Description
Purchasing power parity (PPP) is an economic theory and a technique used to determine the relative value of currencies, estimating the amount of adjustment needed on the exchange rate between countries in order for the exchange to be equivalent to (or on par with) each currency's purchasing power.
Case Study on Purchasing Power Parity (PPP) in the Long-Run: A
Cointegration Approach
Abstract: This paper intends to test the long-run purchasing power parity (PPP) in Bangladesh
economy during the period 1971/72-2007/08. The cointegration tests using exchange rate and
price indices from annual observations reject the PPP proposition for Bangladesh. The results
indicate that deviations in domestic and foreign price levels are not reflected in nominal
exchange rate movements. Instead of considering PPP as a complete model of exchange rate
determination, it should be used in providing a guideline in setting exchange rates in the presence
of monetary disturbances.
1. Introduction
The Purchasing Power Parity (PPP) doctrine states that the exchange rate between two
currencies should be equal to the ratio of the price levels in two countries so that a given
commodity has the same price in both countries when expressed in terms of the same
currency. The intellectual origins of the doctrine can be attributed to the works of Wheatley
(1807) and Ricardo (1821), where it appears as an extension of the quantity theory of money.
Its latest revival owes much to Gustav Cassel's writings throughout the 1920s to explain the
behaviour of the dislocated European exchanges during World War I (Humphrey and
Kelehar, 1982). The emergence of the floating exchange rate system after 1973 inspired an
enormous resurrection of interest in PPP theory.
Numerous studies have been carried out in testing the validity of the PPP theory. Early
studies of PPP centered on the European and United States economies during the 1920s. The
results support the PPP hypothesis as exchange rates could not be separated from the price
levels. On the contrary, PPP collapsed during the 1970s due to various structural changes in
the United States economy with its trade partners (Frenkel, 1976, 1980; Krugman, 1978). In
these studies, estimations were carried out without examining the time series properties of the
variables. If the variables are nonstationary, we can study their behaviour only for the time
period under consideration without generalizing it to other time periods. Provided that the
variables are stationary as well as cointegrated, we may consider a long-run relationship
among them. Besides, a number of studies were conducted on the basis of cointegration tests
to identify the long-run relationship between exchange rate and price levels. Basher and
Mohsin (2004) test the PPP hypothesis using panel cointegration framework for ten Asian
countries. The results did not indicate any evidence in favor of PPP. The studies undertaken
by Corbae and Ouliaris (1988) and Eatzaz et al. (2002) on US and Pakistan economies
respectively, did not find any evidence in favor of the PPP hypothesis.
*
Associate Professor, Department of Economics, Jahangirnagar University, Savar, Dhaka.
**Lecturer, Department of Economics, Asian University of Bangladesh, Uttara, Dhaka.
Purchasing Power Parity (PPP) in the Long-Run: A Cointegration Approach
This article aims at assessing the long-run PPP relationship in Bangladesh economy. Instead
of regressing exchange rate on relative prices, the cointegration approach is adopted in
testing PPP through analyzing the time series properties of the variables. Unless the two
variables are cointegrated, one cannot show that there exists a long-run relationship between
them. In such a case, the observed relationship may be entirely spurious.
The outline of this paper is as follows. Section 2 presents the theoretical framework, while
section 3 discusses the econometric methodology. Section 4 reports the data sources and
empirical results. Finally, the concluding remarks are provided in section 5.
2. Theoretical Framework
The 'absolute' version of the purchasing power parity (PPP) states that the equilibrium
exchange rate equals the ratio of domestic to foreign general price levels. If E is the nominal
exchange rate measured as the domestic currency price of a unit of foreign currency and P
d
and P
f
are the domestic and foreign price indexes respectively, then PPP can be written as:
E = P
d
/ P
f
(2.1)
The logarithmic version of the PPP is as follows:
Ln E
t
= o
0
+ o
1
Ln (P
d
/ P
f
)
t
+ e
t
(2.2)
where, E is the nominal exchange rate (Taka per US dollar), P
d
and P
f
are the price indexes
in Bangladesh and United States (US) respectively, o's are the coefficients to be estimated
and e is the disturbance term representing short-run deviations from PPP.
