This paper tests the relative version of purchasing power parity (PPP) for a set of ten Asian developing countries using panel cointegration framework. We employ 'between-dimension' dynamic OLS estimator as proposed by Pedroni (2001b). The test results overwhelmingly reject the PPP hypothesis.Purchasing Power Parity, Panel Cointegration, Unit Root

Mohammed Mohsin

Syed A. Basher

English

Research Papers in Economics

PPP TESTS IN COINTEGRATED PANELS: EVIDENCE FROM ASIAN 
DEVELOPING COUNTRIES 
 
 
 
 
 
Syed Abul Basher 
Department of Economics 
York University 
Toronto, ON M3J 1P3 
basher@yorku.ca 
 
 
and 
 
 
Mohammed Mohsin
* 
Department of Economics 
University of Tennessee 
Knoxville, TN 37996 
mmohsin@utk.edu 
 
 
 
 
Abstract: This paper tests the relative version of purchasing power parity (PPP) for a set of 
ten Asian developing countries using panel cointegration framework. We employ ‘between-
dimension’ dynamic OLS estimator as proposed by Pedroni (2001b). The test results 
overwhelmingly reject the PPP hypothesis. 
 
 
JEL classifications: F31, C22, C23  
Key Words: Purchasing Power Parity, Panel Cointegration, Unit Roots.  
 
 
 
 
 
 
 
------------------------------ 
* Corresponding author: Mohammed Mohsin, Assistant Professor, Department of Economics, 
University of Tennessee, TN 37996, USA. Tel: +1 865-974-1690; Fax: +1 865-974-4601;  
E-mail: mmohsin@utk.edu  1. Introduction 
 
The purpose of this study is to examine the empirical validity of relative 
purchasing power parity (PPP) doctrine in the context of a set of Asian developing 
economies.  In the literature there has been an influx of empirical studies on PPP 
especially in the 90s with mixed findings.  The main concern of these studies is to 
find any possible common stochastic trend(s) between exchange rates and relative 
prices in a bilateral context by employing a number of different unit root and 
cointegration tests.  Majority of them use the post Bretton Woods data. Obviously 
these studies do not have sufficiently longer time series to overcome the possible 
problem of ‘small sample distortions’ that the traditional unit root and cointegration 
tests encounter.  Of course there are other studies that use longer time span. However, 
the traditional tests for PPP using longer univariate time series usually overlook the 
potential problem of structural break as the data set covers both the fixed and floating 
exchange rate regimes [Qian and Strauss (2001)].  
To circumvent these problems, researchers of late started recommending the 
use of panel cointegration framework to get econometrically robust findings [Baltagi 
and Kao (2000), Banerjee (1999), Pedroni(2000, 2001b) and Qian and Strauss 
(2001)]. A major advantage of this approach is that it allows one to selectively pool 
the long run information contained in the panel while permitting the short run 
dynamics (and heterogeneity) among different members.  An important consideration 
regarding ‘pooling’ has to do with the dimension over which they are pooled. One can 
pool across either the ‘within’ or ‘between’ dimensions. Pedroni concluded that the 
‘between dimension’ has relatively lower small sample distortions.  The goal of this 
study is to employ this improved panel cointegration method to evaluate the PPP 
doctrine in the context of a set of somewhat homogeneous developing countries.   
2. Methodological Discussions 
Pedroni evaluates the asymptotic properties of three versions of panel 
estimators.  “Residual-FM” and the “adjusted-FM” pooled the data along the ‘within’ 
dimension and “group-FM” pooled the data along the ‘between dimension’.  He 
shows that the “group-FM” has relatively lower small sample distortions and more 
flexibility in terms of hypothesis testing.  For example, in the panel unit root 
regression  it it i it Y Y ε µ + = −1
i ∀
 for t = 1,2…T, and i = 1,2…N, pooled tests imply 
H i =1 : 0 µ  and  1 : < = A i A H µ µ   i ∀  where as grouped mean tests imply 
  1i H i ∀ =1 : 0 µ  and  1 : < i A H µ   .  It is clear that  i ∀ i µ under the alternative hypothesis 
is not required to be the same among different   members of the panel.  Hence the 
grouped tests often allow for a greater flexibility.   
i
it it i X µ β α + + =
it it X ε + = −1
) 1 ( ~ ) I Xit ′ ( Zit = ( I ~ ′
= i i L i L
β
Γ + Ω = Ω i i i
0 0
i
− 

∑ ∑
= =
T
t
it
N
i
X (
1 1
− X = NT β
*
i X )
it
i
i
i X
L
L
Y ∆ −
22
21
ˆ
ˆ
) it Y Y =
* ( ˆ
ˆ
22
21
i
i
L
L ˆ τ
K
k
+
− = ∑
−
it
*
it i i X β α + =
β






