The link between economic development and
selected economic indicators in the case of Brazil.
Results and discussion
According to the data, it can be seen that Brazil’s selected economic indicators such as
inflation, interest rate, unemployment, exchange rate, industry, export, FDI inflators
are trending in an upwards direction over the years from 1996 to 2014. Moreover,
country’s standard of living and economic development which is GDP per capita
increased by around $3,000 in 2014.
The variables that represent the economic indicators like inflation, interest rate,
unemployment, exchange rate, industry, export, FDI inflators were selected as an
independent variable, while GDP per capita was taken as a dependent variable in our
model.
Economic indexes give information different aspects of a country’s economic
performance and show how country’s GDP per capita is affected by these indicators.
While according to the World Bank methodology, GDP per capita reflects the level of
economic development of a country. For instance, we can see that Brazil was
considered a low-income country in terms of GDP per capita in 1996. According to
World Bank data, Brazil’s GDP per capita in 1996 was $3,720, which was below the
threshold for upper-middle-income country. However, Brazil’s economy has grown
significantly since then, and is now classified as an upper-middle-income country with
a GDP per capita of $9,183 in 2014.The reason why we chose these economic indexes
is to show how these variable can contribute to the improvement of country’s GDP per
capita.
Before analyzing the independent vaeriables, firstly, it is important to test our GDP per
capita in terms of the Dickey-Fuller test.
Table 1. Results of the Dickey-Fuller test on GDP per capita
. dfuller GDPpercapita
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
0.612
-3.750
=
18
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
MacKinnon approximate p-value for Z(t) = 0.9879
-3.000
-2.630
It is illustrated in the table that there are 18 number of observations. 1%, 5% and 10%
critical values are normal, but test statistic is not lower than critical values. In order to
achieve stationary outcome there is need for integration.
Table 2. Results of the Dickey-Fuller test on GDP per capita
. dfuller d.GDPpercapita
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-4.004
-3.750
=
17
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.000
-2.630
MacKinnon approximate p-value for Z(t) = 0.0014
After making the Dickey-Fuller derivate test, we achieve normal value for test
statistics, which is -4.004 and lower than other critical values. P-value for Z(t) shows
highly stationary data (0.0014). Also, the number of observations has decreased to 17.
Furthermore, since our study is conducted in multi-factor series, the next step in the
criterion of multifactor times series is to examine the variables which are nonstationary in the Dickey-Fuller test and find if they are cointegrated or not. After that,
appropriate model can be selected.
According to the table 3, the Dickey-Fuller test was conducted on the Inflation. The
test statistic value has been found to be -4.463, which is negative and lower than the
three critical values. The critical values for the 1 percent, 5 percent, and 10 percent
levels were -3.750, -3.000 and -2.630, respectively. Since the statistical test value is
lower than all three critical values, it indicates that the data is strongly stationary and
meets the criterion requirement of the Dickey-Fuller test.
Table 3. Results of the Dickey-Fuller test on Inflation
. dfuller Inflation
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-4.463
-3.750
=
18
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
MacKinnon approximate p-value for Z(t) = 0.0002
-3.000
-2.630
This result has been attained when checking for stationary and it showed the data was
already stationary. The result does not need to derived. Additionally, the p-value is
0.0002 which indicates a strong stationary presence with a small value.
In the next step, another variable FDI will be tested in the Dickey-Fuller test.
Table 4. Results of the Dickey-Fuller test on FDI
. dfuller FDI
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-0.828
-3.750
=
18
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.000
-2.630
MacKinnon approximate p-value for Z(t) = 0.8107
.
After getting the result, we discovered that FDI has a value at -0.828 and is lower than
1%, 5% and 10% critical values. This indicates that the data is strongly stationary,
similar to the result obtained for Inflation. P-value is 0.8107 which means that the result
tends to be passed over in silence.
The next step is to examine unemployment according to the Dickey-Fuller test.
Table 5. Results of the Dickey-Fuller test on Unemployment
. dfuller Unemployment
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-0.037
-3.750
=
18
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.000
-2.630
MacKinnon approximate p-value for Z(t) = 0.9554
. dfuller d.Unemployment
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-3.424
-3.750
=
17
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
MacKinnon approximate p-value for Z(t) = 0.0102
-3.000
-2.630
. dfuller d2.Unemployment
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-6.572
-3.750
=
16
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.000
-2.630
MacKinnon approximate p-value for Z(t) = 0.0000
We have to derive this variablwe times, because the test statistic is to be quite higher
than three critical values and after second integration, we got the excellent result which
is -6.572. P-value is 0, meaning that the null hypothesis is rejected and our test is
statistically significant.
Moreover, now we will examine Exchange rate in the Dickey-Fuller test.
