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REGRESSION ANALYSIS
Research Question:
Test a hypothesis if finance-led growth hypothesis is confirmed for Japan using an annual
data for the 1960-2012 period (n = 53 years)
Model:
DC 
 M2
lnGDP = f  ln
, ln

GDP 
 GDP
Equation (1)
where,
lnGDP = the natural log of real gross domestic product in Japan (GDP, 2005 = 100)
lnM2 = the natural log of money supply as percent of GDP
lnDC = the natural log of domestic credit provided by banking sector as percent of GDP
In order to test the hypothesis mentioned above, a double logarithmic function will be adapted for
the functional relationship mentioned above:
 M2 
 DC 
ln GDP   0  1  ln
  2 
  t
 GDP 
 GDP 
Equation (2)
You are given the following EVIEWS output for this model:
Correlation Results:
LGDP
1
0.941879501947232
0.9833712628015627
LM2
0.941879501947232
1
0.9487282398692911
LDC
0.9833712628015627
0.9487282398692911
1
Regression Results:
Dependent Variable: lnGDP
Method: Least Squares
Date: 01/09/14 Time: 15:35
Sample: 1960 2003
Included observations: 44
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
lnM2
lnDC
1.443938
0.229074
1.069379
0.527789
0.227242
0.105481
2.735824
1.008063
10.13815
0.0092
0.3193
0.0000
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
0.967817
0.966247
0.108020
0.478400
37.03966
616.4765
0.000000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
8.015673
0.587958
-1.547257
-1.425608
-1.502144
0.572494
White Test Results:
Heteroskedasticity Test: White
F-statistic
Obs*R-squared
Scaled explained SS
3.513351
13.91006
41.92729
Prob. F(5,38)
Prob. Chi-Square(5)
Prob. Chi-Square(5)
0.0104
0.0162
0.0000
Questions:
1. Write the estimated parameters of equation (2). Make economic interpretation of
estimated parameters.
2. What is R2 of the model? Make econometric interpretation.
3. Run t-tests and F-test in order to test the validity of parameters and the overall model
respectively. Write your null and alternative hypotheses clearly and explain your results.
4. Do you observe multicollinearity in the model? Why? Why not?
5. Carry out White Test for heteroskedasticity? Write your null and alternative hypotheses
clearly and explain your results.
6. Carry out Durbin Watson “d” test for autocorrelation. Write your null and alternative
hypotheses clearly and explain your results.
7. Is your model validated in overall?
8. Do you confirm or reject your research question? Explain!
Answers:
1. Write the estimated parameters of equation (2).
 M2 
 DC 
ln GDP  1.443  0.229 ln
  1.069
  t
 GDP 
 GDP 
0 = 1.443 “suggests that if there is no change in the volumes of M2 and DC as percent of GDP
separately from one year to another, then, GDP in Japan will continue to grow (increase) by
1.443 percent.
1 = 0.229 “suggests that if M2 as percent of GDP changes by 1 percent, then, GDP in Japan will
change by 0.229 percent in the same direction (positively inelastic effect since it is less than 1).
2 = 1.069 “suggests that if DC as percent of GDP changes by 1 percent, then, GDP in Japan will
change by 1.069 percent in the same direction (positively elastic effect since it is greater than 1).
2. What is R2 of the model? Make econometric interpretation.
R2 = 0.967 “suggests that 96.7 percent of changes in GDP can be explained by the changes in M2
and DC, while 3.3 percent (1 – 0.967) are explained by the other external factors which are not
included in the model.
3. Run t-tests and F-test in order to test the validity of parameters and the overall model
respectively. Write your null and alternative hypotheses clearly and explain your results.
t-tests for individual parameters:
Intercept:
H0: 0 = 0 (the estimated intercept is not statistically significant)
H1: 0  0 (the estimated intercept is statistically significant)
t-computed value: 2.735
t-critical value (df = n – 2 = 51;  = 0.01) = 2.660
t-critical value (df = n – 2 = 51;  = 0.05) = 2.000
t-critical value (df = n – 2 = 51;  = 0.10) = 1.671
Since t-computed value is greater than t-critical value, we reject H0 and accept H1 that the
estimated intercept is statistically significant at 99 percent confidence interval. We reach the
same conclusion by p-value approach where t-prob value (p = 0.0092) is less than  = 0.01.
