THE J-CURVE EFFECT ON THE TRADE BALANCE IN MALAWI AND SOUTH
AFRICA
The members of the Committee approve the master’s
thesis of Eric B. Kamoto
William J. Crowder
Supervising Professor
______________________________________
Craig Depken II
______________________________________
Michael Ward
______________________________________
Copyright © by Eric B. Kamoto
All Rights Reserved
THE J-CURVE EFFECT ON THE TRADE BALANCE IN MALAWI AND SOUTH
AFRICA
by
ERIC BEN KAMOTO
Presented to the Faculty of the Graduate School of
The University of Texas at Arlington in Partial Fulfillment
of the Requirements
for the Degree of
MASTER OF ARTS IN ECONOMICS
THE UNIVERSITY OF TEXAS AT ARLINGTON
May 2006
ACKNOWLEDGEMENTS
I would like to thank Dr. William J. Crowder, my thesis supervisor for his
guidance and support during the entire period of writing this paper. He constantly
monitored my progress toward the completion of this paper. Dr. Crowder, thank you
very much.
I also would like to acknowledge Dr. Craig Depken II for being a source of
encouragement and motivation. He was always welcome and helpful whenever I visited
him for advice. To Dr. Michael Ward, I appreciate the role you played in my
completion of this paper. Many thanks to Dr. Shushanik Papanyan for the statistical
support I got from her. Dr. Papanyan even recommended me to read some books which
proved to be very useful in my study.
Finally, I appreciate my family for their understanding during the rest of the
time I wasn’t available for them. To God, all glory be unto Him for seeing me through
out many challenges.
April 26, 2006
iv
ABSTRACT
THE J-CURVE EFFECT ON THE TRADE BALANCE IN MALAWI AND
SOUTH AFRICA
Publication No. ______
Eric B.Kamoto, M.A.
The University of Texas at Arlington, 2006
Supervising Professor: William J. Crowder
The purpose of this paper is to investigate the effects of devaluation on the trade
balance in Malawi and South Africa using a vector error correction model (VECM).
The generalized impulse response functions are used to trace the response of the trade
balance to the shocks in the exchange rate. The vector error correction model suggests
the existence of a long-run equilibrium relationship among the variables for both
Malawi and South Africa. There is a positive relationship between the trade balance and
the real effective exchange rate indicating that a real depreciation will improve the trade
balance in the long run. The study finds evidence of the J-curve on the South African
v
trade balance. This suggests that following a real depreciation the South African trade
balance will initially deteriorate but improve in the long run. However, Malawi does not
exhibit a statistically significant J-curve phenomenon.
vi
TABLE OF CONTENTS
ACKNOWLEDGEMENTS.......................................................................................
iv
ABSTRACT ..............................................................................................................
v
LIST OF ILLUSTRATIONS.....................................................................................
ix
LIST OF TABLES.....................................................................................................
xi
Chapter
1. INTRODUCTION.........................................................................................
1
1.1 The J-curve ..............................................................................................
1
1.2 Background Setting .................................................................................
2
1.3 The Purpose of the Study.........................................................................
4
2. LITERATURE REVIEW..............................................................................
6
3. METHODOLOGY…….. ..............................................................................
12
3.1 Theoretical Framework............................................................................
12
3.2 Empirical Model ......................................................................................
14
3.3 Data Description and Sources..................................................................
18
3.4 Time Series Properties of Data ................................................................
23
4. EMPIRICAL ANALYSIS AND RESULTS.................................................
27
4.1 Cointegration Analysis ............................................................................
27
4.2 The Long Run-Equilibrium Relationship ................................................
28
4.3 Dynamic Relationships............................................................................
32
vii
4.3.1 Variance Decompositions ........................................................
32
4.4 Generalized Impulse Response Analysis.................................................
34
4.5 Diagnostic Tests for the Long-Run Models.............................................
41
4.6 Final Discussion.......................................................................................
42
5. CONCLUSIONS ...........................................................................................
44
Appendix
A. SUMMARY STATISTICS ...........................................................................
47
B. GRAPHICAL REPRESENTATION OF RESIDUALS...............................
51
REFERENCES ..........................................................................................................
60
BIOGRAPHICAL INFORMATION.........................................................................
64
viii
LIST OF ILLUSTRATIONS
Figure
Page
1 Malawian real effective exchange rate and trade ratio in levels........................ 20
2 South African real effective exchange rate and trade ratio in levels ................. 21
3 Malawian real effective exchange rate and trade ratio in first differences ........ 22
4 South African real effective exchange rate and trade ratio in levels ................. 22
5 The impulse response of South African trade ratio to one standard
deviation shock to REER ................................................................................... 38
6 The impulse response of the Malawian Trade Ratio to one standard
deviation shock in REER................................................................................... 40
B.1 Graphs of residuals from the real effective exchange rate
equation for South Africa. .............................................................................. 52
B.2 Graphs of residuals from the domestic income equation
for South Africa .............................................................................................. 53
B.3 Graphs of residuals from the foreign income equation
for South Africa ............................................................................................... 54
B.4 Graphs of residuals from the trade ratio equation
for South Africa .............................................................................................. 55
B.5 Graphs of residuals from the real effective exchange rate
equation for Malawi ....................................................................................... 56
B.6 Graphs of residuals from the domestic income equation for Malawi ............. 57
B.7 Graphs of residuals from the foreign income equation for Malawi ................ 58
ix
B.8 Graphs of residuals from the trade ratio equation for Malawi ......................... 59
x
LIST OF TABLES
Table
Page
1 Augmented Dickey-Fuller Test for Unit Root for Variables in
Malawi ................................................................................................................ 24
2 Augmented Dickey-Fuller Test for Unit Root for Variables in
South Africa......................................................................................................... 25
3 Cointegration Test Results for Malawi and South Africa ................................... 28
4 Estimated Cointegrating Vector for South Africa .............................................. 30
5 Estimated Cointegrating Vector for Malawi ....................................................... 31
6 Variance Decomposition of the Trade Ratio for Malawi .................................. 32
7 Variance Decomposition of the Trade Ratio for South Africa .......................... 33
8 Misspecification Tests for the Models in Malawi and South Africa ................... 42
A.1 Variable Description ....................................................................................... 48
A.2 Descriptive Statistics of Data for Malawi........................................................ 49
A.3 Descriptive Statistics of Data for South Africa ............................................... 50
xi
CHAPTER 1
INTRODUCTION
The Malawi kwacha and South African rand have over the past years
depreciated against their major trading partners. Such depreciations have received
mixed reactions. Some economists argue that the depreciation of both currencies is a
good stimulant for export growth while others argue that the net benefits of depreciation
cannot outweigh its ills on the economy as a whole. Depreciation of the kwacha and the
rand were not initiated by policy makers. These were due to shocks in macroeconomic
environment. Malawi has been failing to maintain adequate foreign reserves for
currency stabilization. This has been due to over dependency on agriculture as the main
source of foreign exchange. This lack of diversification has been the main source of
depreciation of the Malawi kwacha. In South Africa, slow down in economic activities
and general deterioration in the current account balance led to the slump in the rand
(Gunnar, 2001). It is against this background that this paper would investigate the
behavior of the trade balance with respect to a real depreciation in both countries.