Two common price indexes used in the empirical verification of PPP are the consumer price
index (CPI) and the wholesale price index (WPI). However, there exists a great deal of
debate over the choice of the price index. One of the views emphasizes on commodity
arbitrage in the determination of exchange rates and considers WPI to be the appropriate
price index which represents the prices of tradable goods (Pigou, 1920). On the contrary,
proponents of asset equilibrium in the determination of exchange rates, relies on CPI which
covers a broad range of commodities (Cassel, 1928). However, WPI has been criticized to
assign too much weight to traded goods. This study considers CPI to be the appropriate price
index to be used in the empirical verification of the PPP hypothesis which has a greater
representation of nontraded goods.
This article attempts to test of the 'absolute' version of the PPP hypothesis. Various
disturbances from monetary shocks may not lead to the equilibrium relationship between
exchange rate and the ratio of domestic to foreign general price levels in the short-run. A
necessary condition for PPP to hold requires e to follow a stationary process. In such a case,
the deviations from the equilibrium value are corrected over time. A cointegrated system
offers a strong evidence for the 'absolute' version of PPP theory.
2
The Jahangirnagar Economic Review
Vol. 21. June 2010
3. Methodology
3.1 Unit Roots
The econometric methodology first examines the stationarity properties of the time series.
Two procedures for detecting a unit root in exchange rate and price level data are used in our
analysis: (i) The Dickey-Fuller (DF) test (Dickey and Fuller, 1979), and (ii) the Augmented
Dickey-Fuller (ADF) test (Dickey and Fuller, 1981). The DF test is derived from the regression
equation:
X
t
= ¸
0
+ ¸
1
t + oX
t
÷
1
+ u
t
÷1 s o s 1 (3.1)
where, X
t
is a random walk with drift around a stochastic trend and u
t
is a white noise error
term which is assumed to be uncorrelated. Ifo = 1, then X
t
is nonstationary. Alternatively, we
can estimate the model:
?X
t
= ¸
0
+ ¸
1
t + ?X
t
÷
1
+ u
t
(3.2)
where ? = (o ÷1) and ? is the first-difference operator, and test the null hypothesis that ? = 0. If ? = 0, o
=1, we have a unit root, implying that the time series under consideration is
nonstationary. The ADF test is undertaken by adding lagged values of the dependent variable
?X
t
if the error terms are correlated. Thus, the following regression is estimated for unit root
testing:
p
?X
t
= ¸
0
+ ¸
1
t + ?X
t
÷
1
+ o
j
¿ ?X
t
÷
j
+ c
t
j=1
(3.3)
In model (3.3) X
t
is a random walk with drift around a stochastic trend, ? is the first-
difference operator, c
t
is a white noise error term and p is the number of lags in the dependent
variable. The null hypothesis of a unit root implies that the coefficient of X
t
÷
1
is zero i.e., ?
= 0. Rejection of the null hypothesis implies that the series is stationary and no differencing
in the series is necessary to induce stationarity. The number of lags in the dependent variable
is chosen by the Akaike Information Criterion (AIC). Unit root test identifies whether the
variables are stationary or nonstationary. The test is applied on both the original series (in
logarithmic form) and to the first differences. In addition, both models with and without trend
are tried. The DF and ADF tests are carried out by replacing X
t
with LnE
t
and Ln(P
d
/P
f
)
t
in
equations (3.2) and (3.3) respectively.
3.2 Cointegration Tests
Time series should to be checked for cointegration. For two or more variables to be
cointegrated, the time series must have similar statistical properties i.e., they must be
integrated of the same order. The Engle-Granger two-step method (Engle and Granger, 1987)
is used for this purpose. The order of integration of the variables are identified in the first
step while in the second step the residuals are estimated from the Ordinary Least Squares
3
Purchasing Power Parity (PPP) in the Long-Run: A Cointegration Approach
(OLS) regression on the levels of the variables from equation (2.2). Thus, accordingf to the
Engle-Granger method, two variables, exchange rate (LnE
t
) and relative price [Ln(P
d
/P )
t
] are
considered to be cointegrated if they ared inftegrated of the same order i.e., I(d) and the
residuals in the regression of LnE
t
on Ln(P /P )
t
(or vice versa) is integrated of order less than
d.
