on system guarantees after exiting the job market; for the unemployed, we consider the proportion of net labour income replaced by net benefits during the first year of unemployment;

ü the monetary benefits that, on average, national governments provide to the disabled (in the form of disability pensions or monetary transfers, to pay medical expenses and for care and assistance); in particular, we consider the monetary amount net of taxes―the corresponding data are directly available from Eurostat;

ü the Gini index calculated based on after-tax and transfers disposable income for income inequality; these data are directly available from OECD;

ü the poverty index (calculated as the percentage of households with disposable incomes at least 60 percent lower than the median national income) is considered as an indicator of the effectiveness of social policies aimed at ensuring a given standard of living; the source of data is the OECD “Income distribution and poverty” database, that refers to the “equivalised disposable household income”, that is, household income net of taxes and inclusive of transfers received adjusted for household composition based on equivalence scales.

3.1. Calculating the Social Protection Performance Index (SPPI)

Our performance index for the ith country and jth sector of social policy at time t is thus given by:

$0\le {P}_{i,j,t}=\frac{{x}_{i,j,t}-{x}_{\mathrm{min},j,t}}{{x}_{\mathrm{max},j,t}-{x}_{\mathrm{min},j,t}}\le 1$

$i=1,2,\cdots ,22;\text{\hspace{0.17em}}j=1,2,\cdots ,8$

where xi,j,t is the value of the outcome indicator associated to the sector j of social policy in country i at time t, while xmin,j,t and xmax,j,t represent, respectively, the minimum and maximum values for the same indicator within the group of the 22 countries under consideration. Therefore, the performance index ranges be- tween 0 and 1. Pi,j,t = 0 indicates the case in which the ith country exhibits the worst performance in the jth sector at time t within the group of countries under consideration; conversely, Pi,j,t = 1 represents the best outcome in the jth sector at time t for the ith country. To ensure that the highest values of the index are representative of the best performances, we transform three variables: the unemployment rate, the poverty index and the Gini index. In these cases, higher values of the index would indicate worse―and not better―performances for the country concerned. We therefore consider the complement to one of the preceding three outcome variables interpretable as the employment rate, a “welfare index” (representative of the percentage of households with disposable income of over 60 percent of the median disposable income) and an index of equidistribution of disposable income, respectively.

For the sectors with several outcomes’ indicators (for example family, labour market, elderly, unemployment, etc.), we consider their average value, following the methodology used in calculating the Human Development Indices (see the Appendix for details; methodological notes available at the following link. http://hdr.undp.org/en/content/calculating-indices). Finally, the aggregate indicator for the whole area of the social sector was obtained by adding together the individual partial indicators in accordance with the existing literature [6] . We give equal weight to each sector indicator in compiling the aggregate performance indicator; the assumption is strong, but stronger alternatives are lacking. It facilitates the comparison with the existing literature, where either the same assumption is made [2] or some sectors are not considered at all (thus being assigned a zero weight). For country i at time t we thus have:

$SPP{I}_{i,t}=\underset{j=1}{\overset{8}{\sum }}{P}_{i,j,t}$

The final values are characterized by a high degree of heterogeneity within the group of countries considered, ranging from 1.96 (Greece) to 6.34 (Norway). Higher indicators (greater than the median value 4.43) are associated with the Nordic countries (Norway, Denmark, the Netherlands, Finland and Sweden) and Luxembourg, Austria, France, Germany, Belgium and Slovenia (Table 1).

The disaggregated analysis of the index shows diversity in its composition. Performance levels of the “family”, “health”, “unemployment”, “income inequality” and “poverty” sectors are higher in the Nordic systems (Norway, Denmark, Sweden, the Netherlands) and in some continental countries, notably Luxembourg.

Table 1. The social protection performance index (2013).

Source: Our elaborations on OECD and Eurostat Data.

In the Mediterranean countries, in contrast, the better-performing components are represented by “health” and “the elderly”, while markedly poor performances are highlighted by context indicators relating to the fight against poverty and to policies reducing income inequality. Anglo-Saxon countries perform well in the unemployment and poverty sector.

3.2. Performance, Median Income and Distribution

Equations (8) and (8’) imply that $\beta g$ is directly related to kmYm. Given that

${k}_{m}=\frac{{Y}_{m}+\stackrel{¯}{{Y}_{\mathrm{min}}}}{2{Y}_{m}}$ , km increases with $\frac{\stackrel{¯}{{Y}_{\mathrm{min}}}}{{Y}_{m}}$ . This ratio corresponds to the inverse of

the percentile ratio P50/P10, among the common measures of inequality, basically representing a distributional parameter (see claim 1).

Figure 1 shows the relationship between our SPPI for the year 2013 and the average value of the product between the percentile ratio and the median income for the period 2009-2013 for the countries under consideration. We take the average value of Ym(P10/P50) for the period 2009-2013 to consider the lag between the outcome of social policies in a given year and the expenditure decisions of previous years.