Coefficient of M2:
 M2 
H0: 1 = 0 (the estimated coefficient of  ln
 is not statistically significant)
 GDP 
 M2 
H1: 1  0 (the estimated coefficient of  ln
 is statistically significant)
 GDP 
t-computed value: 1.008
t-critical value (df = n – 2 = 51;  = 0.01) = 2.660
t-critical value (df = n – 2 = 51;  = 0.05) = 2.000
t-critical value (df = n – 2 = 51;  = 0.10) = 1.671
Since t-computed value is less than t-critical values at  = 0.01, 0.05, and finally 0.10 levels
 M2 
respectively; therefore, we cannot reject H0; it means the estimated coefficient of  ln
 is
 GDP 
not statistically significant. We reach the same conclusion by p-value approach where t-prob
value (p = 0.3193) is greater than  = 0.01, 0.05, and finally 0.10 levels. This is to conclude that
1 = 0.229 in the model is not statistically valid. We cannot make this inference for M2.
Coefficient of DC:
 DC 
H0: 1 = 0 (the estimated coefficient of  ln
 is not statistically significant)
 GDP 
 DC 
H1: 1  0 (the estimated coefficient of  ln
 is statistically significant)
 GDP 
t-computed value: 10.138
t-critical value (df = n – 2 = 51;  = 0.01) = 2.660
t-critical value (df = n – 2 = 51;  = 0.05) = 2.000
t-critical value (df = n – 2 = 51;  = 0.10) = 1.671
Since t-computed value is greater than t-critical value at  = 0.01 level; therefore, we reject H0
 DC 
and accept H1 that the estimated coefficient of  ln
 is statistically significant at 99 percent
 GDP 
confidence interval. We reach the same conclusion by p-value approach where t-prob value (p =
0.0000) is less than  = 0.01 level. This is to conclude that 2 = 1.069 in the model is statistically
valid.
F-test for the Overall model fit:
H0: 1 = 2 = 0 (The overall model is not statistically significant or not best fitted)
H1: 1  2  0 (The overall model is statistically significant or it is best fitted)
F-computed value: 616.476 (Prob. : 0.000)
Degrees of freedom for F-critical value:
numerator / denominator
= (k-1) / (n-k)
k = the number of parameters including intercept = 3 (intercept, M2, DC)
df for numerator = (3-1) = 2
df for denominator = (53- 2) = 51
F-critical value ( = 0.01, 2, 51): 4.980 (we look to 60 observations since 51 is not available)
F-critical value ( = 0.05, 2, 51): 3.150
F-critical value ( = 0.10, 2, 51): 2.390
Since, F-computed value (616.476) is greater than F-critical value at  = 0.01 (4.980), we reject
H0 and accept H1 that the overall model is statistically significant and the model is best fitted.
Also, F-prob value (0.000) is less than  = 0.01; therefore, we reach the same conclusion. So, our
model is significant at 99 percent confidence level.
4. Do you observe multicollinearity in the model? Why? Why not?
In regression model, we see that DC is not statistically significant, its t value is very low, R2 is
high (0.967), and correlation coefficient between GDP and DC is very high (0.983); therefore,
DC should be definitely significant in the model; but it’s not. Therefore, we conclude that there is
multicollinearity problem in our model. Our model suffers from multicollinearity which should
be solved.
5. Carry out White Test for heteroskedasticity? Write your null and alternative hypotheses
clearly and explain your results.
H0: Distribution of error residuals are HOMOCEDASTIC
H1: Distribution of error residuals are HETEROSCEDASTIC
We run white test for heteroscedasticity. Results are below:
Heteroskedasticity Test: White
F-statistic
Obs*R-squared
Scaled explained SS
3.513351
13.91006
41.92729
Prob. F(5,38)
Prob. Chi-Square(5)
Prob. Chi-Square(5)
0.0104
0.0162
0.0000
We see that chi-square statistic (obs * R2) is 13.910 and its prob value is 0.0162; therefore, we
reject H0 and accept H1 that there is heteroscedasticity problem in the model. So, model results
on the estimated parameters are not valid.
6. Carry out Durbin Watson “d” test for autocorrelation. Write your null and alternative
hypotheses clearly and explain your results.
DW statistic in the model is 0.572 which is very low; and it shows the possibility of
autocorrelation.
Lower critical value from the table is: 1.452 while upper value is 1.681.
H0: There is no positive autocorrelation
H1: There is positive autocorrelation
Please look at autocorrelation decision table in Gujarati’s textbook.
DW (0.572) is lower than DL = 1.452; therefore, we reject H0 and accept H1 that there is positive
autocorrelation in the model. So, our model also suffers from autocorrelation problem; thus, in
addition to heteroscedasticity problem, one more time our model is not valid.
7. Is your model validated in overall?
Since we found that there are multicollinearity, heteroscedasticity, and autocorrelation problems,
our model is not validated overall. We need to fix these problems by alternative approaches.
8. Do you confirm or reject your research question? Explain!
Becuse of the above mentioned problems, we cannot validate our research question; we cannot
validate finance-led growth hypothesis for Japan by using this model estimation. These problems
should be solved firstly, and then, the model should be re-estimated.