Is real GDP per capita panel stationary with structural breaks in African countries? Econometric evidence.
Murthy, Vasudeva N.R. ; Anoruo, Emmanuel
Abstract
This paper applies a battery of first and second generation panel
unit root tests in addition to the recently developed
Carrion-i-Silvestre et al. (2005) test to investigate the stochastic
properties of real GDP per capita (PRGDP) for a panel of 27 African
countries from 1960-2005. The results reveal that there is
cross-sectional dependence in PRGDP series among the 27 countries
included in the sample. The results further reveal that the PRGDP series
in the panel are stationary with multiple structural breaks taking place
in different countries at different dates. Thus, the series are found to
be stationary with broken trends. These results are robust to the
assumption of either homogeneity or heterogeneity in computing the
long-run variance in the Carrioni-Silvestre et al. panel stationarity
tests. Policy implications of the findings are discussed in the paper.
Keywords: Panel unit roots--Cross-sectional
independence--Structural breaks--Real GDP per Capita
JEL Classification: 011; C22; C23
I. INTRODUCTION
In recent years, economists and policy makers have been interested
in understanding the nature of the stochastic properties of many
macro-economic time series, especially the real GDP per capita series,
of various economies. Their main interest is to find out whether the
real GDP per capita series is stationary or non-stationary in levels.
Here, stationarity of a time-series is understood to mean that the
moments, especially the mean and variance, do not depend on time and
therefore the series does not contain a unit root. The concerns of the
economists and the policy makers are understandable, given the fact that
the implications of series that are non-stationary in levels, and hence
their mean and variance are a function of time, for the effectiveness of
economic policies, economic modeling and economic forecasting are
enormous. For instance, using nonstationary time-series in Ordinary
Least squares (OLS) regression analysis would lead to spurious results
and the forecasts based on the series would cease to be reliable, in
addition to rendering monetary and fiscal policy actions based on these
series permanent and not mean-reverting.
A literature review in time-series econometrics reveals that there
is a plethora of studies that examine the presence of a unit root in the
aggregate real GDP (RGDP) and real GDP per capita series of various
countries. Many of these studies deal with empirically examining the
order of integration of output series- in advanced economies and the
OECD (Organization of Economic Co-operation and Development) countries.
Some of the famous studies in this regard include the empirical
investigations conducted by Kormendi and McQuire (1990), Ben-David and
Papell (1998), Cheung and Chinn (1996), Fleissig and Strauss (1999),
Gerdham and Lothgren (2000), Rapach (2002), Gaffeo et al. (2005) and
Carrion-i-Silvestre et al. (2005). In this context, it is interesting to
observe that Kormendi and McQuire (1990), Cheng and Chinn (1996),
Gerdtham and Lothgren (2000) and Rapach (2002) find the real output
series of many advanced countries, including many OECD countries to be
non-stationary and conclude that therefore, the series are integrated of
the order, I(1). In contrast, empirical investigations by Fleissig and
Strauss (1999), Graffeo et al. (2005) and Carrion-i-Silvestre et al.
(2005) conclude that the series are stationary and hence they are
integrated of the order zero, I (0).
Although in the literature there exist many empirical
investigations of the time-series properties of the PRGDP series for
developed countries, one finds that there are a limited number of
studies that examine the phenomenon under consideration for developing
countries, especially African economies. Some of these studies are
undertaken by Ben-David and Papel (1998), Li (2000), Aguirre and
Ferreira (2001), Smyth and Inder (2004), Narayan (2004), Chang et al.
(2005), Chang et al. (2008), and Narayan (2008a, 2008b). While,
Ben-David and Papel (1998) present empirical evidence to show that for
16 developing countries the PRGDP series are stationary in levels,
Aguirre and Ferreira (2001) found that the PRGDP in the Brazilian
economy to be stationary, and Narayan (2008) finds the PRGDP series for
15 Asian countries to be panel stationary for the period 1950-2002.
Chang et al. (2008) consider the per capita RGDP to be stationary with
broken trend during the period 1960-2000. The only study on the
time-series properties of the African economies is found in Chang et al.
(2005). They, using the data on PRGDP of 26 select African countries for
the period 1960-2000, conclude that for the majority of the countries,
the series are non-stationary. But, Chang et al. (2005) do not consider
the possibilities of multiple-structural breaks in the context of unit
root tests and the tests that they have used do not allow for the
presence of cross-sectional dependence. Another excellent study
undertaken by Romero-Avila (2009) tests the unit root hypothesis for a
panel of 46 African countries over the period 1950-2001 using the data
from Maddison (2003) and the data for the period 1960-2004 collected
from Penn World Table, PWT 6.2 (2006). He concludes that the real GDP
per capita series in these African countries experienced multiple breaks
and also are regime-wise trend stationary the present paper uses the
recently available consistent data on strictly African countries, where
as Romero-Avila's paper includes the data on the North African
countries and other African countries such as, Angola, Eritrea and
Ethiopia, Somalia, Sudan and Uganda that have experienced persistent
political, ethnic and economic instability. Another distinguishing
feature of our paper is that the present paper focuses, for testing and
analysis, the period during which most of the African became independent
and thus were able to undertake autonomous economic policies that were
not influenced by colonial economic priorities and philosophy.
Furthermore, it applies, in addition to the first-generation panel unit
root tests, the recently developed second-generation panel unit root
tests, such as the Pesaran's Cross-Sectional Augmented
Dickey-Fuller test (CADF, 2003), the Cross-Sectional Im,Pesaran and Shin
(CIPS, 2003) test and the Moon-Perron panel unit root test (MP, 2004)
that are designed to handle cross-sectional dependence and correlation.