The presence of a long-run equilibrium relationship between exchange rate and relative price
is also tested through Johansen (1988) maximum likelihood procedure. In Johansen's
procedure, exchange rate and relative price are assumed to follow the first order Vector Auto
Regressive (VAR) representation as follows:
E
t
=
HE 11
t÷1
+
HR 12
t÷1
+
c
Et
(3.4)
R
t
=
HE 21
t÷1
+
HR 22
t÷1
+
c
Rt
(3.5)
Subtracting lagged dependent variables from the respective equations, the system can be
written in matrix notation as follows:
?
? E
t
?
?
I11
I
12
?
?
E t ÷
1
?
?
c
Et
?
? ? R t ? ?I21
?
?=? ?+?
I
??
22 ? ? Rt ÷1 ?
?
c
?
Rt ?
where I
11
= H
11
-1, I
22
= H
22
-1, I
12
= H
12
and I
21
= H
21
and E
t
and R
t
are first difference
stationary i.e., I(1). The existence of a cointegrating relationship depends on the rank of the
matrix I which must be equal to one as there can be up to one linearly independent cointegrating
vectors. Johansen's procedure gives two likelihood ratio tests for the number of cointegrating
vectors (r) which are found by the trace and the maximum eigen value tests
as follows:
k
ì
trace ( r )
= ÷N
¿ ln (1
÷
ìˆ ) ii =
r +1
(3.6)
ì
max( r ,r +1)
= ÷ N ln(1
÷
ìr+
1
) ˆ
(3.7)
where, ì
i
's are the characteristic roots of the matrix I and N is the sample size. The null
hypothesis of at most r cointegrating vectors is tested in both the trace test as well in the
maximum eigen value test. In the trace test, the alternative hypothesis is that the number of
cointegrating vectors is equal to or less than r+1, whereas it is equal to r+1 in the maximum
eigen value test. The Johansen'sf maximum likelihood procedure is carried out by replacing
E
t
with LnE
t
and R
t
with Ln(P
d
/P )
t
in equations (3.4) and (3.5) respectively.
4. Data Sources and Empirical Results
The study is based on annual data for the period 1971/72-2007/08. Nominal exchange rates
(period average) are expressed as units of local currency (Taka) per US dollar. Data on
exchange rates have been gathered from various issues of Economic Trends, published by the
4
The Jahangirnagar Economic Review
Vol. 21. June 2010
Bangladesh Bank. The relative price is the domestic price index divided by a similar US
price index. The CPI (Base: 1989-90=100) has been used as the appropriate price index. Data
on CPI for Bangladesh and US have been obtained from different publications of Statistical
Yearbook of Bangladesh and IMF International Financial Statistics (IFS) Yearbook,
respectively. Econometric estimations have been performed using STATA (version 9.2).
The results in Table-1 indicate that in all cases, the level of the logarithm of exchange rate
and relative price (measured by consumer price index) are nonstationary. Thus to achieve
stationarity the variables must be first-differenced. The DF and ADF statistics are significant
only for the first-differenced series. Thus, exchange rate and relative price series appear to be
?I(1).
Table-1: Unit Root Tests with DF and ADF for the period 1971/72 to 2007/08
With Trend
DF ADF
Variables Levels First Difference Levels First Difference
Ln E -2.20 -4.18*** -1.89 (2) -4.67*** (2)
Ln (P
d
/P
f
) -2.29 -4.31*** -2.84 (1) -4.91*** (1)
Without Trend
DF ADF
Variables Levels First Difference Levels First Difference
Ln E -2.46 -3.79*** -1.33 (2) -3.11** (2)
Ln (P
d
/P
f
) -2.74 -4.47*** -2.31 (1) -5.28*** (1)
Notes: i) Figures within parentheses indicate lag lengths chosen by the Akaike information criterion
(AIC); ii) *** and ** denote rejection of the null hypothesis of unit root at the 1% and 5% levels
respectively.
Table 2: Unit Root Rest for the Residuals'e
t
'
With Trend Without Trend
Cointegrating Regressions DF ADF DF ADF
Ln E
t
= 3.91+1.83 Ln (P
d
/P
f
)
t
-3.13 -3.19 (1) -2.27 -2.23 (1)
Ln (P
d
/P
f
)
t
= -1.70+0.42 Ln E
t
-3.11 -3.14 (1) -2.19 -2.17 (1)
Notes: i) Figures within parentheses indicate lag lengths chosen by the Akaike information criterion
(AIC); ii) The null hypothesis of unit root in the residuals cannot be rejected at the 1%, 5% and 10%
levels respectively.
