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Russian Journal of Agricultural and Socio-Economic Sciences, 6(18)
8
ARE THE REAL GDP SERIES IN ASIAN COUNTRIES NONSTATIONARY OR
NONLINEAR STATIONARY?
Nurun Nahar Jannati, Researcher
Nayeem Sultana, Associate Professor
Md. Israt Rayhan, Associate Professor
University of Dhaka, Dhaka-1000, Bangladesh
E-mail: nnahar@isrt.ac.bd, sultana_nayeem@yahoo.ca, israt@isrt.ac.bd
Phone: +880-1924752885
ABSTRACT
This paper checks whether per capita real gross domestic product (GDP) series in 16 Asian
countries are nonstationary or nonlinear and globally stationary during the period from 1970
to 2009, by applying the nonlinear unit root tests developed by Kapitanios, Shin and Snell
(2003). In five out of the sixteen countries that is approximately one-third of the countries, the
series are found to be stationary with asymmetric or nonlinear mean reversion. Analyses
depict that nonlinear unit root test are suitable for some cases compare to the commonly
used unit root test, Augmented Dickey-Fuller (ADF) and Dickey-Fuller Generalized Least
Square (DF-GLS) tests.
KEY WORDS
Autoregressive model; Nonlinearity; Unit root test.
The moments of the statistical distribution of a stationary time series remain same no
matter at what point they are measured, that is, those are time invariant. Such a series will
tend to its mean (called mean reversion) and fluctuations around this mean will have a
broadly constant amplitude . A nonstationary time series will not revert to its mean path if the
series receives any shocks or experiences policy interventions that are following a negative
shock automatic return to a normal trend may not occur. Using such series in regression
modeling would yield spurious statistical test results. Furthermore, for the purpose of
forecasting, such time series may be of little practical value. Therefore, it is must to check
stationarity of a time series before analyzing the series. Per capita real gross domestic
product (PRGDP) is an important macroeconomic variable for analyzing the impact of
economic policies. Therefore, it is essential to determine statistically whether the PRGDP
series of an economy of interest has a unit root or nonstationary.
Nelson and Plosser (1982) found for the first time that the US real GDP to be a non-
stationary process. Since their findings questioned the business cycle behavior of real GDP,
the issue of a unit root in real GDP has become an intensively researched topic in
macroeconomics. Stock and Watson (1986); Perron and Phillips (1987); Nelson and Murray
(2000) have examined US real GDP whose findings have supported those of Nelson and
Plosser (1982). Cheung and Chinn (1996) found real GDP to be non-stationary for 26 out of
29 high-income countries. Rapach (2002) found that real GDP and real GDP per capita were
non-stationary for Economic Cooperation and Development (OECD) countries. Duck (1992),
Fleissig and Strauss (1999) found real GDP to be trend stationary. Raj (1992), Perron (1994)
and Ben-David et al. (2003), found mixed results on the integrational property of real GDP.
However, most of the studies mentioned above are on developed countries. Studies for
developing countries are scarce. Ben-David and Papell (1998) applied a one-break unit root
test and found real GDP per capita to be stationary for 16 developing countries. Smyth and
Inder (2004) examined real GDP data for 24 Chinese provinces. When they allowed for a
single structural break in the data series for the period 1952-1998, found real GDP per capita
to be nonstationary and when they allowed for two structural breaks the results were mixed.
Recently Murthy and Anoruo (2009) applying nonlinear univariate unit root test developed by
kapetanios et al. (2003), on the per capita real GDP time series in 27 African countries over
the period from 1960 to 2007, found one-third of the countries, the series are stationary with
nonlinear mean reversion that is nonlinear stationary.
Russian Journal of Agricultural and Socio-Economic Sciences, 6(18)
9
However, studies dealing with this phenomenon for Asian countries are found hardly.
