**4. Results**

#### *4.1. Ranking Public Poverty Policies by the EU-28 States*

The results of PPPs efficiency are given in 10a,10b and 2 of the annex A. It can be checked in Table 10b that all hierarchies in RRP and DF index present a correlation close to 1. This fact does not depend on the coefficient λ used to defuzzify *RRP i*and

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*DF i*, *i* = 1, 2, . . . , 28. Hence, by applying fuzzy linguistic interpretation of correlation proposed in Section 2.2, we can conclude that all the expected values of RRP and DF present a perfect(+) correlation.

**Table 10a.** Ranking social policy in UE-28 countries on the basis of the expected value of RRP and DF in Table 2 for several values of λ.


Source: own elaboration from data provided by EU-SILC (2008–2018) and ESSPROS (2008–2017). V–F stands for the rank in [10] within the period 2007–2015.

**Table 10b.** Spearman correlations between the expected values of RRP and/or DF for several values of the index of optimism λ.


Source: own elaboration from data provided by EU-SILC (2008–2018) and ESSPROS (2008–2017). Note: As V–F, we symbolize the value of RRP and DF obtained by Valls-Fonayet et al. (2020) within the period 2007–2015.

> The results that we have obtained are similar to those in [7,9,12]. Better performances are attained by Anglo-Saxon welfare states (Ireland and Great Britain), Scandinavian welfare states (Finland, Sweden and Denmark) and some Visegrad pact countries like Hungary and Czechia. The less efficient PPPs are those from the Mediterranean welfare states (Italy, Greece, Spain) and some Mediterranean and Baltic former communist republics as Romania, Bulgaria, Latvia or Estonia. In intermediate positions, we find continental

welfare states (as, e.g., France, Belgium, etc.) and a heterogeneous set of non-UE-15 as, e.g., Cyprus, Malta or Slovakia. Table 10b shows that the hierarchies in Valls-Fonayet et al. in [10] and those in our paper present a Spearman correlation coefficient that Table 2 labels as very strong (+).

#### *4.2. Fuzzy Assessment of the Relation between Social Expense Effort and Efficiency in Poverty Reduction*

Tables 11 and 12 show the relation of the volume of social expenses with the reduction of poverty and its efficiency. As we expected, in the whole EU-28, the relation between SER and RRP is positive (strong (+)). However, the behavior of that relation is completely different in EU-15 and non-EU 15. In non-EU 15 countries it is very strong (+), i.e., there is a direct relation between the volume of social expenses and poverty reduction. On the other hand, in EU-15 countries that relation is negligible. Hence, this result is in accordance with the statement in [16] that showed that despite there is a strong negative correlation between SER and poverty rates in several European countries, it cannot be concluded that increases in SER lead directly to reductions in poverty.

**Table 11.** Correlations of SER with RRP and DF efficiency index.


Source: own elaboration from data provided by EU-SILC (2008–2018) and ESSPROS (2008–2017).

**Table 12.** Value of the compatibility indexes (7b) of the correlations between SER with RRP and DF and the labels of linguistic variable "correlation coefficient".


Source: own elaboration from data provided by EU-SILC (2008–2018) and ESSPROS (2008–2017).

> Likewise, in whole EU-28 countries, the relation between the volume of social expenditure and its efficiency is weak (+). Again, the relation between these variables in non-EU-15 countries and EU-15 states is completely different. In EU-15 countries, that relation is weak ( −), whereas in non-EU-15 countries is strong (+). Notice that the value of SER in non-EU-15 countries is substantially lower than in EU-15 countries. Therefore, its marginal productivity of SER is clearly positive when social expenses are relatively low, and so a greater diminution of poverty comes fair from increasing SE. However, when a critical level of SER is reached, the relationship between increases in SER and diminutions in RRP is not so direct. This fact motivates a detailed analysis of the influence of the social expenditure composition over the value of DF reached by every PPP.

From Tables 13 and 14a, we can state that in overall EU-28, there is not any SE item with a high positive relation with DF. Hence, the greater positive relation is reached by the expenses in family/children and social exclusion with a moderate (+) relation. Those results are in accordance with [19–23] where it is pointed out the limited impact in poverty reduction of social assistance policies as those for family and children or housing in a grea<sup>t</sup> deal of countries due to its reduced value. To consult those values, see Table A1.

On the other hand, pension expenses (old age and survivors, not disability) are strong (−) correlated with DF measure. That finding is in accordance with [17], where it is indicated that benefits for the elderly people generally have a low redistributive impact. However, Tables 13 and 14b,14c shows that those patterns are not uniform within EU-28.

**Table 13.** Value of the correlations between DF and the proportion that each kind of social expense suppose in overall SER.


Source: own elaboration from data provided by EU-SILC (2008–2018) and ESSPROS (2008–2017).

**Table 14a.** Value of the compatibility indexes (7b) of the correlations between DF and the proportion that each kind of social expense suppose in overall SE and the labels of the linguistic variable "correlation coefficient" (EU-28).


Source: own elaboration from data provided by EU-SILC (2008–2018) and ESSPROS (2008–2017).


**Table 14b.** Value of the compatibility indexes (7b) of the correlations between DF and the proportion that each kind of social expense suppose in overall SE and the labels of the linguistic variable "correlation coefficient" (Non-EU-15 countries).

> Source: own elaboration from data provided by EU-SILC (2008–2018) and ESSPROS (2008–2017).

**Table 14c.** Value of the compatibility indexes (7b) of the correlations between DF and the proportion that each kind of social expense suppose in overall SE and the labels of the linguistic variable "correlation coefficient" (EU-15 countries).


Source: own elaboration from data provided by EU-SILC (2008–2018) and ESSPROS (2008–2017).

> There are clear differences in the relation between SE items and DF of PPP within EU-15 with respect to non-EU-15 countries. In non-EU-15 countries, six of eight types of expenses are low correlated with the productivity measure. Only social exclusion miscellanea (moderate(+)) and disability benefits (strong ( −)) show a significant correlation. Notice that, in general, non-EU-15 countries present lower levels of SER than EU-15 states. Hence, it seems that the efficiency of social expenses within non-EU-15 is improved by simply increasing them. Hence, except in the case of disability benefits, increasing a given type of social expense may not lead to a greater result in poverty reduction than increasing any other.

On the other hand, in EU-15, the correlations of each type of social expense and DF is often more intense. Likewise, we can check that not necessarily a given kind of expense has the same sign in its correlation with DF within EU-15 and non-EU-15 countries. That is the case of Sick, Dis, Old and Surv. As [10] we also obtain that Sick, Fam and Dis expenses have a significant positive relationship with the efficiency pf PPPs (strong in two first cases and moderate in the third). Likewise, as [10] we find that benefits due to old age or survival have a significant negative relation with DF (strong and very strong, respectively). Likewise, we must point out that in the case of Une, Hou and Soc, the sign and the intensity of the correlation are essentially the same in EU-15 and non-EU-15 countries. Hence, the relation of DF with housing benefits is negligible, with unemployment is weak (−) and lastly, with Soc is weak/moderate(+) in both EU-15 non-EU-15 countries. Notice that results obtained for the correlation between unemployment benefits and DF are according with Cantillon [18] who outlines that financial aid for the unemployed has not the desired effects in reducing poverty.