1.1 The J-curve
Most economists and policy makers believe that currency devaluations bring
about competitive advantage in international trade. When a country devalues its
currency, domestic export goods become cheaper relative to its trading partners
resulting in an increase in quantity demand. Devaluation as a policy prescription is
1
mainly aimed at improving the trade balance. However, there is a time lag before the
trade balance improves following a real depreciation. The short run and long run effects
of depreciation on the trade balance are different. Theoretically, the trade balance
deteriorates initially after depreciation and some time along the way it starts to improve
until it reaches its long-run equilibrium. The time path through which the trade balance
follows generates a J-curve. The time lag comes about as an impact of several lags such
as recognition, decision, delivery, replacement and production (Junz and Rhomberg,
1973). Following a real depreciation, traders take time to recognize the changes in
market competitiveness, and this may take longer in international markets than in
domestic markets before information is passed on the stakeholders because of distance
and language problems. Some time is spent on deciding on what business relationships
to venture into and for the placement of new orders. There is a delivery lag that explains
the time taken before new payments are made for orders that were placed soon after the
price shocks. Procurement of new materials may be delayed to allow inventories of
materials to be used up, this is a replacement lag. Finally, there is a production lag
before which producers become certain that the existing market condition will provide a
profitable opportunity.
1.2 Background Setting
One explanation for the J-curve phenomenon is that the prices of imports rise
soon after real depreciation but quantities take time to adjust downward because current
imports and exports are based on orders placed some time back (Yarbrough and
Yarbrough 2002). On the other hand, domestic exports become more attractive to
2
foreign markets but quantities do not adjust immediately for the same reason. An
increase in value of imports against a constant or a small change in the value of exports
results in a trade deficit in the short run. As time passes by, importers have enough time
to adjust their import quantities with respect to the rise in prices while quantity demand
for exports increases and this result in an improvement in the trade balance. The
long-run improvement in the trade balance occurs when the Marshall-Lerner condition
holds. In the long-run the volume effect dominates the price effect of a real
depreciation. In order for the trade balance to improve the sum of imports and exports
demand and supply elasticities must be greater than unity. For the J-curve phenomenon
to hold the assumption is that exports are denominated in domestic currency and
imports in foreign currency. This condition suggests that small economies compared to
large economies, may not exhibit a J-curve after a real depreciation since its exports are
invoiced in foreign currency. And the expectation is that trade balance will improve
following devaluation if initially, the trade balance was in equilibrium.
The conventional model for the J-curve theory explains the trade balance as
function of exchange rate, domestic income and foreign income. An increase in foreign
income increases demand for domestic goods thus foreign income is positively related
to trade balance while domestic income exhibits a negative relationship with trade
balance. Since the long-run generalization about the effect of currency devaluation is an
improvement on the trade balance, it is important to consider the impact of such policies
on the economy as a whole. Gylfason and Risager (1984) find that a real devaluation
has important effects on national incomes. They suggest that developed countries are to
3
benefit more from devaluation than would small economies. Small countries tend to
register a decline in national income as a result of devaluation.
1.3 The Purpose of the Study
This study attempts to investigate the response of the trade ratio to shocks in the
real effective exchange rate in both Malawi and South Africa. For South Africa
quarterly data from 1976:1 to 2003:4 are used while annual data from 1970:1 to 2004:1
are used for Malawi. The paper employs the cointegration methodology to estimate the
long-run equilibrium relationship between the trade ratio and the real exchange rate.
The generalized impulse response analysis and the vector error correction models are
used to investigate the short-run and feedback effects of the shock in the exchange rate
on the trade balance. The use of the generalized impulse response as opposed to
traditional impulse response analysis is advantageous because the ordering of the
variables in the model does not affect the outcome of the results and the shocks are
unique. The model sets trade balance as a function of real exchange rate, domestic
income and world income. In this paper, the trade balance is defined as the ratio of
exports to imports. This presentation allows the trade ratio to be logged without
worrying about negative values in case of trade deficits. Since aggregated trade data is
used the real effective exchange rate is used instead of the bilateral real exchange rate
and U. S. income is used as a proxy for foreign income. The aggregate data helps to
have an average overview of what is happening on the trade balance and the economy at
large compared to case by case analysis. Considering a small economy like Malawi,
disaggregated data would give no significant data worth study.
4
This paper finds that a real depreciation has a long-run positive effect on the
trade balance in South Africa with a significant J-curve. Responding to 1 percent
depreciation in the rand, the trade balance deteriorates for about 5.2 percent. About four
quarters after the shock, the trade balance starts to improve. There is a positive
long-run relationship between the real effective exchange rate and the trade balance in
Malawi. However, the data in Malawi does not exhibit a statistically significant J-curve.
The long-run elasticities of exchange rate with respect to the trade balance are 0.620
and 0.202 for South Africa and Malawi respectively.
The organization of this paper is as follows, Chapter 2 provides the literature
review for similar studies under the subject in question. Chapter 3 develops a theoretical
framework and empirical model to assist in the analysis of the J-curve. Chapter 4
provides the analysis of the empirical results. In chapter 5 the conclusion of this study is
provided.
5
CHAPTER 2
LITERATURE REVIEW
The effects of devaluation in the exchange rate on the trade balance are related
to the determinants of the demand and supply elasticities of exports and imports. In the
short run, the elasticities are relatively smaller (inelastic demand and supply), than in
the long run (elastic) hence the trade balance may deteriorate in the short run, BahmanOskooee (2004). Due to currency contracts, initially, the trade balance worsens as a
result of a real depreciation since prices and trade volumes are not allowed to change.
This situation assumes that exports are invoiced in domestic currency and imports in
foreign currency. The degree of foreign and domestic producer’s price pass-through to
consumers and the scale of supply and demand elasticities of exports and imports,
determine the value of the effect, Hsing (1999). The J-curve effect can be explained by
both a perfect pass-through and a zero pass-through. Under a perfect pass-through
domestic import price increases while domestic export price remains unchanged. The
resulting effect is a deterioration in the trade balance. In zero pass-through situation,
domestic export price increases and domestic import prices remain constant hence the
real trade balance improves following devaluation. According to Bahman-Oskooee
(2004), the Marshall-Lerner condition is the necessary and sufficient condition for an
improvement in the trade balance following a devaluation. For a currency devaluation
to have a positive impact on the trade balance, the sum of import and export demand
6
elasticities should be greater than one. The Marshall-Lerner condition is a long-run
condition because exporters and importers have enough time to adjust to changes in the
exchange rate by coming up with alternative choices in demand and supply.