The recent study, using the Carrion-i-Silvestre et al.(2005) panel stationarity unit root test
allowing for multiple breaks conducted by Narayan (2008), found overwhelming evidence of
panel stationarity of per capita real GDP for different panels of Asian countries. But unit root
studies based on panel data, despite enhancing the power of unit root tests have some
shortcomings. It has been demonstrated that in most of the widely used panel unit root tests
such as the Levin-Lin-Chu (LLC) and Im-Pesaran-Shin(IPS) tests, there is a possibility that
the panel outcome, where the data generating series of a panel as a whole is stationary is
driven often by a small number of stationary panel members [Breuer et al. (2002),
Chortareas and Kapetanios (2004)]. Thus, the existence of a few stationary series in the
panel might warrant the rejection of the null hypothesis of the presence of a unit root for the
whole panel [Breuer et al. (2002)].
The present paper attempts to study the time series properties of individual Asian
counties, as to increase the rate of economic growth by undertaking new economic policies,
information based on individual country unit root tests is warranted. In this paper, the focus is
on the individual country time series mainly for the availability of the data for 16 Asian
countries, for a relatively long span, 1970-2009 (WDI, 2010 ) and for the presence of some
major theoretical pitfalls of commonly used panel unit root tests leading to misleading
inferences, especially when the panel members included in the sample exhibits pronounced
variations in economic, political and structural characteristics or heterogeneities [Breuer et
al.(2002)].Therefore, we aim to perform univariate unit root test by employing the recent non-
linear univariate unit root test developed by Kapetanios et al.(2003), to determine empirically
whether real GDP per capita series in levels are nonstationary or nonlinear stationary
processes.
DATA AND METHODOLOGY
This study covers a total of 16 Asian countries GDP series. The countries are chosen
on the basis of the availability of required data. The data are collected for the period of 1970
to 2009. The data are obtained from World Development Indicators (WDI, 2010). All
observations are annual. The data used for estimation and analysis on per capita real GDP
for the countries constant in 2000 US dollars. For estimation, the data are expressed in
logarithms.
The application of traditional unit root tests as the ADF and Phillips-Perron tests are
less powerful and more size distorted when the data exhibit nonlinearity. Nonlinearity arise
may be due to high transition costs, high regulatory costs, transportation costs, corruption
and frequent policy interventions. Kapetanios Shin and Snell (2003) extended the
Augmented Dickey–Fuller (ADF) test to tackle the problem of traditional tests in case of
nonlinearity in the Exponential Smooth Transition Autoregressive (ESTAR) framework which
is known as KSS or nonlinear ADF (NLADF) test. They state the null hypothesis of the
presence of a unit root and hence is nonstationary against the alternative of globally
stationary ESTAR process. The ESTAR model can be written as:
t = βt-1 + β*t-1 [1 - exp (- θ2
t-d)] + Єt (1),
where Єt ~ iid (0, σ2). The null hypothesis of a unit root which in terms of the above model
implies that β = 1 and θ = 0. Taking β = 1 in equation (1) and assuming d = 1, the ESTAR
model can be written as:
Δt = β*t-1 {1 - exp (- θ2
t-1)} + Єt (2),
where t is the demeaned or demeaned and de-trended series of interest and [1-exp(-θ2
t-d)]
is the exponential transitional function. Since β* is not identified under the null, testing the
null hypothesis H0 : θ = 0 directly is not feasible [ Davies (1977) ]. Therefore, using a first–
Russian Journal of Agricultural and Socio-Economic Sciences, 6(18)
10
order Taylor series approximation Kapetanios, et al. (2003) obtained the following auxiliary
regression:
Δt = 3
t-1 + νt (3).
To handle the presence of serial correlation in the error terms, the above equation can
be extended as follows:
Δt = ∑∅∆
+ 3
t-1 + νt (4).
Here is the coefficient of interest for testing the presence of a unit root. Kapetanios et al.