5
Purchasing Power Parity (PPP) in the Long-Run: A Cointegration Approach
The results reported in Table-1 provide the basis for the test of cointegration. The DF and
ADF statistics for the cointegration tests are presented in Table-2. The results show that
exchange rate and relative price series for Taka-US Dollar are not cointegrated. The residuals
of the cointegrating regressions are nonstationary indicating that deviations between
exchange rate and relative price continue indefinitely without reconciling together in the
long-run.
Table-3: Johansen's Maximum Likelihood Procedure
Trace ì-Max
Null r=0 rs1 r=0 r=1 Number
Alternative rs1 rs 2 r=1 r=2 of lags (k)
Ln E, Ln (P
d
/P
f
) 11.97 1.69 10.29 1.69 2
Notes: i) The lag lengths are chosen by Akaike's Final Prediction Error (FPE) criteria;
ii) r denotes the number of cointegrating vectors; iii) The null hypothesis of no
cointegration cannot be rejected at the 1% and 5% levels.
Table-3 provides the results of the Johansen's maximum likelihood procedure for
determining the number of cointegrating vectors r. The results show that the null hypothesis
of no cointegration (r = 0 ) cannot be rejected . Therefore, it can be confirmed that exchange
rate and relative price are not cointegrated i.e., PPP does not hold for the Bangladesh
economy.
5. Conclusion
The aim of this paper has been to test the 'absolute' version of the PPP hypothesis in
Bangladesh Economy for the period 1971/72-2007/08. Exchange rate and relative price were
nonstationary in levels, but stationary in first difference i.e., they are integrated of order one,
I(1). The study applies cointegration technique of economic time series to verify the
existence of a stable relationship between exchange rate and relative price. The results
indicate that there is no cointegrating relationship between the variables i.e., deviations in
domestic and foreign prices due to disturbances are not reflected in nominal exchange rate
movements in Bangladesh. Thus, PPP should not be considered as a complete theory of
exchange rate determination. Instead of providing a general trend, the PPP theory may be
used as a guide for fixing exchange rate in the event of any monetary disturbance.
References
Basher, A. and M. Mohsin, 2004, "PPP Tests in Cointegrated Panels: Evidence from Asian
Developing Countries", Applied Economic Letters, Vol. 11, pp. 163-166.
Cassel, G., 1928, Post-War Monetary Stabilization, Columbia University Press, New York.
6
The Jahangirnagar Economic Review
Vol. 21. June 2010
Corbae, D. and S. Ouliaris, 1988, "Cointegration and Test of Purchasing Power Parity",
Review of Economics and Statistics, Vol. 70, pp. 508-511.
Dickey, D. A. and W. A. Fuller, 1979, "Distribution of the Estimators for Autoregressive
Time Series with a Unit Root", Journal of the American Statistical Association, Vol. 74,
pp. 427-431.
Dickey, D. A. and W. A. Fuller, 1981, "Likelihood Ratio Statistics for Autoregressive Time
Series with a Unit Root", Econometrica, Vol. 49, pp.1057-1072.
Eatzaz, A. and K. Farzana, 2002, "Short Run Dynamics in Purchasing Power Parity: A Case
of Selected Asian Countries", The Middle East Business and Economic Review, Vol. 14,
No.2, pp. 28-40.
Enders, W., 1995, Applied Time Series Econometrics, John Wiley and Sons Inc., New York.
Engle, R. F. and C. W. Granger, 1987, "Co-integration and Error Correction: Representation,
Estimation and Testing", Econometrica, Vol. 55, pp. 251-276.
Frenkel, J. A., 1976, "A Monetary Approach to the Exchange Rate: Doctrinal Aspects and
Empirical Evidence", The Scandinavian Journal of Economics, Vol.78, No.2, pp.200-224.
Frenkel, J. A., 1978, "Purchasing Power Parity: Doctrinal Perspectives and Evidence from
the 1920s", Journal of International Economics, Vol. 8, No. 2, pp. 169-191.