Most studies on the J-curve effect have come up with mixed results. Some
results are consistent with the J-curve phenomenon while others depict non existence or
new evolution of the J-curve effect. Gupta-Kapoor and Ramakrishnan (1999) used the
error correction model and the impulse response function to determine the J-curve effect
on Japan using quarterly data from 1975:1 -1996:4. Their analysis showed the existence
of the J-curve on the Japanese trade balance. Tihomir Stucka (2004) found evidence of
J-curve on trade balance for Croatia. His study employed a reduced form model to
estimate the impact of a permanent shock on the merchandise trade balance. It was
found that 1 percent depreciation in the exchange rate improves the equilibrium trade
balance by the range of 0.94 percent-1.3 percent and it took 2.5 years for equilibrium to
be established.
Koch and Rosensweig (1990) studied the dynamics between the dollar and
components of U. S. trade. They employed time series-specification tests and Granger
tests of causal priority to identify the J-curve phenomenon. Two of the four components
portrayed dynamic relationships that are weaker and more delayed than the standard Jcurve. In the conventional J-curve, the theory asserts a strong and rapid dependency of
imports prices on the currency.
Carter and Pick (1989) found empirical evidence indicating the existence of the
first segment of the J-curve on the U.S. Agricultural trade balance. The results exhibited
7
deterioration in the trade balance that lasted for about 9 months following a 10 percent
depreciation in the U.S. dollar. Using the generalized impulse response function from
the vector error correction model to examine the existence of J-curve for Japan, Korea
and Taiwan, Hsing (2003) found that Japan’s aggregate trade provided evidence of the
phenomenon while Korea and Taiwan did not show any presence of the J-curve effect.
He argues that this may be attributed to a small open economy effect. In small open
economies like Korea and Taiwan, both imports and exports are invoiced in foreign
currency as a result the short run effect of real devaluation is hedged and the trade
balance remains unaffected.
Haynes and Stone (1982) estimated the impact of terms of trade on the U.S
trade balance. Their results showed no improvement in the trade balance following a
deterioration of the terms of trade for the period between 1947 and 1974. This was a
reexamination of McPheters and Stronge (1974) who concluded that there was a lag of
about 2 years before the U.S. trade balance could improve following changes in the
prices giving evidence of J-curve. Miles (1979) found that devaluations do not improve
the trade balance but do improve the balance of payments. He suggests that devaluation
results in a readjustment in investment portfolio resulting in an excess in the capital
account. The data used was from 14 countries for the period ranging from 1956 to 1972.
These results were reexamined by Himarios (1985) and some evidence of a J-curve was
found. He critiqued Miles’ results as to be sensitive to units of measurements, and
argued that the real exchange rate is the one that affect the trade flow and not the
nominal exchange rate. He went further to state that examining what is happening to the
8
trade balance on average is not the same as examining what is happening to the average
trade balance.
Scott Hacker and Abdulansser Hatemi-J (2004) used bilateral trade data to
estimate the short and long-run effect of exchange rate changes on the trade balance in
the transitional Central European economies of Czech Republic, Hungary and Poland
against their trade with Germany. Their study employed export to import ratio as the
measure of trade balance. Other variables included the industrial production index (as a
proxy for foreign and domestic income) and the exchange rate. The use of the industrial
production index, allowed them to estimate the statistical parameters using monthly data
and there were no reliable and consistent data on GDP. Their findings suggest that in all
the three cases, there were some evidence of the J-curve effect after real depreciation of
the currencies in question. They also investigated the J-curve effect replacing the real
exchange rate with the nominal exchange rate and the relative German price level. The
argument for introducing these variables is that real exchange rate changes are either a
result of shocks in the nominal exchange rate or general domestic price changes. In
some case it’s a combination of both variables. Nominal exchange rate changes are
much more observable than real exchange rate changes. Besides, it is easily controlled
by authorities. They found weak forms of the J-curve effect where the trade balance
deteriorates and improves later after the shock but the process was not instantaneous as
predicted in the conventional theory. Paresh Narayan (2004) investigated the J-curve
effect of on the trade balance for New Zealand. He found no cointegrating relationship
between the trade balance and real effective exchange rate, domestic income and the
9
foreign income during the period of 1970-2000. However, the New Zealand trade
balance exhibited a J-curve pattern. Following a real depreciation of the New Zealand
dollar, the trade balance worsens for the first three years and improves thereafter.
Similar study on the Singapore’s trade relations with the U.S. found no significant
impact of the Singapore’s real exchange rate on the trade balance and little evidence of
the J-curve hypothesis. This study was conducted by Wilson and Kua (2000) using the
partial reduced form model of Rose and Yellen (1989) derived from two-country
imperfect substitute model.
Bahmani-Oskooee et al. (2003) conducted a study on India’s trade balance
following up on previous studies which did not find any significant results on the
subject. Researchers argued that the problem could probably be the use of aggregated
data. As a result they employed disaggregated data to investigate the J-curve hypothesis
against India’s trading partners. The empirical results of the study did not support the Jcurve pattern but the long-run real depreciation of India’s rupee had significant effect
on the improvement of the trade balance. The Turkish trade balance supported the
Marshal-Lerner condition where there was evidence of the long-run relationship
following real depreciation. However, the results did not support the short-run effect of
currency depreciation. This clearly suggests that in studying the J-curve phenomenon, it
is crucial to separate and identify both the short and long-run implication of devaluation
on the trade balance. In estimating the J-curve, researchers either use aggregated or
bilateral trade data. Rose and Yellen (1989) argue that use of bilateral data is useful
10
because you do not require a proxy for the world income variable as in the aggregate
analysis which reduces aggregation bias.
Having discussed the expected effects of exchange rate devaluations on the
trade balance, we construct the following hypothesis for this study and will be tested in
Chapter 4.
Hypothesis: There is a long-run relationship between the trade ratio and real effective
exchange rate and the evidence of J-curve in Malawi and South Africa.
To test the hypothesis the cointegaration analysis will be conducted and the
existence of cointegrating vectors will help answer part of our hypothesis about the
long-run relationship. If found that real effective exchange rate variable is positively
related to the trade ratio, this entails that real depreciation will lead to a long-run
improvement in the trade ratio. And the other part of the hypothesis about the J-curve
will be tested using the generalized impulse response functions.
11
CHAPTER 3
METHODOLOGY
3.1 Theoretical Framework
In the imperfect substitutes model as outlined by Goldstein and Khan (1985), the
trade balance comprises only the merchandise components of exports and imports.
Domestic income and prices of imports are the main determinants of demand for
imported goods. Mathematically, we can express the import demand function as
follows,
M d  M d (Y , Pm , Pd )
(1)
Where M d is the domestic demand for imports, Y is domestic income, Pm is the
domestic currency price and Pd is the general price level in the domestic country.
