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论文研究 - 人均GDP购买力平价及其决定因素：金砖国家的面板数据分析.pdf
GDP Purchasing Power Parity per Capita and Its Determinants: A Panel Data Analysis for BRICS
Abstract
Keywords
1. Introduction
2. Review of Literature
3. Data and Methodology
3.1. Nature and Sources of Data
3.2. Panel Unit Root Test
3.3. Fisher-Type Test Using ADF and PP-Test (Maddala and Wu, 1999)
3.4. Panel Cointegration Test
3.5. VAR Specification
3.6. Vector Error Correction Model
3.7. VAR Causality (Block Exogeneity) Wald Tests
4. Results and Discussion
4.1. Descriptive Statistics: (We Need to Put This Statistics)
4.2. Panel Unit Root Tests Results
4.3. Johansen Fisher Panel Co-Integration Test Results
4.4. Variance Decomposition Results
5. Conclusions
References
Theoretical Economics Letters, 2018, 8, 575-591
http://www.scirp.org/journal/tel
ISSN Online: 2162-2086
ISSN Print: 2162-2078
GDP Purchasing Power Parity per Capita and Its
Determinants: A Panel Data Analysis for BRICS
S. Venkata Seshaiah1, Trilochan Tripathy2
1Icfai Business School (IBS), IFHE, Hyderabad, India
2XLRI-Xavier School of Management, Jamshedpur, India
How to cite this paper: Seshaiah, S.V. and
Tripathy, T. (2018) GDP Purchasing Power
Parity per Capita and Its Determinants: A
Panel Data Analysis for BRICS. Theoretical
Economics Letters, 8, 575-591.
https://doi.org/10.4236/tel.2018.83040
Received: January 12, 2018
Accepted: February 11, 2018
Published: February 14, 2018
Copyright © 2018 by authors and
Scientific Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY 4.0).
http://creativecommons.org/licenses/by/4.0/
Open Access
Abstract
This study examines the Gross Domestic product purchasing power parity per
capita (GDP PPP per capita) and its determinants using the panel data me-
thod to test for unit roots in Brazil, Russia, India, China, and South Africa
(BRICS). The main dependent variable in our study is GDP PPP per capita
while the independent variables are real exchange rate, real interest rate, con-
sumer price index (CPI), and money supply. We find strong evidence of a
long-run relationship among the chosen variables. The co-integration equa-
tion reveals positive relationship between GDP PPP per capita and the real
exchange rate, real interest rate, and money supply and a negative relationship
between GDP PPP and CPI. Based on the VEC Granger Causality/Block Ero-
geneity Wald Tests, the study finds that the GDP PPP per capita is influenced
by the exchange rate and CPI. However, based on the overall Chi-square test,
the study shows strong evidence of an influence of all variables on GDP PPP
per capita. We hope this study would help the policy makers to come up with
appropriate policies to bring about homogeneity among the BRICS nations.
Keywords
GDP, Panel Data Analysis, BRICS
1. Introduction
The Purchasing Power Parity (PPP) Theory otherwise known as “Law of One
Price” has remained an inconclusive debate in the academic and policy circles
since it was coined by Cassel, G. [1]. The PPP is an economic theory that states
residents of one country should be able to purchase the goods and services at the
same price as residents of any other country over time. This theory has a linkage
to goods and financial markets and the absence of PPP ignites the arbitrage op-
DOI: 10.4236/tel.2018.83040 Feb. 14, 2018
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Theoretical Economics Letters
S. V. Seshaiah, T. Tripathy
DOI: 10.4236/tel.2018.83040
portunity and in turn such arbitrage activities help establishing parity price for
goods and services across the countries. It is an established fact that consumers
and business persons often make comparisons between spending incomes, spot
exchange rates, forward exchange rates, consumer price indices and interest be-
tween countries. These comparisons are made to understand the state of Pur-
chasing Power Parity (PPP). Against this backdrop, more often policy makers
face major issues such as how to maintain the optimal level of inflation; how to
maintain the optimal level of exchange rates; how to manage the economic is-
sues and policy responses; how to improve the quality of life; and how to manage
the purchasing power parity and determinants of purchasing power parity. Sub-
stantial work has been done by experts to assess the validity of purchasing power
parity in the long run taking either the indices of absolute purchasing parity or
relative purchasing power parity as dependent variables. There are no dearths of
literature that examine whether PPP is holding across the set of countries. How-
ever, even after extensive discourse on the PPP theory, it has remained a puzzle
in the international finance literature. On the one hand a wide array of studies
vehemently argue that validity of purchasing power parity is a myth and it is a
theoretical conceptualization and on the other hand a handful of literature found
evidence of validity of purchasing power parity both in the developed and emerg-
ing economies contexts.