Frenkel, J. A., 1980, "Exchange Rates, Prices, and Money: Lessons from the 1920's", The
American Economic Review, Vol. 70, No. 2, pp.235-242.
Greene, W. H., 2003, Econometric Analysis, Pearson Education, Inc., New Jersey.
Gujarati, D. N., 2003, Basic Econometrics, McGraw Hill, New York.
Humphrey, T. M. and R. E. Kelehar, 1982, The Monetary Approach To The Balance Of
Payments, Exchange Rates, And World Inflation, Praeger Publishers, New York.
Johansen, S. and K. Juselius, 1990, "Maximum Likelihood Estimation and Inference on
Cointegration With the Application to the Demand for Money", Oxford Bulletin of
Economics and Statistics, Vol. 52, pp. 169-210.
Johansen, S., 1988, "Statistical Analysis of Cointegrating Vectors", Journal of Economic
Dynamics and Control, Vol. 12, pp.255-259.
Krugman, P. R., 1978, "Purchasing Power Parity and Exchange Rates: Another look at the
evidence", Journal of International Economics, Vol.8, No.3, pp.397-407.
Officer, L. H., 1976, "The Purchasing Power Parity Theory of Exchange Rates: a Review
Article", IMF Staff Papers, Vol.23, No. 1, pp.1-60.
Pigou, A.C., 1920, "Some Problems of Foreign Exchanges", Economic Journal, Vol. 30, No.
120, pp. 460-472.
Ricardo, D., 1821, Principles of Political Economy and Taxation, G. Bell and Sons, London,
in E. C. Connor, ed. (G. Bell and Sons), 1911.
Rogoff, K., 1996, "The Purchasing Power Parity Puzzle", Journal of Economic Literature,
Vol. 34, No. 2, pp. 647-668.
Wheatley, J., 1807, An Essay on the Theory of Money and Principles of Commerce, London.
7
doc_332041323.docx
Purchasing power parity (PPP) is an economic theory and a technique used to determine the relative value of currencies, estimating the amount of adjustment needed on the exchange rate between countries in order for the exchange to be equivalent to (or on par with) each currency's purchasing power.
Case Study on Purchasing Power Parity (PPP) in the Long-Run: A
Cointegration Approach
Abstract: This paper intends to test the long-run purchasing power parity (PPP) in Bangladesh
economy during the period 1971/72-2007/08. The cointegration tests using exchange rate and
price indices from annual observations reject the PPP proposition for Bangladesh. The results
indicate that deviations in domestic and foreign price levels are not reflected in nominal
exchange rate movements. Instead of considering PPP as a complete model of exchange rate
determination, it should be used in providing a guideline in setting exchange rates in the presence
of monetary disturbances.
1. Introduction
The Purchasing Power Parity (PPP) doctrine states that the exchange rate between two
currencies should be equal to the ratio of the price levels in two countries so that a given
commodity has the same price in both countries when expressed in terms of the same
currency. The intellectual origins of the doctrine can be attributed to the works of Wheatley
(1807) and Ricardo (1821), where it appears as an extension of the quantity theory of money.
Its latest revival owes much to Gustav Cassel's writings throughout the 1920s to explain the
behaviour of the dislocated European exchanges during World War I (Humphrey and
Kelehar, 1982). The emergence of the floating exchange rate system after 1973 inspired an
enormous resurrection of interest in PPP theory.
Numerous studies have been carried out in testing the validity of the PPP theory. Early
studies of PPP centered on the European and United States economies during the 1920s. The
results support the PPP hypothesis as exchange rates could not be separated from the price
levels. On the contrary, PPP collapsed during the 1970s due to various structural changes in
the United States economy with its trade partners (Frenkel, 1976, 1980; Krugman, 1978). In
these studies, estimations were carried out without examining the time series properties of the
variables. If the variables are nonstationary, we can study their behaviour only for the time
period under consideration without generalizing it to other time periods. Provided that the
variables are stationary as well as cointegrated, we may consider a long-run relationship
among them. Besides, a number of studies were conducted on the basis of cointegration tests
to identify the long-run relationship between exchange rate and price levels. Basher and
Mohsin (2004) test the PPP hypothesis using panel cointegration framework for ten Asian
countries. The results did not indicate any evidence in favor of PPP. The studies undertaken
by Corbae and Ouliaris (1988) and Eatzaz et al. (2002) on US and Pakistan economies
respectively, did not find any evidence in favor of the PPP hypothesis.
