Poverty in the Regions of the European Union – Measurement with a Composite Indicator

We measure area-specific human poverty in the European Union (EU) at the second level of the nomenclature of territorial units for statistics (NUTS 2). We construct a regional human poverty index (RHPI), which comprises four dimensions: social exclusion, knowledge, a decent standard of living, and a long and healthy life. The RHPI provides information regarding the relative standing of a given country with respect to its level of poverty and shows the variability of poverty within a country with respect to NUTS 2. The RHPI shows satisfactory statistical coherence, confirmed by the results of correlation analysis and a principal component analysis. As confirmed by an uncertainty analysis, the RHPI also shows satisfactory robustness to the normative assumptions made during the construction process. The RHPI is computed for all NUTS 2 regions in 28 EU countries. Our results show that the poverty scale differs considerably among EU countries, with RHPI scores ranging between 9.23 for Prague and more than 65 for Bulgarian Yugoiztochen and Severozapaden. We also find that substantial differences in levels of poverty between regions are present in all EU countries. The only exceptions to this finding are small EU countries where neither NUTS 1 nor NUTS 2 regions exist.

tors. It is reported not only at the country level but also for different levels of the nomenclature of territorial units for statistics (NUTS) and for areas differently defined with respect to population density.
Nevertheless, the AROPE rate is not reported consistently for all countries. Namely, sub-national estimates of the AROPE rate are not available for several large countries, including Germany and the United Kingdom. With this knowledge, it seems reasonable to provide a composite measure of poverty that, in combination with the AROPE rate, will enable better identification of the NUTS 2 regions where aid is most needed. Therefore, inspired by the Human Poverty Index (HPI) (UNDP, 2007), which measured human poverty between countries, we provide information in this study on the level of human poverty at the subnational level (NUTS 2). This information is presented in the form of the Regional Human Poverty Index (RHPI), which comprises four dimensions: a long and healthy life, standard of living, knowledge, and social exclusion. Additionally, we show the results of the uncertainty analysis performed with respect to the scores and ranks of the RHPI to show the possible volatility of our results.
The approach we propose has three useful properties. First, the RHPI comprises only six indicators, which makes it relatively simple to replicate. Second, the RHPI takes into account both monetary and nonmonetary perspectives in the poverty measurement.
Third, the RHPI not only provides information about the absolute magnitude of human poverty experienced by Europeans in a given country and the relative standing of the country but also shows the variability of human poverty within a country with respect to NUTS 2.
The RHPI also has some limitations. First, the conceptual model of the RHPI corresponds mostly to the conceptualization of HPI and, thus, to the Human Development Index (HDI) proposed by the UNDP (UNDP, 2007) and the availability of indicators at the NUTS 2 level. Second, although research on poverty has developed rapidly in recent years, there is currently no research on the "one-size-fits-all" weights that could be applied in all circumstances; therefore, we apply a weighting scheme resulting from the importance analysis, assuming the equal importance of dimensions.
In the following sections, we first present the concept of poverty with a focus on the multidimensional measurement. Second, we shortly describe the HPI proposed by UNDP (UNDP, 2007). Third, the conceptualization of our approach to poverty measurement is discussed. Fourth, the methods used to construct a composite indicator of poverty are presented. The results section follows, and the final section concludes the paper.