(MP, 2004).
This paper, for empirical investigation purposes, recognizes a need
for classifying the African countries as a group, because despite these
countries having some degree of heterogeneity, they share many common
economic, political and social characteristics. African economies are
basically low income developing countries that are supply-constrained,
suffering from inadequate capital stock, lack of a well-defined"
enforced and maintained system of property rights, with agriculture and
mining as the important sectors of the economy and having dual
markets-formal and informal markets. Most of these countries are export
oriented in producing primary commodities. Many of these countries have
historically experienced ethnic conflicts and military rule, which can
be construed as structural breaks. Therefore, in light of the paucity of
the studies on the time series properties of many macroeconomic
time-series for the African economies, the present paper, using
the' panel data of 27 African countries for the period 19602005,
attempts to test the stochastic properties of the real gross domestic
per capita (PRGDP) by a battery of first and second-generation panel
unit root tests and the recently developed Carrion-i-Silvestre et al.
(2005) panel stationarity test (CBL) that allows for the presence of
endogenously determined multiple structural breaks and adjustments for
cross-sectional dependence among the panel members. Unlike the
first-generation panel unit root tests, the second-generation panel unit
root tests take into consideration the dependence among cross-sections
and therefore they do not suffer from size distortions. The
Carrion-i-Silvestre et al. unit root tests are more flexible than the
other existing panel unit root tests that attempt to statistically
identify the presence of structural breaks. One of the features of these
tests is that they consider the null hypothesis of panel stationarity
with multiple structural breaks for each cross-section member. A
comprehensive panel unit root analysis should include, as stressed by
Karlsson and Lothgren (2000), a battery of both univariate and panel
unit root tests especially given the shortcomings of any single commonly
used panel unit root tests in the literature.
II. SPECIFICATION OF THE MODEL AND THE DATA
As the econometrics details of the univariate unit root tests are
well-known in the literature, no attempts are made in this paper to
explain them [for details, read Breitung and Pesaran (2005) and Murthy
(2007)]. However, since panel unit root tests are relatively new, a
brief description of the panel unit root tests employed in this paper
and the Carrion-i-Silvestre et al. stationary test will be presented in
this section [see for details, Hurlin (2007), Breitung and Pesaran
(2005) and Carrion-i-Silvestre et al. (2005)]. As the central frame-work
for panel unit-root tests, we assume the following data generating
process of a time-series of a cross-sectional unit, X, in its difference
form as:
[DELTA][X.sub.it] = [alpha][X.sub.it-1] + [[p.sub.i].summation over
(j=1)][beta][i.sub.j][DELTA][X.sub.it-j] + Z'[delta] +
[[epsilon].sub.it] (1)
In specified model (1), in the present study we incorporate the
indexes, i = 1, 2, ..., 27 cross-sections and t = 1, 2, ..., 46, T time
period observations. [Z.sub.it] represent the deterministic terms such
as the individual effects and linear trends. In equation (1) [alpha] =
([rho] - 1) and [[rho].sub.i] are the autoregressive coefficients. In
the panel unit root tests of Levin et al. (2002) [LLC] and Breitung
(2000) and Hadri (2000) tests, it is required that the autoregressive
coefficients in (1) are the same across the panel. This assumption is
considered rather too restrictive (common unit root process) by some
econometricians. Therefore recently, Im, Pesaran and Shin (2003) have
designed a new panel unit root test, the IPS test, in which they let the
autoregressive coefficients vary in light of the heterogeneity found in
individual members of the panel. Furthermore, where as the LLC test
states that the null hypothesis is the presence of a unit root for all
the cross-section members, and the alternative hypothesis is defined as
the individual process is stationary for all i, the IPS test maintains
the same null hypothesis, but the alternative hypothesis is modified to
require a non-zero fraction of the individual panel members'
processes as stationary. Technically Im, Pesaran and Shin (2003)
formulate a standardized panel unit root test statistic, based on the
Lindberg-Levy theorem, known as the IPS statistics, tips which can be
computed as follows:
[t.sub.IPS] = [square root of N]([bar.t]-1/N[N.summation over
(i=1)]E[t.sub.iT]|[[rho].sub.i]=0)/[square root of 1/N[N.summation over
i=1]Var[t.sub.iT]|[[rho].sub.i]=0]] (2)
In expression (2), the term t-bar denotes the average of the actual
individual cross-section's ADF statistics. For various T and lags,
Im, Pesaran and Shin compute through Monte Carlo simulations the values
of the moments, E[[t.sub.iT]|[[rho].sub.i] = O] and
Var[[t.sub.iT]|[[rho].sub.i] = O]. They show that the [t.sub.IPS] will
be normally distributed as N (0, 1) as N and T tend to infinity [see,
Baltagi (2005)]. Another widely used panel unit root test, the
Maddala-Wu (1999) panel unit root test has many advantages, the main
positive features being that the test can be applied even to an
unbalanced panel, the cross section's individual ADF regressions
may have different lag lengths, and finally the test can incorporate the
p-values from any other univariate unit root tests such as the Phillips-
Perron unit root test, besides the ADF unit root tests. The Maddala-Wu
test panel statistic, MW[lambda], either [MW.sub.ADF] or [MW.sub.pp]. is
computed by combining the observed p-values of the individual
cross-sectional members' ADF unit root tests or their actual
p-values from the Phillips-Perron unit-root tests (1988). The Maddala-Wu
panel test statistic which is distributed as a Chi-Square distribution
with 2N degrees of freedom, in general can be expressed as,
MW[lambda] = -2[N.summation over (i=1)]ln[[pi].sub.i] (3) i=1
The IPS and Maddala-Wu panel unit root tests belong to the
first-generation panel unit root tests that assume that there is no
cross-sectional dependence among the panel members. Cross-sectional
dependence or cross-sectional correlation are often found among
countries through the spill-over effects, common economic and other
links, transfer of technology, movements of human capital and foreign
private investment, custom unions and the omitted factors.