*
Associate Professor, Department of Economics, Jahangirnagar University, Savar, Dhaka.
**Lecturer, Department of Economics, Asian University of Bangladesh, Uttara, Dhaka.
Purchasing Power Parity (PPP) in the Long-Run: A Cointegration Approach
This article aims at assessing the long-run PPP relationship in Bangladesh economy. Instead
of regressing exchange rate on relative prices, the cointegration approach is adopted in
testing PPP through analyzing the time series properties of the variables. Unless the two
variables are cointegrated, one cannot show that there exists a long-run relationship between
them. In such a case, the observed relationship may be entirely spurious.
The outline of this paper is as follows. Section 2 presents the theoretical framework, while
section 3 discusses the econometric methodology. Section 4 reports the data sources and
empirical results. Finally, the concluding remarks are provided in section 5.
2. Theoretical Framework
The 'absolute' version of the purchasing power parity (PPP) states that the equilibrium
exchange rate equals the ratio of domestic to foreign general price levels. If E is the nominal
exchange rate measured as the domestic currency price of a unit of foreign currency and P
d
and P
f
are the domestic and foreign price indexes respectively, then PPP can be written as:
E = P
d
/ P
f
(2.1)
The logarithmic version of the PPP is as follows:
Ln E
t
= o
0
+ o
1
Ln (P
d
/ P
f
)
t
+ e
t
(2.2)
where, E is the nominal exchange rate (Taka per US dollar), P
d
and P
f
are the price indexes
in Bangladesh and United States (US) respectively, o's are the coefficients to be estimated
and e is the disturbance term representing short-run deviations from PPP.
Two common price indexes used in the empirical verification of PPP are the consumer price
index (CPI) and the wholesale price index (WPI). However, there exists a great deal of
debate over the choice of the price index. One of the views emphasizes on commodity
arbitrage in the determination of exchange rates and considers WPI to be the appropriate
price index which represents the prices of tradable goods (Pigou, 1920). On the contrary,
proponents of asset equilibrium in the determination of exchange rates, relies on CPI which
covers a broad range of commodities (Cassel, 1928). However, WPI has been criticized to
assign too much weight to traded goods. This study considers CPI to be the appropriate price
index to be used in the empirical verification of the PPP hypothesis which has a greater
representation of nontraded goods.
This article attempts to test of the 'absolute' version of the PPP hypothesis. Various
disturbances from monetary shocks may not lead to the equilibrium relationship between
exchange rate and the ratio of domestic to foreign general price levels in the short-run. A
necessary condition for PPP to hold requires e to follow a stationary process. In such a case,
the deviations from the equilibrium value are corrected over time. A cointegrated system
offers a strong evidence for the 'absolute' version of PPP theory.
2
The Jahangirnagar Economic Review
Vol. 21. June 2010
3. Methodology
3.1 Unit Roots
The econometric methodology first examines the stationarity properties of the time series.
Two procedures for detecting a unit root in exchange rate and price level data are used in our
analysis: (i) The Dickey-Fuller (DF) test (Dickey and Fuller, 1979), and (ii) the Augmented
Dickey-Fuller (ADF) test (Dickey and Fuller, 1981). The DF test is derived from the regression
equation:
X
t
= ¸
0
+ ¸
1
t + oX
t
÷
1
+ u
t
÷1 s o s 1 (3.1)
where, X
t
is a random walk with drift around a stochastic trend and u
t
is a white noise error
term which is assumed to be uncorrelated. Ifo = 1, then X
t
is nonstationary. Alternatively, we
can estimate the model:
?X
t
= ¸
0
+ ¸
1
t + ?X
t
÷
1
+ u
t
(3.2)
where ? = (o ÷1) and ? is the first-difference operator, and test the null hypothesis that ? = 0. If ? = 0, o
=1, we have a unit root, implying that the time series under consideration is
nonstationary. The ADF test is undertaken by adding lagged values of the dependent variable
?X
t
if the error terms are correlated. Thus, the following regression is estimated for unit root
testing:
p
?X
t
= ¸
0
+ ¸
1
t + ?X
t
÷
1
+ o
j
¿ ?X
t
÷
j
+ c
t
j=1
(3.3)
In model (3.3) X
t
is a random walk with drift around a stochastic trend, ? is the first-
difference operator, c
t
is a white noise error term and p is the number of lags in the dependent
variable. The null hypothesis of a unit root implies that the coefficient of X
t
÷
1
is zero i.e., ?
