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