of households without any deprivation

Share of households






In sample






In population (estimation)






Source: Author’s calculation

Multi-Dimensional Material Deprivation 155

the population. In the latter case, we used sample weights for each household in order to ensure the results are representative at a national scale.

Almost half the households in the V4 countries did not exhibit any deprivation. The highest share of these households was in Czechia, and the share in the other V4 countries was similar. Moreover, we noted that the percentage of households with each of the nine deprivations in all V4 countries is infinitesimal.

To take a close look at MD in the V4 countries, we examined the impact of various household characteristics on this issue. The set of potential correlates of MD captures information on the entire household and characteristics of the household head (HH). The first group of these correlates includes disposable household income equivalent in terms of purchasing power parity (PPP), the degree of urbanisation, the presence of disabled persons and the type of household. The second group includes age, gender, education, employment, occupation and health status. Most of the explanatory variables considered are standard in MD analyses.


Material Deprivation Scores

This section describes the method used in constructing deprivation scores. Our study is based on the methodology developed by Cerioli and Zani (1990), Cheli and Lemmi (1995) and Betti and Verma (2008), according to which the state of deprivation is seen as a ‘fuzzy set’ to which all households of a given population belong but in varying degrees (Ciani et al., 2019).

The MD score for the /th household results from the weighted sum of nine deprivation items:

where each djk (k = 1,2,..., 9) is a binary indicator variable that takes a value of 1 if the zth household is deprived in terms of a given item or 0 if it has no

deprivation, wk is a weight for item k, in which 0 < wk < 1 and ^ wk = 1.

Weights for aggregating different items can be selected using various different approaches. A common method proposed by Desai and Shah (1988) and Cerioli and Zani (1990) is to weight items in proportion to their prevalence in the population. This approach assigns a higher weight to deprivation items which are less common among households in a given population. This approach, called ‘prevalence’ or ‘frequency-based weighting’ (Fusco et al., 2013; Pi Alperin and Van Kerm, 2014), is used in MD studies by Barcena-Martin et al. (2014) and Busetta et al. (2016). It can be justified in terms of the subjective perception of MD, as the higher the proportion of households that are not deprived of a given item is, the more likely it is that a household unable to afford this item will feel deprived (Fusco et al., 2013).

Another important property that weights should satisfy is limiting the influence of indicators that are highly correlated (Betti et ah, 2006). Thus, the methodology developed by Betti and Verma (2008) comprises two factors: the dispersion of the deprivation indicator and its correlation with other deprivation indicators. According to this methodology, the weights can be defined as follows:

where the first factor is the coefficient of variation of the item, and the second factor is a measure which gives less weight to items that are more highly correlated with others in order to reduce the effect of redundancy. Betti and Verma (2008) give an accurate calculation of factor Wb as follows:

where rkk, is the correlation coefficient between two different indicators dk and dk,, and r is a predetermined cut-off correlation level. Finally, are normalised to sum to one.

We use the Betti and Verma approach in our study because of its properties:

  • (1) Betti and Verma’s weighting ‘lets the data speak for itself’.
  • (2) It takes into account the problem of redundancy in information, limiting the influence of deprivation indicators that are highly correlated.
  • (3) In our binary indicators, Wg equals -1, thus, like other frequency-

V dk

based weighting, this method assigns a higher weight to deprivation items that are relatively infrequent (Pi Alperin and Van Kerm, 2014).

In other words, the Betti and Verma approach enables the calculation of data-driven weights using a sort of ‘prevalence-correlation’ method (Betti et al., 2016; Betti, 2017; Ciani et al., 2019). This approach has been applied across variety fields, including poverty and quality of life (Ciani et al., 2019; Dudek and Szczesny, 2017; Panek, 2010).

We compute weights using mdepriv, the Stata procedure developed by Pi Alperin and Van Kerm (2014). The weights are calculated separately for items in the ‘economic strain’ dimension and in the ‘durables’ dimension. Moreover, like Barcena-Martin et al. (2014), we use national weighting, i.e. the weight for a given item is equal across households in the same country.

In the next step, to gain deeper insights into the socio-economic and demographic correlates of the MD score, we conducted a regression analysis. The following section briefly describes the model used.

Multi-Dimensional Material Deprivation 157 Zero-Inflated Beta Regression Model

Generally, the MD score defined by Equation (10.1) can take values in the interval [0,1]. If the number of boundary values of the unitary interval is not large, the response variable can be transformed to ‘push’ zeros and ones a little inwards. For example, Smithson and Verkuilen (2006) propose rescaling variable s using the transformation s’ = (s{n - 1) + 0,5)/n, where n is the sample size. Another solution is to replace a value of 0 with 0.001 or 0.005 and 1 with 0.999 or 0.995. Nonetheless, these solutions are not appropriate if the number of zeros or ones is considerable, and the boundary values of the unitary interval are values of special interest for research (Masserini et al., 2017). In this situation, to address the issue raised, Ospina and Ferrari (2012) introduced a general class of zero-or-one inflated beta regressions. Because in our study only the problem of excess zeros occurred, we focused on the zero-inflated beta regression model (ZIBRM), which assumes that the response variable has a mixed continuous-discrete distribution with a probability mass of zero. The appropriate mixture density is:

where a. is the probability of observing zero,

f(s,n,g) is the beta distribution density function, defined as:

Г denotes the gamma function, p is the mean of the outcome variable s for se (0,1),

IP" is the scaling factor related to the variance of s, for se (0,1).