Concept of poverty
Poverty both in relative terms, compared to other people in society, and in absolute terms, whether people enjoy life's basic necessities, is a reflection of whether people "have insufficient command of resources over time" (Gordon, 2006, p. 32). However, numerous studies on the notion of poverty show not only that is this concept understood differently in different contexts but also that there are many distinct approaches to the conceptualization of this notion. To list only a few, Wagle (2008) and Saunders (2005)  Alternatively, Foster (1998), Hagenaars and de Vos (1988) and Lok-Dessallien (2000), among others, report that types of poverty can expressed in • absolute terms, meaning that poverty entails having less than an objectively defined, absolute minimum, • relative terms, meaning that poverty entails having less than others in society, and • self-assessed terms, meaning that poverty is a feeling that you do not have enough to get by. It is worth mentioning, however, that the only example of poverty measurement performed on a unidimensional basis is income poverty. Nevertheless, even in this case, the available measures of poverty are sufficient to show it from different perspectives (see Foster, Greer, & Thorbecke, 1984;2010).   (Eurostat, 2010(Eurostat, -2012 Life expectancy at a given age represents the average number of years of life remaining if a group of persons at that age were to experience the mortality rates for a particular year over the course of their remaining life. Life expectancy at birth is a summary measure of the age-specific all-cause mortality rates in an area in a given period I 2 -Infant mortality rate (Eurostat, 2010(Eurostat, -2012 The number of deaths of infants (younger than one year of age at death) per 1,000 live births (based on one year data) Knowledge P 2 -Adults lacking functional literacy skills I 3 -Percentage of population aged 25-64 with low educational attainment (Eurostat, 2011(Eurostat, -2013 The percentage of people aged 25 to 64 with an education level ISCED (International Standard Classification of Education) of 2 or less. ISCED levels 0-2: pre-primary, primary and lower secondary education I 4 -Percentage of population aged 18-24 neither employed nor in education or training (NEET) (Eurostat, 2011(Eurostat, -2013 Youth (aged 18-24) who are either unemployed or inactive and who do not participate in any education or training Decent standard of living P 4 -Rate of long-term unemployment (lasting 12 months or more) I 5 -Long-term unemployment rate (Eurostat, 2011(Eurostat, -2013 Persons unemployed for more than 12 months as a percentage of the labor force based on the International Labour Office (ILO) definition. The labor force is the total number of people employed and unemployed. Unemployed persons comprise persons aged 15 to 74 who (1) are without work during the reference week; (2) are available to start work within the next two weeks; (3) and have been actively seeking work in the past four weeks or had already found a job to start within the next three months.

UNDP Human Poverty Index
Social exclusion P 2 -Population below the income poverty line (50% of median adjusted household disposable income) I 6 -Percentage of population below the income poverty line (60% of median adjusted household disposable income) (Eurostat, 2010(Eurostat, -2012 Persons at risk of poverty are those living in a household with an equivalized disposable income below the risk-of-poverty threshold, which is set at 60% of the national median equivalized disposable income (after social transfers). The equivalized income is calculated by dividing the total household income by its size determined after applying the following weights: 1.0 to the first adult, 0.5 to each other household member aged 14 or over and 0.3 to each household member aged less than 14 years old To eliminate the risk of unexpected transitions or outliers in the data series, we calculate the moving average of the last three available data points in the series. Therefore, the data mostly cover the period of 2010-2012 or that of 2011-2013.

