ECONOMETRIC MODEL OF SOCIAL PROTECTION BENEFITS

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1 NATIONAL AND REGIONAL ECONOMICS VIII ECONOMETRIC MODEL OF SOCIAL PROTECTION BENEFITS Marcel REŠOVSKÝ Technická Univerzita v Košiciach, Ekonomická fakulta resovsky.marcel@gmail.com Abstract The aim of this work is to suggest appropriate econometric model for the social protection benefits based on data from specific country. There is the definition of social protection benefits and opinions of two authors on this field of research. In the second part there is the description of data, suggested econometric model, interpretation of appropriate econometric model and interval prediction for next period based on the econometric model. Keywords: social protection benefits, econometric model 1 INTRODUCTION Social protection benefits can be defined as all services from public or private organizations with the purpose of reducing the burden on households and individuals from specially defined risks or to meet specially defined needs. We recommend that these services do not require a return of services and that they are not based on individual arrangements. The benefits may be either in cash or in kind. [4] Social protection benefits have been influenced by many economic, political and demographic factors in last decades. Mahler [2] has made the empirical analysis of social protection benefits by means of regression analysis in 17 countries of OECD in the period and has studied the most powerful factors of it. The most important determinant by which have been social protection benefits affected in this period were expenditures on elderly. Statistically significant determinants have been also unemployment rate, inflation and foreign trade. Sosvilla-rivero et al. [3] have examined the degree of convergence in social protection in 12 member countries of EU during the period The tests that have been made on time-series data of social protection benefits do not show the strong convergence between social protection benefits and GDP, that can help to predict volume of social protection benefits in the future by the development of GDP. But Sosvilla-Rivero et al. [3] claim that data from Germany and data from EU as a whole

2 ECONOMETRIC MODEL OF SOCIAL PROTECTION BENEFITS indicate weak relationship or that social protection benefits follow the development of GDP. 2 ECONOMETRIC MODEL SUGGESTION 2.1 Data definition, analysis and modifying We suggest following econometric model: social protection benefits (SPB) as dependent variable, unemployment rate (UR), age dependence ratio (ADR), gross domestic product (GDP), food and non-alcoholic beverages (FANAB), inflation rate (IR) as independent variables. We have decided to examine this econometric model on data of Sweden because of obvious reasons. One reason is as study of Statistics Sweden [4] claims that compared to other European countries that present data of social protection, Sweden had among EU countries the highest social protection expenditure in relation to GDP during the whole period and all data were available for the period , which we wanted to analyze. We have downloaded annual data of all variables from website of Eurostat in following units: social protection benefits expressed in euro per inhabitant, unemployment rate annual average, age dependence ratio population aged 0-14 and 65 and more to population aged 15-64, gross domestic product in market prices expressed in euro per inhabitant, food and nonalcoholic beverages as percentage of total consumption, inflation rate measured by HICP and expressed in annual rate of change. Complete data in mentioned units are presented in the Table 1.

3 NATIONAL AND REGIONAL ECONOMICS VIII Table 1 Data of analyzed variables for the period t SPB UR ADR GDP FANAB IR ,6 57, ,1 N/A ,9 56, ,9 1, ,2 56, ,7 1, ,7 56, ,3 0, ,6 55, ,0 1, ,9 55, ,4 2, ,9 54, ,6 1, ,6 54, ,4 2, ,3 53, ,2 1, ,4 53, ,0 0, ,0 52, ,1 1, ,1 52, ,2 1,7 Source: EUROSTAT When we look on the data presented in the Table 1, it is possible to identify some trends in development of variables during the analyzed period. For example age dependence ratio was permanently decreasing every year, while social protection benefits except 1997, 1998 and 2001 and GDP except 2001 were permanently rising. Unemployment rate was decreasing until 2002 and then this trend changed. Data from Eurostat in form presented in Table 1 may cause some problems in process of testing. Four of six variables are expressed in annual rate of change or as a percentage of total and two are expressed in total. Therefore we have modified social protection benefits and GDP from total to annual rate of change, which are in Table 2 and we calculate them as: SPB r SPB 1 / t SPB t SPB t1 GDP 1 / t GDPt GDPt 1 GDP (1) r

4 ECONOMETRIC MODEL OF SOCIAL PROTECTION BENEFITS Table 2 Modified data of analyzed variables for the period t SPBr UR ADR GDPr FANAB IR ,100 9,6 57,0 0,118 13,1 N/A ,003 9,9 56,8 0,024 12,9 1, ,014 8,2 56,6 0,012 12,7 1, ,056 6,7 56,2 0,067 12,3 0, ,072 5,6 55,8 0,103 12,0 1, ,040 4,9 55,3-0,057 12,4 2, ,075 4,9 54,8 0,046 12,6 1, ,072 5,6 54,3 0,041 12,4 2, ,022 6,3 53,8 0,039 12,2 1, ,005 7,4 53,4 0,019 12,0 0, ,029 7,0 52,8 0,058 12,1 1, ,034 6,1 52,3 0,049 12,2 1,7 Source: Own editing based on data by EUROSTAT 2.2 Graphical analysis of selected variables The time series development of the dependent and independent variables are given in Figure 1. Here, we can affirm the negative relationship between social protection benefits and unemployment rate, positive relationship between social protection benefits and GDP. Social protection benefits have also positive relationship with food and non-alcoholic beverages. Based on Figure 1 we assume that the most important variables determining the development of social protection benefits in Sweden during the analyzed period are the unemployment rate and GDP.