Therefore, a zero-inflated beta distribution is a combination of two distributions: a beta distribution when the variable is in the interval (0,1), and another distribution function that is in effect when the variable takes a value of 0.

ZIBRM can be defined by assuming the relationships in the mixture parameter a and the conditional mean ц (Ospina and Ferrari, 2012):

where у and p are vectors of unknown parameters to be estimated, zi and x are vectors of known covariates of the z'th household, (i = 1,2, ... ,n), which may be identical or overlap in part (Masserini et al., 2017), h(-): (0,1) ->R, g(-): (0,1) ->R, are strictly monotonic and twice continuously differentiable functions.

In our study, we estimated the parameters of ZIBRM using the Stata module zoib developed by Buis (2010), with logit link for b(-) and g(-). The ZIBRM applied consists of two sub-models:

  • (1) a logistic regression model for whether the MD score is 0;
  • (2) a beta regression model for the MD scores from the interval (0,1).

Thus, the first model estimates the probability of not experiencing any deprivations, and the second model examines the intensity of MD. The vectors of the parameters у and p in the ZIBRM are estimated using the maximum likelihood. For a detailed description of the estimation and inference of ZIBRM, see Ospina and Ferrari (2012).

Results and Discussion

In the first stage of our study, we computed the weights assigned to each of the nine deprivation symptoms. Using the weights, we aggregated MD items to calculate a household’s score, in which the score equals 1 when the household is deprived of all component indicators and equals 0 if it is not deprived of any indicator. As shown in Table 10.1, almost half the households in the V4 did not exhibit any of the nine deprivation symptoms. By contrast, we found that only six households experienced each of the symptoms considered. In these cases, we replaced an MD score of 1 with 0.999.

We surmise that the only reason for not experiencing MD is income above the poverty threshold. We decided to analyse this aspect, taking into account households that do and do not have income poverty.

Table 10.2 lists the percentage of households which did not experience any deprivation symptoms by their income level.

The results in Table 10.2 show that 18.4% of income-poor households in the V4 did not report any deprivation symptoms, whereas 52.7% of the households there who were not income poor reported not being deprived. This means that the two populations - unambiguously non-deprived and

Table 10.2 Share of households without any deprivation by income level

Income level






Below 60% of national median equivalent income






Above 60% of the national median equivalent income






Source: Author calculations. The results are weighted in order to represent the structure of the population of households in each V4 country income non-poor - do not perfectly overlap. Our findings are confirmed in the literature, showing that income poverty and MD are not closely correlated (Ayllon and Gabos, 2017). Thus, MD indicators provide more specific information on poverty than income data. These results suggest that the relationship between MD and income is complex. Two households with the same income can have different standards of living if their income does not adequately measure all their available resources or if their needs differ (Fusco et al., 2011). Therefore, after we control for income, the identification of other factors that influence households’ MD is a key step. In order to assess the impact of various socio-economic and demographic factors on the risk and the intensity of MD, we estimated the ZIBRM parameters in Table 10.3.

The significance and sign of these estimates indicate the significance and direction of the partial effects. However, the estimates on the risk of deprivation are the opposite of the estimates in the second column in Table 10.3. This is because, when we analyse the risk of deprivation, we consider the probability of being deprived of at least one of the nine items, whereas the ZIBRM estimation indicates the probability of not having any deprivation. Thus, the results of ZIBRM sub-models must be interpreted in the opposite way. As the logistic regression estimates the probability that a household is unambiguously non-deprived (i.e. the probability that the MD score is zero), a negative estimate of a parameter indicates that the corresponding covariate has a positive effect on the risk of being deprived, while a positive coefficient indicates a negative effect. In the beta regression sub-model, a positive estimate indicates an increment in the incidence of MD due to growth (i.e. a change in state) in the covariate, whereas a negative coefficient shows the opposite.

As might be expected, the risk and the intensity in the V4 decline if a household’s income increases. However, there is no perfect one-to-one relationship, which has already been highlighted.

When comparing results for the risk and the intensity of MD, we found that some correlates significantly affected one process but not another. Specifically, the risk of MD did not differ significantly with respect to the degree of urbanisation. However, the intensity was higher in urban areas than in rural areas. Furthermore, the risk of MD was significantly greater for households with disabled members, but there was no statistically significant difference in the intensity of MD between households without disabled members and households with those facing health challenges. This is consistent with Bediik’s (2018) results, confirming that a score of zero is a qualitatively different phenomenon to a score on at least one of nine MD items.