Methods
Our index was based on data with satisfactory coverage, namely, 98.5% of data were available. Missing values were spotted in three out of six indicators, namely, in the percentage of the population aged 18-24 neither employed nor in education or training (I 4 ), the longterm unemployment rate (I 5 ), and the percentage of the population below the income poverty line (I 6 ).
The missing data present in our dataset were imputed using an expected maximization algorithm (Rubin, 1987;Schafer, 1997). The imputations were based on the indicators of the RHPI (see Table 1) and one additional variable, namely, early leavers from education and training, which is expressed as a percentage of the population aged 18-24. In total, 24 of 1,620 values were imputed.
The following step detected outliers. We decided to perform this step because outliers may artificially introduce spurious variability to the data, as clearly stated by JRC-OECD (2008) or implemented in a multi-dimensional case by Białowolski and Węziak-Białowolska (2014). We applied a combination of two criteria. For each indicator, we checked if the distribution of an indicator is characterized by skewness>2 and kurtosis>3.5 (Dybczyński, 1980;Velasco & Verma, 1998), indicating the lack of a normal distribution and the presence of outliers. Using this criterion, the possible presence of outliers was found only with respect to one indicator, infant mortality (I 2 ). However, an analysis of the histogram revealed that no observation stands out. Therefore, no outlier treatment was conducted.
The data were then normalized to the range of 1 to 100 using the min-max method, with the minimum and maximum values taken from the dataset and with 100 meaning the worst observable score (the highest deprivation/human poverty) and 1 meaning the best observable score (the lowest deprivation/human poverty). This type of aggregation implied that the orientation of the indicators was such that the higher the score, the worse the situation with respect to human poverty. The normalized indicators belonging to the same dimension were averaged using the arithmetic mean. In this way, dimension scores for "long and healthy life" and "knowledge" were obtained.
In the next step, we verified the underlying structure of the RHPI data. Because we assumed that the RHPI is more formative than reflective in nature, principal component analysis (PCA) was employed. However, we would like to underline that the PCA was not used to calculate the RHPI scores.  Table A1 in the Appendix).
Having confirmed the one-dimensionality of the RHPI, we aggregated variables into the RHPI. As the RHPI dimensions are believed to be non-compensatory in nature, which implies that an improvement in one dimension cannot fully compensate for equal deterioration in another dimension, we employed a generalized mean with power 0.5. This aggregation method ensures that the compensation of low results in one dimension with high results in others is only partial (Decancq & Lugo, 2013;Ruiz, 2011). Using this approach also means that a rise in the lower tail of the distribution of any variable will improve the composite indicator more than a similar increase in the upper tail. This approach is consistent with recent developments in the field: it has been used to com- We also aimed for the RHPI to be statistically well balanced, implying that the importance of dimensions in the index was relatively equal. We wanted each of four dimensions to explain 25% of the total variation in the RHPI scores. To this end, in the aggregation process, we applied the weighting scheme resulting from the analysis of the "main effect," also known as the correlation ratio or first-order sensitivity measure (Saltelli et al., 2008). This measure, as argued by Paruolo, Saisana and Saltelli (2013), offers a precise definition of importance, i.e., "the expected reduction in variance of the composite indicator that would be obtained if a variable could be fixed." Although the weights we used seem unequal when expressed in the nominal terms, they ensured the equal contribution of each dimension in the aggregating formula toward explaining the total variation in the RHPI scores (more about the relationship between the explicit and normative weights can be found in Paruolo et al. (2013) Finally, to assess the robustness of the RHPI with regard to the normative assumption related to compensability that was made during the conceptualization step, we performed an uncertainty analysis. The aim of this analysis was to measure the overall variation in RHPI scores and ranks resulting from the uncertainty linked to the assumption about the power of the generalized mean. To verify the assumption, we modified the power of the generalized mean, which was allowed to range between 0 and 1, implying that we tested an influence of the range of the generalized means from the arithmetic to geometric means on the RHPI scores and ranks. In particular, in the uncertainty analysis, its values were sampled from the uniform distribution U[0; 1]. As a result, the final scores of the RHPI were presented with uncertainty expressed by the error terms (please see Figure 3 and Figure 4 as well as Table A5 in the Appendix).

Spatial distribution of the RHPI
When taking into consideration country-level estimates of the RHPI (see Figure 1 and Table A3 Table A5 in the Appendix). However, it must be noted that changes in the power value led to some modifications in the index scores and ranks, especially in cases of unequal performance with respect to all dimensions.
In particular, with regard to ranks, we verified the difference between the median simulated score and the reference rank. The maximum observed difference amounted to 2, which corresponds to 0.74% of the maximum possible shift in rank. The length of the 90% confidence interval, constructed as the 5 th and 95 th percentiles of the simulated ranks, was then analyzed.
It appeared that in only 14 cases (noted in Figure 3  Regarding the uncertainty analysis of the RHPI scores, we analyzed the difference between the mean simulated scores and the reference scores. It appeared that in all cases, they were similar. The variation coefficients were then examined. This analysis confirmed low variation of RHPI scores. In only three out of 270 cases (noted in Figure 4) did the coefficient of variation exceed 10%.

Conclusions
In this study, we attempted to measure area-specific    namely, the Regional Human Poverty Index (RHPI).
The RHPI was computed for 28 EU countries. Our results show that levels of poverty in the EU range from 9 to almost 70 RHPI points, with Sweden scoring unequivocally the best and Latvia, Bulgaria, and Romania scoring the worst. We also found that considerable differences in levels of poverty exist in all EU countries sufficiently large to have NUTS 2.
The RHPI has some limitations. When computing the RHPI, we had to make a certain assumption about the compensability rate between RHPI dimensions captured by the power of the generalized mean.
Although the RHPI turned out to be quite robust to this assumption, we also observed that changes in the strength of compensation among dimensions led to some modifications in the index scores and ranks.

Data citation and disclaimer
The responsibility for all results and conclusions presented in this study lies entirely with the author.   Note: In smaller countries, in which the entire country would be placed on the NUTS 2 or even NUTS 3 level (e.g., Luxembourg, Cyprus), levels 1, 2 and/or 3 are identical to the level above and/or to the entire country.   Figure A4. Spatial distribution (NUTS 2) of the social exclusion dimension in the EU Note: Thresholds correspond to quintiles; the darker the color, the worse the conditions