MIT OpenCourseWare
http://ocw.mit.edu
14.384 Time Series Analysis
Fall 2008
For information about citing these materials or our Terms of Use, visit:
http://ocw.mit.edu/terms
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Consumption,
Income,
Wealth
and
Cointegration
1
14.384
Time
Series
Analysis,
Fall
2008
Recitation
by
Paul
Schrimpf
Supplementary
to
lectures
given
by
Anna
Mikusheva
October
31,
2008
Recitation
9
Consumption,
Income,
Wealth
and
Cointegration
There
is
a
long
line
of
papers
that
use
cointegration
to
examine
the
relationship
among
consumption,
income,
and
wealth.
These
notes
go
over
two
such
papers,
one
relatively
old
and
one
more
recent.
Campbell
(1987):
Does
Saving
Anticipate
Declining
Labor
Income?
An
Al
ternative
Test
of
the
Permanent
Income
Hypothesis
Brieﬂy,
the
permanent
income
hypothesis
says
that
consumption
should
only
change
in
response
to
changes
in
expected
lifetime
income,
or
“permanent
income.”
Since
permanent
income
is
unobservable,
the
permanent
�
�
�
�
income hypothesis (PIH) cannot be tested directly. Hall (1978) observed that under rational expectations, the
PIH
implies
that
consumption
should
be
a
martingale
(
E
[
c
t
+1
I
t
] =
c
t
−
1
).
Many
authors
have
implemented
tests
based
on
this
fact,
such
as
Mankiw
and
Shapiro
(1985)
as
mentioned
in
lecture
16.
Tests
based
on
this
fact
generally
reject
the
PIH.
Campbell
develops
an
alternative
test,
both
to
confirm
Hall’s
result
and
to
better
understand
how
the
PIH
fails.
Model
Let
y
kt
and
y
lt
denote
capital
and
labor
income
at
time
t
,
c
t
denote
consumption,
W
t
wealth,
and
r
the
interest
rate.
The
PIH
model
maintains
that
y
kt
=
rW
t
.
Let’s
also
allow
from
some
unforecastable
capital
gains,
η
t
.
Then
the
evolution
of
wealth
is
W
t
=
(1 +
r
)
W
t
−
1
+
y
l,t
−
1
−
c
t
−
1
+
η
t
We
can
rewrite
the
budget
constraint
in
terms
of
capital
and
labor
income
as
y
kt
−
(1
+
r
)
y
k,t
−
1
−
r
(
y
l,t
−
1
−
c
t
) +
η
t
(1)
Consumption
is
proportional
to
wealth
plus
expected
future
income,
r
This is the end of the preview.
Sign up
to
access the rest of the document.
 '09
 Geurrieri
 Macroeconomics, Consumption function, Permanent income hypothesis, labor income

Click to edit the document details