= ∑
=
−
N
i
N
1
1 ∑
=
T
t
Z
1
it Y
*
,... K − , it i it X X ∆ − it Z 1 (K +
                                                          
Consider the following cointegrated system for a panel of i = 1,2…N members 
it Y  
it X         ( 1 )  
where   and  , Yit ) 0 ) , ( it it it = ε µ ξ  with long run covariance 
matrixΩ ( is a lower triangular decomposition of  ′
i L i Ω ).  In this case the 
variables are said to be cointegrated for each member of the panel, with cointegrating 
vector  .  It should be noted that  i α allows the cointegrating relationship to include 
member specific fixed effects. This covariance matrix can also be decomposed as 
, where Ω  is the contemporaneous covariance and Γ  is a weighted 
sum of autocovariances. 
′ Γ + i i
  The panel FMOLS estimator for the coefficient β is given by  






− 

 ∑
=
−
−
i
T
t
it it i T Y X N τˆ ( )
1
*
1
2 1     (2) 
where  it − ,  ) ˆ ˆ ( ˆ ˆ 0
22 22
0
21 21 i i i i i Ω + Γ Ω + Γ ≡ . The associated t-
statistic follows standard normal distribution.
1  
  For the panel DOLS estimation, we need to augment the cointegrating 
regression in (1) as follows:    
k it
K
ik it X Y
i
1
µ γ + ∆ − .       ( 3 )  
where the estimated coefficient  is given by 





 ′ ∑
=
− T
t
it it it DS Z Z
1
1
* β     (4) 
where  ) ( K it X X + ∆ = is   1 ) 2 x  vector of regressors.   
 
 
1 The detail expression of the t-statistic is available in Pedroni (2000). 
  23. Results 
3.1 Data 
The panel consists of 240 monthly (and 80 quarterly) series of ‘end of period’ 
nominal U.S. dollar exchange rates (E) and aggregate consumer price index ratio (P) 
for 10 countries covering the period from January 1980 through December 1999 
(1980:1 to 1999:4 for quarterly data). The sample countries are India, Indonesia, 
South Korea, Malaysia, Nepal, Pakistan, The Philippines, Singapore, Sri Lanka and 
Thailand. The selection of these countries is somewhat arbitrary, except that they 
belong to a set of major Asian developing economies. All data have been taken from 
IMF’s International Financial Statistics CD-ROM.  The required log-transformation 
has been done. The results reported here are only for monthly data
2.  
3.2 The panel unit root and the panel cointegration tests 
In order to determine the presence of a unit root in individual country specific 
data we employ standard ADF test.  For a panel unit root we conduct Levin-Lin 
(1992) and IPS t-bar (1997) tests. Both the panel tests include a constant and a 
heterogeneous time trend in their specifications. The test results show that the unit 
root null could not be rejected and hence the series are generated by an I(1) process. 
Next we perform cointegration tests for all the sample individual countries by 
using Johansen and Juselius (1990) method and for the panel by using Pedroni (1999) 
procedure. We find the evidence of no cointegration from both individual and panel 
cointegration tests.  So, the PPP does not hold in the long-run in this context. To 
conserve space we report only panel unit root (upper panel) and panel cointegration 
(lower panel) results in Table 1. 
3.3 FMOLS and DOLS 
Table 2 reports the results of individual and panel FMOLS and DOLS. 
Individual FMOLS and DOLS estimates and the respective t-statistics for H0: βi = 1 
are provided in the first 10 entries in Table 2, while results for the panel estimators 
with and without common time dummies are shown at the bottom of the table. Both 
individual and panel tests overwhelmingly reject the null hypothesis of strong PPP. 
As for the individual countries, 7 out of 10 cases we find the rejection of the null. We 
should also note that both FMOLS and DOLS test results are in agreement. 
                                                           
2 Similar results on quarterly data will be made available upon request. 
  3For the panel tests, all 4 reported tests reject the null at least at 5% level except 
in the case of within-dimension panel DOLS without time dummies. However, it is 
important to note that the between-dimension estimators consistently produce larger 
estimates than the within-dimension estimators. This finding is thus consistent with 
Pedroni (2001b). Following him, we argue that these higher values to be a more 
accurate representation of the average long-run relationship between nominal 
exchange rates and aggregate price ratios. 
4. Conclusion 
  In this study we employ panel cointegration method for evaluating the 
purchasing power parity doctrine in a panel of ten Asian developing economies for 
the post Bretton Woods period. The empirical findings of this paper do not support 
the relative version of PPP.  The analysis of the individual countries furthermore 
indicates that this failure of the PPP is not driven by the data from only a few 
countries. Rather, the failure of strong PPP appears to be pervasive in the flexible 
exchange rate regime.  
 
Acknowledgements 
 
We would like to thank Don Bruce, Keya Maitra and Peter Predoni for suggestions and 
encouragements. The errors are of course our own.   
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  4References 
 
Baltagi, B.H. and C. Kao, 2000, Nonstationary panels, cointegration in panels and 
dynamic panels: a survey, in B.H. Baltagi, eds., Nonstationary panels, panel 
cointegration, and dynamic panels, advances in econometrics, Vol. 15, (JAI) 7-52. 
 