5 NATIONAL AND REGIONAL ECONOMICS VIII Figure 1 Relationship between analyzed variables Source: Own editing based on data by EUROSTAT 2.3 Methodology of econometric model testing Our assumption is that we have following econometric equation: SPB UR + ADR + GDP+ FANAB IR (2) u t The aim of this part is to verify suggested econometric model. We test statistical significance of regression coefficients. Then we test this model by Jarque-Bera test to verify assumption that distribution of residuals is normal, by Breusch-Pagan test we verify presence of heteroscedasticity, by Durbin-Watson test we test presence of autocorrelation. Then we verify presence of multicollinearity by VIF (Variance inflation factor) and test model as a whole by Ramsey-reset test. At the end we make an interval prediction for the development of dependent variable (Social protection benefits) for the next period by appropriate econometric model.

6 ECONOMETRIC MODEL OF SOCIAL PROTECTION BENEFITS 2.4 Appropriate econometric model By testing different models we get appropriate econometric model that is: SPB - 0, ,013273UR + 0,920690GDP + 0,044395FANAB (3) This model satisfies all econometric conditions on significance level α=0,05. Results of testing distribution of residuals, heteroscedasticity and autocorrelation of appropriate econometric model are in Table 3. Table 3 Testing of econometric model Econometric Distribution of Heteroscedasticity Autocorrelation problem residuals Test J-B test B-P test D-W test Null hypothesis 2 u t ~ N(0, ) k Alternative 2 u ~ N(0, ) hypothesis t i 0 0 p- value 0,573 0,802 0,447 D-W coefficient - - 2,232 Result of testing model by selected condition satisfies the test satisfies the test satisfies the test Source: Own editing Results of testing statistical significance of coefficients and multicollinearity are given in Table 4. Model again satisfies all tests. The coefficients are statistical significant and there is no multicollinearity in model. Table 4 Testing of econometric model Econometric problem Significance of coefficients Multicollinearity (tested by VIF) p-value value Intercept 0, UR 0, , GDP 1.25e-05 1, FANAB 0, , Result of testing model by selected condition satisfies the test satisfies the test Source: Own editing

7 NATIONAL AND REGIONAL ECONOMICS VIII 2.5 Interpretation and interval prediction of the model As we assumed in graphical analysis, social protection benefits in Sweden depend on unemployment rate and GDP. From this model we deduce interpretation: growth of GDP annual rate of change by 1 unit influences the growth of social protection benefits annual rate of change by 0,921 units. Growth of unemployment rate influences the growth of social protection benefits negatively. If unemployment rate increases by 1 unit, social protection benefits rate of change will decrease by 0,013 units in such case. Growth of GDP makes a space for growth of benefits that are provided by the government, but government holds some reserve for unexpected problems, so the growth of benefits is lower than growth of GDP. Unemployment rate has opposite influence to growth of benefits, but this influence is not as strong as the one of GDP. More unemployed people in economy bring fewer amount of taxes and other revenues into state budget and also need and take additional benefits from budget. So the growth of unemployment rate effect on decreasing amount of benefits. Very interesting is also that social protection benefits as dependent variable depend on food and non-alcoholic beverages as independent variable. If we had opposite relationship, it would be clear. The explanation of that would be following: social protection benefits are primary addressed to people with weaker social and economic situation, so those people spend their money mainly for food. But also relationship induced by our econometric model has some justification. By this relationship government can adjust adequate amount of social protection benefits that will be used primary for basic needs (for example food). Prediction of this model using real data of independent variables for 2008 claims that the most probable scenario for next period (2008) is the decrease in annual rate of change of social protection benefits by 0,015 units. Growth of social protection benefits rate of change should not be more than 0,021 units and decrease of social protection benefits rate of change should not be more than 0,052 units. 3 CONCLUSION Approximately 80 million people live on the threshold of poverty in Europe. Social protection benefits are one of government instruments by which government distributes its revenues between social and economic weaker citizens. It is important to suggest appropriate indicators to measure efficiency of this instrument. But the most important is to address adequate amount of benefits to those citizens. Econometric model can help to analyze the factors with those are social protection benefits in relationship and which should determine the amount of benefits for existing period.

8 ECONOMETRIC MODEL OF SOCIAL PROTECTION BENEFITS REFERENCES [1] HATRÁK, M.: Ekonometria, Bratislava: Iura Edition, p. ISBN [2] MAHLER, V.A.: Explaining the growth of social benefits in advanced capitalist countries, Available on: < i1p13-28.html>. [3] SIMÓN SOSVILLA-RIVERO S. HERCE J.A. DE LUCIO J.J.: Convergence in social protection across EU countries, Available on: < repec.org/p/fda/fdaddt/ html>. [4] Social protection in Sweden :Expenditure for social protection continues increase. Available on: < aspx>. [5] ŢELINSKÝ T.: Porovnanie alternatívnych prístupov k odhadu individuálneho blahobytu domácností ohrozených rizikom chudoby. Bratislava: Ekonomický časopis, 3/2010.