What emerges is a positive relationship, which hints at an explanation of differences in national choices about the level of protection based on differences in the level and the position in the distribution of the median voter’s income. This can be connected both to the redistribution and the insurance motives outlined in the previous section. Since the main objective of the paper is to analyse efficiency in social expenditure, we do not elaborate further on this finding, turning, instead, to the analysis of social expenditure efficiency.

4. The Inefficiency Parameter

Our next step is to calculate the inefficiency parameter represented by $\alpha$ in the theoretical framework. Since the per capita social expenditure is $\alpha \beta g$ , the value of $\alpha$ is simply given by $\alpha \beta g$ divided by $\beta g$ , estimated in the previous section. From a conceptual point of view, we are calculating the ratio between the input of social policy (expenditure) and the output (the SPPI).

As an estimate for $\alpha \beta g$ , we take per capita net public social expenditure, as a share of GDP. In particular, we assume a lagged effect from expenditure onto performance: we thus take the average value of per capita net social expenditure over the period 2009-2013 (at constant prices). The method is similar to the one applied in [2] , therefore most of the same caveats apply. Thus, we are aware that

Figure 1. The social protection performance index and income distribution. Source: Our elaborations on OECD data (SOCX Database). Median income in PPP (US dollars).

public expenditure data are not always fully comparable among countries and that its impact on performance cannot be always separated by that of other factors. Note that the existing literature uses gross social expenditure; instead, by using net social expenditure, we can correct for differences across countries stemming from different taxation levels on social benefits.

We can now obtain an estimate of $\alpha$ computing an indicator for social expenditure inefficiency for each country, SEIIi. To do this, we weigh the logarithm of average per capita net social expenditure, NPSEi, by SPPIi (of course, the values of the indexes only give an ordering of countries):

The final values (Table 2) are characterized by a high degree of heterogeneity within the group of countries considered, ranging from 1.47 (Denmark) to 3.83 (Estonia). Based on this ranking, one can distinguish three groups of countries: the Nordic countries, with Luxembourg and Austria, with the lowest inefficiency indexes (between 1.7 and 1.83); the Continental countries, with inefficiency parameters between 1.84 and 2.28; the Mediterranean and Anglo-Saxon countries, with Poland, Hungary and Estonia, with fairly high inefficiency parameters (2.39 - 3.83).

Table 2. The social expenditure inefficiency index (2013).

Unlike the result for general public expenditure in [2] , inefficiency in social expenditure is not positively related to the amount of spending, as shown in Figure 2 (the same applies to the relationship between the SEII and the ratio of net social expenditure to GDP).

Differently from [11] [12] and [13] , Ireland and the United Kingdom are at the same levels of inefficiency as the Mediterranean countries. As for the new Continental countries, differently from [13] , the Czech Republic and Slovenia do not outperform the Northern countries, ranking with the other Continental countries and the Slovak Republic (even if Slovenia is quite near to Sweden), while Hungary joins Poland at the levels of the Mediterranean countries. This difference, besides the different time period under consideration, stems from the different measure of performance that we adopt, based on the outcomes of a set of social policy areas that is wider than those adopted in the above-mentioned literature. For instance, the lag of the Mediterranean countries w.r.t. the Anglo-Saxon ones in the area “unemployment” is compensated by a better performance in the fields of “health” (and “the elderly”, as for the United Kingdom). Consequently, we believe that a general performance index can better assess the overall effect of social protection on social welfare.

As argued in Section 2, a higher level of the inefficiency parameter $\alpha$ should be inversely related to $\beta g$ . This corresponds to an inverse relationship between the SPPI and the SEII. In the perspective of a cross-country comparison, we find that countries with an above average (2.14) inefficiency level have a below average (4.22) level of performance (Figure 3).

5. Conclusions

Our theoretical analysis of the relationship between social performance and efficiency predicts that the size of social protection increases with the median

Figure 2. The social expenditure inefficiency index and net public social expenditure (2013). Source: Our elaborations on OECD Data.

Figure 3. The relationship between the social protection performance index and the Social Expenditure Inefficiency Index Source: Our elaborations on OECD Data.

voter’s income level and its proximity to the bottom end of the distribution and decreases as the inefficiency of social expenditures increases. These claims are supported by the data.

To test the model, we first constructed performance indexes for 22 European countries in 2013. While the literature on the effectiveness and the efficiency of welfare systems proposes sectorial analyses, we construct a composite performance index (SPPI) based on the outcomes of all main sectors of social policy. Then, we calculated an inefficiency index (SEII) as the ratio of net social expenditure to the performance index (existing studies use gross social expenditure).

We obtain a ranking of countries not completely in line with those found in the literature: for instance, Mediterranean and Anglo-Saxon countries end up being quite similar. We also find that, in the field of social protection, efficiency does not appear to be inversely related to the size of public intervention. The type of welfare system appears to be a more relevant factor in determining the effectiveness and efficiency of social expenditure. Of course, given the difficulties in cross-country data comparability and in separating the effect of public expenditure from that of other factors (just take life expectancy as an example), all the results are indicative. Also, the 22 countries have different levels of private social expenditure; these are limited in general, albeit higher in the Nordic countries. These findings can be of relevance within the debate on the link between the characteristics of welfare systems and their efficacy and effectiveness, to which we have already referred in the paper: by comparing the performance and efficiency rankings, we found that countries with higher expenditure efficiency present a greater homogeneity of performance in all subsectors considered.

