GOVERNMENT
CAPITAL EXPENDITURE ON ADMINISTRATION, SOCIAL & COMMUNITY, ECONOMIC
SERVICES, TRANSFERS
CHAPTER FOUR
DATA ANALYSIS
This study was
carried out based the annual time series data on; Gross Domestic Product (GDP) as
the dependent variable and as a proxy for Economic Growth. This is because
Economic Growth is considered a function of the GDP. Government Capital
Expenditure on Administration (GCEA), Government Capital Expenditure on Social
& Community Services (GCESCS), Government Capital Expenditure on Economic
Services (GCEES) and Government Capital Expenditure on Transfers (GCET) were
used as the explanatory variables and as proxies for Federal Government Capital
Expenditure. In this chapter the researcher presented and analyzed the results
from the estimation of the working model as specified.
4.1 Descriptive Statistics
With
the data for the variables covering the sample period employed for this study,
we begin our analysis by observing the descriptive statistics of each of the
variables, all of which are summarized below:
|
|
LOG(GDP)
|
LOG(GCEA)
|
LOG(GCEES)
|
LOG(GCESCS)
|
LOG(GCET)
|
|
Mean
|
16.62315
|
11.91214
|
12.49111
|
11.19788
|
9.338442
|
|
Median
|
16.73677
|
12.12932
|
12.48762
|
11.27316
|
10.17629
|
|
Maximum
|
17.51790
|
12.66312
|
13.13431
|
11.93278
|
12.49088
|
|
Minimum
|
15.71964
|
10.80476
|
11.49254
|
10.23872
|
0.000000
|
|
Std.
Dev.
|
0.640480
|
0.638507
|
0.523594
|
0.611912
|
3.783153
|
|
Skewness
|
-0.088938
|
-0.620441
|
-0.641946
|
-0.330042
|
-1.680142
|
|
Kurtosis
|
1.645476
|
1.975837
|
2.422351
|
1.803890
|
4.476644
|
|
|
|
|
|
|
|
|
Jarque-Bera
|
1.010953
|
1.402211
|
1.073615
|
1.010962
|
7.297323
|
|
Probability
|
0.603218
|
0.496037
|
0.584612
|
0.603215
|
0.026026
|
|
|
|
|
|
|
|
|
Sum
|
216.1009
|
154.8578
|
162.3844
|
145.5724
|
121.3997
|
|
Sum
Sq. Dev.
|
4.922583
|
4.892297
|
3.289812
|
4.493229
|
171.7469
|
|
|
|
|
|
|
|
|
Observations
|
13
|
13
|
13
|
13
|
13
|
Source: Researcher’s Calculations using Eviews
7
Average
(mean) GDP was more than the mean of all other variables within the period.
Same goes with the median. The measure of dispersion/spread (i.e. standard
deviation) is also highest for GDP, with GCET having the lowest. The data for
all the variables are negatively skewed. However, the distribution of GCET has
the longest tail, indicating that it has more extreme large values than others.
The kurtosis of GCET is highest among all. The probability of the Jarque-Bera
statistic for each of the series is low and leads weak rejection of the null
hypothesis of a normal distribution, further confirming that the skewness and
kurtosis of each of the sample data do not match a normal distribution, and
suggesting that the data series for the variables are not normally distributed.
4.2 Augumented Dickeyfuller Unit Root
Test
The
results from stationary test for all the variables of the study are presented
below (see appendix for full results):
|
Null Hypothesis: D(LOG(GCEA)) has a unit root
|
|
|||
|
Exogenous:
Constant, Linear Trend
|
|
|||
|
Lag
Length: 0 (Automatic - based on SIC, maxlag=2)
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
t-Statistic
|
Prob.*
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Augmented
Dickey-Fuller test statistic
|
-4.648111
|
0.0189
|
||
|
Test
critical values:
|
1% level
|
|
-5.124875
|
|
|
|
5% level
|
|
-3.933364
|
|
|
|
10% level
|
|
-3.420030
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
*MacKinnon
(1996) one-sided p-values.
|
|
|||
Since
the ADF t-statistic (absolute value) is greater than the test critical values of
5% as well as 10% and the p-value is less than 0.05, the researcher rejects the
null hypothesis and concludes that LOG(GCEA) is stationary at first difference
level and at both 5% and 10% level of significance.
