Springer Texts in Business and Economics
The backup regressions are given below
a. OLS regression of consumption on a constant and Income using EViews Dependent Variable: Consumption Method: Least Squares
Sample: 1959 2007 Included observations: 49
b. The Breusch-Godfrey Serial Correlation LM Test for serial correlation of the first order is obtained below using EViews. An F-statistic as well as the LM statistic which is computed as T* R-squared are reported, both of which are significant. The back up regression is also shown below these statistics. This regression runs the OLS residuals on their lagged values and the regressors in the original model. We cannot reject first order serial correlation.
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 168.9023 Prob. F(1,46) 0.0000
Obs*R-squared 38.51151 Prob. Chi-Square(1) 0.0000
Test Equation:
Dependent Variable: RESID Method: Least Squares
Sample: 1959 2007 Included observations: 49
Presample missing value lagged residuals set to zero.
|
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
|
C |
-54.41017 |
102.7650 |
-0.529462 |
0.5990 |
|
Y |
0.003590 |
0.005335 |
0.673044 |
0.5043 |
|
RESID(-1) |
0.909272 |
0.069964 |
12.99624 |
0.0000 |
|
R-squared |
0.785949 |
Mean dependent var |
-5.34E-13 |
|
|
Adjusted R-squared |
0.776643 |
S. D. dependent var |
433.0451 |
|
|
S. E. of regression |
204.6601 |
Akaike info criterion |
13.53985 |
|
|
Sum squared resid |
1926746. |
Schwarz criterion |
13.65567 |
|
|
Log likelihood |
-328.7263 |
Hannan-Quinn criter. |
13.58379 |
|
|
F-statistic |
84.45113 |
Durbin-Watson stat |
2.116362 |
|
|
Prob(F-statistic) |
0.000000 |
c. Cochrane-Orcutt AR(1) regression—twostep estimates using Stata
. prais c y, corc two
Iteration 0: rho = 0.0000 Iteration 1: rho = 0.9059
Cochrane-Orcutt AR(1) regression - twostep estimates
48
519.58
0.0000
0.9187
0.9169
183.38
|
c |
Coef. |
Std. Err. |
t |
P>|t| |
[95% Conf. Interval] |
|
y _cons |
.9892295 -1579.722 |
.0433981 1014.436 |
22.79 -1.56 |
0.000 0.126 |
.9018738 1.076585 -3621.676 462.2328 |
|
rho |
.9059431 |
Durbin-Watson statistic (original) 0.180503 Durbin-Watson statistic (transformed) 2.457550
Cochrane-Orcutt AR(1) regression - iterated estimates using Stata 11
|
. prais c y, |
corc |
|
Iteration 0 |
: rho = 0.0000 |
|
Iteration 1 |
: rho = 0.9059 |
|
Iteration 2 |
: rho = 0.8939 |
|
Iteration 3 |
: rho = 0.8893 |
|
Iteration 4 |
: rho = 0.8882 |
|
Iteration 5 |
: rho = 0.8880 |
|
Iteration 6 |
: rho = 0.8879 |
|
Iteration 7 |
: rho = 0.8879 |
|
Iteration 8 |
: rho = 0.8879 |
|
Iteration 9 |
: rho = 0.8879 |
48
689.89
0.0000
0.9375
0.9361
183.26
|
c |
Coef. |
Std. Err. |
t |
P>|t| |
[95% Conf. Interval] |
|
y .cons rho |
.996136 -1723.689 .8879325 |
.0379253 859.2143 |
26.27 -2.01 |
0.000 0.051 |
.9197964 1.072476 -3453.198 5.819176 |
|
Durbin-Watson statistic (original) 0.180503 Durbin-Watson statistic (transformed) 2.447750 |
d. Prais-Winsten AR(1) regression—iterated estimates using Stata 11 . prais c y
Iteration 0: rho = 0.0000 Iteration 1: rho = 0.9059
Iteration 2: rho = 0.9462 Iteration 3: rho = 0.9660 Iteration 4: rho = 0.9757 Iteration 5: rho = 0.9794 Iteration 6: rho = 0.9805 Iteration 7: rho = 0.9808 Iteration 8: rho = 0.9808 Iteration 9: rho = 0.9808 Iteration 10: rho = 0.9809 Iteration 11: rho = 0.9809 Iteration 12: rho = 0.9809
49
119.89
0.0000
0.7184
0.7124
180.74
|
c |
Coef. |
Std. Err. |
t |
P>|t| |
[95% Conf. Interval] |
|
|
y |
.912147 |
.047007 |
19.40 |
0.000 |
.8175811 |
1.006713 |
|
_cons rho |
358.9638 .9808528 |
1174.865 |
0.31 |
0.761 |
-2004.56 |
2722.488 |
Durbin-Watson statistic (original) 0.180503 Durbin-Watson statistic (transformed) 2.314703
e. The Newey-West HAC Standard Errors using EViews are shown below: Dependent Variable: Consum Method: Least Squares
Sample: 1959 2007 Included observations: 49
Newey-West HAC Standard Errors & Covariance (lag truncation = 3)
|
Coefficient |
Std. Error |
t-Statistic |
Prob. |
|
|
C |
-1343.314 |
422.2947 |
-3.180987 |
0.0026 |
|
Y |
0.979228 |
0.022434 |
43.64969 |
0.0000 |
|
R-squared |
0.993680 |
Mean dependent var |
16749.10 |
|
|
Adjusted R-squared |
0.993545 |
S. D. dependent var |
5447.060 |
|
|
S. E. of regression |
437.6277 |
Akaike info criterion |
15.04057 |
|
|
Sum squared resid |
9001348. |
Schwarz criterion |
15.11779 |
|
|
Log likelihood |
-366.4941 |
Hannan-Quinn criter. |
15.06987 |
|
|
F-statistic |
7389.281 |
Durbin-Watson stat |
0.180503 |
|
|
Prob(F-statistic) |
0.000000 |