It can be noted that African economies are not immune to
cross-sectional dependence as they are economically and culturally
interlinked and share many common features as it is found in the
literature that cultural traits do affect economic behavior of the
economic participants. It has been demonstrated by Banerjee et al.
(2004), Gengenbach et al. (2005), Strauss and Yogit (2003) and
O'Connel (1998) that in the presence of cross-sectional dependence
among the residuals, the panel unit root tests suffer from adverse
effects of size and power. O'Connel shows how the presence of
cross-sectional dependence leads to enhanced empirical significance
level of tests with a nominal size of 5% to a dramatic level of 50%,
often leading to an over-rejection of the null hypothesis. Therefore,
there is a need for applying some of the second-generation panel unit
root tests such as the Pesaran's Cross-Sectional IPS (CIPS) test
(2007) and the Moon and Perron (2004) panel unit root test which control
for the presence of cross-sectional dependence. Before applying these
tests, we have to find out whether the data sample suffers from
cross-sectional correlation. The most widely used test to detect
statistically the presence of cross-sectional correlation in a panel is
the Cross-Section Dependence test (CD) developed by Pesaran (2007).
Pesaran (2007) shows how the observed CD test statistic, which is
distributed as N (0, 1), can be computed as follows:
CD = [[TN(N - 1)/2].sup.-1/2][^/[rho] (4)
In the mathematical expression (4), [^/[rho] denotes the pair-wise
cross-section correlation coefficients and N and T, respectively are the
number of cross-sections in the panel and time period included for each
cross-section. In the CD test, the null hypothesis is that the
cross-sectional units are independent. Pesaran's CIPS test is
derived as an average of the cross-sectionally augmented Dickey-Fuller
(CDF) tests of all the cross-sectional units. In the presence of serial
correlation in the data generating processes, the CDF can be modified to
be cross-sectionally augmented Dickey-Fuller test (CADF) and is
expressed as:
[DELTA][x.sub.it]=[[alpha].sub.i][[beta].sub.i][x.sub.i,t-1] +
[[gamma].sub.i][[bar.x].sub.t-1] + [[PHI].summation over
j=0][[delta].sub.ij][DELTA][[bar.x].sub.t-j] + [[PHI].summation over
j=1][[theta].sub.ij][DELTA][x.sub.i,t-j] + [e.sub.it] (5)
Similarly, the CIPS statistics can be derived as:
CIPS = (1/N)[N.summation over (i=1)][CADF.sub.i] (6)
Where it is posited that [[bar.x].sub.t-1] = (1/N)[N.summation over
(i-1)][x.sub.it-1], [DELTA][[bar.x].sub.t] = (1/N)[N.summation over
(i=1)][DELTA][x.sub.it]. In equation (5), for CADF unit root test, the
observed t-statistics of the estimate of [[beta].sub.i] is used in
conducting the unit root testing. Pesaran also provides an average of
the truncated version of the CADF statistics, CIPS*. The critical values
for CADF, CIPS and CIPS* for various deterministic terms in the CADF
regressions are provided by Pesaran (2007). Pesaran's CIPS test
explicitly assumes that there is only one common factor in the error
structure of the series.
The Moon and Perron panel unit root test (2004), unlike the
Pesaran's CIPS test, assumes that the error structure of the data
generating processes possess more than one common factor. In order to
conduct the panel unit root tests, they develop two modified test
t-statistics, [t.sup.*.sub.-a] and [t.sup.*.sub.-b], that are based on
the pooled estimation of the first-order serial correlation coefficient
of the data generating process series [for details, see Moon and Perron
(2004)]. Furthermore, they demonstrate that the test statistics are
asymptotically normally distributed.
The above discussed panel unit root tests do not take into
consideration the presence of structural breaks in the data generating
process. But, it has been demonstrated by Perron (1989) that ignoring
the presence of structural breaks in a Unit root test results in biased
results and often the presence of a structural break in the data
generating process can be mistaken for a unit root. Therefore in this
paper, we apply the panel stationarity test developed recently, by
Carrion-i-Silvestre et al. (2005) which, unlike the Zivot-Andrews
univariate structural break unit root test (1992) and Im et al. (2005)
panel unit LM unit root tests, has many desirable econometric features.
The main advantages of the Carrion-i-Silvestre et al. test) test are
that the test allows for the possible presence of a multiple number of
structural breaks for each panel member at different dates and the test,
unlike other panel structural break tests, maintains the null hypothesis
of stationarity. Generally, one needs strong evidence to reject the null
hypothesis. Additionally, the CBL test, a panel version of the
Hadri's univariate KPSS (2000) test with structural breaks, is
flexible enough so that we can control for the presence of
cross-sectional dependence via empirical bootstrapping technique.