Similarly, the supply for domestically produced goods (equivalent to export demand by
foreigners) to the rest of the world is expressed as,
X d  X d (Y * , Px , E , Pf )
(2)
Where X d is the quantity of export goods to the rest of the world, Y * is the foreign
income, Px is the foreign currency price paid by domestic importers, Pf is the general
price level in the foreign country and E is the nominal exchange rate defined as the
number of units of domestic currency per one unit of foreign currency. The key
assumptions in equations (1) and (2) are that both domestic and foreign income
elastisties are positive, so is the cross price elasticity while the own price elasticity is
12
negative. In this model, demand variables are represented by current income and not
permanent or transitory income. This condition makes economists assume homogeneity
of the demand function. As a result consumers make their decisions based on real
values as opposed to nominal values (money illusion). In order to effect the
homogeneity assumption, the right hand sides of equations (1) and (2) are divided by
their respective prices and the following equations are derived
M d  M d (Y r , RPm )
(3)
Where Yr is the real domestic income and RPm is relative price of imports and
X d  X d (Yr* , RPx )
(4)
Where Yr* real foreign income and RPx is relative price of exports. When the foreign
currency price of foreign exports Px is adjusted for exchange rate, it is equivalent to the
relative price of imports thus we come up with the following equation,
RPm 
Pm EPx* EPf Px*


 QPx*
Pd
Pd
Pd Pf
(5)
Where Px* is the real foreign currency price of exports and Q is the real exchange rate,
in this formulation, an increase in Q is associated with a depreciation of the domestic
currency. Since domestic exports are foreign imports and the collolary is true, domestic
import demand is equivalent to foreign export supply and domestic export supply is
equivalent to foreign import demand, thus
M d  X s* , X d  M s*
13
(6)
Where X s* and M s* are foreign export supply and foreign import supply respectively.
We then derive the long-run equation for the trade balance as
TB  Px* X d  QM d
(7)
Thus the trade balance is the difference between the value of exports and imports. A
negative value in the trade balance implies a trade deficit and is associated with an
increase in the value of imports relative to exports. The interaction of the variables in
equation (7) yield the following reduced form equation in real values
TB  TB (Y , Y * , Q),
TB
TB
TB
 0, *  0,
0
Y
Q
Y
(8)
The equation above is the traditional Keynesian function for the trade balance where
real domestic income, real foreign income and the real exchange rate are the main
determinants of net exports.
3.2 Empirical Model
In equation (7) we defined the trade balance as the difference between the value
of exports and imports. In this study, we define the trade balance as the ratio of exports
(X) to imports (M). This study adopts Gupta-Kapoor and Ramakrishnan (1999) reduced
form equation to investigate the J-curve using real variables. When using disaggregated
(bilateral) data the trade balance is a function of domestic income, foreign income and
exchange rate. This study looks at the effect of shocks in the real exchange rate on the
total trade as compared to bilateral trade relations. We therefore use GDP for the United
States as a proxy for world income and real effective exchange rate as a measure of
terms of trade. The reason for choosing the United States income is none other than the
14
important role the United States economy plays in world trade. Thus the empirical
model used in this study is
ln( X / M )   0   1 ln Y   2 ln Y *   3 ln REER  
(9)
Where ln ( X / M ) is the natural log of trade ratio, ln Y is the natural log of real
domestic income, ln Y * is the natural log of foreign income, ln REER is the natural log of
real effective exchange rate,  0 , 1 ,  2 and  3 are the parameters to be estimated and 
is an i.i.d. normal error term. The use of export to import ratio as dependent variable
over trade balance is of the advantage that we can take logs without worrying for the
possible negative values of the trade balance in case of trade deficit, Han-Min Hsing
(2003). Other than real effective exchange rate, the trade ratio is also affected by real
domestic and foreign incomes. All the variables are logged such that the parameter
estimates would be interpreted as elasticities. We expect the trade ratio to be negatively
related to the domestic real income and positively related to foreign income and the real
effective exchange rate. Thus a currency depreciation will lead to a decrease in the
export-import ratio in the short run due to price effect. In the long run when the volume
effect takes over, the trade ratio improves. An increase in demand for foreign goods put
much constraint on the domestic income hence the negative relationship while exports
bring in income from abroad increasing the value of trade balance. A real depreciation
has two effects, direct and feedback effects. The direct effect on the trade ratio is
demonstrated by taking the partial derivative the trade ratio with respect to the real
effective exchange rate. According to Gupta-Kapoor and Ramakrishna (1999), the
feedback effects arise from a contemporaneous effect of the exchange rate on both the
15
trade balance as well as the future exchange rate. To capture both the direct and
feedback effects, the vector error correction model is used in this study. In order for the
VECM to be applicable there need be a stationary relationship among the variables
implying that they are cointegrated. The cointegration tests are be carried out as
outlined by Jonhansen (1995). This methodology is advantageous because it allows for
analysis in the case of multiple cointegrating vectors. The resulting vector error
correction model is
n 1
Z t    j  t 1   t 1   t
(10)
i 1
Where  t is a vector of variables in equation (9),  j is a matrix of coefficients for the
growth rate of the variables,    / where  is the matrix of the speed of the
adjustment parameters and  / is the matrix of the cointegrating vectors, i and n are lag
order and maximum lag respectively, t is a time index and vt is the vector of error term.
In estimating the error correction model, it is necessary to select the appropriate
lag order that will effect the residuals white noise. The likelihood ratio, SBC and AIC
information criteria are used to select the lag order. Of course much emphasis is put on
the SBC and AIC because they have small sample properties as characterized by our
data. All variables are also tested for unit root using the Augmented Dickey-Fuller test.
The choice of the ADF is the fact that the procedure automatically selects for the lag
length to be included in the test. A variable with no unit root is stationary. According to
Enders (2004), stationarity implies that a variable has a constant time invariant mean,
variance and zero auto covariances. A non-stationary variable can be made stationary
16
by either differencing or detrending. If a variable becomes stationary by differencing
once, the variance is said to be integrated of the order one, denoted I(1). Consequently,
if a variable is differenced twice in order to attain stationarity, such variable is
integrated of the order two, denoted I(2). Unit root testing in macroeconomic data is
much more important because it determines the appropriate model for estimating
parameters. When non-stationary variables are treated as stationary in a classical
regression model, this results in spurious regression where the t-statistics appear to be
significant, with high R-Squared values but the results are of no economic meaning.
Using the Johansen procedure (Johansen 1995), we test for the existence of
long-run relationship between the trade ratio and the real effective exchange rate. The
generalized impulse response function derived from the VECM is used to estimate the
J-curve effect. According to Hsing (2003) the impulse response function shows the
response of current and future trade ratio to one standard deviation change in the real
exchange rate. The superiority of using the generalized impulse response functions is
that the order in which the variables are arranged does not affect the outcome of the
results. Variance decompositions analysis is used to estimate the forecast error of the
trade ratio as attributable to its own innovation as well as innovations in other variables
in the system. The main interest in using the variance decomposition analysis in this
paper is to estimate the contribution of the shocks in the real effective exchange rate to
the forecast error of the trade ratio.
17
3.3 Data Description and Sources
In this section we give a detailed description of the data, the variables included,
author’s calculations, sources, limitations and problems encountered during data
sourcing and their implication and finally the time series properties of the variables. For
both Malawi and South Africa the variables used in the empirical model are the trade
ratio, real effective exchange rate, domestic income and the U.S income all in log form.