However, there are not many studies which attempt to examine the factors
determining the GDP PPP in emerging market space. Against this backdrop, this
study makes an attempt to examine the influence of real exchange rates, real in-
terest rates, and inflation on the movement of GDP PPP per capita across major
emerging market spaces. The findings here suggest that the influence of real ex-
change rates, real interest rates, and inflation on the movement of GDP PPP per
capita, exhibiting long-run relationships among the variables in question. It is
evidenced that except money supply, all the variables influence the movement of
GDP PPP per capita, thus confirming the theory. We hope this study would help
the policy makers to come up with appropriate policies to bring about homo-
geneity among the BRICS nations.
The paper is organized under five broad sections. The section one captures the
introduction. The broad contours of literature on PPP theory along with the gap
and objectives of the study is captured in section two. Data and Methodology
engaged in this study are delineated in the section three. The section four cap-
tures the results and discussion. The conclusion, contribution and limitations of
the study is presented in the last section.
2. Review of Literature
John C.B. Cooper [2], using co-integration analysis, concluded that PPP does
not hold in the long run for Australia, New Zealand, and Singapore. Thomas E.
Schweigert [3], analyzed the nominal, real exchange rates, and purchasing power
parity during the Guatemalan float for the period 1897-1922 and found a
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Theoretical Economics Letters
S. V. Seshaiah, T. Tripathy
co-integration relationship among exchange rate, money supply, and the foreign
consumer price index (CPI). The author observed a random walk with drift, im-
plying a stationary real exchange rate. He then concluded that the real exchange
behavior was inconsistent with theory. Salah A. Nusair [4] made an attempt to
assess the validity of purchasing power parity for a sample of developing coun-
tries in the Asian Financial Crisis during current float. The author concluded
that PPP does not hold in four out of the six Asian countries under study and
also concluded that deviations in PPP are transitory. Ahmad Zubzid Baharum-
shah et al. [5] investigated the behavior of real exchange rates of six East-Asian
countries along with their trading partners United States and Japan and used the
ARDL model to test long-run PPP. The authors found no evidence of a weak
form of PPP in the pre-crisis period but found small persistent PPP deviations
during the post crisis period by concluding some form of PPP-oriented rule as a
basis of their exchange rate policies.
Hsu-Ling Chang, Chi-Wei Su, Meng-Nan Zhu, and Pei Liu [6], examined the
long-run purchasing power parity among BRICS using the Momentum Thre-
shold Co-integration Test and the Engle Granger Test and found evidence of
long-run PPP for BRICS and no co-integration based on the Engle-Granger Test.
Finally, the authors concluded the importance of nominal exchange rates in eli-
minating the deviations from long-run PPP. Bulent Gologlu et al. [7], found
evidence of quasi validity of purchasing power parity for 18 Turkish real ex-
change rate using the Panel Unit Root Test with structural breaks. Fizari Abu
Hassan Asari, et al. [8] using the co-integration approach, studied the short run
and long run determinants of purchasing power parity in Malaysia. The authors
found the positive influence of real interest rates and consumer price index and
the negative influence of real exchange rates and money supply in the movement
of purchasing power parity of Malaysia. A. Oznur Umit [9] using the Traditional
Unit Root Test and Unit Roots Test with structural breaks, assessed the statio-
narity of real exchange rate for five fragile countries—Brazil, India, Indonesia,
Turkey, and South Africa. Based on the Traditional Unit Root Test, the author
concluded that purchasing power parity does not hold true in these countries.
