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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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8/10/2019 Rapach (2002)

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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

rapachd@seattleu.edu.

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