Solutions to Computer Exercises in Assignment 4
C10.10
(i)
. tsset t
time variable: t, 1948
to 2003
. correlate inft deft
(obs=56)
| inft deft
-------------+------------------
inft | 1.0000
deft |
0.0975 1.0000
The correlation is small (.098). From a statistical point of view,
this implies that the parameters of the model can be estimated more
precisely.
(ii)
. gen inft1 = L.inft
. gen deft1 = L.deft
. reg i3t inft deft inft1 deft1
Source |
SS
df
MS
Number of obs = 55
-------------+------------------------------
F( 4, 50) = 27.18
Model |
299.516929 4
74.8792323
Prob > F = 0.0000
Residual | 137.722545
50
2.7544509
R-squared = 0.6850
-------------+------------------------------
Adj R-squared = 0.6598
Total |
437.239474 54
8.0970273
Root MSE = 1.6597
------------------------------------------------------------------------------
i3t
| Coef. Std.
Err. t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
inft |
.3426159 .1253973 2.73
0.009 .090748 .5944837
deft |
-.1896663 .2212844 -0.86
0.395 -.6341291 .2547964
inft1 |
.3819795 .1335847 2.86
0.006 .1136667 .6502922
deft1 |
.5692731 .1967706 2.89
0.006 .1740477 .9644985
_cons |
1.611482 .4007615 4.02
0.000 .8065291 2.416435
------------------------------------------------------------------------------
(iii) The estimated long-run propensity is .343 + .382 = .725
which is larger than .606.
(iv)
. test inft1 deft1
( 1) inft1 = 0
( 2) deft1 = 0
F( 2, 50)
= 5.22
Prob
> F = 0.0087
The F-statistic is 5.22 (p-value = .009). Therefore, the lagged
values
of inflation and deficit are joinlty significant at 5% level.
C11.8
(i)
. tsset t
. gen unemt1 = L.unemt
. gen inft1 = L.inft
. reg unemt unemt1
Source
|
SS
df
MS
Number of obs = 55
-------------+------------------------------
F( 1, 53) = 69.17
Model |
69.0545684 1
69.0545684
Prob > F = 0.0000
Residual | 52.9097954
53
.998298026
R-squared = 0.5662
-------------+------------------------------
Adj R-squared = 0.5580
Total |
121.964364 54
2.25859933
Root MSE = .99915
------------------------------------------------------------------------------
unemt
| Coef. Std.
Err. t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
unemt1 |
.7425353 .0892793 8.32
0.000 .5634636 .921607
_cons |
1.488356 .5199931 2.86
0.006 .4453819 2.53133
------------------------------------------------------------------------------
The predicted unemployment rate for 2004 is 1.49 + .742*6 = 5.94,
which overpredicts the actual rate of 5.5.
(ii)
. reg unemt unemt1 inft1
Source |
SS
df
MS
Number of obs = 55
-------------+------------------------------
F( 2, 52) = 59.57
Model |
84.9046984 2
42.4523492
Prob > F = 0.0000
Residual | 37.0596653
52
.712685871
R-squared = 0.6961
-------------+------------------------------
Adj R-squared = 0.6845
Total |
121.964364 54
2.25859933
Root MSE = .84421
------------------------------------------------------------------------------
unemt
| Coef. Std.
Err. t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
unemt1 |
.6496298 .0779645 8.33
0.000 .4931825 .806077
inft1 |
.1829481 .0387936 4.72
0.000 .1051029 .2607932
_cons |
1.295166 .4412616 2.94
0.005 .4097097 2.180622
------------------------------------------------------------------------------
The regression results show that lagged inflation is statistically
significant.
(iii) Predicted unemployment rate for 1997 is 1.295 + .650*6
+ .183*2.3 = 5.62 which still overpredicts the actual rate but the
magnitude
of overprediction is slightly smaller.