Based on the results of Zivot-Andrews (one structural break)/Lee Strazicich (Two
structural breaks) respectively, the author observed the validity of PPP for India
and Brazil, and for India alone. The results of the Carrion-i-Silvestre (CS) Unit
Root Test which allows five structural breaks revealed that PPP is not valid for
India and South Africa and also concluded that Indians and South African banks
are not under pressure to establish exchange rate stability.
Based on the backdrop of the paper, we make a modest attempt to use panel
data analysis to assess the determinants of GDP PPP per capita for the BRICS
countries. The main reasons for studying the BRICS countries emanates due to
the following three reasons. These reasons are: 1) in a globalized world the pro-
duction lag and demand lag have shortened, 2) across the countries people have
started imitating the eating habits and production techniques, and 3) movement
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Theoretical Economics Letters
DOI: 10.4236/tel.2018.83040
S. V. Seshaiah, T. Tripathy
of goods and services due to technical as well economic substitution. We hope
this study will help the policy makers to develop appropriate economic policies
to integrate the BRICS economies. Our main equation that helps us determining
GDP PPP is:
GDP PPP percapita
f=
(
(
)
Realex changerate EX ,Real interestrate Int ,
(
y M3
Consumer price index CPI ,Money Suppl
(
)
(
)
(1)
))
.
3. Data and Methodology
3.1. Nature and Sources of Data
The present study employs yearly data on GDP PPP per capita, real interest rates,
real exchange rates, consumer price index (CPI), and money supply over the pe-
riod 1990-2016 from World Development Indicators. This data has been col-
lected for Brazil, Russia, India, China, and South Africa (BRICS). Before con-
ducting panel co-integration, we used Newey-West Automatic Bandwidth Selec-
tion and the Bartlett Kernel Summary Panel Unit Root Test, without which con-
clusions drawn from the co-integration estimation may not be valid. After con-
firming from the unit root and stationary tests that all the variables are non sta-
tionary in their levels form and stationary at the first difference, we proceed to
co-integration analysis. For co-integration analysis we used Johansen Fisher Panel
Co-integration. Pedroni and Kao Co-integration Tests are residual-based tests taken
from the Engle Granger Two-step Test and both are one-way co-integration whereas
the Johansen Fisher Panel Co-integration Test is a system-based co-integration
test for the whole panel set. Further, we also estimated Granger Causality using
VECM, Variance decomposition, VEC Granger Causality/Block Exogeneity Wald
Tests, and pair-wise Granger Causality Tests. The details of these aforesaid me-
thodologies used in this study are delineated hereunder sequentially.
3.2. Panel Unit Root Test
A wide array of literature delineates that individual time series based unit root
tests have relatively lower power than the panel-based unit root tests. Some of
the landmark study engages the panel based unit root tests in the context of the
purchasing power parity (PPP) and growth convergence in macro panels using
country data over time (Levin, Lin and Chu [10], Im, K.S. Persaran, M.H and
Shin [11], and Breitung [12]. In this study we have focused on three types of
panel unit root tests such as Levin, Lin and Chu (2002), Im, Pesaran and Shin;
2003, Fisher-Type test using ADF and PP-test (Maddala and Wu [13], These
unit root methods also see more detail in Chaitip, P., Chaiboonsri, C. and N.
