NATIONAL AND REGIONAL ECONOMICS VIII
ECONOMETRIC MODEL OF SOCIAL PROTECTION
BENEFITS
Marcel REŠOVSKÝ
Technická Univerzita v Košiciach, Ekonomická fakulta
[email protected]
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 1960-1980 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 1970-1999. 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
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 1993-2008 and all data were
available for the period 1996 – 2007, 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,



gross domestic product in market prices 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,
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.
NATIONAL AND REGIONAL ECONOMICS VIII
Table 1 Data of analyzed variables for the period 1996 – 2006
t
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
SPB
8 135
8 112
7 998
8 447
9 053
8 692
9 341
10 011
10 233
10 286
10 589
10 950
UR
9,6
9,9
8,2
6,7
5,6
4,9
4,9
5,6
6,3
7,4
7,0
6,1
ADR
57,0
56,8
56,6
56,2
55,8
55,3
54,8
54,3
53,8
53,4
52,8
52,3
GDP
24 600
25 200
25 500
27 200
30 000
28 300
29 600
30 800
32 000
32 600
34 500
36 200
FANAB
13,1
12,9
12,7
12,3
12,0
12,4
12,6
12,4
12,2
12,0
12,1
12,2
IR
N/A
1,8
1,0
0,5
1,3
2,7
1,9
2,3
1,0
0,8
1,5
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:
SPBr  SPBt  SPBt 1  / SPBt 1
GDPr  GDPt  GDPt 1  / GDPt 1
(1)
ECONOMETRIC MODEL OF SOCIAL PROTECTION BENEFITS
Table 2 Modified data of analyzed variables for the period 1996 – 2006
t
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
SPBr
0,100
-0,003
-0,014
0,056
0,072
-0,040
0,075
0,072
0,022
0,005
0,029
0,034
UR
9,6
9,9
8,2
6,7
5,6
4,9
4,9
5,6
6,3
7,4
7,0
6,1
ADR
57,0
56,8
56,6
56,2
55,8
55,3
54,8
54,3
53,8
53,4
52,8
52,3
GDPr
0,118
0,024
0,012
0,067
0,103
-0,057
0,046
0,041
0,039
0,019
0,058
0,049
FANAB
13,1
12,9
12,7
12,3
12,0
12,4
12,6
12,4
12,2
12,0
12,1
12,2
IR
N/A
1,8
1,0
0,5
1,3
2,7
1,9
2,3
1,0
0,8
1,5
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.
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   0 + 1UR +  2 ADR +  3GDP +  4 FANAB +  5 IR  ut
(2)
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.
ECONOMETRIC MODEL OF SOCIAL PROTECTION BENEFITS
2.4 Appropriate econometric model
By testing different models we get appropriate econometric model that is:
SPB  - 0,465761 - 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
problem
Test
Distribution of
residuals
J-B test
Null hypothesis
ut ~ N (0,  )
 0  ...   k   0
Alternative
hypothesis
p- value
D-W coefficient
Result of testing
model by selected
condition
ut ~ N (0,  2 )
 i   0
 0
0,573
-
0,802
-
0,447
2,232
satisfies the test
satisfies the test
satisfies the test
2
Heteroscedasticity
Autocorrelation
B-P test
D-W test
 0
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
p-value
0,02835
0,00372
1.25e-05
0,01853
Intercept
UR
GDP
FANAB
Result of testing model
satisfies the test
by selected condition
Source: Own editing
Multicollinearity
(tested by VIF)
value
1,723458
1,079790
1,623128
satisfies the test
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.
ECONOMETRIC MODEL OF SOCIAL PROTECTION BENEFITS
REFERENCES
[1] HATRÁK, M.: Ekonometria, Bratislava: Iura Edition, 2007. 502 p. ISBN
9788080781507.
[2] MAHLER, V.A.: Explaining the growth of social benefits in advanced capitalist
countries, 1960 – 80. Available on: <http://ideas.repec.org/a/pio/envirc/v8y1990
i1p13-28.html>.
[3] SIMÓN SOSVILLA-RIVERO S. – HERCE J.A. – DE LUCIO J.J.: Convergence
in social protection across EU countries, 1970-1999. Available on: <http://ideas.
repec.org/p/fda/fdaddt/2003-01.html>.
[4] Social protection in Sweden 1993-2008:Expenditure for social protection
continues increase. Available on: < http://www.scb.se/Pages/PressRelease
294038.aspx>.
[5] ŢELINSKÝ T.: Porovnanie alternatívnych prístupov k odhadu individuálneho
blahobytu domácností ohrozených rizikom chudoby. Bratislava: Ekonomický
časopis, 3/2010.