|
Null Hypothesis: D(LOG(GCEES),2) has a unit root
|
||||
|
Exogenous:
Constant, Linear Trend
|
|
|||
|
Lag
Length: 1 (Automatic - based on SIC, maxlag=2)
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
t-Statistic
|
Prob.*
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Augmented
Dickey-Fuller test statistic
|
-17.13786
|
0.0001
|
||
|
Test
critical values:
|
1% level
|
|
-5.521860
|
|
|
|
5% level
|
|
-4.107833
|
|
|
|
10% level
|
|
-3.515047
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
*MacKinnon
(1996) one-sided p-values.
|
|
|||
|
|
||||
Since
the ADF t-statistic (absolute value) is greater than the test critical values
for all percentage levels and the p-value is less than 0.05, the researcher
rejects the null hypothesis and concludes that LOG(GCEES) is stationary at 2nd
difference level and at both 1%, 5% and 10% level of significance.
|
Null Hypothesis: D(LOG(GCESCS)) has a unit root
|
||||
|
Exogenous:
Constant, Linear Trend
|
|
|||
|
Lag
Length: 0 (Automatic - based on SIC, maxlag=2)
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
t-Statistic
|
Prob.*
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Augmented
Dickey-Fuller test statistic
|
-6.180769
|
0.0027
|
||
|
Test
critical values:
|
1% level
|
|
-5.124875
|
|
|
|
5% level
|
|
-3.933364
|
|
|
|
10% level
|
|
-3.420030
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
*MacKinnon
(1996) one-sided p-values.
|
|
|||
Since
the ADF t-statistic (absolute value) is greater than the test critical values
for all percentage levels and the p-value is less than 0.05, the researcher
rejects the null hypothesis and concludes that LOG(GCESCS) is stationary at 1st
difference level and at both 1%, 5% and 10% level of significance.
|
Null Hypothesis: LOG(GCET) has a unit root
|
|
|||
|
Exogenous:
Constant, Linear Trend
|
|
|||
|
Lag
Length: 1 (Automatic - based on SIC, maxlag=2)
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
t-Statistic
|
Prob.*
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Augmented
Dickey-Fuller test statistic
|
-7.657553
|
0.0005
|
||
|
Test
critical values:
|
1% level
|
|
-5.124875
|
|
|
|
5% level
|
|
-3.933364
|
|
|
|
10% level
|
|
-3.420030
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
*MacKinnon
(1996) one-sided p-values.
|
|
|||
Since
the ADF t-statistic (absolute value) is greater than the test critical values
for all percentage levels and the p-value is less than 0.05, the researcher
rejects the null hypothesis and concludes that LOG(GCET) is stationary at level
and at both 1%, 5% and 10% level of significance.
|
Null Hypothesis: D(LOG(GDP)) has a unit root
|
|
|||
|
Exogenous:
Constant, Linear Trend
|
|
|||
|
Lag
Length: 0 (Automatic - based on SIC, maxlag=2)
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
t-Statistic
|
Prob.*
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Augmented
Dickey-Fuller test statistic
|
-4.088843
|
0.0405
|
||
|
Test
critical values:
|
1% level
|
|
-5.124875
|
|
|
|
5% level
|
|
-3.933364
|
|
|
|
10% level
|
|
-3.420030
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
*MacKinnon
(1996) one-sided p-values.
|
|
|||
Since
the ADF t-statistic (absolute value) is greater than the test critical values
of 5% as well as 10% and the p-value is less than 0.05, the researcher rejects
the null hypothesis and concludes that LOG(GCEA) is stationary at first
difference level and at both 5% and 10% level of significance.
4.3 Estimation of the Model
The
result from the model estimation using Eviews 7 is presented below:
|
Dependent Variable: LOG(GDP)
|
|
|
||
|
Method: Least Squares
|
|
|
||
|
Date: 12/10/14 Time: 13:55
|
|
|
||
|
Sample: 1 13
|
|
|
|
|
|
Included
observations: 13
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
C
|
5.817319
|
2.386775
|
2.437313
|
0.0407
|
|
LOG(GCEA)
|
0.666456
|
0.278461
|
2.393353
|
0.0436
|
|
LOG(GCEES)
|
0.053479
|
0.332434
|
0.160872
|
0.8762
|
|
LOG(GCESCS)
|
0.188220
|
0.323939
|
0.581037
|
0.5772
|
|
LOG(GCET)
|
0.010792
|
0.016381
|
0.658845
|
0.5285
|
|
|
|
|
|
|
|
|
|
|
|
|
|
R-squared
|
0.825071
|
Mean dependent var
|
16.62315
|
|
|
Adjusted R-squared
|
0.737606
|
S.D. dependent var
|
0.640480
|
|
|
S.E. of regression
|
0.328082
|
Akaike info criterion
|
0.892619
|
|
|
Sum squared resid
|
0.861105
|
Schwarz criterion
|
1.109908
|
|
|
Log likelihood
|
-0.802026
|
Hannan-Quinn criter.