(2003) perform the KSS unit root test as the following t-test:
NLADF =
..(
) (5),
where and s.e. are respectively, the estimated coefficient and the standard error of .
The test statistic NLADF does not have an asymptotic standard normal distribution and
therefore, Kapetanios, et al. (2003) provide the critical values on p. 364 of their article which
is reproduced in table 1. If the computed absolute value of the test statistic exceeds the
critical values, the hypothesis of = 0, will be rejected in which case the time series is
stationary.
Table1 – Asymptotic critical values for the KSS test
Significance Level Case 1 Case 2 Case 3
1% -2.82 -3.48 -3.93
5% -2.22 -2.93 -3.40
10% -1.92 -2.66 -3.13
Note: Case 1, Case 2 and Case 3 refer to the underlying model with the raw data, demeaned data and de-trended
data, respectively.
When the data have non-zero mean such that t = µ + t, the demeaned data t - ̅ ,
where ̅ is the sample mean, is used to perform KSS test. When the data have non-zero
mean and non-zero linear trend such that t = µ + δt + t, the demeaned and de-trended data
are obtained by t - µ - t, where µ and are the OLS estimators of µ and δ.
The unit root tests described above are sensitive to the choice of lag length p for
augmenting unit root regressions in the presence of serial correlation. If p is too small then
the remaining serial correlation in the errors will bias the test. If p is too large then the power
of the test will suffer. So an important practical issue for the implementation of the unit root
tests is the specification of the lag length p. The most common way of selecting an
appropriate (optimal) lag structure is using information theoretic criteria such as the AIC
[Akaike (1974)], BIC [Schwarz (1978)] or HQ [Hannan & Quinn (1979)]. Hall (1994) and Ng
and Perron (1995, 2001) shows that the use of too short lag lengths lowers power for ADF
tests and makes DF-GLS tests oversized. They recommend a general-to-specific procedure
for ADF tests and a modified Akaike information criterion (MAIC) for DF-GLS tests. These
procedures have become standard practice for conducting unit root tests. This study
performs unit root tests using standard lag selection techniques. The procedure provided by
Hall (1994) is as follows: Set an upper bound pmax for p and estimate the test regression with
p = pmax. If the last included lag is significant at the 10% level, then set p = pmax and perform
the unit root test. However, if p is insignificant, reduce by one lag until the last lag becomes
significant. If no lags are significant then set p equal to zero. A useful rule of thumb for
determining pmax, suggested by Schwert (1989), is:
Russian Journal of Agricultural and Socio-Economic Sciences, 6(18)
11
pmax = int. 12.
(6),
where int. stands for integer and T is the sample size. Although Liew et al. (2004) fixed the
number of lags to 8, the optimum number of lags chosen on the basis of statistical criteria
may be better than fixed arbitrarily. In MAIC procedure lag is selected by minimizing the
MAIC.
ANALYSES AND RESULTS
Tables 2 and 3 present the results from the most commonly used tests of the unit root
in time-series, the ADF and DF-GLS unit root tests for the level series. Due to capture
different possibilities in the data generating process, this study apply the tests for both, with
constants and with constants and trend terms in the test equations. The tests are designed to
test the null hypothesis of a unit root against the alternative that the series is stationary.
These tests are not very efficient tests because sometimes exhibit less power and more size
distortion. The size distortion could result from excluding moving average (MA) components
from the model or if the model is not appropriate. However, the DF-GLS test has the
advantage of allowing for higher power in the sense that the test is more likely to reject the
null hypothesis of a unit root.
However, in table 2 the traditional ADF test results show that for only one country,
Singapore, the null hypothesis of the presence of a unit root is rejected at the 10% level of
significance when only a constant term was included in the model. When a constant and a
linear trend were incorporated as the deterministic term, it is apparent that the null
hypothesis of nonstationarity is rejected at10% level of significance for China and at 1% level
of significance the null hypothesis is rejected for the two countries, Israel and Turkey.