Following Carrion-i-Silvestre et al. (2005)'s notations and their
exact specification, we can express the data generating model,
[y.sub.it], used for estimation as follows:
[y.sub.i,t]=[[alpha].sub.i]+ [[m.sub.i].summation over (k=1)]
[DU.sub.i,k,t] + [[beta].sub.i]t + [[m.sub.i].summation over
(k=1)][[gamma].sub.i,k][DT.sup.*.sub.i,k,t] + [[epsilon].sub.i,t] (7)
In the specified model (7), [DU.sub.i,k,t] and [DT.sup.*.sub.i,k,t]
represent dummy variables with [DU.sub.i,k,t] = 1 for [T.sup.t.sub.b], k
and 0 elsewhere and [DT.sup.*.sub.i,k,t] = t - [T.sup.i.sub.b,k] and 0
elsewhere. [T.sup.i.sub.b], k is the kth date of structural break for
the ith member of the panel with k = 1, ..., [m.sub.i], [m.sub.i] > /
= 1. The model (7) can be used to allow structural breaks in both the
mean and the time trend depending on the presence or absence of a
discernible trend in the data generating process. The model allows for a
potential maximum of 5 structural breaks for each cross-sectional member
in the panel. The location of the structural breaks are determined by
the sequential procedure recommended by Bai and Perron (1998) [for
details, see Carrion- i-Silvestre (2005) and Bai and Perron (1998)]. In
order to decide the optimum number of breaks, the CBL model recommends
one of the three criteria, depending on the trending nature of the
regressors in model (7). The proposed three criteria are the Bai-Perron
(2001) Criterion (BP), the Bayesian Information Criterion (BIC) and
finally, the modified Schwartz Information Criterion (SIC) of Liu, Wu
and Zidek (LWZ, 1997). In this paper, the optimal number of breaks is
chosen using the modified SIC criterion of Liu, Wu and Zidek (1997).
Carrion-i-Silvestre et al. (2005), for hypothesis testing purposes,
derive the following standardized panel test statistic:
Z([lambda]) = [square root of
N](LM([lambda])-[bar.[epsilon]])/[bar.[zeta] (8)
In expression (8), LM ([lambda]) is the average of the individual
KPSS statistics estimated using the OLS procedure. The vector of the
relative position of the chosen structural break points is denoted by
[lambda]. Furthermore, the CBL test shows that the panel test statistic
Z ([lambda]), standardized by [xi]-bar and [??]-bar, is normally
distributed as (0, 1). In (8), [xi]-bar and [??]-bar are the average of
the individual mean and variance of [[eta].sub.I] ([lambda]i).
III. EMPIRICAL FINDINGS
The data on real per capita GDP, in constant 2000 U.S. dollars for
the period 1960-2005 on all the 27 countries, used for empirical
estimation and analysis, are obtained from the World Bank's World
Development Indicators 2007 [World Bank (2007)]. For estimation and
analysis, the data are expressed in natural logarithms.
Table 1 presents some of the important summary statistics related
to the real per capita GDP series in the African countries included in
the study. Table 1 reveals in terms of the summary statistics, a high
degree of heterogeneity in the level of economic development over the
period 1960-2005 in the African economies included in the study, despite
these economies having many structural similarities. In terms of the
average real per Capita GDP during the period under investigation,
Gabon, Seychelles and South Africa have experienced relatively speaking,
high level of PRGDP, whereas Burundi has ranked the lowest in terms of
the PRGDP. The overall evidence from the Jarque-Bera (JB) normality test
results, reported in Table 1, point out that for the real per capita GDP
data series of the African countries in the included sample, the
assumption of normality holds well. The minor exceptions are the two
sets of countries, Gabon and Kenya, and Mauritania and South Africa, for
which we reject the null hypothesis of normality at the 5% and 1% level,
respectively.
The univariate unit root tests results for the level PRGDP series
are reported in Table 2. It is clear from the reported ADF (1979,1981),
Phillips-Perron (1988) and the KPSS (1992) tests results, with the
exceptions of Burkina Faso, Kenya, Lesotho, Niger, Nigeria and
Seychelles, in all African countries the real GDP per capita series are
found to be non-stationary in levels and thus they are not integrated of
the order zero, I (0). While the ADF and the Phillips-Perron unit root
tests maintain the null-hypothesis of non-stationarity, the KPSS states
the null of stationarity. Table 3 presents the results of the ADF,
Phillips-Perron and the KPSS univariate unit root tests for
first-differenced series. The ADF test results overwhelmingly reject for
all the countries the null-hypothesis of non-stationarity at the 5 %
level. The findings from the Phillips-Perron tests echo the same
conclusion, with the sole exception of Botswana, for which the null
hypothesis is not rejected at the 5 % level. The KPSS tests results show
that with the sole exception of Senegal, for all the countries we cannot
reject the null-hypothesis of stationarity at the 5% level. Therefore,
the results in general indicate that the PRGDP series are difference
stationary and thus in levels they are integrated of the order, I (1).
As it has been demonstrated in the time-series literature that the
univariate unitroot tests lack sufficient power, information from a
panel of 27 African countries for the period 1960-2005 is used to
investigate the stochastic properties of the PRGDP series in these
countries. In Table 4, we report the results of the first-generation
panel unit-root tests. For the level PRGDP series, the LLC, Breitung,
IPS, Maddala-[Wu.sub.ADF] and the Maddala-[Wu.sub.PP] panel unit- root
tests fail to reject the null-hypothesis of non-stationarity as
indicated by larger p-values. For the level and first-differenced
series, the Hadri test rejects the null-hypothesis of joint stationarity
against the alternative of the presence of a unit root in at least one
of the panel members at the 1% level. This finding of the Hadri tests
could be due to the tests' shortcomings. For the first-differenced
series, all the panel unit-root tests, with the exception of the Hadri
test, strongly reject the null-hypothesis of non-stationarity. Thus, the
results from the first-generation panel unit root tests, as in the case
of univariate unit-root test results overwhelmingly support the
conclusion that the PRGDP series are integrated of the order one, I(1).
