This document presents the results of a model examining the impact of various factors on government expenditure for Eurozone countries from 2002-2013. It finds that approximately 48.89% of changes in government expenditure can be explained by changes in gross debt, inflation rate, investment, and real GDP growth rate. A positive correlation exists between debt and expenditure, while a negative correlation exists between growth rate and expenditure. Tests for heteroskedasticity show that the model exhibits homoskedasticity.

1. Author: Antonia Ficova
Possible title: ESTIMATING THE IMPACT OF PUBLIC FINANCE FOR THE
COUNTRIES OF EUROZONE: EXPENDITURE MODEL
Introduction, - research metodology, research onjectives, goal
Main Body, about: previous research,
Key words – expenditure in context of gross debt, inflation, growth rate – Eurozone
countries
Methodology: by using Eviews – MLS, Scatter Graphs, Heteroskedasticity: The Park
Test, White test
Source of Data: Eurostat (2002-2013)
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4 Expenditure Model
At this section we use method of least squares (MLS) by using economic software Eviews for
examination observed variables (216) since 2002 to 2013 at 95 percent of probability, that
include: General government gross debt (% of GDP); HICP - inflation rate; Investment (% of
GDP), Real GDP growth rate - volume of observed countries of Eurozone. Countries include:
Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Latvia,
Luxembourg, Malta, Netherlands, Portugal, Slovakia, Slovenia, Spain. We examine impact of
variables that were mentioned above on investments (% of GDP).
According to the results from Expenditure Model bellow, N=216, k=4; shows that
coefficient of determination increased in comparisom with previous model; R2=0.488
indicates that 48,89% changes of total general government expenditure in countries of
Eurozone is being explained by changes in variables that were mentioned above, on the other
hand 51.11% could be caused by variables that are not included in this model. Prob (F-
statistic) is 0.000 < 0.01; that means model is high statistically significant (++). For N = 216,
k = 4, and significant level = 5%, the significant Durbin-Waston statistic dL is 1.745 and dU
is 1.803; 4-0.642=3.358, moreover a value toward 4 indicates negative autocorrelation.
Table 6 Expenditure
Dependent Variable: EXPENDITURE
Method: Least Squares
Sample: 1 216
Included observations:216
Variable Coefficient Std. Error t-Statistic Prob.
GROSS DEBT 0.070 0.011 6.000 0.000
INFLATION RATE -0.529 0.166 -3.179 0.001
INVESTMENT OF GDP -0.617 0.348 -1.769 0.078
REAL GDP GROWTH RATE -0.462 0.089 -5.148 0.000
C 45.318 1.639 27.635 0.000
R-squared 0.488 Mean dependent var 45.632
Adjusted R-squared 0.479 S.D. dependent var 6.137
S.E. of regression 4.428 Akaike info criterion 5.837
Sum squared resid 4138.796 Schwarz criterion 5.915
Log likelihood -625.402 F-statistic 50.474
Durbin-Watson stat 0.642 Prob(F-statistic) 0.000

2. Source: Author´s estimation by using Eviews
In this model, as is shown in Table above, we get estimation equation as follows:
Expenditure = β0 + β1*debt - β2*inflation rate - β3*investment - β4*growth rate
Than we get following formula:
Expenditure = 45.318 + 0.070*debt - 0.529*inflation rate - 0.617*investment - 0.462*growth
rate
Relations between variables are illustrated by scatter graphs as follows. Moreover, a
positive correlation is between debt and expenditure, on the other hand is negative correlation
between growth rate and expenditure.
Figure 5-8 Simple Scatter Graph of observed variables in Expenditure Model
Source: Author´s estimation by using Eviews.
* Note: The data is displayed as a collection of points, each having the value of one variable determining the
position on the horizontal axis and the value of the other variable determining the position on the vertical axis. If
the pattern of dots slopes from lower left to upper right, it suggests a positive correlation between the variables
being studied, e. g. debt to expenditure. If the pattern of dots slopes from upper left to lower right, it suggests a
negative correlation, e.g. growth rate to expenditure.

3. 4.1 Testing for heteroskedasticity
4.1.1 The Park Test
At this point, we use Park test for estimating linear regression parameters in the presence of
heteroscedastic error terms. As were mentioned in previous model, first we take formula from
regression analysis (OLS):
Yi = β0 + β1X1i + β2X2i + εi; (6)
Expenditure = β0 + β1*debt - β2*inflation rate - β3*investment - β4*growth rate+ εi.
Second, we collect the residuals ei and get following table the auxiliary regression as follows:
LOG(RESID02^2) = -22.450 - 0.256*LOG(inflation rate) + 0.924* LOG(debt) - 3.194
*LOG(expenditure)+ 6.947*LOG(employment)
Than we formulate hypothesis as follows:
H0: There is homoscedasticity; var(εi)=(σ)2
H1: There is heteroscedasticity; var(εi)=(σi)2
Table 7 Park Test
Dependent Variable: LOG(RESID03^2)
Method: Least Squares
Sample (adjusted): 1 214
Included observations:157 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 3.381 1.495 2.261 0.025
LOG(debt) -0.238 0.284 -0.837 0.403
LOG(inflation rate) -0.603 0.320 -1.883 0.061
LOG(investment) -0.450 0.504 -0.894 0.372
LOG(growth rate) 0.107 0.226 0.474 0.635
R-squared 0.032 Mean dependent var 1.586
Adjusted R-squared 0.006 S.D. dependent var 2.243
S.E. of regression 2.235 Akaike info criterion 4.478
Sum squared resid 759.939 Schwarz criterion 4.575
Log likelihood -346.567 F-statistic 1.262
Durbin-Watson stat 0.855 Prob(F-statistic) 0.287
Source: Author´s estimation by using Eviews.
According to the results from Table above Park test show that t-Statistics (Park-t) is not larger
than 2 of the regressors Xi (the thumb than critical t), therefore we accept H0. The model
confirmed Homoscedasticity.
4.1.2 White test of Expenditure Model
We use this test for estimation of heteroscedasticity of the model. We formulate hypothesis as
follows:
H0: There is homoscedasticity; var(εi)=(σ)2
H1: There is heteroscedasticity; var(εi)=(σi)2
The Lagrange multiplier (LM) test statistic is the product of the R2 value and sample size:

4. LM = n . R2 (7)
In our case LM= 216*0.118= 25.583
Moreover, the squared residuals from the original model serve as a proxy for the variance of
the error term at each observation. We use formula from regression analysis (OLS) and take
White Heteroscedasticity (cross terms) as follows:
Table 8 White Heteroskedasticity Test
F-statistic 1.928 Probability 0.025
Obs*R-squared 25.583 Probability 0.029
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 10/25/14 Time: 18:14
Sample: 1 216
Included observations:216
Variable Coefficient Std. Error t-Statistic Prob.
C -17.771 42.586 -0.417 0.676
GROSS DEBT 0.367 0.604 0.606 0.544
GROSS DEBT^2 -0.002 0.002 -0.876 0.381
GROSS DEBT*INFLATION_RATE -0.104 0.054 -1.908 0.057
GROSS DEBT*INVESTMENT 0.036 0.112 0.329 0.742
GROSS DEBT*GROWTH RATE -0.015 0.023 -0.644 0.520
INFLATION RATE 5.496 7.407 0.741 0.459
INFLATION RATE^2 0.031 0.256 0.124 0.900
INFLATION RATE*INVESTMENT -0.814 1.470 -0.553 0.580
INFLATION RATE*GROWTH RATE -0.339 0.258 -1.312 0.190
INVESTMENT 22.491 17.616 1.276 0.203
INVESTMENT^2 -4.152 2.203 -1.884 0.060
INVESTMENT*GROWTH RATE 0.458 0.781 0.586 0.557
GROWTH RATE -0.771 3.460 -0.222 0.823
GROWTH RATE^2 0.116 0.083 1.396 0.164
R-squared 0.118442 Mean dependent var 19.161
Adjusted R-squared 0.057040 S.D. dependent var 28.284
S.E. of regression 27.46636 Akaike info criterion 9.530
Sum squared resid 151634.6 Schwarz criterion 9.765
Log likelihood -1014.317 F-statistic 1.928
Durbin-Watson stat 1.201186 Prob(F-statistic) 0.025
Source: Author´s estimation by using Eviews.
The test statistic is nR2, where n is the sample size and R2 is the proportion of variation
explained in Table above. Test regression (k is the number of slope coefficients; k=14 in this

5. model). Critical values of the Chi-square; χ2 distribution is calculated as follows:
=@qchisq(0.90,14). We get value of Scalar=29.141 that appears in the lower left of the
EViews screen. Since the nR2 value of 25.58342 is lower than the 10% critical χ2 value of
29.1412, we can accept the null hypothesis, there is homoscedasticity. The probability printed
to the right of the nR2 value in the EViews output for White’s heteroskedasticity test (i.e.,
0.029226<0.05) represents the probability that we would be incorrect if we accepted
alternative hypothesis of heteroskedasticity. Nevertheless, the advantages of presenting
summary descriptive statistics for all variables in a data set in Model of Expenditure are
presented in following Table 9.
Table 9 Descriptive Statistics: Expenditure Model
EXPENDITURE GROSS DEBT
INFLATION
RATE INVESTMENT
GROWTH
RATE
Mean 45.63241 61.15602 2.623148 2.969444 1.637500
Median 45.60000 62.10000 2.400000 3.100000 1.800000
Maximum 65.50000 175.1000 15.30000 5.700000 11.00000
Minimum 33.20000 3.700000 -1.700000 1.000000 -17.70000
Std. Dev. 6.137590 34.44325 1.912656 1.066484 3.847576
Skewness 0.020125 0.453730 2.150160 0.092863 -0.946854
Kurtosis 2.732047 3.178257 13.48162 2.310914 6.627432
Jarque-Bera 0.660769 7.697331 1155.215 4.584002 150.6996
Probability 0.718647 0.021308 0.000000 0.101064 0.000000
Sum 9856.600 13209.70 566.6000 641.4000 353.7000
Sum Sq. Dev. 8099.053 255062.5 786.5243 244.5383 3182.826
Observations 216 216 216 216 216
Source: Author´s estimation by using Eviews