|
0.847957
|
|
|
F-statistic
|
9.433180
|
Durbin-Watson stat
|
0.500317
|
|
|
Prob(F-statistic)
|
0.004027
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Source: Eviews 7.0
4.4
Interpretation of Result
From the regression
result presented 4.3, other factors (affecting GDP) remaining constant, the
researcher deduced as follows:
1.
As
Government Capital Expenditure on Administration (GCEA) increased by, say, N1,
Gross Domestic Product (GDP) on the average increased by about N0.7 (70
kobo).
2.
As
Government Capital Expenditure on Economic Services (GCEES) increased by, say, N1,
Gross Domestic Product (GDP) on the average increased by about N0.05 (5
kobo).
3.
As
Government Capital Expenditure on Social & Community Services (GCESCS) increases
by, say, N1, Gross Domestic Product (GDP) on the average increased by about
N0.19 (19 kobo).
4.
As
Government Capital Expenditure on Transfers (GCET) increased by, say, N1,
Gross Domestic Product (GDP) on the average increased by about N0.01 (1
kobo).
4.3 EVALUATION OF RESULT
Evaluation and
test of hypothesis as regards estimated parameters consists of ascertaining
whether the estimated parameters are theoretically meaningful and statistically
satisfactory. We shall evaluate the parameters using economic a priori
criterion and some key statistics from the result the model estimation.
1. Economic A
Priori Criterion
Economic theory
imposes a restriction on the signs and magnitudes of economic relationships. In
view of this, the coefficients of the explanatory variables in the estimated
model presented in 4.3 all conform to the a priori expectations as analyzed
below:
Table 4.1: Evaluation Based on a priori Criterion
|
Variable
|
Parameter
estimate
|
Expected Sign
|
Remark
|
|
C
|
b0 = 5.817319
|
+
|
Conforms
|
|
GCEA
|
b1 = 0.666456
|
+
|
Conforms
|
|
GCEES
|
b2 = 0.053479
|
+
|
Conforms
|
|
GCESCS
|
b3 = 0.188220
|
+
|
Conforms
|
|
GCET
|
b4 = 0.010792
|
+
|
Conforms
|
From the
analysis in table 4.1, it can be observed that all the variables of the model
in this study, met the a priori expectations with respect to size and magnitude
of their coefficients/parameter estimates.
2.
Coefficient of Determination R2
Being a measure
of goodness of fit, an R2 of
0.825071 (82 percent) as
in the estimated model presented in 4.1, shows that the regression line fits
the data well. Also GDP is highly responsive to the changes in the explanatory
variables in the model.
3.
The t-statistic/Test of Hypotheses
Hypothesis
One: H0: Government
Capital Expenditure on Administration (GCEA) has not impacted significantly on
Nigeria’s Economic Growth.
Decision:
From the regression result presented
in section 4.3, the low probability of the critical value of 0.0436 (which is lower than
the corresponding t-statistic 2.393353) indicates the significance of the null hypothesis.
Thus, the researcher rejects the null hypothesis at 5% level of significance,
and concludes that Government Capital Expenditure on Administration (GCEA) has
impacted significantly on Nigeria’s Economic Growth. Hence the observed impact
as indicated by the parameter estimate of GCEA is statistically significant. Hypothesis
Two: H0: As Government Capital Expenditure on Economic Services
(GCEES) has not impacted significantly on Nigeria’s Economic Growth.
Decision: The high
probability of the critical value of 0.8762 which is higher than the absolute
value of the t-statistics (0.160872) indicates the acceptance of the null
hypothesis. The researcher as such accepts the Ho at 5% significance level and
concludes that Government Capital Expenditure on Economic Services (GCEES) have
not impacted significantly on Nigeria’s Economic Growth. The observed positive
impact as indicated by the parameter estimate of GCEES in the estimated model
is therefore proved to be statistically significant. There is therefore need to
beef up the GCEES and as well as ensure an implementation system that would
translate to a significant impact on the economic growth of Nigeria. This is
because economic services/activities are the major driver of economic growth in
any economy.