However, it should be noted that the first-generation panel unit-root
tests assume that the members of the panel are independent and there is
no cross-sectional dependence among them. But, given the fact that the
African countries included in the investigation trade amongst themselves
share many economic similarities, have spillover effects, and are
well-integrated financially, it is reasonable to expect cross-sectional
dependence among the panel. It has been recently demonstrated by
O'Connel (1998), Banerjee et al. (2005), Gengenbach et al. (2005)
and Strauss and Yogit (2003) that in the presence of cross-sectional
dependence or correlation, panelunit root tests suffer from size
distortions resulting in frequent rejections of the null-hypothesis.
Therefore in the literature, it is recommended that the researchers
apply the so-called second-generation panel unit-root tests that control
for cross-sectional dependence. Some of the well-known second-generation
panel unit-root tests are the Pesaran Cross-sectional IPS (CIPS) test
(2003, 2007) and the Moon-Perron (MP) test [see, Pesaran (2007), Moon
and Perron (2004), Breitung and Perron (2005)]. It is recommended in the
literature that before applying these tests, one has to find out whether
there is any statistical evidence of cross-sectional dependence or
correlation in the panel data sample used for investigation. One widely
employed test to statistically determine the presence of cross-sectional
dependence is the CD test developed recently by Pesaran (2006, 2007).
Table 5 shows the results of the CD tests, using various
deterministic terms, for the panel data used in the study. It is clear
from the results of the Pesaran's CD tests reported in Table 5, the
computed CD test statistics are greater than the critical 1% value and
thus the null-hypothesis of cross-sectional independence is strongly
rejected. This finding is robust to both the chosen lag order and the
inclusion of various deterministic terms. Therefore, some of the
second-generation panel unit-root tests need to be applied to control
for the presence of cross-sectional dependence.
In Table 6, the results of the individual cross-section's CADF
test results are reported. For CADF specification incorporating both the
intercept and the trend deterministic terms, with the exceptions of the
Central African Republic, Liberia, Mauritania, Sierra Leone, and Togo,
we fail to reject the null of non-stationarity. The results of the
Pesaran's CIPS tests (2007) and the Moon and Perron (2004) panel
unit root tests are shown in Table 7. The results show that both these
tests fail to reject the null-hypothesis of non-stationarity at the 5%
level.
Table 8 reports the Carrion et al. panel stationarity unit root
test that allows for endogenously determined multiple structural breaks
and is flexible enough to control for cross-sectional dependence by
accommodating the appropriate critical values by the bootstrapping
procedure. In Panel A of Table 8, the last two columns show the computed
10% and 5% finite KPSS critical values, by means of Monte Carlo
simulations of 20,000 draws. These critical values are used to control
for the finite sample bias that might be present in small samples used
in the paper. Comparing the observed KPSS statistics with the finite
sample KPSS 5% critical values, we reject the null hypothesis of
stationarity for Benin, Botswana, Burkina Faso, Burundi, Chad, Congo
Democratic Republic and Cote d'Ivoire, Gabon, Liberia ,Mauritania
and Senegal.
Therefore, in these eleven countries the PRGDP series are
integrated of the order 1, I ~ (1), and hence non-stationary. However,
for the majority of the countries included in the study, the series are
integrated of the order zero, I ~ (0), implying that they are stationary
in levels. Furthermore, as shown in Table 9, all the African countries
included in the study have experienced multiple structural breaks, with
the exceptions of Mauritania. Benin, Botswana, Ghana and Lesotho that
have witnessed a maximum number of five structural breaks. Another
interesting observation is that each of 17 of the 27 countries studied
has gone through four structural breaks in its PRGDP series. The test
results show that different countries have experienced a different
number of structural breaks at different dates. These findings further
reveal the presence of heterogeneity in the included data sample. With
regard to the dates of the structural breaks noted in Table 9, the
majority of them have occurred in the 1970s, 1980s, and 1990s. Some of
the possible causes of these statistically discernible structural breaks
could be the lagged effects of the famous energy crisis. In addition,
most African countries gained their independence in the 1960s and 1970s.
During the 1980s and 1990s many of these countries embraced trade and
financial liberation policies, and frequent political regime changes,
debt and structural adjustment problems of 1980s and 1990s, and the
price reductions of primary agricultural commodities in the 1960s.
Comparing the observed panel KPSS test statistics, using the
assumptions of homogeneous and heterogeneous variance, with the
bootstrapped empirically distributed critical values at the 1%, 5% and
10% levels we fail to reject the joint null hypothesis of stationarity.
Specifically, for both the homogeneous and heterogeneous variance
assumptions, we find the actual panel KPSS test statistics are less than
the bootstrapped critical values at the 1%, 5%, and 10% levels of
significance. Thus, we can conclude that, after allowing for multiple
structural breaks and controlled for cross-sectional dependence, the
PRGDP series in African economies are integrated of the order zero, I
(0), and therefore they are stationary with broken trends. Overall the
panel unit root test results are consistent with those of the individual
country KPSS test results reported in Panel A of Table 8.
