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Are Real GDP Levels Nonstationary? Evidence from Panel Data Tests
Author(s): David E. Rapach
Source: Southern Economic Journal, Vol. 68, No. 3, (Jan., 2002), pp. 473-495
Published by: Southern Economic Association
Stable URL: http://www.jstor.org/stable/1061713
Accessed: 11/04/2008 12:57
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Southern Economic Journal
2002,
68(3),
473-495
r e
R e a l
G P
e v e l s
Nonstationary
v idence
f r o m
P a n e l
a t a
T e s t s
David E.
Rapach*
Ever since
the seminal
paper
of Nelson and Plosser
(1982),
researchershave focused on
the
potential
nonstationarity
f
important
macroeconomic
variables,
and unit root
tests are now a
standard
procedure
n
empirical analyses.
While there are
many findings
of unit
roots
in
mac-
roeconomic variables
using
the
popularaugmentedDickey
and Fuller
(1979)
test,
this test has
low
power
against
near-unit-root lternatives.
Recently, panel
data
procedures
have been
pro-
posed
as an
avenue to
increased
power.
This
paper applies panel
unit root
tests to international
real
GDP
and real
GDP
per capita
data.
The results
overwhelmingly
ndicate
that international
real GDP and real GDP
per capita
levels are
nonstationary.
1. Introduction
In the wake of the seminal
paper
of
Nelson and Plosser
(1982),
the
potential presence
of
unit
roots
in macroeconomic
variables has received a
great
deal
of attention. The
time-series
properties
of real
output
levels have been of
special
interest to
researchers. As stressed
by
Nelson
and Plosser
(1982),
a unit root in real
output
is
inconsistent with the view
that business
cycles
are stationary fluctuations around a deterministic trend; instead, shocks to real output levels
have
permanent
effects.
This
is
generally
interpreted
as
implying
that real
factors,
such as
technology
shocks,
play
a
leading
role in economic
fluctuations-although,
as
noted
by
Camp-
bell and Mankiw
(1987),
it
might
also mean that
aggregate
demand
shocks have
permanent
effects on real
output
levels
(in
opposition
to the natural-rate
hypothesis).
A
large
literature
supports
the Nelson and Plosser
(1982)
conclusion that real
output
levels are
nonstationary.'
This conclusion has not
gone
uncontested,
however. The
most
popular
unit
root
test,
the
aug-
mented
Dickey
and Fuller
(ADF) (1979)
test,
takes the
presence
of a unit root
as the null
hypothesis
and has low
power against
near-unit-root but
stationary
alternatives.2 This
casts doubt
on the
many findings
of unit
roots
in
real
output
levels.
A
recently proposed
avenue to
increased
power
in
testing
for
unit roots is the
use of
panel
data. Levin and Lin
(1992)
and
Im, Pesaran,
and
Shin
(1997)
develop
the
asymptotic theory
and
finite-sample properties
of ADF
tests of
panel
data.
They
demonstrate that even
relatively
small
panels
offer
large improvements
in
power.
Panel unit root tests
have been used
extensively
*
Department
f Economics and
Finance,
Albers
School of Business and
Economics,
Seattle
University,
900 Broad-
way,
Seattle,
WA
98122-4340, USA;
E-mail
The author thanks Alan Isaac and two
anonymous
referees for
very
helpful
comments on
earlier drafts.
Any
remaining
errorsare
solely
the author's
responsibility.
The
GAUSS
programs
used to
generate
the results in this
paper
are availableon
request
rom
the author.
ReceivedFebruary1999; acceptedMarch2001.
See,
for
example,
Stulz and Wasserfallen
1985)
and
Wasserfallen
1986).
A
more
recent
representative tudy
s
Cheung
and Chinn
(1996).
They
find that the unit root null
hypothesis
cannot
be
rejected
or 26 of
29
high-income
countries.
2
See,
for
example, DeJong
et al.
(1992).
473
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474 David E.
Rapach
in the recent
empirical
literature on
purchasing power parity.
Jorion and
Sweeney
(1996),
Oh
(1996),
Wu
(1996),
and
Papell
(1997),
among
others,
use
international
panel
data to
test the
stationarity
of
real
exchange
rates. In
addition,
Wu and
Zhang
(1996),
Culver and
Papell
(1997),
and
Song
and Wu
(1998)
test for a unit root in nominal
interest
rates,
inflation
rates,
and
unemployment
rates,
respectively, using panels
of
OECD countries.
All
of these studies contain
many rejections
of the unit root null
hypothesis.
These results are
noteworthy
in that
single-
country
ADF tests for real
exchange
rates,
nominal interest
rates,
inflation
rates,
and unem-
ployment
rates
typically
cannot
reject
the unit root
null
hypothesis.
For
example,
Culver and
Papell
(1997)
reject
the
nonstationary
null
hypothesis
for
only
three
of the thirteen
inflation rate
series
that
they
consider
when
they apply
the ADF test to each
country individually.
However,
the unit root
null
hypothesis
is often
rejected
for
panels
of
only
two countries and
is
always
rejected
for
panels
of seven or more countries.
This paper contributes to the existing unit root literature by applying panel unit root tests
to international
real GDP and
real
GDP
per capita
data.
Interestingly,
the estimation results
overwhelmingly
demonstrate
that the
typical finding
of
nonstationary
real
output
behavior in
industrialized OECD
countries is robust to
panel
unit root tests.
In
particular, using
two
postwar
real GDP
data
sets,
one annual and
one
quarterly,
the
unit
root null
hypothesis
is
rarely rejected
at standard
significance
levels for a
variety
of
panel
unit root
tests. The same holds true for
two annual
real GDP
per capita
data
sets,
one
spanning
the
postwar
era and the other most of
the 20th
century.
Unlike some
other macroeconomic variables that have been
investigated
re-
cently,
the
unit root null
hypothesis
is not often
rejected by applying
more
powerful panel
unit
root
tests. This can be viewed
as
strong
evidence that international real
output
levels
are,
in
fact, nonstationary.
The rest of the
paper
is
organized
as
follows. Section
2
outlines the
panel
unit root test
methodology,
section 3
presents
the estimation
results,
and section
4
concludes.
2. Panel
ADF
Tests
The well-known
single-country
ADF test for a unit root
in
Yi,
for
country
i,
allowing
for
a linear deterministic
trend,
is
based on
the
following regression
model:
k
AYit
=
ca,
Pi
+
i Yi,
+
E
6
Ai,
t-j
+
i,,
(1)
j=l
where
A
is
the difference
operator
(i.e.,
Ayit
=
Yi
-
Yi,t-),
E,i
s a white-noise
disturbance term
with variance
cr2,
and
t
=
1,
. .
,T
indexes time.
The
AYi,j
terms on the
right-hand-side
of
Equation
1
allow for serial
correlation and are
designed
to
ensure that
Eit
s
white
noise.
Fol-
lowing
standard
practice
in
the real
output
unit root
literature,
I
include
a linear deterministic
trend
in
Equation
1. The null
hypothesis
is that
Pi
=
0,
which
corresponds
to a unit root
in
Yi,
(i.e.,
Yit
s
nonstationary).
The unit root null
hypothesis
is tested
against
the one-sided
(lower-
tail)
alternative
hypothesis
that
Pi