|
Q1 |
|
|
|
|
|
|
|
|
|
|
i |
The model that the researcher tests can be described as |
|
|
|
|
|
|
|
|
|
|
ln(wage)t=k*ln(wage)(t-1)+ut |
|
|
|
|
|
|
|
|
|
|
Where ut is a random error variable, normally distributed
with mean 0 |
|
|
|
|
|
|
|
|
|
|
If this is a random walk, k=1. |
|
|
|
|
|
|
|
|
|
|
However, to test that, it is more convenient to express it
in difference form, and test |
|
|
|
|
|
|
|
|
|
|
whether the coeficient(delta) is 0. For empirical reasons,
constant is added |
|
|
|
|
|
|
|
|
|
|
ln(wage)t-ln(wage)(t-1)=a+delta*ln(wage)(t-1)+ut |
|
|
|
|
|
|
|
|
|
|
Ho:delta=0 |
|
|
|
|
|
|
|
|
|
|
H1:delta<>0 |
|
|
|
|
|
|
|
|
|
|
Yt-Y(t-1)=a+delta Y(t-1) + ut |
|
|
|
|
|
|
|
|
|
|
if the absolute value of the computed DF statistics
exceeds critical value, reject H0 |
|
|
|
|
|
|
|
|
|
|
Unit root tests for variable LNREAL |
|
|
|
|
|
|
|
|
|
|
The
Dickey-Fuller regressions include an intercept but not a trend |
|
|
|
|
|
|
|
|
|
|
******************************************************************************* |
|
|
|
|
|
|
|
|
|
|
130
observations used in the estimation of all ADF regressions. |
|
|
|
|
|
|
|
|
|
|
Sample
period from 1960Q4 to 1993Q1 |
|
|
|
|
|
|
|
|
|
|
******************************************************************************* |
|
|
|
|
|
|
|
|
|
|
Test Statistic LL AIC SBC
HQC |
|
|
|
|
|
|
|
|
|
|
DF -.42894 360.3673
358.3673 355.4998 357.2022 |
|
|
|
|
|
|
|
|
|
|
95%
critical value for the augmented Dickey-Fuller statistic = -2.8837 |
|
|
|
|
|
|
|
|
|
|
|DF|<|Critical value| |
|
|
|
|
|
|
|
|
|
|
Do not reject H0, it can be a random walk. |
|
|
|
|
|
|
|
|
|
ii |
Ho:delta=0 |
|
|
|
|
|
|
|
|
|
|
H1:delta<>0 |
|
|
|
|
|
|
|
|
|
|
Yt-Y(t-1)=a+delta Y(t-1) + ut |
|
|
|
|
|
|
|
|
|
|
if the absolute value of the computed DF statistics
exceeds critical value, reject H0 |
|
|
|
|
|
|
|
|
|
|
Unit root tests for variable LO |
|
|
|
|
|
|
|
|
|
|
The
Dickey-Fuller regressions include an intercept but not a trend |
|
|
|
|
|
|
|
|
|
|
******************************************************************************* |
|
|
|
|
|
|
|
|
|
|
130
observations used in the estimation of all ADF regressions. |
|
|
|
|
|
|
|
|
|
|
Sample
period from 1960Q4 to 1993Q1 |
|
|
|
|
|
|
|
|
|
|
******************************************************************************* |
|
|
|
|
|
|
|
|
|
|
Test Statistic LL AIC SBC
HQC |
|
|
|
|
|
|
|
|
|
|
DF -1.1729 413.7883
411.7883 408.9208 410.6231 |
|
|
|
|
|
|
|
|
|
|
95%
critical value for the augmented Dickey-Fuller statistic = -2.8837 |
|
|
|
|
|
|
|
|
|
|
|DF|<Critical value |
|
|
|
|
|
|
|
|
|
|
Do not reject H0, it can be a random walk. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
iii |
Ho:delta=0 |
|
|
|
|
|
|
|
|
|
|
H1:delta<>0 |
|
|
|
|
|