IV. CONCLUSIONS AND POLICY IMPLICATIONS
This paper, for the first time in the literature, by using a panel
data sample of 27 African economies over the period 1960-2005, applies a
battery of both univariate and panel unit root tests and attempts to
investigate the stochastic properties of the per capita real GDP
time-series. The findings are that the per capita real GDP series in
this panel are both individually and jointly stationary with broken
trends. The presence of structural breaks experienced by the African can
be explained by the fact that many of the countries gained their
independence in the 1960s and 1970s. Similarly, a number of structural
breaks occurred during. During the 1980s and 1990s many African
countries embraced trade and financial liberation policies. The results
of univariate unit root tests and the panel test that allows for the
presence of endogenously determined structural breaks and controls for
the presence of cross-sectional dependence by empirical distribution of
the panel test statistic using bootstrap techniques overwhelmingly show
that in these countries the per capita real GDP time-series are
stationary in levels. The finding of stationary per capita real GDP has
both theoretical and policy implications. For econometric modeling and
forecasting, if other relevant variables in an econometric model that
includes the per capita real GDP series of these African countries
during the period under investigation are found stationary, then there
is no need for using the cointegration technique. Instead, one can use
the Ordinary Least Squares (OLS) for modeling. From the policy
perspective, fiscal and monetary policy actions that are designed to
bring changes in the level of per capita real GDP in these countries
will have a temporary rather than any permanent effects. The policy
shocks that the output levels receive in these countries will be
transitory in nature, but will dampen and disappear with time. The
equilibrium level of per capita real GDP in these countries will be mean
reverting.
Acknowledgements
The authors are grateful to M. Hashem Pesaran, Takeshi Yamagata,
Syed Basher and Carrion-i-Silvestre for providing Gauss codes for
running the CD, CADF and CIPS tests, and the CBL panel stationarity
tests with multiple-structural breaks, respectively.
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VASUDEVA N. R. MURTHY
Creighton University, Omaha, NE, U.S.A.
EMMANUEL ANORUO
Coppin State University, Baltimore, MD, U.S.A.
Table 1
Real Per Capita GDP in African Countries,
1960-2005: Summary Statistics
Country Mean Maximum Minimum
Benin 290.858 326.308 258.366
Botswana 1678.736 4648.541 228.712
Burundi 123.978 156.754 83.450
Cameroon 669.785 1020.278 475.434
Central African
Republic 296.859 359.259 225.187
Chad 196.371 266.699 141.112
Congo Democratic
Republic 229.144 344.103 82.158
Cote d'Ivoire 746.494 1118.092 563.497
Gabon 3871.620 7714.232 1659.427
Ghana 242.486 291.050 180.821
Kenya 382.619 450.584 233.176
Lesotho 323.819 550.373 140.439
Liberia 509.736 862.529 56.520
Madagascar 306.485 410.061 209.399
Malawi 137.766 166.104 98.127
Mauritania 405.161 465.693 267.624
Niger 224.692 347.214 152.632
Nigeria 381.428 479.593 258.175
Rwanda 237.666 292.806 152.007
Senegal 429.814 483.822 377.322
Seychelles 4545.133 7478.851 2188.276
Sierra Leone 239.339 346.280 139.523
South Africa 3056.598 3561.262 2207.367
Togo 269.479 346.280 181.964
Zambia 432.076 604.430 295.034
Zimbabwe 756.292 690.372 426.373
Country Standard JB
Deviation
Benin 17.031 2.038
Botswana 1293.239 4.023
Burundi 20.332 2.576
Cameroon 146.984 4.226
Central African
Republic 44.741 4.442
Chad 30.441 1.150
Congo Democratic
Republic 93.627 4.564
Cote d'Ivoire 156.187 5.175
Gabon 1172.050 7.116 *
Ghana 29.883 2.338
Kenya 65.174 9.398 *
Lesotho 125.077 5.033
Liberia 294.101 5.899 *
Madagascar 65.730 5.033
Malawi 18.221 4.994
Mauritania 41.783 47.380 **
Niger 65.048 4.635
Nigeria 53.947 0.603
Rwanda 31.615 0.470
Senegal 28.851 1.955
Seychelles 1738.887 3.697
Sierra Leone 44.214 3.924
South Africa 318.464 12.302 **
Togo 36.669 0.598
Zambia 98.652 4.283
Zimbabwe 74.822 3.665
* and ** denote significant at the 5% and 1% levels, respectively.
Source: World Development Indicators 2007 (World Bank, 2007).
Table 2
Univariate Unit Root-Test Results: Level Series
Phillips-
Country ADF Perron KPSS
Benin -2.010 (0.578) -2.182 (0.488) 0.096 *
Botswana -1.388 (0.850) -1.145 (0.909) 0.189 *
Burkina Faso -3.892 (0.21) -3.953 (0.018) * 0.087
Burundi -0.813 (0.956) -0.733 (0.964) 0.213 *
Cameroon -2.895 (0.175) -1.531 (0.804) 0.144 *
Central African
Republic -2.198 (0.479) -2.268 (0.442) 0.176 *
Chad -0.769 (0.961) -0.911 (0.946) 0.198 *
Congo Democratic
Republic -2.947 (0.158) -1.851 (0.663) 0.196 *
Cote d'Ivoire -2.179 (0.489) -2.179 (0.489) 0.142
Gabon -1.962 (0.605) -1.975 (0.599) 0.186 *
Ghana -0.254 (0.989) -0.254 (0.989) 0.180 *
Kenya -4.181 (0.011) * -1.299 (0.875) 0.211 *
Lesotho -4.166 (0.010) * -3.103 (0.118) 0.089
Liberia -2.255 (0.448) -2.004 (0.584) 0.125 *
Madagascar -2.154 (0.504) -2.162 (0.498) 0.107
Malawi -2.040 (0.562) -1.960 (0.607) 0.166 *
Mauritania -3.621 (0.039) * -4.529 (0.004) * 0.149 *
Niger -2.534 (0.311) -2.809 (0.202) 0.103
Nigeria -2.420 (0.364) -2.066 (0.550) 0.096
Rwanda -3.397 (0.065) -3.321 (0.076) 0.157 *
Senegal -1.778 (0.699) -1.319 (0.870) 0.192 *
Seychelles -1.844 (0.667) -2.127 (0.517) 0.082
Sierra Leone -1.720 (0.723) -1.917 (0.623) 0.177 *
South Africa -3.061 (0.128) -2.523 (0.316) 0.186 *
Togo -3.216 (0.094) -3.346 (0.072) 0.181 *
Zambia -1.592 (0.783) -1.581 (0.785) 0.118
Zimbabwe -1.124 (0.913) -0.640 (0.971) 0.173 *
* Significant at the 5% level in rejecting the
null-hypothesis. P-values are in parentheses. The
5% and 10% critical values for the KPSS test are
0. 146 and 0.119 ,respectively (Eviews 6.0).