Banerjee, A., 1999, Panel data unit roots and cointegration: an overview, Oxford 
Bulletin of Economics and Statistics, S1, 61, 607-629 
 
Im, K.S., M.H. Pesaran, and Y. Shin, 1997, Testing for unit roots in heterogeneous 
panels, Discussion paper, University of Cambridge, December. 
 
Johansen, S. and K. Juselius, 1990, Maximum likelihood estimation and inferences on 
cointegration—with applications to the demand for money, Oxford Bulletin of 
Economics and Statistics, 52, 169-210.  
 
Levin, A. and C.F. Lin, 1992, Unit root tests in panel data: asymptotic and finite 
sample properties, Department of Economics, University of California at San Diego, 
Discussion paper no. 92-93.  
 
Mark, N. and D. Sul, 1999, A computationally simple cointegration vector estimator 
for panel data, manuscript, Ohio State University. 
 
Pedroni, P., 1996, Fully modified OLS for heterogeneous Cointegrated panels and the 
case of purchasing power parity, Working paper 96-020, Department of Eocnomics, 
Indiana University. 
 
Pedroni, P., 1999, Critical values for cointegration tests in heterogeneous panels with 
multiple regressors, Oxford Bulletin of Economics and Statistics, S1, 61, 653-670. 
 
Pedroni, P., 2000, Fully modified OLS for heterogeneous Cointegrated panels, in B.H. 
Baltagi, eds., Nonstationary panels, panel cointegration, and dynamic panels, 
advances in econometrics, Vol. 15, (JAI) 93-130. 
 
Pedroni, P., 2001a, Asymptotic and finite sample properties of pooled time series tests 
with an application to the PPP hypothesis, Indiana University Working Paper. 
 
Pedroni, P., 2001b, Purchasing power parity in cointegrated panels, The Review of 
Economics and Statistics, 83, 4, 727-731. 
 
Qian, H. and J. Strauss, 2001, Panel PPP tests with unknown cross-sectional 
dependence and heteroscedasticity, unpublished manuscript. 
 
 
 
 
 
 
 
 
 
 
  5Table 1: Panel Unit Root and Cointegration Test Statistics 
Panel Unit Root Tests
a,b,c 
  Log of E Log  of  P 
Levin-Lin rho-stat 
Levin-Lin t-rho-stat 
Levin-Lin ADF-stat 
 
IPS ADF-stat 
-0.40220 
-0.08784 
-0.63467 
 
-0.77409 
1.96964 
0.88196 
1.19161 
 
0.45507 
Panel Cointegration Tests
d 
  Constant Constant  +  trend 
Panel v-statistics 
Panel ρ-statistics 
Panel t-statistics (non-parametric) 
Panel t-statistics (parametric) 
 
Group ρ-statistics 
Group t-statistics (non-parametric) 
Group t-statistics (parametric) 
0.03497 
0.38135 
0.35931 
-0.12432 
 
-0.00968 
0.29615 
-0.15929 
1.06003 
0.74992 
0.90140 
0.57380 
 
1.35524 
1.26993 
0.80218 
  Notes: 
a.  The critical values are from Levin and Lin (1992) Table 3 (with N=10 and T=250). 
b.  IPS indicates the Im et al. (1997) test. The critical values are taken from Table 4. 
c.  Unit root tests include a constant and heterogeneous time trend in the data.  
d.  The critical values for the panel cointegration tests are base on Pedroni (2001a).   
 
 
Table 2: Purchasing Power Parity Tests 
Country  FMOLS t-stat  DOLS  t-stat 
 
India 
Indonesia  
Korea  
Malaysia  
Nepal 
Pakistan  
The Philippines 
Singapore 
Sri Lanka 
Thailand 
 
1.80 
-0.03 
1.07 
-0.42 
1.63 
1.64 
1.16 
1.21 
0.98 
1.97 
 
16.27*** 
-6.19*** 
0.38 
-3.04*** 
20.66*** 
8.64*** 
3.55*** 
1.52 
-0.89 
3.28*** 
 
1.80 
-0.19 
1.04 
-0.49 
1.64 
1.55 
1.15 
1.20 
0.96 
1.77 
 
15.79*** 
-5.99*** 
0.20 
-3.67 
23.88*** 
6.76*** 
3.27*** 
1.50 
-1.91* 
2.42** 
 
  Panel Results 
  without time dummies 
within
a 
between
b 
0.80 
1.10 
-1.72* 
13.97*** 
0.95 
1.04 
-0.44 
13.35*** 
  with time dummies 
within 
between 
0.43 
1.07 
-6.34*** 
-2.26** 
0.57 
1.19 
-5.06*** 
2.55** 
Notes: t-stats are for H0: βi = 1. ***,**,* indicate, 1%,5%,10% rejection level, respectively. 
a. “within-dimension” reports Mark and Sul (1999) unweighted within-dimension DOLS 
and an analogous unweighted FMOLS. 
b. “between-dimension” reports Pedroni (1996) group mean panel FMOLS and the group 
mean panel DOLS introduced in Pedroni (2001b). 
  6

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