Hypothesis
Three: H0:
Government Capital Expenditure on Social & Community Services (GCESCS) has not
impacted significantly on Nigeria’s Economic Growth.
Decision: The regression result presented in 4.3 above indicates the
probability of the critical value as 0.5772 which is lower
than the absolute value of t-statistics (0.581037). This is
indicative of the rejection of the null hypothesis. Thus the researcher as such
rejects the Ho at 5% significance level and concludes that GCESCS has impacted
significantly on Nigeria’s Economic Growth. This also indicates that the
observed impact as indicated by the parameter estimate of GCESCS as seen in the
result of the estimated model (in 4.1) is statistically significant.
Hypothesis Four:
H0:
Government Capital Expenditure on Transfers (GCET) has not impacted
significantly on Nigeria’s Economic Growth.
Decision: The regression result presented in 4.3 above indicates the
probability of the critical value as 0.5285 which is lower
than the absolute value of t-statistics (0.581037). This is
indicative of the rejection of the null hypothesis. Thus the researcher as such
rejects the Ho at 5% significance level and concludes that Government Capital
Expenditure on Transfers (GCET) has impacted significantly on Nigeria’s
Economic Growth. This also indicates that the observed impact as indicated by
the parameter estimate of GCET as seen in the result of the estimated model (in
4.1) is statistically significant.
4.
Durbin Watson
Test Statistic
Durbin Watson
statistic is used to test for the presence of autocorrelation with the
following decision rule: if D.W < dl (lower limit), it implies there is an
evidence of positive first order serial correlation (autocorrelation). But if
D.W > du (upper limit), there is no evidence of positive first-order serial
correlation. However, if dl<DW<du, there is inconclusiveness regarding
the presence or absence of autocorrelation.
At 5 percent level
of significance; where n = 13, k’ = 4, dl = 0.4991 and du = 1.126. Also, observed
D.W for the estimated model is 0.500317. Since dl > DW < du (i.e 0.4991>0.500317< 1.126), the
researcher therefore concludes that there is inconclusiveness regarding the
presence or absence of autocorrelation.
APPENDIX
DATA
FOR ANALYSIS
|
Year
|
GDP
|
GCEA
|
GCEES
|
GCESCS
|
GCET
|
|
2000
|
6,713,574.84
|
53,279.5
|
111,508.6
|
27,965.2
|
46,697.6
|
|
2001
|
6,895,198.33
|
49,254.9
|
259,757.8
|
53,336.0
|
76,347.8
|
|
2002
|
7,795,758.35
|
73,577.4
|
215,333.4
|
32,467.3
|
0.0
|
|
2003
|
9,913,518.19
|
87,958.9
|
97,982.1
|
55,736.0
|
11.3
|
|
2004
|
11,411,066.91
|
137,765.9
|
167,721.8
|
30,032.5
|
15,729.8
|
|
2005
|
14,610,881.45
|
171,574.1
|
265,034.7
|
71,361.2
|
11,500.0
|
|
2006
|
18,564,594.73
|
185,224.3
|
262,207.3
|
78,681.3
|
26,272.9
|
|
2007
|
20,657,317.67
|
226,974.4
|
358,375.6
|
150,895.2
|
23,036.0
|
|
2008
|
24,296,329.29
|
287,103.6
|
504,286.9
|
152,174.6
|
17,325.0
|
|
2009
|
24,794,238.66
|
315,880.0
|
506,010.0
|
120,710.0
|
210,200.0
|
|
2010
|
33,984,754.13
|
264,554.2
|
412,245.2
|
147,409.5
|
59,661.1
|
|
2011
|
37,409,860.61
|
232,600.0
|
386,500.0
|
91,900.0
|
207,500.0
|
|
2012
1
|
40,544,099.94
|
190,500.0
|
321,000.0
|
97,400.0
|
265,900.0
|
Source:
CBN Statistical Bulletin, CBN Annual Report and Financial Statements
RESULT
OF THE ESTIMATED REGRESSION MODEL
|
Dependent Variable:
LOG(GDP)
|
|
|
||
|
Method: Least Squares
|
|
|
||
|
Date: 12/10/14 Time: 13:55
|
|
|
||
|
Sample: 1 13
|
|
|
|
|
|
Included
observations: 13
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
Variable
|
Coefficient
|
Std. Error
|
t-Statistic
|
Prob.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
C
|
5.817319
|
2.386775
|
2.437313
|
0.0407
|
|
LOG(GCEA)
|
0.666456
|
0.278461
|
2.393353
|
0.0436
|
|
LOG(GCEES)
|
0.053479
|
0.332434
|
0.160872
|
0.8762
|
|
LOG(GCESCS)
|
0.188220
|
0.323939
|
0.581037
|
0.5772
|
|
LOG(GCET)
|
0.010792
|
0.016381
|
0.658845
|
0.5285
|
|
|
|
|
|
|
|
|
|
|
|
|
|
R-squared
|
0.825071
|
Mean dependent var
|
16.62315
|
|
|
Adjusted R-squared
|
0.737606
|
S.D. dependent var
|
0.640480
|
|
|
S.E. of regression
|
0.328082
|
Akaike info criterion
|
0.892619
|
|
|
Sum squared resid
|
0.861105
|
Schwarz criterion
|
1.109908
|
|
|
Log likelihood
|
-0.802026
|
Hannan-Quinn criter.