Rangaswamy [14]. Levin, Lin and Chu (2002) delineate panel unit root test by
consider the following basic ADF specification:
Y
∆
i t
,
=
(
ρ
i
−
)
1
Y
i t
, 1
−
+
φ
∑
j
1
=
β
i t
,
Y
∆
i t
,
−
j
+
X
δ
i t
,
+
ε
i t
,
(2)
DOI: 10.4236/tel.2018.83040
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Theoretical Economics Letters
S. V. Seshaiah, T. Tripathy
,i tY∆ is the difference terms associated with panel data variable
,i tY ;
where,
,i tX is the ex-
1ρ− is …; n is the number of lag order for difference terms;
ogenous variable in model such as country fixed effects and time trend and
,i tε
is the error term of equation. In the presence of autocorrelation and determinis-
tic component in the above model is rewritten with the removal of these effects
as follows:
*
Y
∆
i t
,
=
(
ρ
i
−
)
1
Y
i t
, 1
−
+
φ
∑
j
1
=
*
β
i t
,
Y
∆
i t
,
−
j
+
*
δ
X
*
i t
,
+
ε
i t
,
. (3)
We can define the analogous
*
i ty − using the second set of coefficients and it
, 1
is presented in the following equation
n
*
y
i t
, 1
−
=
Y
i t
, 1
−
+
*
β
i t
,
Y
∆
i t
,
−
j
+
X
δ
*
i t
,
. (4)
∑
j
1
=
*
While
i ty − are transformed by dividing the regression standard
,i tY∆ and
*
, 1
error (si) so as to get
− also can express more detail of these va-
,i tY +∆
, 1
riable following that
. Where si are estimated
and
+∆
Y
i t
,
standard errors from each ADF in Equation (9) and lastly an estimate of the
coefficient α can be realized from the following Equation (5).
i ty +
*
Y s
i t
i
,
and
= ∆
*
y
i t
, 1
−
+
y
i t
,
s
i
=
+
Y
∆
i t
,
=
(
)
+
yρ
1
i t
,
−
i
+
ξ
i t
,
(5)
where resulting α coefficient in the above equation would be asymptotical
having finite sample properties and normally distributed [N ~ (0, 1)] as per Le-
vin and Lin (1993). However, if the t statistic diverges to minus infinity, it has to
be reentered and normalized to induce convergence towards a well-defined li-
miting distribution as demonstrated by Levin et al. (2002). Thus the modified
statistics would be as follows:
(
T
µ σ
m
NTS STD
(6)
∗ =
T
m
ˆ
Φ
t
φ
)
(
)
−
NT
ˆ
t
where T is the average effective sample size across the individual units and
STD Φ is the standard deviation of
(
)ˆ
ˆΦ (see Levin et al., 2002).
1
N
N =
i
1
= ∑ .
s
i
ˆ
S
NT
(7)
The Null hypothesis for the panel unit root test is:
H
0 :
ρΦ =
i
i
− = .
1 0
i
1,
= .
For
That means, panel data has unit root (assumes common unit root process).
N
,
The alternative hypothesis for the panel unit root test is:
H
1 :
ρΦ =
i
i
− ≠ .
1 0
That means the panel data has not unit root. If t* is significant then conclusion
that reject null hypothesis or panel data has not unit root. Otherwise If t* is not
significant then conclusion that accept null hypothesis or panel data has unit
root.
579
Theoretical Economics Letters
DOI: 10.4236/tel.2018.83040
S. V. Seshaiah, T. Tripathy
Panel Unit root test of Im, Pesaran and Shin (1997 & 2002) presented two
group-mean panel unit root tests designed against the heterogeneous alternative.
The test takes into account the individual specific autoregressive structures and
individual specific variances to develop the test statistic. We have presented in
detail the test procedure hereunder.
The model proposed to test panel unit root is:
ε−
it
1
Yα β
= +
it
Y
it
+
where
t
=
1,2,3,
.
T
,
(8)
They use separate unit root test for the N cross section units. Let Yit be the
observation on the ith cross-section unit at time t and suppose that it is generat-
ed according to following simple dynamic linear heterogeneous panel data mod-
el and can be written in equation in Dicky Fuller format:
where
t
1,2,
= .
