Using data for SAARC region, we found real GDP per capita is nonlinear stationary implying that shocks to economy by economic policies (external or internal) have permanent effects on real per capita GDP of SAARC countries. This finding reveals that classical growth model works better to boost economic growth in long run.GDP, Non-stationarity, panel unit root tets

Shabbir, Muhammad

Shahbaz, Muhammad

Tiwari, Aviral

English

Research Papers in Economics

Is Per Capita GDP Non-linear Stationary in SAARC Countries? 
 
Aviral Kumar Tiwari 
Faculty of Management, ICFAI University Tripura, India 
 
Muhammad Shahbaz 
COMSATS Institute of Information Technology, Lahore, Pakistan 
 
Muhammad Shahbaz Shabbir 
University of Illinois at Urbana Champaign, Champaign, USA 
 
 
 
Abstract:  
Using data for SAARC region, we found real GDP per capita is nonlinear stationary implying 
that shocks to economy by economic policies (external or internal) have permanent effects on 
real per capita GDP of SAARC countries. This finding reveals that classical growth model works 
better to boost economic growth in long run. 
  
Keyword: GDP, Non-stationarity 
JEL Codes: C23, E3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Introduction 
Economic  growth  is  basic  indicator  to  measure  economic  prosperity  of  any  nation  while 
economic  wellbeing  is  judged  by  economic  development.  To  measure  economic  growth, 
normally,  we  use  real  GDP  per  capita.  This  variable  is  also  used  to  analyse  the  effect  of 
economic policies as well as to forecast future trends of economic growth. The fundamental 
problem with time series as pointed in econometeric literature is, if data generating process is 
influenced by linear trend then series will contain unit root problem i.e., series is considered non-
stationary at its level form. The unit root problem in series opens up new directions not only for 
macroeconomic theories but also for policy makers (Mishra et al., 2009). This issue was raised in 
pioneering paper by Nelson and Plosser (1982) who investigated the nonstationarity of real GDP 
and latter on by Campbell and Mankiw (1987), Perron and Philip (1987), Zivot and Andrews 
(1992), Nelson and Murray (2000), Sen (2004), Chang et al. (2005), Narayan (2007) and Hurlin 
(2008) etc.  
        
Economic literature has provided many studies who investigated whether there was a unit root 
problem in real GDP per capita. For instance, Li (2000), Smyth (2003), Narayan (2004a, 2008b) 
and Smyth and Inders (2004) for Chinese economy, Narayan and Narayan (2008) for Fiji islands, 
Aguirre and Ferreira (2001) for Brazil, reported that real GDP per capita contained a unit root. 
Further,  Alba  and  Papell  (1995)  for  newly  industrialized  economies,  Ben-David  and  Papell 
(1998) for 16 developing economies, Narayan (2008b)
1 for 15 Asian countries found unit root 
problem in real GDP per capita series i.e. real GDP per contained a unit root.   
    
In African economies, Chang et al. (2005) used nonlinear (logistic) unit root test developed by 
Leybourne et al. (1998) to investigate the unit root problem containing the series of real GDP per 
capita of African countries over the period of 1960-2000
2. Their findings indicated that real GDP 
per capita contained unit root problem in Botswana, Central African Republic, Cote d' Ivoire, 
Ghana, Madagascar, Mali, Mozambique, Mauritius, Niger, Rwanda, Zambia, Burundi, Guinea, 
Guinea-Bissau and Lesotho. Stationarity in real GDP per capita was found in the rest countries 
accompanied with stabilization in economic policies. Romero-Avila (2007) used panel unit root 
test to examine stationarity of  real GDP per  capita by incorporating structural breaks in the 
series. But, Murthy and Anoruo (2009) pointed out that the findings by Romero-Avila (2009) 
may provide inconsistent and misleading inferences due to the variations in economic, political 
and structural changes in the economies. Using time series data for real GDP per capita of 27 
African countries, Murthy and Anoruo (2009) conducted a study to examine unit root property of 
                                                           
