This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied,
or distributed without the prior consent of the publisher.
52
CHAPTER 10
SOLUTIONS TO PROBLEMS
10.1
(i) Disagree.
Most time series processes are correlated over time, and many of them
strongly correlated.
This means they cannot be independent across observations, which simply
represent different time periods.
Even series that do appear to be roughly uncorrelated – such as
stock returns – do not appear to be independently distributed, as you will see in Chapter 12 under
dynamic forms of heteroskedasticity.
(ii) Agree.
This follows immediately from Theorem 10.1.
In particular, we do not need the
homoskedasticity and no serial correlation assumptions.
(iii) Disagree.
Trending variables are used all the time as dependent variables in a regression
model.
We do need to be careful in interpreting the results because we may simply find a
spurious association between
y
t
and trending explanatory variables.
Including a trend in the
regression is a good idea with trending dependent or independent variables.
As discussed in
Section 10.5, the usual
R
-squared can be misleading when the dependent variable is trending.
(iv) Agree.
With annual data, each time period represents a year and is not associated with
any season.
10.3
Write
y*
=
α
0
+ (
δ
0
+
δ
1
+
δ
2
)z*
=
α
0
+
LRP
⋅
z
*,
and take the change:
Δ
y
*
=
LRP
⋅
Δ
z
*.
10.5
The functional form was not specified, but a reasonable one is
log(
hsestrts
t
)
=
α
0
+
α
1
t
+
δ
1
Q2
t
+
δ
2
Q3
t
+
δ
3
Q3
t
+
β
1
int
t
+
β
2
log(
pcinc
t
) +
u
t
,
Where
Q2
t
,
Q3
t
, and
Q4
t
are quarterly dummy variables (the omitted quarter is the first) and the
other variables are self-explanatory.
This inclusion of the linear time trend allows the dependent
variable and log(
pcinc
t
) to trend over time (
int
t
probably does not contain a trend), and the
quarterly dummies allow all variables to display seasonality.
The parameter
β
2
is an elasticity
and 100
⋅
β
1
is a semi-elasticity.
10.7
(i)
pe
t
-1
and
pe
t
-2
must be increasing by the same amount as
pe
t
.
(ii) The long-run effect, by definition, should be the change in
gfr
when
pe
increases
permanently.
But a permanent increase means the level of
pe
increases and stays at the new
level, and this is achieved by increasing
pe
t
-2
,
pe
t
-1
, and
pe
t
by the same amount.

This ** preview** has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*