T
,
Y
it
Yα β
= +
it
ε−
it
1
+
(9)
The above first order Auto Regressive (AR) model contains a dependent vari-
able Yit and independent variable with its first order lag in the panel framework.
, N are cross-section units;
In the panel framework, where i varies from 1,
t
1,
= are observed over periods;
itε denotes the error term of equation.
This can be presented in Augmented Dicky fuller model:
t
,
Y
∆ =
it
Y
+ ∆
α β
it
i
i
1
−
+
pi
∑
Y
∆
θ
it
1
=
j
+
ε
it
−
j
(10)
t
T
,
=
1,2,3,
. The null hypothesis or unit root hypothesis of can now
where
be expressed as H0: β = 1 (for all i against the alternative hypothesis as H1: β < 0,
N
i
. The estimated t statistics for testing unit roots in
=
1
individual series is:
1,2,
N
1
1,
2,
N
+
+
,
,
t
NT
1 N
= ∑
N
i
1
=
t
iT
(
p
θ
i
i
)
. (11)
NTt
The
is the standardized and it is shown that the standardized NTt
sta-
tistic converges to the standard normal distribution as N and T → ∞ . IPS (1997)
showed that
test has better performance when N and T are small. They
proposed a cross-sectionally demeaned version of both test to be used in the case
where the errors in different regressions contain a common time-specific com-
ponent.
NTt
3.3. Fisher-Type Test Using ADF and PP-Test
(Maddala and Wu, 1999)
Madala and Wu (1999) proposed the use of the Fisher (Pl) test which is based on
combining the P-values of the test-statistics for unit root in each cross-sectional
unit. Let pi are U[0, 1] and independent, and
has a χ2 distribution
with 2N degree of freedom and can be written in the following Equation (12).
2loge
−
ip
(12)
where Pl = Fisher (Pl) panel unit root test, N = all N cross-section and
2
= −
log
SN
P1
p
i
=
e
i
DOI: 10.4236/tel.2018.83040
580
Theoretical Economics Letters
S. V. Seshaiah, T. Tripathy
=
log
SN
2
−
Fisher (Pl) Chi Square panel unit root test has non-stationary as null hypothe-
it has a χ2 distribution with 2N degree of freedom.
p
i
e
i
sis as well as to show below that:
H0: panel data has unit root (assumes individual unit root process), against the
alternatives.
H1: panel data has not unit root.
If both Fisher (Pl) Chi-square panel unit root test and Choi Z-statistics panel
unit root test are significant then conclusion that reject null hypothesis or panel
data has not unit root. Otherwise both If Fisher (Pl) Chi-square panel unit root
test is not significant then conclusion that accept null hypothesis or panel data
has unit root.
3.4. Panel Cointegration Test
Johansen (1988) proposes two different approaches; one of them is the likelih-
ood ratio trace statistics and the other one is maximum eigenvalue statistics, to
determine the presence of cointegration vectors in non-stationary time series.
The trace statistics and maximum eigenvalue statistics have shown in Equations
((13) and (14)) respectively.
n
λ
trace
( )
r
T
= −
i
∑
i r
= +
−
)
(
(13)
ln 1
λ
i
(
)
ln 1
λ+
−
r
1
(14)
.
λ
max
(
r r
,
+
)
1
T
= −
For the trace statistic test the null hypothesis is to check for at most r cointe-
grating vectors against the alternative Hypothesis: Full rank r = n cointegrating
vector. The Null hypothesis for the maximum eigenvalue statistics is to be
checked for the for r cointegrating vectors against the alternative hypothesis of r
+ 1 cointegrating vectors.