1 Narayan (2008b) applied ADF and KPSS univariate tests without structural breaks. 
2  Botswana,  central  African  Republic,  Cote  d'  Ivoire,  Gabon,  Ghana,  Kenya,  Madagascar,  Mali,  Mozambique, 
Mauritius,  Niger,  Nigeria,  Rwanda,  Senegal,  Tanzania,  Uganda,  South  Africa,  Zambia,  Zimbabwe,  Burundi, 
Burkina Fasco, Ethiopia, Guinea, Guinea-Bissau and Lesotho.  GDP series by using non-linear unit root test developed by  Kapetanios et al. (2003)
3. Their 
analysis indicated the rejection of hypothesis of non-stationarity of per capita GDP in African 
countries namely Burundi, Central African Republic, Chad, Congo Democratic Republic, Ghana, 
Kenya, Lesotho, Liberia, Madagascar, Malawi, Seychelles, Sierra Leone and Togo and shocks of 
economic policies on these economies are transitory.          
 
Recently, Mishra et  al.  (2009) examined nonstationarity property of real GDP per capita by 
accommodating  structural  change  in  the  trend  function  for  Pacific  islands.  Their  findings 
indicated that momentary variations due to irregular changes in trend affected the permanent 
secular component of real GDP while in real GDP per capita in Kiribati and Fiji island contained 
unit root due to structural breaks in series indicating political instability along with shocks on 
economic growth path in Fiji and affect of external disaster on commodity prices in Kiribati.    
 
To the best of our knowledge there is no study in the context of SAARC countries in the context 
of analyzing the stationary property of the per capita GDP as these countries have been tiding 
their relations strongly in order to boost the economic growth of the region by implementing 
various  kinds of  economic  and financial, bilateral  and  multilateral environmental and liberal 
trade  policies.  Therefore,  through  this  study  we  contribute  in  this  direction.  Our  second 
contribution lies in implementing a recently developed nonlinear panel unit root test.  
 
The rest part of study is organized as following: section-II describes methodology and data and 
results interrelations are discussed in section-III. Finally, section-IV concludes the study. 
 
II. Methodological Framework 
However, we preferred a panel nonlinear unit root test developed by Ucar and Omay (2009) in 
the framework of Kapetanios et al. (2003). Breitung and  Pesaran (2008) and Baltagi (2005) 
suggested that  in  the time-series  econometrics  literature,  the  usual procedure  to  increase the 
power of unit root tests, in light of shorter univariate time series data, is to use the panel data. 
Therefore, for the analysis we have used a more recent test proposed by Ucar and Omay (2009) 
for heterogeneous panel. This test can be explained as follows. Let  it y be Panel Exponential 
Smooth  Transition  Autoregressive  Process  of  order  one  )) 1 ( (PESTAR on  the  time  domain 
T t ,......., 2 , 1 = for the  cross section  units N i ,...., 2 , 1 = .  Now  suppose that  it y follows  the DGP 
with fixed effect (heterogeneous intercept) parameter i a : 
 
t i d t i i t i i t i i i t i y y y y ,
2
, 1 , 1 , , )] exp( 1 [ e q g f a + - - + + = D - - -        (1) 
 
                                                           
3  Benin,  Botswana,  Burkina  Fasco,  Burundi,  Cameroon,  Central  African  Republic,  Chad,  Congo  Democratic 
Republic,  Cote d' Ivoire, Gabon, Ghana, Kenya, Lesotho, Liberia, Madagascar, Malawi, Mauritania, Niger, Nigeria, 
Rwanda, Senegal, Seychelles Sierra Leon, South Africa, Sudan, Tango and Zambia. Where  1 ³ d is the delay parameter and  0 > i q implies the speed of mean reversion for all i. 
Further, they set  0 = i f for all i (i.e.  it y has a unit root process in the middle regime) and 1 = d , 
which gives specific  )) 1 ( (PESTAR  model: 
 
t i t i i t i i i t i y y y ,
2
1 , 1 , , )] exp( 1 [ e q g a + - - + = D - -         (2) 
 
Therefore, in the equation (2) testing the presence of nonlinear unit root in panel framework is 
simply to test the null hypothesis  1 = i q for all i against  0 > i q  for some i under the alternative 
hypothesis. However, direct testing of the  0 = i q  is somewhat problematic because  i g is not 
identified under the null hypothesis. This problem has been sorted out by applying first-order 
Taylor series approximation to the  ) 1 ( PESTAR   model around  0 = i q  for all i. Hence, we obtain 
the auxiliary regression: 
 
t i t i i i t i y y ,
3
1 , , e d a + + = D -               (3) 
. i i i where g q d =  
 