= 0. Rejection of the null hypothesis implies that the series is stationary and no differencing
in the series is necessary to induce stationarity. The number of lags in the dependent variable
is chosen by the Akaike Information Criterion (AIC). Unit root test identifies whether the
variables are stationary or nonstationary. The test is applied on both the original series (in
logarithmic form) and to the first differences. In addition, both models with and without trend
are tried. The DF and ADF tests are carried out by replacing X
t
with LnE
t
and Ln(P
d
/P
f
)
t
in
equations (3.2) and (3.3) respectively.
3.2 Cointegration Tests
Time series should to be checked for cointegration. For two or more variables to be
cointegrated, the time series must have similar statistical properties i.e., they must be
integrated of the same order. The Engle-Granger two-step method (Engle and Granger, 1987)
is used for this purpose. The order of integration of the variables are identified in the first
step while in the second step the residuals are estimated from the Ordinary Least Squares
3
Purchasing Power Parity (PPP) in the Long-Run: A Cointegration Approach
(OLS) regression on the levels of the variables from equation (2.2). Thus, accordingf to the
Engle-Granger method, two variables, exchange rate (LnE
t
) and relative price [Ln(P
d
/P )
t
] are
considered to be cointegrated if they ared inftegrated of the same order i.e., I(d) and the
residuals in the regression of LnE
t
on Ln(P /P )
t
(or vice versa) is integrated of order less than
d.
The presence of a long-run equilibrium relationship between exchange rate and relative price
is also tested through Johansen (1988) maximum likelihood procedure. In Johansen's
procedure, exchange rate and relative price are assumed to follow the first order Vector Auto
Regressive (VAR) representation as follows:
E
t
=
HE 11
t÷1
+
HR 12
t÷1
+
c
Et
(3.4)
R
t
=
HE 21
t÷1
+
HR 22
t÷1
+
c
Rt
(3.5)
Subtracting lagged dependent variables from the respective equations, the system can be
written in matrix notation as follows:
?
? E
t
?
?
I11
I
12
?
?
E t ÷
1
?
?
c
Et
?
? ? R t ? ?I21
?
?=? ?+?
I
??
22 ? ? Rt ÷1 ?
?
c
?
Rt ?
where I
11
= H
11
-1, I
22
= H
22
-1, I
12
= H
12
and I
21
= H
21
and E
t
and R
t
are first difference
stationary i.e., I(1). The existence of a cointegrating relationship depends on the rank of the
matrix I which must be equal to one as there can be up to one linearly independent cointegrating
vectors. Johansen's procedure gives two likelihood ratio tests for the number of cointegrating
vectors (r) which are found by the trace and the maximum eigen value tests
as follows:
k
ì
trace ( r )
= ÷N
¿ ln (1
÷
ìˆ ) ii =
r +1
(3.6)
ì
max( r ,r +1)
= ÷ N ln(1
÷
ìr+
1
) ˆ
(3.7)
where, ì
i
's are the characteristic roots of the matrix I and N is the sample size. The null
hypothesis of at most r cointegrating vectors is tested in both the trace test as well in the
maximum eigen value test. In the trace test, the alternative hypothesis is that the number of
cointegrating vectors is equal to or less than r+1, whereas it is equal to r+1 in the maximum
eigen value test. The Johansen'sf maximum likelihood procedure is carried out by replacing
E
t
with LnE
t
and R
t
with Ln(P
d
/P )
t
in equations (3.4) and (3.5) respectively.
4. Data Sources and Empirical Results
The study is based on annual data for the period 1971/72-2007/08. Nominal exchange rates
(period average) are expressed as units of local currency (Taka) per US dollar. Data on
exchange rates have been gathered from various issues of Economic Trends, published by the
4
The Jahangirnagar Economic Review
Vol. 21. June 2010
Bangladesh Bank. The relative price is the domestic price index divided by a similar US
price index. The CPI (Base: 1989-90=100) has been used as the appropriate price index. Data
on CPI for Bangladesh and US have been obtained from different publications of Statistical
Yearbook of Bangladesh and IMF International Financial Statistics (IFS) Yearbook,
respectively. Econometric estimations have been performed using STATA (version 9.2).