Table 2 – Linear unit root test (ADF) results for level PRGDP series
Country ADF
c
ADF
t
Bangladesh 3.905(6) 1.687(6)
China 1.751(1) -3.289(8)*
Indonesia -1.659(0) -1.954(1)
India 3.389(9) 0.769(9)
Iran
,
Islamic Rep. -1.912(1) -1.894(1)
Israel -0.277(5) -4.297(1)***
Japan -2.434(1) -0.223(0)
Korea, Rep. -1.724(0) -0.353(0)
Malaysia -1.619(0) -1.746(0)
Nepal 0.371(4) -2.866(2)
Pakistan -0.729(1) -2.382(7)
Philippines -1.549(1) -2.389(1)
Saudi Arabia -2.547(2) -2.980(7)
Singapore -2.656(8)* -0.984(8)
Thailand -1.343(1) -1.542(1)
Turkey -0.280(4) -4.118(3)***
Note: ADF test with constant and with constant and trend are denoted by ADFc and ADFt respectively.
*,**,*** indicate 10%, 5% and 1% significance level respectively.
The figures in parentheses are the optimal lags. Hall(1994), procedure is used to determine the lag length. We set
an upper bound pmax = 9 and estimate the test regression. If the last included lag is significant at the 10% level,
then we set p = 9 and perform the unit root test. However, if p is insignificant, it is reduced by one lag until the last
lag becomes significant. If no lags are significant then we set p equal to zero. We obtain pmax= 9 by using the rule
of thumb for determining pmax, suggested by Schwert (1989).
pmax = int. 12.
, where, int. stands for integer and T is the sample size.
Russian Journal of Agricultural and Socio-Economic Sciences, 6(18)
12
In table 3 the DF-GLS tests reject the null hypothesis only for one country, Saudi
Arabia. Therefore, for a vast majority of the Asian countries included in this study, the
overwhelming evidence of nonstationarity in levels is supported.
Table 3 – Linear unit root test (DF-GLS) results for level PRGDP series
Country DF-GLSc DF-GLSt
Bangladesh -0.794(8) -1.432(5)
China -0.664(9) -1.556(2)
Indonesia 1.240(1) -1.496(1)
India -0.408(7) -0.105(1)
Iran
,
Islamic Rep. -0.766(3) -1.208(3)
Israel 1.242(1) -1.778(3)
Japan -0.477(1) -0.267(1)
Korea, Rep. -0.309(5) -0.905(1)
Malaysia 0.367(3) -1.890(1)
Nepal -0.207(5) -0.731(2)
Pakistan -0.106(2) -2.280(1)
Philippines 0.341(2) -1.978(2)
Saudi Arabia -3.622(1)*** -3.270(1)*
Singapore 0.130(3) -0.608(4)
Thailand 0.063(1) -1.664(1)
Turkey 0.954(2) -2.787(1)
Note: *,**,*** indicate 10%, 5% and 1% significance level respectively.
Optimal lag lengths are selected by MAIC procedure.
Table 4 reports the results of non-linear ADF (KSS or NLADF) tests. The KSS test
results show that for two countries (Israel and Saudi Arabia) in the case of NLADFM (NLADF
based on demeaned data) and for five countries (Israel, Malaysia, Nepal, Pakistan, Saudi
Arabia) in the case of NLADFT (NLADF based on de-trended data), the null hypothesis of the
presence of a unit root is rejected. That means for the two countries, Israel and Saudi Arabia,
the per capita real GDP series are stationary and they exhibit asymmetric or nonlinear mean
reversion. However, in almost all of these countries where the series on per capita real GDP
exhibit upward trends, the unit root tests based on NLADFT are more relevant. The empirical
findings from the KSS unit root test results using de-trended series, NLADFT, shows that the
null hypothesis of nonstationarity is rejected only in 5 out of 16 countries indicating
asymmetric mean reversion and nonlinear stationarity.