However, we needed data on exports and imports to calculate the trade ratio hence data
on exports and imports variables was also collected, data on real exchange rate between
South Africa and USA, consumer price indices in South Africa and USA are used to
convert GDP for South Africa form rands to dollars. The data set for South Africa
covers the period from 1976 to 2003 in quarterly frequencies. To be consistent in the
interpretation of the estimates, all the variables needed to be in the same currency
except for the real effective exchange rate since it is an index. As such, we choose the
US dollars as the units of measure of value. For South Africa, data were available in US
dollars for all variables except for the domestic income. As a result, we had to convert
the domestic income from rands to dollars using purchasing power parity (PPP) method.
The following equation describes how the, PPP methodology was applied
Y$  YR
CPI US
E$ R
CPI SA
(11)
Where, Y$ is South African GDP in United States dollars, YR is GDP for South Africa
in rands, CPI US and CPI SA are the United States and South African consumer price
18
index for all items in urban areas respectively, E$ R is the exchange rate between the U.S
and South African. The CPI and exchange rates are based on 2000 constant values.
The series used for the analysis of the empirical model for Malawi are all
defined as those of South Africa and they are all in US dollars with an exception for the
real effective exchange rate since it is and index. The series stretch from 1970 to 2004
in annual frequency. The study preferred the employment of quarterly data to increase
the number of possible observations, but could not find GDP data for Malawi in the
preferred frequency. As a result used annual data were used. Taking into account for the
number of observations one may be hesitant to implement a policy prescription from the
results of this study as far as Malawi is concerned. However, for academic purpose the
series befit the objective of this paper. The real effective exchange rate for both Malawi
and South Africa are all based on consumer price index. There was no specific reason
for choosing the CPI based REER other than convenience in the availability of the data.
The main source of data used in this study is Microsoft Excel for Datastream Advance,
courtesy of University of Texas at Arlington Central library. Other source of data
includes the St. Louis Federal Reserve Bank for data on consumer price index for
United States and the exchange rate between the dollar and the rand. Otherwise the rest
of the series were sourced from Microsoft Excel for Datastream Advance. The
descriptive statistics and definition of the variables are provided in Appendix A. Figure
1 and 2 provide the trends in the real effective exchange rate and the trade ratio in
Malawi and South Africa respectively.
19
5.1
0.2
5.0
0.1
-0.0
4.9
-0.1
4.8
-0.2
4.7
-0.3
4.6
-0.4
4.5
-0.5
4.4
-0.6
4.3
-0.7
1970
1974
1978
1982
1986
REER
1990
1994
1998
2002
Trade Ratio
Figure 1 Malawian real effective exchange rate and trade ratio in levels
On average, Malawi had been running a trade deficit. Significant part of the trade ratio
is below zero except for 1984 where a surplus was registered. Malawi’s real effective
exchange rate against time portrayed a continuous downward trend implying a
depreciation of the Malawi kwacha.
20
0.8
5.4
0.6
5.2
0.4
5.0
0.2
4.8
0.0
4.6
-0.2
4.4
-0.4
4.2
1976
1979
1982
1985
1988
1991
REER
1994
1997
2000
2003
Trade Ratio
Figure 2 South African real effective exchange rate and trade ratio in levels
In figure 2, there are some volatilities in the South African rand implying either
a depreciation or appreciation. However, the rand has been depreciating through out
time. The average trade ratio is above zero except for the year 2000. This signifies that
South Africa has been achieving a trade surplus.
21
DREER
0.32
0.24
0.16
0.08
0.00
-0.08
-0.16
-0.24
-0.32
-0.40
1971
1974
1977
1980
1983
1986
1989
1992
1995
1998
2001
2004
1989
1992
1995
1998
2001
2004
D(X/M)
0.50
0.25
0.00
-0.25
-0.50
1971
1974
1977
1980
1983
1986
Figure 3 Malawian real effective exchange rate and trade ratio in first differences
DREER
0.25
0.20
0.15
0.10
0.05
-0.00
-0.05
-0.10
-0.15
-0.20
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
1992
1994
1996
1998
2000
2002
D(X/M)
0.3
0.2
0.1
-0.0
-0.1
-0.2
-0.3
-0.4
-0.5
1976
1978
1980
1982
1984
1986
1988
1990
Figure 4 South African real effective exchange rate and trade ratio in first differences
22
In figures 3 and 4, all the series look stationary after first differencing. However, to
substantiate this claim, unit root tests in both levels and first difference will be
conducted in the next section to identify the time series properties of the data.
3.4 Time Series Properties of Data
To test for unit root of the variables the Augmented Dickey-Fuller (ADF) test
procedure is employed as described by Enders (1995). The ADF test compared to the
ordinary Dickey-Fuller unit root test, allows the inclusion of lagged dependent variable
terms in order to correct for serially correlated residuals. Plots of domestic and foreign
incomes for both South African and Malawian models exhibit a presence of a trend in
the series. As a result, the unit root tests for these variables include a constant and a
time trend, equation (13) applies. The rest of the variables from both models do not
have a time trend in the series as a result, equation (12) is used to test for presence of
unit root in the series. Thus, the following equation is used
P
z t  a 0  z t 1    i z t i 1   t
(12)
i 2
Where a 0 ,  and  i are parameter estimates and  t is the error term. The number of
augmented lags is denoted by p. The null hypothesis of the ADF in this specification is
that   0 (the data needs to be differenced to make it stationary) and the alternative
hypothesis is that   0 (the data is stationary and doesn’t need to be differenced). For
the equations that include a time trend (domestic and foreign incomes), the following
specification is employed
23
P
zt  a0  zt 1  a2t   i zt i 1   t
(13)
i 2
Where t is a time trend and a 2 is a parameter estimate.   0 (the data needs to be
differenced to make it stationary) and the alternative hypothesis is that   0 (the data is
trend stationary and needs to be treated by means of using a time trend in the regression
model instead of differencing the data). The results of the tests are provided in the
following tables (1) and (2).
Table 1 Augmented Dickey-Fuller Test for Unit Root for Variables in Malawi
H0: I(1), H1:(0)
T-Value
H0: I(2), H1:(1)
T-Value
Trade Ratio
-3.59**
Trade Ratio
-7.36**
Real Effective
-0.53
Real Effective
-6.96**
Exchange Rate
Exchange Rate
Domestic Income
-2.07
Domestic Income
-7.50**
Foreign Income
-0.30
Domestic Income
-4.59**
Notes. H0: I(1), H1:(0), the null hypothesis is that the series are unit root against the alternative that the
series are stationary. H0: I(2), H1:(1), the null is that the series are integrated of the order two against the
alternative hypothesis that the series are integrated of order one. ** represents significant at 99%
confidence level.
24
Table 2 Augmented Dickey-Fuller Test for Unit Root for Variables in South Africa
H0: I(1), H1:(0)
T-Value
H0: I(2), H1:(1)
Trade Ratio
-2.87
Trade Ratio
Real Effective
-1.98
Real Effective
Exchange Rate
T-Value
-12.61**
-4.64**
Exchange Rate
Domestic Income
-0.15
Domestic Income
-10.06**
Foreign Income
-2.89
Domestic Income
-5.58**
Notes. H0: I(1), H1:(0), the null hypothesis is that the series are unit root against the alternative that the
series are stationary. H0: I(2), H1:(1), the null is that the series are integrated of the order two against the
alternative hypothesis that the series are integrated of order one. ** represents significant at 99%
confidence level.