The results in Table-1 indicate that in all cases, the level of the logarithm of exchange rate
and relative price (measured by consumer price index) are nonstationary. Thus to achieve
stationarity the variables must be first-differenced. The DF and ADF statistics are significant
only for the first-differenced series. Thus, exchange rate and relative price series appear to be
?I(1).
Table-1: Unit Root Tests with DF and ADF for the period 1971/72 to 2007/08
With Trend
DF ADF
Variables Levels First Difference Levels First Difference
Ln E -2.20 -4.18*** -1.89 (2) -4.67*** (2)
Ln (P
d
/P
f
) -2.29 -4.31*** -2.84 (1) -4.91*** (1)
Without Trend
DF ADF
Variables Levels First Difference Levels First Difference
Ln E -2.46 -3.79*** -1.33 (2) -3.11** (2)
Ln (P
d
/P
f
) -2.74 -4.47*** -2.31 (1) -5.28*** (1)
Notes: i) Figures within parentheses indicate lag lengths chosen by the Akaike information criterion
(AIC); ii) *** and ** denote rejection of the null hypothesis of unit root at the 1% and 5% levels
respectively.
Table 2: Unit Root Rest for the Residuals'e
t
'
With Trend Without Trend
Cointegrating Regressions DF ADF DF ADF
Ln E
t
= 3.91+1.83 Ln (P
d
/P
f
)
t
-3.13 -3.19 (1) -2.27 -2.23 (1)
Ln (P
d
/P
f
)
t
= -1.70+0.42 Ln E
t
-3.11 -3.14 (1) -2.19 -2.17 (1)
Notes: i) Figures within parentheses indicate lag lengths chosen by the Akaike information criterion
(AIC); ii) The null hypothesis of unit root in the residuals cannot be rejected at the 1%, 5% and 10%
levels respectively.
5
Purchasing Power Parity (PPP) in the Long-Run: A Cointegration Approach
The results reported in Table-1 provide the basis for the test of cointegration. The DF and
ADF statistics for the cointegration tests are presented in Table-2. The results show that
exchange rate and relative price series for Taka-US Dollar are not cointegrated. The residuals
of the cointegrating regressions are nonstationary indicating that deviations between
exchange rate and relative price continue indefinitely without reconciling together in the
long-run.
Table-3: Johansen's Maximum Likelihood Procedure
Trace ì-Max
Null r=0 rs1 r=0 r=1 Number
Alternative rs1 rs 2 r=1 r=2 of lags (k)
Ln E, Ln (P
d
/P
f
) 11.97 1.69 10.29 1.69 2
Notes: i) The lag lengths are chosen by Akaike's Final Prediction Error (FPE) criteria;
ii) r denotes the number of cointegrating vectors; iii) The null hypothesis of no
cointegration cannot be rejected at the 1% and 5% levels.
Table-3 provides the results of the Johansen's maximum likelihood procedure for
determining the number of cointegrating vectors r. The results show that the null hypothesis
of no cointegration (r = 0 ) cannot be rejected . Therefore, it can be confirmed that exchange
rate and relative price are not cointegrated i.e., PPP does not hold for the Bangladesh
economy.
5. Conclusion
The aim of this paper has been to test the 'absolute' version of the PPP hypothesis in
Bangladesh Economy for the period 1971/72-2007/08. Exchange rate and relative price were
nonstationary in levels, but stationary in first difference i.e., they are integrated of order one,
I(1). The study applies cointegration technique of economic time series to verify the
existence of a stable relationship between exchange rate and relative price. The results
indicate that there is no cointegrating relationship between the variables i.e., deviations in
domestic and foreign prices due to disturbances are not reflected in nominal exchange rate
movements in Bangladesh. Thus, PPP should not be considered as a complete theory of
exchange rate determination. Instead of providing a general trend, the PPP theory may be
used as a guide for fixing exchange rate in the event of any monetary disturbance.
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