Spatial Modeling of Social Expenditure in EU Countries

The age structure of EU countries has changed significantly in recent years. These changes are mainly due to longer life expectancy, low fertility rates, and population migrations. Countries are trying to cope with the consequences of demographic changes by reforming the social care system, extending the retirement age, introducing additional social benefits promoting parenthood and supporting large families. Social security programs in EU countries are very diverse. The financial aspect plays an important role in social security systems. Social security is based on the redistribution of income between persons receiving remuneration from work and persons who, due to reaching retirement age, poor health, lack of employment or having many children receive social benefits. In view of the changing demographic situation, social security functions such as health care, pensions and benefits for large families require Member States to take immediate structural and financial change. In the study will carry out spatial analysis of social care system development in the European Union and will research the impact of social spending on the unemployment rate, household structure, birth rate or poverty level. In addition, the forecast of social expenditure in the EU will be designated. The use of spatial analysis will allow to determine the existing relations between the studied countries due to the level of development of the studied phenomenon. The analysis will be carried out on the basis of actual data from Eurostat.


Introduction
In recent years, the analysis of economic phenomena has been increasingly carried out based on methods and tools of spatial statistics or spatial econometrics.These tools allow the assessment and comparison of phenomena in terms of spatial relationships, i.e. similarity and diversity of objects located at a certain distance from each other.Spatial methods are used in such issues as demographic phenomena, analysis of the labor market, study of the standard of living of the population, economic and trade concentration, analysis of electoral support, real estate valuation, analysis of industrial structures (Pietrzykowski, 2011;Pośpiech, 2015).The ongoing process of population aging around the world leads to significant changes in the structure of societies, and thus to changes in the volume of demand and supply for basic social services related not only to the proper functioning of the health service, care institutions, education but also the social security system (disability and retirement benefits, benefits for large families, unemployment benefits).The aim of the study is to examine the spatial relationships between EU countries in terms of the development of the social care system.The article analyzes the development of the social care system in EU countries and builds an econometric model explaining the impact of social spending on, among others, the unemployment rate, household structure, birth rate or the level of poverty.

Social Protection in the EU
The first legal regulations on social policy in the EU Community appeared more than 60 years ago (Treaty of Rome (1957)).At that time, Member States were to improve both the economic and social situation of the poorest social groups, as well as to protect workers against the effects of adverse and unfortunate accidents and life events.Initially, EU social policy was not a priority for Member States and focused mainly on creating appropriate social, economic and legal conditions on a Community and national scale.These conditions concerned equal treatment of men and women on the labor market, pensions, mobility of the labor force on the EU labor market and improvement of the working and living conditions of the citizens of the community.Intensive growth of interest in social issues occurred only in the 70s, when on the Conference in Paris in 1972 highlighted the social dimension of economic and political integration.A year later, the First Social Program on European labor law was developed.In 1975, the European Regional Development Fund was created, which deals with the regional policy of the member states.The Single European Act (1986) introduced further changes in the social dimension of the single market.As a consequence, the Community Charter of Fundamental Social Rights of Workers was adopted at the Strasbourg summit (1989).These rights included, among others, the improvement of living and working conditions, social protection, health protection, protection of children and young people, protection of the disabled and protection of the elderly.Amendments introduced by the Mastricht Treaty (1992) to implement this policy in accordance with the principle of subsidiarity are essential for EU social policy.On its basis, in subsequent years, the European Commission formulated strategies assuming, among others ensuring a high level of health protection for residents of EU countries, improving living conditions and hygiene, promoting a healthy lifestyle.In 2000, the Charter of Fundamental Rights was adopted to guarantee respect for human rights, which was attached in the form of a declaration to the Treaties on European Union (Treaty of Mastricht since 1993) and the Treaty establishing the European Community (1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009), later the Treaty on the Functioning of the European Union (from 2009 ) (Głąbicka, 1997;Ulman, Eichengreen, Dickens, 2010 ).At present, total expenditure on social benefits in the EU amounts to EUR 8388.39 per capita and is almost 80% higher than in 1995.These expenses cover seven areas: sickness / health care, disability, old age, family/children, unemployment, housing and social exclusion.In addition, social expenditure also covers administrative and other costs, representing around GBP 1.1%.Fig. 1 presents the distribution of spending on social objectives in the EU in the years 1995-2017.Total expenses for social benefits are expressed as% GBP, while the remaining data as purchasing power standard (PPS) per inhabitant.Based on the data in Fig. 1, it can be seen that total social spending is systematically growing.The disorder of the upward trend is 2007, in which two countries Bulgaria and Romania joined to the community.The largest percentage of social expenditure is old age spending (about 40% of total expenditure), which is understandable in the light of an aging society.The largest percentage of social expenditure is old age expenditure (about 40% of total expenditure), which is understandable in the light of an aging society.Expenditure on health care comes second (about 30% of total expenditure).In addition, an increase in old age expenditure by 3.3 pp and health care expenditure by nearly 2 pp can be observed during the period under review.In the case of expenditure on unemployment, in 2017 there was a decrease of 3.7 percentage points compared to 1995, which may indicate an improvement in the situation on the EU labor market and a decrease in the level of unemployment.