Using Johansens [15] test for cointegration for Maddala and Wu (1999) con-
sider Fisher’s [16] suggestion to combine individual tests to propose an alterna-
tive to the two previous tests for testing the cointegration in the full panel by
combining individual cross section tests for cointegration. If µi is the p value
from an individual cointegration test for cross section i then under the null hy-
pothesis for the whole panel cointegration is as follows:
2
−
n
∑
i
1
=
log
e
(
Π
i
)
~
2
χ
N
2
. (15)
This is having a chi square distribution with 2N degrees of freedom. The null
and alternative hypotheses are the same as in the Im, Pesaran and Shin (1997 & 2002)
test. Applying the ADF estimation equation in each cross-section, we can compute
the ADF t-statistic for each individual series, find the corresponding p-value
from the empirical distribution of ADF t-statistic and compute the Fisher-test sta-
tistics and compare it with the appropriate χ2 critical value. The Maddala-Wu
(1999) test using Fisher’s test is suitable due to the fact that: 1) this test can be
performed with any unit root test on a single time-series, and 2) this does not
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DOI: 10.4236/tel.2018.83040
S. V. Seshaiah, T. Tripathy
require a balanced panel as the Im, Pesaran and Shin [11] test does, so T can dif-
fer over cross sections.
=
=
x
it
y
it
b x
it
12
+
3.5. VAR Specification
b
−
10
c x
+
it
12
1
−
b y
b
−
it
20
12
c x
+
+
it
1
12
−
b
b y
−
it
30
12
c x
+
+
it
12
1
−
b x
m b
−
it
12
40
c x
+
+
it
12
1
−
b x
b
−
it
50
12
c x
+
+
it
12
n
it
z
it
=
=
=
1
−
it
b z
+
it
12
c z
it
12
1
−
b z
+
it
12
c z
it
12
1
−
b x
+
it
12
c z
it
12
1
−
b z
+
it
12
c z
it
12
1
−
b z
+
it
12
c z
it
12
1
−
it
it
it
1
−
1
−
1
−
+
1
−
+
+
+
+
+
(17)
1
−
+
+
1
−
+
+
(16)
c y
it
11
ε
+
yt
c y
it
11
+
ε
xt
c y
it
11
+
ε
zt
c y
it
11
+
ε
mt
b m b n
it
12
12
c n
c m
it
it
1
12
12
−
b m b n
+
+
it
12
12
c m
c n
+
it
it
12
12
b m b n
+
it
12
12
c m
c n
+
it
it
1
12
12
−
b y
b n
+
it
it
12
12
c n
c m
+
it
it
1
12
12
−
c y
b m b y
+
it
it
11
12
12
c n
c m
+
ε
nt
it
it
12
12
)2
(
0,
εσ and covariance across the
1
−
+
+
(18)
(19)
(20)
+
+
+
+
i i d
. .
1
−
+
1
−
1
−
1
−
1
−
it
The error series are distributed with
i
errors are 0.
where,
y indicates per capita GDPppp for the country i in the year t,
xit indicates Real Exchange for the country i in the year t,
zit indicates the real interest rate for the country i in the year t,
mit indicates Consumer Price Index (CPI) for the country i in the year t,
nit indicates the money supply (M3) for the country i in the year t.
While determining the optimal lag length for the VAR, we have conducted the
following LR tests and the information criteria statistics. The LR tests are as follows:
(21)
(
qχ
T m
Σ −
LR
ln
ln
Σ
~
=
−
(
)
2
)(
)
u
r
where T =#observations (after accounting for lags), m = number of parameters
estimated in each equation of the unrestricted system, including the constant.
ln rΣ natural log of the determinant of the covariance matrix of residuals of
the restricted system. q = total number of restrictions in the system (=number of
2n ) and n =number of variables (or equations).If the LR statistics <
lags times
critical value, reject the null of the restricted system.
Further, we have also used the following Information criteria
AIC
=
T
ln
Σ +
SBC
=
T
ln
Σ +
2
N
N T
ln
.
Choose the # lag that minimizes the criteria. Note that these criteria are not
tests; they mainly indicate goodness of fit of alternatives, so used this as com-
plements to the LR tests.
3.6. Vector Error Correction Model
A Vector Error Correction Model (VECM) can lead to a better understanding of
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DOI: 10.4236/tel.2018.83040
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