All variables are found to be non-stationary at 95% significant level except for
the trade ratio in Malawi where the null hypothesis of unit root was rejected. The trade
ratio in South Africa exhibited a borderline case. However, for the interest of this study,
it was treated as non-stationary. All the variables became stationary after first
differencing at 99% significant level. Hence we denoted all but the trade balance ratio
in Malawi I(1) variables. The unit root characteristics of the variables have important
implication when testing for cointegration of the variables in a specified empirical
model. It is often, wrongly assumed that all the variables in the error correction model
(ECM) need to be I(1). However, a necessary condition to finding a cointegrating
relationship among non stationary variables is that only two of the variables have to be
integrated of the order one (Hansen and Juselius, 1995). According to Guptor-Kapoor
and Ramakrishnan, (1999) economic relevance should be a key determinant of the
25
system of the variables in the VECM and not the time series properties of the data.
Having tested the time series properties of the variables, we continue to estimate the
long-run relationships of the variables using the cointegration analysis.
26
CHAPTER 4
EMPIRICAL ANALYSIS AND RESULTS
4.1 Cointegration Analysis
Prior to estimating the cointegrating vectors it is important to select an optimal
lag length that will give white noise residuals. This is one of the important stages in this
analysis. Lag lengths have significant influence on the outcome of the results. There is
always a trade off between using too many lags and too few lags. Too many lags tend to
make the model less parsimonious and reduce the degrees of freedom while using very
few lags leads to correlation of the residuals. The work of information criteria is to
compromise between the number of parameters and lag length by minimizing the linear
combination of the residual sum of squares and the number of parameters (Johansen,
1995). We used the Akaike Information Criterion (AIC), Schwartz Bayesian Criterion
(SBC) and the Likelihood ratio test to select the optimal lag length. Both AIC and SBC
selected two lags as the optimal lag length for the model in Malawi while the model in
South Africa, the optimal lag length is five. The likelihood ratio test was not applied in
Malawi because of the small sample size. The LR test has asymptotic properties hence
applying it to the model in Malawi would not give consistent results. The lag length for
South Africa was arrived at after conflicting results from the three criteria. The AIC and
the LR test selected five lags while the SBC selected two lags. As a result, the test
results from the two criteria were chosen. We applied the Johansen procedure to test for
27
cointegration of the variables in our models. The Johansen method uses the maximum
eigenvalue statistics and the trace statistics to determine the rank of the cointegrating
vectors. The results of this test are given in table 4, with 95 % critical values. The test
statistics are obtained from Enders (2004) reproduced from Osterwald-Lenum (1992).
Both statistics reject the null hypothesis of r ≤ 1 against the alternative hypothesis of r ≥
2 for both Malawi and South Africa.
Table 3 Cointegration Test Results for Malawi and South Africa
Eigenvalues
South
Africa
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
0.2599
0.1958
0.1256
0.0464
Null
Alternative 5 % CV
Hypothesis Hypothesis
Malawi
0.7510
0.5986
0.2337
0.1703
r=0
r≤1
r≤2
r≤3
λ trace tests:
r>0
r>1
r>2
r>3
λ max tests:
r=1
r=2
r=3
r=4
53.12
34.91
19.96
9.24
Test Values
South
Africa
Malawi
72.86*
41.56*
18.89
4.94
85.44*
42.33*
14.04
5.79
0.2599
0.7510
r=0
28.14
31.30*
43.10*
0.1958
0.5986
r=1
22.00
22.66*
28.29*
0.1256
0.2337
r=2
15.67
13.96
8.25
0.0464
0.1703
r=3
9.24
4.94
5.79
Note. λ trace is the stochastic matrix trace test that the number of cointegrating vectors is less than or
equal to r and λmax is the maximal eigenvalue statistic for at most r cointegating vectors against the
alternative of r + 1 cointegrating vectors. * indicates significance at 5 percent critical value.
4.2 The Long-Run Equilibrium Relationship
The existence of two cointegrating vectors implies that the long-run relationship
is not unique. This is a potential identification problem. The maximum eigenvalue
statistics and economic reasoning make us choose the first vectors in both models as the
28
most likely long-run relationships (Tarlok Singh, 2002). Hence the first vectors are the
long-run relationship for our models. The second vectors when normalized on the trade
ratio provided overly large coefficients with inconsistent signs without meaningful
economic interpretation. In South Africa (table 4), the long-run model predicts a
positive relationship between the trade ratio and the real effective exchange rate, with a
long run elasticity of 0.62. This is consistence with theory that real depreciation
improves the trade ratio in the long run. However, the coefficients on domestic and
foreign income have inconsistent signs to those predicted by economic theory when
demand is the main determining factor of exports and imports. In our results domestic
and foreign incomes are positively and negatively related to the trade ratio, respectively.
This may suggest that as far as domestic and foreign incomes are concerned, their
influence on the South African trade ratio is supply driven.
29
Table 4 Estimated Cointegrating Vector for South Africa
Standardized β′ eigenvectors
X/M
1.000
REER
-0.62
(0.041)
Standardized α coefficients
Variable
X/M
REER
Y
Y*
Y
-1.182
(0.013)
Value
0.352
-0.018
0.012
0.001
Y*
3.841
(0.144)
Constant
6.553
T-Statistics
3.63
2.485
5.11
0.731
Note. Standardized β′ eigenvectors are normalized on X/M and the standardized
α coefficients are the speed of adjustment parameters. Standard errors are
enclosed in parentheses.
The alpha coefficients represent the adjustment parameters. The t-values,
suggest that the trade ratio, real effective exchange rate and the domestic income are the
variables that adjust to deviation from the long-run equilibrium. The estimators are
fairly small in size implying that they characterize a slow adjustment to the
disequilibrium. We may as well conclude that the foreign income is weakly exogenous
and is consistent with our expectation. The long-run relationship for the variables in
Malawi is presented in table 4 below.
30
Table 5 Estimated Cointegrating Vector for Malawi
Standardized β′ eigenvectors
X/M
1.000
REER
-0.202
(0.094)
Standardized α coefficients
Variable
(X/M)
REER
Y
Y*
Y
1.160
(0.033)
Value
-0.247
-0.046
-0.052
-0.105
Y*
-1.180
(0.011)
Constant
12.224
T-Statistics
-1.277
-0.381
-1.311
7.228
Note. Standardized β′ eigenvectors are normalized on X/M and the standardized
α coefficients are the speed of adjustment parameters. Standard errors are
enclosed in parentheses.
In table 5, the beta coefficients on the long-run model for Malawi are all consistent
with theory. The trade ratio is positively related to the real effective exchange rate with
an elasticity of 0.202. The implication of this relationship is that real devaluation will
improve trade ratio in the long run. The coefficients on domestic and foreign income
bear the expected signs. This suggests that in Malawi, exports and imports are
determined by demand side effects. Looking at the speed of adjustment parameters
(alpha coefficients), their sizes suggest a slow adjustment to a deviation from the long
run equilibrium. At conventional siginificance levels all variables but the foreign
income are weakly exogenous. This however, is not consistent with reality considering
that Malawi is a small economy compared to U.S. economy such that we would expect
the U.S. income to be exogenous in this model.