Deterministic terms include both the individual
effects and individual linear trends.
Table 3
Univariate Unit-Root Test Results: First-Differenced Series
Country ADF Phillips-Perron KPSS
Benin -5.903 (0.000) * -5.892 (0.000) * 0.085
Botswana -3.618 (0.040) * -2.691 (0.255) 0.090
Burkina Faso -8.932 (0.000) * -9.920 (0.000) * 0.060
Burundi -8.517 (0.000) * -8.517 (0.000) * 0.058
Cameroon -2.157 (0.500) * -4.821 (0.001) * 0.089
Central African
Republic -5.234 (0.000) * -5.314 (0.000) * 0.141
Chad -6.233 (0.000) * -6.232 (0.000) * 0.064
Congo Democratic
Republic -5.180 (0.000) * -5.5412 (0.000) * 0.098
Cote d'Ivorie -7.141 (0.000) * -7.131 (0.000) * 0.063
Gabon -4.872 (0.001) * -4.680 (0.002) * 0.074
Ghana -4.956 (0.001) * -4.872 (0.002) * 0.143 *
Kenya -7.414 (0.000) * -8.101 (0.000) * 0.086
Lesotho -6.710 (0.000) * -8.071 (0.000) * 0.251 ***
Liberia -3.774 (0.028) * -3.857 (0.023) * 0.080
Madagascar -6.913 (0.000) * -6.952 (0.000) * 0.124 *
Malawi -7.156 (0.000) * -7.202 (0.000) * 0.111
Mauritania -7.790 (0.000) * -7.888 (0.000) * 0.155 *
Niger -5.993 (0.000) * -5.993 (0.000) * 0.076
Nigeria -4.045 (0.015) * -4.649 (0.003) * 0.093
Rwanda -8.410 (0.000) * -10.983 (0.000) * 0.126 *
Senegal -8.729 (0.000) * -11.607 (0.000) * 0.500 ***
Seychelles -6.078 (0.060) * 6.082 (0.000) * 0.087
Sierra Leone -5.509 (0.000) * -5.549 (0.000) * 0.117
South Africa -3.704 (0.033) * -3.729 (0.036) * 0.215 **
Togo -6.327 (0.000) * -6.327 (0.000) * 0.132 *
Zambia -6.835 (0.000) * -6.835 (0.000) * 0.132 *
Zimbabwe -4.691 (0.003) * -4.683 (0.003) * 0.069
* , ** and *** imply the rejection of the null-hypothesis
at the 10%, 5% and 1% levels, respectively. P-values are
in parentheses. The 5% and 10% critical values for the KPSS
test are 0.146 and 0.119, respectively (Eviews 6.0).
Deterministic terms include both the individual
effects and individual linear trends.
Table 4
The First-Generation Panel Unit-Root Test Results
Test Level Series First-Differenced Series
LLC 0.779 (0.782) 6.212 (1.000)
IPS -0.096 (0.462) -5.465 (0.000) *
BREITUNG 0.748 (0.773) -3.581 (0.000) *
[MW.sub.ADF] 51.658 (0.565) 112.833 (0.000) *
[MW.sup.PP] 54.554 (0.453) 683.706 (0.000) *
[HADRI.sub.Z] 10.689 (0.000) ** 7.184 (0.000) **
P-values are in parentheses (Eviews 6.0) . Deterministic terms
incorporated in the tests are both individual effects and
individual linear trends. Specified lags are four. * denote the
rejection of the null-hypothesis at the 1% level of
significance. ** indicate the rejection of the null of
stationarity
Table 5
Results of the Pesaran's CD Tests
Deterministic Lags CD
Terms Statistic
Intercept 0 9.30 *
1 6.97 *
2 6.57 *
3 6.80 *
Intercept 0 10.32 *
and Trend 1 7.99 *
2 7.68 *
3 7.49 *
* Significant at the 1% level, in rejecting
the null-hypothesis (See Pesaran, 2007).
Table 6
The Pesaran CADF Unit-Root Test Results
With
With Intercept
Intercept and Trend
Country [CADF.sub.i] [CADF.sub.i]
Benin -1.205 -2.352
Botswana -0.633 -2.100
Burkina Faso 0.235 -2.137
Burundi -1.304 -1.342
Cameroon -2.743 -3.061
Central African Republic -0.462 -3.540 *
Chad 2.473 -2.135
Congo Democratic Republic -0.700 -2.994
Cote d'Ivoire 0.339 -1.378
Gabon -2.225 -2.233
Ghana -2.233 -2.017
Kenya -1.835 -2.049
Lesotho -0.623 -2.629
Liberia -1.639 -3.653 *
Madagascar -1.096 -2.020
Mauritania -6.296 * -5.636 *
Niger -1.791 -2.924
Nigeria -2.451 -3.138
Rwanda -2.458 -2.992
Senegal -2.648 -0.798
Seychelles -0.919 -2.239
Sierra Leone -1.697 -4.450 *
South Africa -2.115 -2.508
Togo -2.252 -3.812 *
Zambia -1.458 -1.519
Zimbabwe -2.237 -1.514
Lags = 3. For [CADF.sub.i] with intercept and trend the
5% critical values, respectively are -3.34 and -3.80
(Pesaran, 2007, Table 1(b) and 1(c)).
