Assinment 3
Q1
a)
̂ 𝑡 = −0.609 + 0.7851𝑙𝑛_𝑖𝑛𝑐𝑜𝑚𝑒𝑡 + 0.246𝑙𝑛_𝑤𝑒𝑎𝑙𝑡ℎ𝑡 + 𝑢1𝑡
𝑙𝑛_𝑝𝑐𝑒
N=263
R2=0.998
adjR2=0.998
̂ 𝑡 = −2.146 + 0.312𝑙𝑛_𝑔𝑑𝑝𝑡 + 0.877𝑙𝑛_𝑝𝑝𝑖𝑡 − 0.007𝑡𝑏3𝑚𝑠𝑡 + 𝑢2𝑡
𝑙𝑛_𝑐𝑝𝑖
N=288
R2=0.9953
adjR2=0.9952
b)
𝜏Stat
Variable name
ln_pce
ln_income
ln_wealth
ln_cpi
ln_ppi
ln_gdp
tb3ms
4.800
5.224
3.153
3.292
3.060
5.944
-1.268
5% Critical
-1.950
-1.950
-1.950
-1.950
-1.950
-1.950
-1.950
Unit Root (not
stationary)
Y
Y
Y
Y
Y
Y
Y
c)
𝜏Stat
Variable name
∆ln_pce
∆ln_income
∆ln_wealth
∆ln_cpi
∆ln_ppi
∆ln_gdp
∆tb3ms
-4.160
-4.574
-5.092
-2.695
-5.295
-4.310
-5.835
5% Critical
-1.950
-1.950
-1.950
-1.950
-1.950
-1.950
-1.950
Unit Root (not
stationary)
N
N
N
N
N
N
N
d)
H0: u has unit root
H1: u has no unit root
Leval of significance = 0.01
T stat is smaller than we reject the null hypothesis an conclude that there is long run
relationship (cointegration)among these variables.
e)
H0: u has unit root
H1: u has no unit root
Leval of significance = 0.01
T stat is bigger than t stat, so we accept the null hypothesis an conclude that there is no
cointegration among these variables.
f)
̂ 𝑡 = 0.690 − 0.1054∆𝑙𝑛_𝑔𝑑𝑝𝑡 + 0.3369∆𝑙𝑛_𝑝𝑝𝑖𝑡 − 0.01578∆𝑡𝑏3𝑚𝑠𝑡 + 𝑢2𝑡
∆𝑙𝑛_𝑐𝑝𝑖
N=287
R2= 0.5403
adjR2= 0.5354
Q2
a)
̂ 𝑡 = 0.7109 − 0.6992𝐸𝐶𝑇𝑡−1 𝑐𝑜𝑠𝑢𝑚 − 0.1967𝐸𝐶𝑇𝑡−1 𝑐𝑝𝑖 − 0.1074∆𝑙𝑛_𝑔𝑑𝑝𝑡
∆𝑙𝑛_𝑐𝑝𝑖
+ 0.3013∆𝑙𝑛_𝑝𝑝𝑖𝑡 − 0.01808∆𝑡𝑏3𝑚𝑠𝑡 + 𝑢2𝑡
N=263
R2= 0.5406
adjR2= 0.5317
Q3
In this case they cannot be positive because the model is shoeing that its growing to fast, so in
order to correct for this the y1 and y2 must be negative or else if they were positive it would
just add to the problem. However if a model had the opposite problem than they could be
positive.