Table 4 – Nonlinear unit root test (KSS) results for level PRGDP series
Country NLADF
M
NLADF
T
Bangladesh - 0.30(6) -0.97(6)
China 0.02(9) -2.16(9)
Indonesia -1.14(1) -3.08(1)
India 0.34(7) -1.40(0)
Iran
,
Islamic Rep. -2.77(1) -2.93(1)
Israel -1.39(1)* -4.48(1)***
Japan -0.68(3) -0.71(1)
Korea, Rep. -0.97(5) -1.20(5)
Malaysia -0.79(3) -3.25(3)*
Nepal -0.18(4) -3.87(0)**
Pakistan -2.13(2) -3.17(7)*
Philippines -0.97(1) -2.49(1)
Saudi Arabia -2.66(2)* -3.70(7)**
Singapore -1.31(5) -0.64(4)
Thailand -1.39(1) -1.97(1)
Turkey -0.91(0) -1.79(0)
Note: 1%, 5%, 10% critical values for NLADFM test are -3.48,-2.93, -2.66 and for NLADFT are -3.93, -3.40, -3.13.
Optimal lags are selected by Hall (1994).
Russian Journal of Agricultural and Socio-Economic Sciences, 6(18)
13
CONCLUSION
There is now a large literature on testing for a unit root in time series and panel data.
Standard univariate and multivariate unit root tests can be expected to have low power if the
time series contain a nonlinear type of dynamics (e.g. structural breaks). The use of panel
data benefits the analysis by enhancing the power of univariate unit root tests but there is the
possibility of the time series properties of a minority of panel members influencing the
statistical outcome that the panel as a whole is stationary. So if sufficient degrees of freedom
are available we need to conduct the individual country unit root test. In this paper we apply
the recently developed KSS nonlinear unit root tests to both the demeaned and de-trended
per capita real GDP series of 16 Asian countries for the period 1970-2009.
Figure 1 – Plot of real GDP per capita for Asian countries
The results from KSS tests shows that in about one-third of the Asian countries (Israel,
Malaysia, Nepal, Pakistan, Saudi Arabia) included in the study sample, per capita real GDP
series are found to be stationary with asymmetric non-linear mean reversion. It is apparent
that the results were conflicting between the linear and nonlinear unit root tests, since the
test developed by Kapetanios et al. (2003) is a stationarity test for nonlinear models, and is
deemed to have better power than the standard ADF unit root test for nonlinear series.
However, for a majority of the countries the real GDP per capita series are found to be
1970 1990 2010
200 450
Bangla desh
Time
GDP per capita
1970 1990 2010
500
China
Time
GDP per capita
1970 1990 2010
400
Indonesia
Time
GDP per capita
1970 1990 2010
200 700
India
Time
GDP per capita
1970 1990 2010
1200
Iran
Time
GDP per capita
1970 1990 2010
10000
Israel
Time
GDP per capita
1970 1990 2010
20000
Japan
Time
GDP per capita
1970 1990 2010
2000
Korea
Time
GDP per capita
1970 1990 2010
1000 5000
Malaysia
Time
GDP per capita
1970 1990 2010
140 240
Nepal
Time
GDP per capita
1970 1990 2010
300 600
Pakistan
Time
GDP per capita
1970 1990 2010
800
Philippines
Time
GDP per capita
1970 1990 2010
8000
Saudi Arabia
Time
GDP per capita
1970 1990 2010
5000
Singa pore
Time
GDP per capita
1970 1990 2010
500 2500
Thailand
Time
GDP per capita
1970 1990 2010
2000 5000
Turkey
Time
GDP per capita
Russian Journal of Agricultural and Socio-Economic Sciences, 6(18)
14
nonstationary. Shocks have permanent effects on the economy of these countries. If there is
a unit root in real output, it suggests that following a negative shock automatic return to a
normal trend may not occur.
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