|
0.847957
|
|
|
F-statistic
|
9.433180
|
Durbin-Watson stat
|
0.500317
|
|
|
Prob(F-statistic)
|
0.004027
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
UNIT
ROOT TEST
LOG(GCEA)
@ 1st dif
|
Null
Hypothesis: D(LOG(GCEA)) has a unit root
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Exogenous:
Constant, Linear Trend
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Lag
Length: 0 (Automatic - based on SIC, maxlag=2)
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||||
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t-Statistic
|
Prob.*
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Augmented
Dickey-Fuller test statistic
|
-4.648111
|
0.0189
|
||
|
Test
critical values:
|
1% level
|
|
-5.124875
|
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|
5% level
|
|
-3.933364
|
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|
10% level
|
|
-3.420030
|
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*MacKinnon
(1996) one-sided p-values.
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Augmented
Dickey-Fuller Test Equation
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|||
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Dependent
Variable: D(LOG(GCEA),2)
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Method:
Least Squares
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Date:
12/16/14 Time: 05:17
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Sample
(adjusted): 3 13
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Included
observations: 11 after adjustments
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|||
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Variable
|
Coefficient
|
Std.
Error
|
t-Statistic
|
Prob.
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D(LOG(GCEA(-1)))
|
-1.038310
|
0.223383
|
-4.648111
|
0.0016
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|
C
|
0.530681
|
0.119255
|
4.449956
|
0.0021
|
|
@TREND(1)
|
-0.057512
|
0.013649
|
-4.213572
|
0.0029
|
|
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R-squared
|
0.768977
|
Mean dependent var
|
-0.011011
|
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|
Adjusted
R-squared
|
0.711221
|
S.D. dependent var
|
0.232999
|
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|
S.E.
of regression
|
0.125209
|
Akaike info criterion
|
-1.090657
|
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|
Sum
squared resid
|
0.125419
|
Schwarz criterion
|
-0.982140
|
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Log
likelihood
|
8.998615
|
Hannan-Quinn criter.
|
-1.159062
|
|
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F-statistic
|
13.31431
|
Durbin-Watson stat
|
2.102071
|
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Prob(F-statistic)
|
0.002849
|
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LOG(GCEES)
@ 2nd dif
|
Null
Hypothesis: D(LOG(GCEES),2) has a unit root
|
||||
|
Exogenous:
Constant, Linear Trend
|
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Lag
Length: 1 (Automatic - based on SIC, maxlag=2)
|
||||
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t-Statistic
|
Prob.*
|
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|
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Augmented
Dickey-Fuller test statistic
|
-17.13786
|
0.0001
|
||
|
Test
critical values:
|
1% level
|
|
-5.521860
|
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|
5% level
|
|
-4.107833
|
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|
10% level
|
|
-3.515047
|
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|
*MacKinnon
(1996) one-sided p-values.
|
|
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|
||||
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|
||||
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|
Augmented
Dickey-Fuller Test Equation
|
|
|||
|
Dependent
Variable: D(LOG(GCEES),3)
|
|
|||
|
Method:
Least Squares
|
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|
||
|
Date:
12/16/14 Time: 05:27
|
|
|
||
|
Sample
(adjusted): 5 13
|
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|
||
|
Included
observations: 9 after adjustments
|
|
|||
|
|
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|
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|
Variable
|
Coefficient
|
Std.
