Q1 









i 
The model that the researcher tests can be described as 









ln(wage)t=k*ln(wage)(t1)+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)tln(wage)(t1)=a+delta*ln(wage)(t1)+ut 









Ho:delta=0 









H1:delta<>0 









YtY(t1)=a+delta Y(t1) + ut 









if the absolute value of the computed DF statistics
exceeds critical value, reject H0 









Unit root tests for variable LNREAL 









The
DickeyFuller 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 DickeyFuller statistic = 2.8837 









DF<Critical value 









Do not reject H0, it can be a random walk. 








ii 
Ho:delta=0 









H1:delta<>0 









YtY(t1)=a+delta Y(t1) + ut 









if the absolute value of the computed DF statistics
exceeds critical value, reject H0 









Unit root tests for variable LO 









The
DickeyFuller 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 DickeyFuller statistic = 2.8837 









DF<Critical value 









Do not reject H0, it can be a random walk. 


















iii 
Ho:delta=0 









H1:delta<>0 









YtY(t1)=a+delta Y(t1) + ut 









if the absolute value of the computed DF statistics
exceeds critical value, reject H0 









Unit root tests for variable LC 









The
DickeyFuller 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 2.9646 352.2209
350.2209 347.3534 349.0557 









95%
critical value for the augmented DickeyFuller statistic = 2.8837 









DF>Critical value 









Reject H0, we dont have a random walk 








iv 
Although two variables seem to follow the random walk, a
linear combination of them does not do so. Thus although we cannot predict
which way the real wage and output per head go we can predict the movements
in cost. This is probably because real wage and output depend so heavily on
technological improvements, that are arguably ranom, however, costs depend
other things as well, on trade cycle, etc. Thus one can predict how much the
cost is going to be on the next period, despite the fact that the magnitudes
of the components that make up costs, wages and output, cannot be determined. 




































































Q2 
X1 is wages, X2 prices, X3 capital/employment ratio and X4
unemployment rate. 









Ordinary Least Squares Estimation 









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Dependent
variable is X1 









32
observations used for estimation from 1959 to 1990 









******************************************************************************* 









Regressor
Coefficient Standard
Error TRatio[Prob] 









C .035507 .14685 .24178[.811] 









X1(1)
.44479 .13727 3.2402[.003] 









X2 .95014 .064631 14.7011[.000] 









X2(1)
.40682 .14319 2.8411[.009] 









X3 .52885 .13224 3.9991[.000] 









X4 .040442 .013155 3.0744[.005] 









X4(1)
.0057808
.013578
.42576[.674] 









******************************************************************************* 









RSquared
.99988 RBarSquared .99985 









S.E. of
Regression .012351 Fstat. F( 6, 25)
35372.8[.000] 









Mean of
Dependent Variable .90632 S.D. of Dependent Variable 1.0220 









Residual
Sum of Squares .0038134 Equation Loglikelihood 99.1536 









Akaike
Info. Criterion 92.1536 Schwarz Bayesian Criterion 87.0235 









DWstatistic
1.9135 Durbin's
hstatistic .38824[.698] 









* A:Serial Correlation*CHSQ( 1)=
.10516[.746]*F( 1, 24)=
.079127[.781]* 









* B:Functional Form *CHSQ( 1)= 1.4509[.228]*F( 1, 24)= 1.1399[.296]* 









* C:Normality *CHSQ( 2)= .16545[.921]* Not applicable
* 









* D:Heteroscedasticity*CHSQ( 1)=
.84065[.359]*F( 1, 30)=
.80937[.375]* 









All the regressors, except lagged unemployment and
the constant term, are significant. The R squared is very high. Which means
the regression model is very good. We had no previous reason to expect the
wages to be determined by a constant anyway. Also there is no problem with
heteroscedacity, autocorrelation, different functional form or nonnormality
of errors 


























































ii 
It is all given in the previous table. 









So for example, 1% change in X1 will lead to 0.44% change
in level of wages 









Roughly, to test for the unity a value t=(b1)/(se)<2.
B is the coefficient we are testing and se its standard error 



















It is clear that only the prices can possibly be unity,
test statistics is 









=(0.950141)/0.064631 
= 
0.771456422 







meaning that x2 can be unity 








iii 
Original RSS 
0.003813 


















1. Restricted by leaving lagged UE out 









Residual
Sum of Squares .0038410 Equation Loglikelihood 99.0380 



















2. Restricted by including only lagged UE out 









Residual
Sum of Squares .0052551 Equation Loglikelihood 94.0227 



















3. Restricted by including the difference 









Residual
Sum of Squares .0051453 Equation Loglikelihood 94.3604 



















I will use the restricted least squares F test approach
for which F=RSS(r)RSS(ur)(nk)/RSSur*m 









Follows the F distribution with m, nk df. Ur means
unrestricted. M is number of linear restrictions, 1 









k number of parameters in ur=7, n=32, df=25, F critical at
5% level =4.25 









For restriction 

1 
F= 
0.180940 





For restriction 

2 
F= 
9.451539 





For restriction 

3 
F= 
8.731709 





So I reject restrictions 2 and 3, restriction one, leaving
lagged UE out is reasonable 








iv 
Chow test 









H0:structural stability 









H1:break in the structure 



















* F:Chow Test *CHSQ( 6)= 2.4940[.869]*F( 6, 20)= .41567[.860]* 









Do not reject H0, structuraly stable. 