Further, they established the hypotheses for unit root testing based on regression (3) as follows: 
0 : = i H d o ; for all i (i.e. linear nonstationarity) 
0 : < i a H d ; for some i (i.e. nonlinear stationarity) 
 
They proposed a panel unit root test which is computed through taking the simple average of 
individual  KSS  statistics.  The  KSS  statistic  for  the  th i individual  is  simply  t-ratio  of  i d   in 
regression (3) defined by 
 
2 / 3
1 ,
'
1 , ,
3
1 ,
'
, ) ( - -
- D
=
i i NL i
i i
NL i y M y
y M y
t
t
t
s )
              (4)   
       
Where NL i, s ) is  the  consistent  estimator  such  that 
2
,NL i s )   =  ), 1 /(
' - D D T y M y i i t  
. ) (
' 1 '
T T T T T I M t t t t t
- - =   Here,  , ) ,..., , (
'
, 2 , 1 , t i i i i y y y y D D D = D  
' 3
1 ,
3
1 ,
3
0 ,
3
1 , ) ,..., , ( - - = T i i i i y y y y   and 
. ) 1 ,..., 1 , 1 (
' = T t  Furthermore, for a fixed T, they defined  
 
∑
=
=
N
i
NL i NL t
N
t
1
,
1
                (5)
 
 Which is invariant average statistic when  NL i t ,  is invariant with respect to initial observations yi,0, 
heterogeneous moments 
2
i s σi
2 and 
4
i s  if yi,0=0 for all  N i ,...., 2 , 1 = . 
 
In addition to that when the invariance property (as just defined above for  NL i t ,  holds for each i) 
and the existence of moments (by truncating  NL i t ,  distribution) are satisfied (that is the individual 
statistics  NL i t ,  are iid random variables with finite means and variances) the usual normalization 
of  NL t  statistic have the limiting standard normal distribution as N→∞ such that  
 
) 1 , 0 (
) (
)) ( (
,
, N
t Var
t E t N
Z
d
NL i
NL i Nl
NL ¾® ¾
-
=
          (6)
 
 
Therefore, they produced critical values of  NL Z statistic as well as its truncated version because 
those values may be different from the fractiles of the standard normal distribution, particularly 
for small N observations, to which they converge as N goes to infinity. Further, just for sake for 
comparison we have conducted other panel unit root test (that is Im et al. 2003) based on linear 
regression.  
 
III. Data analysis and findings  
We have used time series data of real GDP per capita for SAARC countries namely, Pakistan, 
India, Bangladesh, Bhutan, Maldives, Sri Lanka, Nepal and Afghanistan over the period of 1980-
2010. World development indicators (WDI-CD-ROM, 2010) is combed to collect data for real 
GDP per capita ($ US). Nonlinear unit root test developed by Ucar and Omay (2009) and linear 
unit root test advanced by Im et al. (2003) have applied to examine whether real GDP per capita 
contains a unit root or not. The results of both tests are reported in Table-1. 
     
Table-1: Results of Nonlinear and Liner Unit Root Analysis
4. 
Intercept  NL t *   ANL Z *   NBAR t*   NBAR W *  
Lag 1 
1.2230 
(0.9983) 
8.8709 
(0.9983) 
1.2183 
(0.9988) 
8.7278 
(0.9988) 
Lag 2 
0.8300 
(0.9924) 
7.6490 
(0.9924) 
0.8274 
(0.9911) 
7.4879 
(0.9911) 
                                                           