Error
|
t-Statistic
|
Prob.
|
|
|
|
|
|
|
|
|
|
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|
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|
D(LOG(GCEES(-1)),2)
|
-2.090403
|
0.121976
|
-17.13786
|
0.0000
|
|
D(LOG(GCEES(-1)),3)
|
0.581303
|
0.075978
|
7.650951
|
0.0006
|
|
C
|
0.673489
|
0.156876
|
4.293115
|
0.0078
|
|
@TREND(1)
|
-0.083441
|
0.018526
|
-4.504087
|
0.0064
|
|
|
|
|
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|
|
|
|
|
|
|
|
R-squared
|
0.985452
|
Mean dependent var
|
0.053182
|
|
|
Adjusted
R-squared
|
0.976723
|
S.D. dependent var
|
0.925912
|
|
|
S.E.
of regression
|
0.141263
|
Akaike info criterion
|
-0.775278
|
|
|
Sum
squared resid
|
0.099777
|
Schwarz criterion
|
-0.687622
|
|
|
Log
likelihood
|
7.488750
|
Hannan-Quinn criter.
|
-0.964438
|
|
|
F-statistic
|
112.8973
|
Durbin-Watson stat
|
1.470436
|
|
|
Prob(F-statistic)
|
0.000052
|
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|
LOG(GCESCS)
@ 1st dif
|
Null
Hypothesis: D(LOG(GCESCS)) has a unit root
|
||||
|
Exogenous:
Constant, Linear Trend
|
|
|||
|
Lag
Length: 0 (Automatic - based on SIC, maxlag=2)
|
||||
|
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|
|
|
|
t-Statistic
|
Prob.*
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Augmented
Dickey-Fuller test statistic
|
-6.180769
|
0.0027
|
||
|
Test
critical values:
|
1% level
|
|
-5.124875
|
|
|
|
5% level
|
|
-3.933364
|
|
|
|
10% level
|
|
-3.420030
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
*MacKinnon
(1996) one-sided p-values.
|
|
|||
|
|
||||
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Augmented
Dickey-Fuller Test Equation
|
|
|||
|
Dependent
Variable: D(LOG(GCESCS),2)
|
|
|||
|
Method:
Least Squares
|
|
|
||
|
Date:
12/16/14 Time: 05:29
|
|
|
||
|
Sample
(adjusted): 3 13
|
|
|
||
|
Included
observations: 11 after adjustments
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
Variable
|
Coefficient
|
Std.
Error
|
t-Statistic
|
Prob.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
D(LOG(GCESCS(-1)))
|
-1.618245
|
0.261819
|
-6.180769
|
0.0003
|
|
C
|
0.352756
|
0.321394
|
1.097580
|
0.3043
|
|
@TREND(1)
|
-0.033020
|
0.041084
|
-0.803730
|
0.4448
|
|
|
|
|
|
|
|
|
|
|
|
|
|
R-squared
|
0.828550
|
Mean dependent var
|
-0.053411
|
|
|
Adjusted
R-squared
|
0.785688
|
S.D. dependent var
|
0.904356
|
|
|
S.E.
of regression
|
0.418661
|
Akaike info criterion
|
1.323493
|
|
|
Sum
squared resid
|
1.402220
|
Schwarz criterion
|
1.432010
|
|
|
Log
likelihood
|
-4.279210
|
Hannan-Quinn criter.
|
1.255088
|
|
|
F-statistic
|
19.33044
|
Durbin-Watson stat
|
1.248972
|
|
|
Prob(F-statistic)
|
0.000864
|
|
|
|
|
|
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|
LOG(GCET)
@level
|
Null
Hypothesis: LOG(GCET) has a unit root
|
|
|||
|
Exogenous:
Constant, Linear Trend
|
|
|||
|
Lag
Length: 1 (Automatic - based on SIC, maxlag=2)
|
||||
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
t-Statistic
|
Prob.*
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Augmented
Dickey-Fuller test statistic
|
-7.657553
|
0.0005
|
||
|
Test
critical values:
|
1% level
|
|
-5.124875
|
|
|
|
5% level
|
|
-3.933364
|
|
|
|
10% level
|
|
-3.420030
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
*MacKinnon
(1996) one-sided p-values.
|
|
|||
|
|
||||
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
Augmented
Dickey-Fuller Test Equation
|
|
|||
|
Dependent
Variable: D(LOG(GCET))
|
|
|||
|
Method:
Least Squares
|
|
|
||
|
Date:
12/16/14 Time: 05:33
|
|
|
||
|
Sample
(adjusted): 3 13
|
|
|
||
|
Included
observations: 11 after adjustments
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
|
|
Variable
|
Coefficient
|
Std.