Table 6. Results of the Dickey-Fuller test on Exchange rate
. dfuller Exchangerate
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-1.829
-3.750
=
18
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.000
-2.630
MacKinnon approximate p-value for Z(t) = 0.3661
. dfuller d.Exchangerate
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-2.466
-3.750
=
17
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.000
-2.630
MacKinnon approximate p-value for Z(t) = 0.1240
. dfuller d2.Exchangerate
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-5.379
-3.750
=
16
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
MacKinnon approximate p-value for Z(t) = 0.0000
-3.000
-2.630
Accordng to the results of the Dickey-Fuller test for Exchange rate, the statistical test
value is -5.379 and it is smaller than three critical values. This indicates that there is
strong stationary too. This result has been achieved after two integrations. As it can be
seen that p value is smaller than 0.05 and shows a strong stationary.
Besides, we have another independent variable, interest rate to be analyzed.
Table 7. Results of the Dickey-Fuller test on Interest rate.
. dfuller Interestrate
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-1.712
-3.750
=
18
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.000
-2.630
MacKinnon approximate p-value for Z(t) = 0.4249
The result shows that test statistic is -1.712 and 1% critical value is -3.750, 5% critical
value is -3.000, 10% critical is -2.630. It is clear that test statistic is higher rather than
other three other values. Also, p-value is 0.4249 and this means that our result is not
appropriate. Then we will have to do integration of the Dickey-Fuller test.
Table 8. Results of the Dickey-Fuller test on Interest rate.
. dfuller d.Interestrate
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-5.283
-3.750
=
17
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.000
-2.630
MacKinnon approximate p-value for Z(t) = 0.0000
Although the number of observations has shown a decrease by one unit, we have
reached our true result (test statistic is -5.283). Our p-value is 0.0000 indicates strong
stationary with a small value.
As it can be seen from the testing, the variables selected for this observation were
nonstationary, but after integrated one or even two times some variables has become
stationary and the condition of cointegration dependence is satisfied.
Our study’s primary objective is to create a regression and correlation model that
examines the relationship between selected independent variables in respect to GDP
per capita. The next step in achieving this goal is to develop the model.
The factor influencing GDP per capita is expressed in the following regression and
correlation econometric formula:
GDPpercapit 𝑎𝑖 = 𝛽0 + 𝛽1 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝛽2 𝑢𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 + 𝛽3 FDI+ + 𝛽4 exchange
rate+ 𝛽5 interest rate + ��
(1)
As our indicators of the resultant factor in the formation of a simple regression and
correlation econometric model are different, we changed them to a natural logarithm
and bring them to the form of a simple regression and correlation econometric formula.
lnGDPpercapit 𝑎𝑖 = 𝛽0 + 𝛽1 𝑙𝑛𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 + 𝛽2 𝑙𝑛𝑢𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 + 𝛽3 𝑙𝑛 FDI+
+𝛽4 𝑙𝑛exchange rate+ 𝛽5 𝑙𝑛interest rate + ��
(2)
An economic model was created using the “Ordinary least squares method” to perform
simple regression and correlation.
The findings of this analysis are displayed in Table 6.
Table 9. Results of simple regression and correlation analysis
GDPper~a FDIinf~r Intere~e Exchan~e Unempl~t Inflat~n
GDPpercapita
FDIinflator
Interestrate
Exchangerate
Unemployment
Inflation
1.0000
0.8921
-0.6855
0.0628
-0.9374
-0.3344
Source
SS
1.0000
-0.5305
-0.1502
-0.8258
-0.3458
1.0000
-0.4155
0.5561
0.1406
df
1.0000
0.0834
0.1281
MS
Model
Residual
.283248924
.007960216
5
13
.056649785
.000612324
Total
.29120914
18
.016178286
lnGDPpercapita
Coefficient
Std. err.
lnInflation
lnFDIinflator
lnUnemployment
lnExchangerate
Interestrate
_cons
-.0536472
.0134157
-.3040298
.0490052
-.0018247
9.37593
.0197331
.0188467
.0360878
.0253834
.0009604
.5521427
t
-2.72
0.71
-8.42
1.93
-1.90
16.98
1.0000
0.1559
1.0000
Number of obs
F(5, 13)
Prob > F
R-squared
Adj R-squared
Root MSE
P>|t|
0.018
0.489
0.000
0.076
0.080
0.000
=
=
=
=
=
=
19
92.52
0.0000
0.9727
0.9622
.02475
[95% conf. interval]
-.0962779
-.0273
-.3819927
-.0058324
-.0038995
8.183098
-.0110165
.0541315
-.2260669
.1038428
.0002502
10.56876
The table above provides the calculations for the formation of a one-factor regression
model, as follows:
lnGDPpercapit
𝑎𝑖
=
9.38 − 0.054𝑙𝑛𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 − 0.30𝑙𝑛𝑢𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 +
0.13𝑙𝑛FDI+ 0.05𝑙𝑛exchange rate − 0.002𝑙𝑛interest rate + �� (3)
Based on the correlation between the model indicators, it can be inferred that there is a
long-term correlation between them. The regression coefficient of -0.054 indicates that
a 1% change in inflation is associated with a 0.054 decrease in GDP per capita. Also,
1% change in unemployment rate causes a decrease in GDP per capita by 0.3 and 1 %
change in interest rate also negatively affects the GDP per capita by 0.002, there is
almost no effect on GDP per capita. It can be seen that there is a negative relationship
between inflation, unemployment, interest rate and GDP per capita.