We found that the type of household has a clear impact on the risk and intensity of MD. Specifically, we observed that one-person households and single-parent households face a difficult situation. Our results also show the importance of the characteristics of the head of household (HH), such as the

Table 10.3 Estimates of ZIBRM


Logistic regression sub-model on the probability of not experiencing any MD

Beta regression sub-model on the intensity of MD

Estimates of у


Estimates of p







Income in thousands of PPP





Urbanisation (Ref.: Sparse (rural) areas)











Disability (Ref.: Without any disability)

Activity limited due to health status





Activity strongly limited due to health status





Household type (Ref.: One-person households)

Single parent





Multi-person households without children





Two adults with one child





Two adults with two children





Two adults with 3+ children





Other households with children





Education of household head (Ref.: Higher)











Age of household head (Ref.: Below 40)

40-60 years





More than 60 years





Sex of household head






Health of household head (Ref.: Very good)
















Very bad





Economic activity of household head (Ref.: Retired)
















Occupation of household head (Ref.: Intermediate)

High skill










Country (Ref.: Czechia)
















Note: SE are standard errors of estimated parameters. All reported standard errors are robust to heteroscedasticity. Values in boldface are significant at the 0.05 level.

level of education, gender, economic activity, health status, occupation and age. We note that:

  • • when the HH has a low level of education, the risk and the intensity of MD are higher;
  • • the risk of MD was higher with female HH than male HH, but the intensity showed no statistical difference due to sex;
  • • the perceived health of the HH has a negative relationship with the risk and intensity of MD;
  • • households headed by unskilled persons have a higher risk and intensity of MD than households headed by persons with intermediate occupational positions;
  • • lower risk and intensity of MD was noted among households with an older person as the HH than those headed by people aged below 40;
  • • households headed by people who are unemployed were significantly more likely to report MD than those whose HH is retired. However, households headed by economically active people have a higher intensity of MD than households headed by retirees.

These results regarding HH characteristics that influence MD are largely consistent with other studies conducted in similar socio-economic contexts (Nelson, 2012; Barcena-Martin et al., 2014; Israel, 2016; Saltkjel, 2018). However, what distinguishes our study from these investigations is that we considered the risk and the intensity of MD. Furthermore, unlike other studies, we examined how the level of urbanisation affects both phenomena. Our estimates reveal that, ceteris paribus, households in rural areas are not more materially deprived than urban households. Moreover, the intensity of MD is lower among the former than the latter. This finding sheds new light on the issue of rural-urban disparity in the V4.

Apart from these household-level correlates, we found that the country in which households are located significantly differentiated the risk and intensity of MD after all other household-level covariates are controlled for. Specifically, Poland, Slovakia and Hungary have a higher risk of MD than Czechia. Our results show that not only is MD a problem that arises from each household characteristic, but various economic and social country- level features may also affect MD. For example, differences among countries in the risk and the intensity of MD might depend on the structure of the welfare state and the different levels of social support. Our results regarding the differences across countries are supported by the Eurostat Database (2020), revealing that in 2017 the expenditure on social protection per inhabitant was much higher in Czechia than in other V4 countries. Moreover, Czechia is a leader among V4 countries in indicators of wellbeing, such as the Human Development Index (UNDP, 2020) and the Better Life Index (OECD, 2020). Thus, people in countries with higher well-being in general have a lower risk of MD.

162 H. Dudek and W. Szczesny Concluding Remarks

In recent years, the European Commission has drawn attention to the need for greater emphasis on MD, which is currently measured by nine indicators related to financial stress and the enforced lack of durable goods. The MD of a household in the EU can be assessed using different approaches. In our study, we adopted the methodology proposed by Betti and Verma (2008), which enables us to simultaneously capture the multi-dimensional character of MD and its vagueness. In effect, we constructed scores in the interval [0,1], in which a higher score indicates a higher intensity of MD. Moreover, we considered the risk of MD, which in our study indicates the probability of experiencing at least one symptom of MD. We modelled the risk and intensity of households’ MD by applying a two-part ZIBRM and thus jointly estimating both issues.

We focused on conditions in member countries of the Visegrad Group, which in recent years has gained the attention of the international community and analysts because it is regarded as a bloc of countries. Although many studies have been conducted on political and economic conditions in Central Europe, there is a shortage of research papers on MD in the V4 countries. Thus, by looking at these countries in terms of the potential for meeting basic material needs, we aim to fill this research gap.

We found that MD is a multi-faceted phenomenon, with risk and intensity distributed unevenly across the V4 population. It is affected by the income and health conditions, demographic composition, level of education, gender, economic activity, occupation and age of the HH. Furthermore, we showed that correlates of the risk and the intensity of MD do not fully overlap, including the degree of urbanisation and the presence of disabled members of a household. We also revealed that the country in which a household is located significantly differentiates the risk and intensity of MD after all other household-level covariates are controlled for. Various country-level features, such as the social policy, prices and the structure of the welfare state, can affect the risk as well as the intensity of MD.

We hope that our study will lead to a better understanding of the multidimensional aspects of MD in the V4 countries. By identifying the factors correlated with the risk and intensity of MD, our approach can be useful for implementing socio-economic policies to reduce MD.


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