Error
|
t-Statistic
|
Prob.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
LOG(GCET(-1))
|
-1.561499
|
0.203916
|
-7.657553
|
0.0001
|
|
D(LOG(GCET(-1)))
|
0.502582
|
0.149488
|
3.362020
|
0.0121
|
|
C
|
5.001276
|
1.549317
|
3.228051
|
0.0145
|
|
@TREND(1)
|
1.282558
|
0.203420
|
6.304973
|
0.0004
|
|
|
|
|
|
|
|
|
|
|
|
|
|
R-squared
|
0.901273
|
Mean dependent var
|
0.113438
|
|
|
Adjusted
R-squared
|
0.858961
|
S.D. dependent var
|
4.414185
|
|
|
S.E.
of regression
|
1.657752
|
Akaike info criterion
|
4.124090
|
|
|
Sum
squared resid
|
19.23699
|
Schwarz criterion
|
4.268779
|
|
|
Log
likelihood
|
-18.68249
|
Hannan-Quinn criter.
|
4.032883
|
|
|
F-statistic
|
21.30086
|
Durbin-Watson stat
|
1.350074
|
|
|
Prob(F-statistic)
|
0.000676
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
LOG(GDP)
@ 1st dif
|
Null
Hypothesis: D(LOG(GDP)) has a unit root
|
|
||||||
|
Exogenous:
Constant, Linear Trend
|
|
||||||
|
Lag
Length: 0 (Automatic - based on SIC, maxlag=2)
|
|||||||
|
|
|
|
|
|
|||
|
|
|
|
|
|
|||
|
|
|
|
t-Statistic
|
Prob.*
|
|||
|
|
|
|
|
|
|||
|
|
|
|
|
|
|||
|
Augmented
Dickey-Fuller test statistic
|
-4.088843
|
0.0405
|
|||||
|
Test
critical values:
|
1% level
|
|
-5.124875
|
|
|||
|
|
5% level
|
|
-3.933364
|
|
|||
|
|
10% level
|
|
-3.420030
|
|
|||
|
|
|
|
|
|
|||
|
|
|
|
|
|
|||
|
*MacKinnon
(1996) one-sided p-values.
|
|
||||||
|
|
|||||||
|
|
|||||||
|
|
|
|
|||||
|
|
|
|
|||||
|
Augmented
Dickey-Fuller Test Equation
|
|
||||||
|
Dependent
Variable: D(LOG(GDP),2)
|
|
||||||
|
Method:
Least Squares
|
|
|
|||||
|
Date:
12/16/14 Time: 05:34
|
|
|
|||||
|
Sample
(adjusted): 3 13
|
|
|
|||||
|
Included
observations: 11 after adjustments
|
|
||||||
|
|
|
|
|
|
|||
|
|
|
|
|
|
|||
|
Variable
|
Coefficient
|
Std.
Error
|
t-Statistic
|
Prob.
|
|||
|
|
|
|
|
|
|||
|
|
|
|
|
|
|||
|
D(LOG(GDP(-1)))
|
-1.256857
|
0.307387
|
-4.088843
|
0.0035
|
|||
|
C
|
0.245933
|
0.078712
|
3.124447
|
0.0141
|
|||
|
@TREND(1)
|
-0.006396
|
0.008807
|
-0.726171
|
0.4884
|
|||
|
|
|
|
|
|
|||
|
|
|
|
|
|
|||
|
R-squared
|
0.694185
|
Mean dependent var
|
0.004887
|
||||
|
Adjusted
R-squared
|
0.617731
|
S.D. dependent var
|
0.148427
|
||||
|
S.E.
of regression
|
0.091769
|
Akaike info criterion
|
-1.712076
|
||||
|
Sum
squared resid
|
0.067373
|
Schwarz criterion
|
-1.603559
|
||||
|
Log
likelihood
|
12.41642
|
Hannan-Quinn criter.
|
-1.780480
|
||||
|
F-statistic
|
9.079789
|
Durbin-Watson stat
|
2.368791
|
||||
|
Prob(F-statistic)
|
0.008747
|
|
|
|
|||
|
|
|
|
|
|
|||
|
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|
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