However, FDI and exchange rate variables have a positive effect on GDP per capita,
giving 0.13 rise to GDP per capita by 1% change in FDI inflator. Also, 1% change in
exchange rate increases GDP per capita by 0.05.
According to Table 9, there is a high level of correlation between independent variables
(unemployment, FDI, and interestrate) and dependent variable (GDP per capita) in our
model. This means that measuring the coefficient between our some indepent and
dependent variables matched very well. When the adjusted coefficient of determination
is close to -1 or 1, it tells that unemployment, FDI and interest rate, which are
independent variables, are a good predictor of changes in GDP per capita which is our
dependent variable. As a result, we can forecast exact values of GDP per capita based
on changes in independent variables.
The coefficient of determination (R-squared) in the model indicates that 97,27% of the
variation in GDP per capita can be explained by the volume of our five independent
variables, meaning that the model is in a good fit for the data and the volume of
variables is considered to be highly strong predictor of changes in GDP per capita. We
must mention that there are also other factors not taken into account in our model, but
they make contribution to 2.73% of variation in GDP per capita.
Besides, the probability of p-value is equal to 0 and at this point value for the
independent variables in the regression model is less than 0.05% which indicates that
the ratio is a significant predictor of changes in GDP per capita. This suggests that if
unemployment, FDI, exchange rate, inflation and interest rate increase in some points,
GDP per capita will also increase.
Simple regression and correlation analysis are successfully defined and we know how
1% change in independent variables can affect to dependent variable. Now, the next
step is to examine residual model in detail.
Table 10. Residual model.
. dfuller qoldiq
Dickey-Fuller test for unit root
Z(t)
Number of obs
Test
Statistic
1% Critical
Value
-4.247
-3.750
=
18
Interpolated Dickey-Fuller
5% Critical
10% Critical
Value
Value
-3.000
-2.630
MacKinnon approximate p-value for Z(t) = 0.0005
In residual model, we also need the Dickey-Fuller test to define that our data is
stationery or not. The table shows that test statistic is -4.247 and lower than 1%, 5%
and 10% critical values. P-value is 0.005, meaning that data is incredibly statistically
significant.
It is highly mentioned that GDP per Capita indicates how well the economy is doing,
scaled for the population size of a country. The summary of GDP per capita tells about
standard deviation, mean, number of observations and its maximum, and minimum
points.
Table 11. Summary of GDP per capita.
. summ GDPpercapita model
Variable
Obs
Mean
GDPpercapita
model
19
19
7632.006
8.932345
Std. Dev.
Min
Max
989.0721 6551.235 9216.143
.1249531 8.787707 9.168406
As can be seen from the table that there are 19 observations taken in our study. The
mean of GDP per capita is 7632 while model has nearly 9 mean
Additionally, while researching data, errors can appear and our model is not except
from this. To find these errors, we need to use Breusch-Pagan test (or hettest). It is used
to test heteroskedasticity in a linear regression model and assumes that the error terms
are normally distributed. It tests whether the variance of the errors from a regression is
dependent on the values of the independent variables. It is a χ2 test.
Table 12. Breusch-Pagan test.
. hettest
Breusch-Pagan / Cook-Weisberg test for heteroskedasticity
Ho: Constant variance
Variables: fitted values of lnGDPpercapita
chi2(1)
=
Prob > chi2 =
0.21
0.6440
Chi-square is 0.21, greater than 0.05 and it means that the deviations are significant
and the hypothesis being tested must be rejected.
Here, we also make use of Cameron and Trivedi’s tests of heteroscedasticity and
normality.
Table 13. Cameron and Trivedi’s test.
. imtest
Cameron & Trivedi's decomposition of IM-test
Source
chi2
df
p
Heteroskedasticity
Skewness
Kurtosis
14.99
3.50
0.24
14
4
1
0.3788
0.4777
0.6234
Total
18.73
19
0.4741
Based on the result of the test statistic shown in Table 13, p-value is 0.4741.
What’s more, we find autocorrelation in the residuals from a statistical model or
regression analysis. We apply Durbin-Watson statistic test to indentify this correlation.
Table 14. Durbin-Watson statistic test.
. estat dwatson
Durbin-Watson d-statistic( 1, 19) = .0504137