Spatial Modeling
Spatial modeling has become an important research area when the first law of geography was formulated by W. Tobler in 1970(Tobler, 1970), which says that everything is related, but near objects are more related than distant ones.The construction of the spatial model is aimed at improving the quality of the econometric model.Inclusion of spatial relationships within a given area as well as within neighboring areas can have a positive influence on the translation of the variability of the features under consideration.The following basic groups of spatial models are distinguished: spatial lag models, spatial error models, cross-regression models and mixed variants.In paper the first two models were considered.

Spatial Lag Model
The spatial lag model includes the spatially delayed endogenous variable Wy, ie it is an autoregressive model (the basis of the model is spatial dependence).The general form of this model is described by formula (Arbia, 2006;Suchecki, 2010): (1) Where: − spatial autocorrelation coefficient, W− spatial weight matrix,  − vector of model coefficients, X− matrix of exogenous variables,  − model error.
The model tests if 0 =  ie the significance of the dependent variable which is spatially delayed.Spatial delay Wy is interpreted as the level of the dependent variable y in neighboring regions.If this is significant, then the level of y in the i-th region can be explained by the level of the phenomena in the neighborhood and other factors represented by the remaining explanatory variables.

Spatial Error Model
The spatial error model contains spatially delayed error.This model assumes the spatial autocorrelation of the rest of the model.The general form of the model is given by the formula (Kopczewska, 2006;Suchecki, 2010): (2) where:  − spatial autocorrelation coefficient, other signs as above. W is a spatially delayed error, which should be interpreted as the average error from neighboring locations, and  is an independent error of the model.In the model we test whether 0 =  ie lack of spatial autocorrelation.