Table 7
The Second-Generation Panel Unit-Root Tests *
Moon and
Perron
Pesaran's Pesaran's [T.sup.* [T.sup.
CIPS CIPS * .sub.a] *.sub.b]
With Intercept -1.749 -1.745 0.074 0.868
With Intercept -2.464 -2.464 -1.225 -1.172
and Trend
* For levels, with lags = 3. For CIPS with intercept and
Intercept and Trend the 5 % critical values are respectively,
-2.16 and -2.58 (Pesaran, 2007, Table 2 (b) and 2 (c).
Table 8
Carrion et al. Panel Stationarity Test Results
Panel A: Individual Panel Member Statistics and Structural Breaks
Finite
Finite Sample
Sample KPSS
KPSS Critical
Individual Critical Values
KPSS Values Values
Statistics [m.sup.i] (10%) (5%)
Benin 0.121 * 5 0.046 0.051
Botswana 0.133 * 5 0.050 0.057
Burkina Faso 0.095 * 4 0.064 0.076
Burundi 0.132 * 4 0.056 0.063
Cameroon 0.079 3 0.085 0.100
Central African
Republic 0.096 2 0.105 0.126
Chad 0.128 * 4 0.071 0.084
Congo Democratic
Republic 0.136 * 3 0.088 0.106
Cote dlvoire 0.088 * 4 0.071 0.084
Gabon 0.179 * 4 0.080 0.101
Ghana 0.081 5 0.059 0.072
Kenya 0.051 3 0.151 0.196
Lesotho 0.086 5 0.074 0.096
Liberia 0.124 * 3 0.108 0.137
Madagascar 0.078 3 0.082 0.095
Malawi 0.057 4 0.067 0.078
Mauritania 0.295 *** 1 0.277 0.360
Niger 0.057 4 0.063 0.074
Nigeria 0.068 3 0.076 0.089
Rwanda 0.100 2 0.099 0.118
Senegal 0.156 * 4 0.059 0.068
Seychelles 0.068 3 0.076 0.089
Sierra Leone 0.123 2 0.188 0.145
South Africa 0.099 3 0.095 0.114
Togo 0.093 3 0.084 0.100
Zambia 0.073 3 0.084 0.100
Zimbabwe 0.078 2 0.170 0.219
Panel B: Panel Test Statistics
Z ([lamba]) Homogeneous Variance 7.333 (0.013)
Z ([lamba]) Heterogeneous Variance 5.632 (0.009)
Panel C Bootstrap distribution (Allowing for cross-sectional dependence)
Critical Values 90% 95% 97.50% 99%
Homogeneous Variance 12.960 13.604 14.239 15.095
Heterogeneous Variance 11.495 11.900 12.286 12.800
* Significance at the 5% level. P-values are shown in
parentheses. Maximum number of breaks, mi, allowed is 5.
Table 9
Individual Panel Member's Structural Breaks
Structural
Break Dates
[T.sup.i [T.sup.i [T.sup.i
Country [m.sub.i] .sub.b,1] .sub.b,2] .sub.b,3]
Benin 5 1965 1974 1980
Botswana 5 1970 1976 1982
Burkina Faso 4 1966 1975 1981
Burundi 4 1975 1984 1994
Cameroon 3 1974 1980 1989
Central African
Republic 2 1979 1990 --
Chad 4 1965 1978 1984
Congo Democratic
Republic 3 1977 1991 1997
Cote d'lvoire 4 1965 1971 1982
Gabon 4 1966 1973 1979
Ghana 5 1974 1981 1987
Kenya 3 1965 1971 1977
Lesotho 5 1965 1971 1977
Liberia 3 1982 1989 1997
Madagascar 3 1974 1980 1990
Malawi 4 1965 1971 1986
Mauritania 1 1965 -- --
Niger 4 1966 1972 1983
Nigeria 3 1969 1980 1989
Rwanda 2 1977 1993 --
Senegal 4 1968 1977 1990
Seychelles 4 1970 1977 1988
Sierra Leone 2 1968 1991 --
South Africa 4 1965 1971 1989
Togo 3 1965 1982 1991
Zambia 3 1976 1982 1991
Zimbabwe 2 1969 1999 --
Structural
Break
Dates
[T.sup.i [T.sup.i
Country .sub.b,4] .sub.b,5]
Benin 1988 1997
Botswana 1988 1998
Burkina Faso 1996 --
Burundi 1996 --
Cameroon -- --
Central African
Republic -- --
Chad 1999 --
Congo Democratic
Republic -- --
Cote d'Ivoire 1989 --
Gabon 1986 --
Ghana 1993 1999
Kenya -- --
Lesotho 1988 1995
Liberia -- --
Madagascar -- --
Malawi 1994 --
Mauritania
Niger 1991 --
Nigeria -- --
Rwanda
Senegal 1998 --
Seychelles 1996 --
Sierra Leone -- --
South Africa -- --
Togo -- --
Zambia -- --
Zimbabwe -- --