31
4.3 Dynamic Relationships
4.3.1 Variance Decompositions
The dynamic relationships of the variables with respect to the trade ratio are
provided in terms of variance decomposition from the generalized approach. One
important properties of variance decomposition analysis is that it provides some
information about the relative importance of random innovations (Narayan P. and
Narayan S., 2004). With variance decomposition you get some information on the
percentage of variation in the forecast error of a variable as explained by its own
innovation and proportion explained by innovations in other variables in the system.
Tables 6 and 7 provide results of the variance decomposition of trade ratio as
attributable to its own innovations and to shocks in the other variables for a forecast
horizon of 1 through 12.
Table 6 Variance Decomposition of the Trade Ratio for Malawi
Period
1
2
3
4
5
6
7
8
9
10
11
12
X/M
100
97.03
93.74
91.10
89.11
87.62
86.48
85.59
84.87
84.28
83.79
83.38
REER
0
1.60
3.38
4.80
5.87
6.68
7.29
7.78
8.16
8.48
8.74
8.97
Y
0
1.22
2.57
3.66
4.47
5.08
5.55
5.92
6.21
6.46
6.66
6.83
32
Y*
0
0.15
0.31
0.44
0.54
0.62
0.67
0.72
0.75
0.78
0.81
0.83
The results of the variance decomposition suggest that for Malawi (table 6) the
significant source of variation in the trade ratio forecast error is its own innovations and
declines overtime with an average of 89.41% for the forecast horizon. The real effective
exchange rate explains about an average of 5.71% of the variation in the trade ratio. The
domestic income and foreign income explains an average of 4.34% and 0.53 %
respectively. In general the results suggest that foreign income and real effective
exchange rate have little influence on the variations in the trade ratio in Malawi.
Table 7 Variance Decomposition of the Trade Ratio for South Africa
Period
1
2
3
4
5
6
7
8
9
10
11
12
X/M
90.80
86.51
80.46
73.43
67.06
61.83
57.76
54.70
52.42
50.73
49.47
48.52
REER
2.09
8.50
15.77
23.41
30.13
35.58
39.79
42.95
45.31
47.05
48.32
49.23
Y
7.11
4.84
3.66
3.06
2.71
2.50
2.37
2.27
2.19
2.12
2.07
2.03
Y*
0.00
0.15
0.11
0.10
0.09
0.09
0.08
0.08
0.09
0.11
0.15
0.21
From table 7 the results of the variance decomposition of the trade ratio in South
Africa suggest that the most important shocks that affect the trade ratio are its own
innovations with an average of 65.92% for the forecast horizon. However, contrary to
Malawi, here we see that the real effective exchange rate has significant contribution to
the variations in the trade ratio at longer horizons. On average about 30.8% and 3.2% of
the variations of the forecast errors in the trade ratio are attributable to the real effective
33
exchange rate and domestic income respectively. In both systems for South Africa and
Malawi, the foreign income explains a very insignificant proportion of the variations in
the trade ratio. This suggests that the trade ratio evolves independently of the shocks of
the foreign income sequence.
4.4 Generalized Impulse Response Analysis
In this section we answer the existing hypothesis as to whether the J-curve exists
on the trade ratios in both South Africa and Malawi. Similar to auto-regression, a vector
auto-regression can also be written as a moving average representation. In the vector
moving average representation the variables in a given VAR system are expressed in
terms of current and past values of their respective shocks. Importantly, the vector
moving average representation through the coefficients of the error terms can be used to
estimate the interaction between the variables in the dynamic system (Enders 2004).
The parameters of the error terms are called impact multipliers and they measure the
instantaneous response of a given variable to one unit change in a shock. When the
impact multipliers are considered over time, they are called impulse response functions
and when plotted against time, the behavior of the variables in the dynamic system is
represented in response to various shocks.
This is the traditional way of impulse response analysis where orthogonalized
impulse responses are used. The most popular way of orthogonalizing the shocks is the
use of the Cholesky decomposition. The setback with using this method is that the
ordering of the variables in the VAR system affects the outcome and the magnitude of
the shocks. Consequently, the shocks are not unique. To correct this problem, the
34
impulse responses are identified by imposing restrictions on the VAR system. Such
restrictions are based on either economic theory or statistical acceptability. One
alternative method to the traditional impulse response analysis is the generalized
impulse response analysis suggested by Pesaran and Shin (1998). The advantage of this
approach is that the impulse responses are unique since the ordering of the variables in
the system does not affect the outcome of the impulse responses and fully take account
of the historical patterns of correlations observed amongst different shocks. According
to Elif Akbostanci (2004), the generalized impulse responses are an average of the
current and the past shocks, and the impulse responses are expressed as conditional
expectations based on historic information.
This paper applies the generalized impulse response analysis as discussed in
Persaran and Shin (1998). An impulse response function measures the time profile of
the effect of shocks at a given point in time on the (expected) future values of variables
in a dynamical system. The best way to describe an impulse response is to view it as the
outcome of a conceptual experiment in which the time profile of the effect of a
hypothetical k×1 vector of shocks of size δ = (δ1,…,δm)′, say, hitting the economy at
time t is compared with a base-line profile at time t+n, given the economy's history.
There are three main issues: (i) The types of shocks hitting the economy at time t; (ii)
the state of the economy at time t-1 before being shocked; and (iii) the types of shocks
expected to hit the economy from t+1 to t+n.
35
Denoting the known history of the economy up to time t−1 by the nondecreasing information set Ωt−1, the generalized impulse response function of Xt at
horizon n, is defined by
GI x (n,  ,  t 1 )  E ( X t  n  t   ,  t 1 )  E ( X t  n  t 1 ) .
(14)
Alternatively, instead of shocking all the elements of  t , we could choose to shock only
one element, say its ith element, and integrate out the effects of other shocks using an
assumed or the historically observed distribution of the errors. In this case we have
GI x (n,  i ,  t 1 )  E ( X t  n  it   i ,  i 1 )  E ( X t  n  t 1 ) .
(15)
Assuming that  t , has a multivariate normal distribution, it is now easily seen that,
E ( t  it   i )  ( 1i ,  2i ,...,  mi ) /  ii1 i  ei ii1 i
(16)
Where, ei is a selection vector. Hence, the k×1 vector of the (unscaled) generalized
impulse response of the effect of a shock in the ith equation at time t on Xt+n is given by
 An ei

 
ii

  i

   ii


, n  0,1, 2, ... .

(17)
Where, An is the coefficient of the moving average representation. By setting
 i   ii , we obtain the scaled generalized response function
GI i (n) 
36
An ei
 ii
, n  0,1, 2, ... ,
(18)
which measures the effect of one standard error shock  i   ii , to the ith equation at
time t on expected values of X at time t+n. Therefore, impulse responses can be thought
of as the difference between two realizations of the future value of a variable Xt+n. The
first realization is disturbed by a shock, while the second is a standard realization.