Empirical Analysis
The subject of the study were 28 EU countries in 2008 and 2017.The data used for the analysis come from the Eurostat database.MS Excel and R-Cran were used for calculations and graphic presentation of data.In the first stage of the study, countries were compared by level of spending on social benefits.Figure 2 shows the division of EU countries according to the amount of social benefits into 4 groups according to the following rules: class I (high levels of the studied phenomenon), class II (medium levels of the studied phenomenon), class III (low levels of the studied phenomenon), class IV (very low levels of the studied phenomenon).The results of obtained classes spatial distribution for Europe territorial division into countries in 2008 and 2017 due to the social expenditures is shown in the following table (Fig. 2).The first group (dark green color) includes the countries with the highest social benefits, while the fourth group (light yellow color) -the lowest social benefits.Analyzing the data in Fig. 2, it can be seen that in 2008 the highest social benefits (group I) were paid by: France, Denmark, Sweden, Austria, Germany, Italy and Belgium, while the lowest (group IV): Latvia, Romania, Bulgaria, Estonia, Slovakia and Lithuania.In 2017 the situation changed.Group I was joined by Finland and Nederlands, while Belgium and Sweden fell to group II.However, Ireland were additionally included in group IV, while Slovakia and Malta moved to group III.In the analyzed years 20 countries did not change or improved their position in the ranking, which may indicate on improving the social situation in these countries.The largest changes were recorded for Ireland (decrease in the ranking by 10 positions) and Finland (increase in the ranking by 7 positions).Analyzing social expenditure in individual countries, 6 areas mentioned in point 1 were taken into account, i.e. sicknes/health care, disabled, old age, family/children, unemployment, housing, social exclusion.Table 1 presents the ranking of EU countries by each of the above areas.By far the best situation in terms of social security can be seen in Luxembourg, which ranks 1-2 in the ranking in almost every category.However, the worst situation is observed for Bulgaria and Romania, occupying the last positions in the ranking in each of the areas.
In the next stage of the study, statistical analysis of the impact of demographic and socioeconomic factors on the level of social expenditure was carried out for 28 countries of the European Union.The study began with the selection of variables based on which two regression models will be estimated.The dependent variable (Y) characterizing the level of social spending was total social spending in EUR million / inhabitant.For the set of potential explanatory variables, 14 indicators were selected: payments for social purposes in total EUR million / inhabitant (X1), percentage of active population (X2), people at risk of poverty or social exclusion (X3), life expectancy (X4), birthrate(X5), infant mortality rate (X6), total fertility rate (X7), young-age dependency ratio (population aged 0-14 to population 15-64 years) (X8), old dependency ratio (population 65 and over to population 15-64 years) (X9), structure of households by number of children -1 (X10), structure of households by number of children -2 (X11), structure of households by number of children -3 (X12), structure of households by number of children -4+ (X13), Gini coefficient of equivalised disposable income (X14).
Using the Hellwig parametric method (Hellwig, 1981), variables strongly correlated with other features were eliminated, i.e. variables which are carriers of similar information.This allowed to identify central and satellite variables.As a result, eight features were included in the final set of diagnostic variables: X3, X4, X5, X7, X8, X10, X12, X14.
Next, linear econometric models were estimated, which were developed for 2008 and 2017.Table 1 presents the results of estimation of the econometric models.The symbol "-" means that the parameter wasn't statistically significant.Each model contains only four statistically significant explanatory variables.The coefficient of determination for both models is at the medium level, which is why model matching is sufficient, i.e. the model only explains about 60% of the variability of the dependent variable.
In the next step of the analysis, spatial autocorrelation of errors was examined.For this purpose, Moran I test (Moran, 1950) was used for the residuals of the estimated models.The test results are presented in Table 3.Only in one model (2017) Moran I statistic is positive and statistically significant.This situation indicates the presence of spatial autocorrelation, i.e. no randomness in the distribution of model residues.The value of this statistic for the model estimated on the basis of data from 2008 is not statistically significant, which indicates the lack of spatial autocorrelation.Continuing the model diagnostics, the LM test was used and it was checked which of the models, spatial lag or spatial error would be better.The results of this analysis are included in Table 4.The LMerror tests for the estimated models are irrelevant, so it can be assumed that it is better to use spatial lag models.In addition, table 5 presents the values of information criteria: Akaike (AIC) and logLik.Obtained results allow comparison of the linear model with spatial models (SEM -spatial error model, SLM -spatial lag model).The best model is the one for which the AIC criterion takes the lowest value, while the logLik criterion takes the highest value.The information criteria values for models (2008 and 2017) clearly indicate the spatial lag model.The results of the estimation of the parameters of the suggested spatial model are given in Table 6.To improve the quality of forecasts, you can perform parametric bootstraping for the parameters of the estimated model and on this basis forecast

Conclusion
The study carried out an analysis of the development of the social care system in EU countries in the years 2008-2017, and also examined the spatial relationships between variables affecting the size of social expenditure in these countries.During the study, the spatial dependence of spending on social purposes on the socio-economic environment was proved.Particularly significant turned out to be variables: people at risk of poverty or social exclusion by age and sex, life expectancy, birthrate, young-age dependency ratio, structure of households by number of children -3 and Gini coefficient of equivalised disposable income i.e.Based on the conducted research, it can be seen that the progressing aging process of societies causes changes in the social care system.

Figure 1 .
Figure 1.Expenditure on social purposes in the EU in 2008-2017 (Source: own elaboration)

Figure 2 .
Figure 2. The classification of EU countries due to the value of social expenditures in years: 2008 and 2017 (Source: own elaboration)

Table 1 .
Ranking of EU countries for social spending in years 2008 and 2017

Table 2 .
Estimation results of linear models

Table 3 .
Moran I statistics values for the residuals of the linear model

Table 4 .
Selection of the spatial model

Table 5 .
Information criteria values

Table 6 .
Results of the spatial lag model estimation