4 Results of Levin, Lin & Chu, ADF - Fisher Chi-square, PP - Fisher Chi-square and Breitung test statistics are reported in table 
1and 2 in appendix for models when only constant term is included in regression and when constant and trend both are included 
in regression respectively.  Result of these statistics shows that PCRGDP series is nonstationary in both case when constant and 
constant and trend is included.  Lag 3 
0.8300 
(0.9924) 
7.6490 
(0.9924) 
0.8274 
(0.9911) 
7.4879 
(0.9911) 
Lag 4 
1.0801 
(0.9959) 
8.4266 
(0.9959) 
1.0855 
(0.9944) 
8.3066 
(0.9944) 
Trend and intercept          
Lag 1 
-2.3234 
(0.0464) 
-0.6200 
(0.0464) 
-2.1728 
(0.4694) 
0.1012 
(0.4694) 
Lag 2 
-2.3234 
(0.0464) 
-0.6200 
(0.0464) 
-2.1728 
(0.4694) 
0.1012 
(0.4694) 
Lag 3 
-2.3234 
(0.0464) 
-0.6200 
(0.0464) 
-2.1728 
(0.4694) 
0.1012 
(0.4694) 
Lag 4 
-2.3234 
(0.0464) 
-0.6200 
(0.0464) 
-2.1728 
(0.4694) 
0.1012 
(0.4694) 
Note: (1) p-values in parenthesis with 10000 bootstrap replications. (2)  NL t * and  ANL Z *  are 
the statistics of Ucar and Omay (2009) while  NBAR t* and  NBAR W *  are the statistics of Im et al. 
(2003). 
 
It is evident from Table-1 that when model includes only constant term in regression results 
obtained from both tests that is Ucar and Omay (2009) and Im et al. (2003) are same even if we 
are changing the lag structure in order to test the sensitivity of the results. Therefore, analysis 
through this model does not provide sufficient evidence to reject the null hypothesis of linear 
nonstationarity and hence from this model we can conclude that per capita GDP of SAARC 
countries are linear nonstationarity. However, when we incorporate trend in our model as most of 
the macroeconomic series posses the trend and our series too, we find that test statistics of Ucar 
and Omay (2009) rejects the null hypothesis of linear nonstationarity while Im et al. (2003) does 
not. This implies that these results are again robust to change in the lag structure. Hence, we can 
conclude that per capita GDP of SAARC countries are nonlinear stationarity. These findings are 
contradictory with view by Libanio (2005) that after an off-putting shock, an automatic return to 
a normal  trend will  not work and  Keynesian stabilization  policies  have to  play their role  to 
stimulate aggregate demand in an economy with full employment. Our empirical findings imply 
that fiscal and monetary stabilization policies are ineffective and in turn real GDP turns to its 
natural rate which indicates that Keynesian economic policies will have transitory impact on 
output.  In  context  of  policy  implication,  governments  of  SAARC  region  should  implement 
classical growth model as an economic stabilization policy to enhance output levels for long span 
of time.   
 
IV. Conclusion 
The present paper contributes to times series economic literature by applying the Im et al. (2003) 
and Ucar and Omay (2009) non-linear unit root tests to examine the nonlinear stationarity of real 
GDP per capita for SAARC region over the period of 1980-2010. The use of panel data increases 
the power of univariate unit root tests. The results of non-linear unit root tests pointed that real 
GDP per capita in SAARC region are nonlinear stationarity implying that business cycles are 
stationary fluctuations around a deterministic trend in SAARC countries i.e., shocks to economy by  economic  policies  have  permanent  effects.  Further,  this  also  implies  that  fiscal  and/or 
monetary or any other stabilization policies would only have permanent effects on the real output 
levels of SARC countries.  
 
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Further Evidence of the Great Ccrash, the Oil-price Shock and the Unit-root Hypothesis,

Is Chinese Provincial Real GDP Per Capita Non-stationary? Evidence from Multiple Trend Break Unit Root Tests,

Is Per Capita Real GDP Stationary? Evidence from Selected African Countries Based on More Powerful Nonlinear (logistic) Unit Root Tests,

Is There a Unit Root in Per Capita Real GDP? Panel Data Evidence from Chinese Provinces,

Slowdowns and Meltdowns: Postwar Evidence from 74 Countries,

Testing for a Unit Root in the Non-linear STAR Framework,

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Trends and Random Walks in Macroeconomic Time Series,

Unit Roots and Cointegration

What would Nelson and Plosser Find had They Used Panel Unit Root Tests? Applied Economics, Im KS,

Is per capita GDP non-linear stationary in SAARC countries?

Is per capita GDP non-linear stationary in SAARC countries?

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