This might be related to the cross effects of sectorial policies, that thus tend to reinforce each other. For instance, a higher expenditure level in support of families, like childcare, encourages female participation in the labour market and can therefore contribute to reduce poverty and income inequality. As a policy implication, the paper suggests that expenditure policy should follow a multitarget approach, not devoting resources only to contrast some particular social risks, given that some sectorial policies can have indirect positive effects on other areas, thus guaranteeing a more efficient use of resources.

Appendix

Methodological notes and data for outcomes indicators

This appendix provides some methodological notes on some outcomes’ indi- cators used to calculate the performance index. In the paper, we consider 7 sectors of social expenditure (family, health, labour market, elderly, disabled, unemployment, inequality) and 8 sector indicators (we add poverty) for their related outcomes (Figure A1).

In some cases, the outcomes’ indicators are data (maternal employment, life expectancy, unemployment rate, Gini index, poverty index) directly available on OECD databases. In other cases, some elaboration was needed. For example, for family and disabled, we use monetary amounts considered net of fiscal measures and expressed in PPP (US dollar) to make the international comparison possible. While for the disabled, we directly use the available Eurostat data on the monetary benefits that, on average, national governments allocate in the form of disability pensions or monetary transfers, for the family available income we simulated the net disposable income of a “typical” family―which we adopt as a benchmark―consisting of two children and two working parents with, respectively, a gross income from employment equal to 100 percent and 67 percent of

Figure A1. Outcomes indicators for social policies.

the average income from employment in their country of residence. Net disposable income is calculated by subtracting the income tax (considering deductions or tax credits) and social contributions from gross taxable income (adjusted for deductions) and adding monetary benefits. For the simulation analysis, the OECD’s tax-benefit calculator model (available at the following link: http://www.oecd.org/els/soc/benefitsandwagestax-benefitcalculator.htm) was used. The results of the simulation are in Table A1.

Other income support policies target groups of individuals who exhibit a certain degree of vulnerability, due to life cycle and market risks, within the framework of the market economy: the elderly, the unemployed. For each of these categories, the benchmark indicator that we have identified is the average amount of available resources which the various national welfare systems guarantee to them. In all cases, we consider monetary benefits in net terms, i.e. net of

Table A1. Net family income (2013).

Source: elaboration on OECD tax-benefit calculator data.

fiscal measures (direct taxation, resulting from social transfers, indirect taxation of consumption by recipients of transfers and tax benefits for social welfare purposes). For the elderly, we have used the net replacement rate relating to compulsory pension schemes, which represents the percentage of individual income, net of contributions and taxes, that the pension system guarantees after exiting the job market. Formally, this is the ratio of the net pension to the labour income net of tax. Three levels of labour income were considered: 50 percent, 100 percent and 150 percent of national average labour income (AW) (Table A2).

From a methodological point of view, we repeat a simulation analysis to calculate the net replacement rate of unemployment benefits during the first year of unemployment, which represents the proportion of net labour income replaced by net benefits received in the event of unemployment.

Table A2. Net replacement rate for pensions (2013).

Source: Pensions at a Glance, OECD Pensions Statistics (database).

The latter, in turn, depend on both labour income and the recipient’s family situation. Therefore, two income categories were considered (67 percent and 100 percent of national average labour income) and, within each of them, six types of family: three typical families (single parent, single-earner households and families with both partners in employment) without children and three families of the same types with two underage children (Table A3 and Table A4). In both

Table A3. Net replacement rates unemployed: case 1 (67% AW) (2013).

Source: OECD Benefits and wages statistics http://www.oecd.org/els/benefits-and-wages-statistics.htm

Table A4. Net replacement rates unemployed: case 1 (67% AW) (2013).

Source: OECD Benefits and wages statistics http://www.oecd.org/els/benefits-and-wages-statistics.htm

cases, we consider families which do not qualify for cash housing assistance or social assistance while working.

Databases

Eurostat, Social Protection Benefits Data available at http://ec.europa.eu/eurostat/tgm/table.do?tab=table&init=1&plugin=1&language=en&pcode=tps00107

OECD, Social Expenditure Database (SOCX) available at
http://www.oecd.org/social/expenditure.htm

OECD, Family Database available at http://www.oecd.org/els/family/database.htm

OECD, Tax-benefit calculator available at http://www.oecd.org/social/soc/benefitsandwagestax-benefitcalculator.htm

OECD, Unemployment Data available at https://data.oecd.org/unemp/harmonised-unemployment-rate-hur.htm

OECD, Pensions at Glance- Pensions Statistics available at http://www.oecd-ilibrary.org/social-issues-migration-health/data/oecd-pensions-statistics/pensions-at-a-glance-2

OECD, Benefits and wages statistics available at http://www.oecd.org/els/benefits-and-wages-statistics.htm

OECD, Income Distribution and Poverty Database available at http://stats.oecd.org/Index.aspx?DataSetCode=IDD

Conflicts of Interest

The authors declare no conflicts of interest.

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