Having discussed the theoretical aspects of the generalized impulse response
analysis, we now investigate the J-curve hypothesis on the trade ratios in Malawi and
South Africa. Figures 5 and 6 present the impulse responses of the trade ratio to one
standard deviation shock in the real effective exchange rate.
37
Figure 5 The response of South African trade ratio to one standard deviation shock to
REER
In the short run (Figure 5), South Africa’s trade ratio deteriorates by a maximum
of about 5.2% due to a 1% real depreciation in the rand. The deterioration of the trade
ratio is due to price effect which implies that the unit value of imports has increased
resulting in an increase in total value of imports against a constant or an insignificant
change in the value of exports. About four quarters after the initial shock, the trade ratio
starts to improve. At this time the impact of depreciation is almost decimated, thus the
price effect is now approximately equal zero. The improvement in the trade balance is
38
due to volume effect here both supply and demand elasticities increase in absolute
values. The domestic export volume has increased due to a decrease in price in foreign
currency and a decrease in import volume due to price increase in domestic currency.
On average the trade ratio adjust to its equilibrium paths at about 1 % above the old
equilibrium level. At the given confidence interval, the South African J-curve seems to
be significant. Therefore, we fail to reject the hypothesis about the existence of the Jcurve in South Africa’s trade ratio. However the rate at which the trade ratio responds to
the shock in the real effective exchange rate may not go without comment. Generally
the rate has been slow which may imply a weak form of the J-curve as opposed to a
textbook example where the form of the J-curve is rapid and strong. For instance, it
takes about 24 quarters before the trade ratio reaches its balance. These results are
consistent with what H. Hsing (2005) found when four quarters after a shock in the
Japanese yen, the Japan’s trade with the world economy started to improve.
39
Figure 6 The impulse response of the Malawian trade ratio to a shock in REER
In figure 6, the plot of the impulse response of the trade ratio to one standard
deviation shock in the real effective exchange rate in Malawi. We clearly see that after
the shock on the REER the trade ratio deteriorates by a maximum of about 3%.
However, the impact of the price effect doesn’t stay long as evidenced in the figure.
About nine months after the initial shock, the trade ratio reaches its balance. On
average, 1 % real depreciation of the Malawi kwacha has a long-run positive impact of
about 3 % on the trade ratio. However, at the given confidence level, the J-curve is
40
insignificant. It should be noted that the wider the confidence interval the more
insignificant the results become. We therefore reject the null hypothesis that the J-curve
phenomenon exist on the trade ratio in Malawi.
4.5 Diagnostic Tests for the Long Run Models
The misspecification tests for the long-run models are provided in table 6. We
apply the autoregressive conditional heteroskedasticity (ARCH) and the normality tests
for individual models. The test results suggest that the individual variables in both
models do not suffer from these problems except for the normality test in DREER
equation in Malawi where the normality hypothesis is rejected. For ARCH (5 and 2),
the chi-squared distributions have a 95 % critical values of 11.0705 and 5.9915
respectively. The multivariate tests for the general models are given by LM (1) and
LM (4). These are tests for residual autocorrelation of order 1 and 4 respectively. Both
models do not suffer from residual autocorrelation. Graphical representations of the
actual and fitted values of the variables are provided in appendix B and do not show any
signs of misspecification.
41
Table 8 Misspecification Tests for the Models in Malawi and South Africa
Univariate Statistics
Variable
Malawi
Arch(2)
D(X/M)
3.041
DREER
1.144
DY
3.060
DY*
1.978
Multivariate Statistics
Value
LM(1)
21.558[0.16]
LM(4)
20.675[0.19]
2
Normality χ (8) 3.447[0.9]
2
Normality χ (2)
0.168
7.238*
0.889
0.288
South Africa
Arch(5)
6.189
2.339
1.879
2.939
Normality χ2(2)
1.599
2.236
2.374
1.184
Value
15.195[0.229]
20.206[0.208]
10.536[0.62]
* is significant at 95 percent significance level
Notes: Arch is test for residual heteroskedasticity while LM(1) and LM(4) are tests for general and
seasonal residual correlations respectively. All the tests are χ 2 distributed. The figures in brackets are
p-values.
4.6 Final Discussion
From the long-run equilibrium models of both Malawi and South Africa, we see
that the trade ratio is positively related to the real effective exchange rate. From
theoretical point of view this implies that real currency devaluation will lead to a
long-run improvement in the trade ratio. It signifies that exports are increase more than
imports and the trade balance is expected to be positive. It is also found that the trade
ratio in South Africa is positively and negatively related to the domestic and foreign
income respectively. This is contrary to the assumptions we made in the framework
about demand as the driving force of both exports and imports. When the demand is the
driving force, we expect domestic income to be negatively related to the trade balance.
However, the conflicting signs from the empirical results suggest that supply side
42
effects are the main determinants of imports and exports in South Africa. One
explanation about this is that an increase in real income increases productivity or
production of import substitute goods. This outstrips domestic consumption due to high
marginal propensity to save in home country or low domestic absorption. Exports need
to rise to dispose of some of the surplus (Onafowura, 2003). The results for Malawi are
consistent with demand side expectations.
The empirical results about the generalized impulse response function
from the vector error correction model suggest that only South Africa support the Jcurve hypothesis that soon after a real depreciation, the trade balance deteriorates as a
result of price effects. The unit value of imports increases relative to exports but as time
passes by, the volume effect takes over and the trade balance starts to improve. In case
of Malawi, we did not find evidence of J-curve hypothesis. The lack of evidence of Jcurve in Malawi is consistent with theory that countries that are consistently devaluating
their currency do not experience any improvement in the balance of payments because
they use debt to finance current accounts (Kulkarn, 1996). De Silva (2004) argues that
continuous devaluations keep postponing the desired effects. The discussion above
leads us to confirm our hypothesis that,
There is a long-run relationship between the trade ratio and the real effective exchange
rate in Malawi and South Africa and we fail to reject the hypothesis about the existence
of J-curve phenomenon in South Africa which is rejected for Malawi.
43
CHAPTER 5
CONCLUSIONS
This paper employs the cointegration analysis and vector error correction model
to investigate the J-curve effect on the trade balance in Malawi and South Africa. The
overall conclusion is that real depreciation has a long-run positive impact on the trade
balance in South Africa and we find evidence of J-curve hypothesis. Although we find a
long-run positive relationship between the trade balance and real effective exchange rate
in Malawi, the empirical results did not exhibit a statistically significant J-curve. Using
variance decomposition analysis, we find that shocks in the real effective exchange rate
have significant attributes on the forecast error variance in the trade ratio in South
Africa. For Malawi, shocks in REER have little influence on the trade ratio forecast
error variance. About 30.8% and 5.7 % of shocks in REER were attributable to
variation in the forecast error of the trade ratio for South Africa and Malawi
respectively.
Much as we find evidence of the J-curve hypothesis in South Africa, this does
not provide enough information to prescribe a devaluationary policy on South Africa. It
is important to assess the effect of such a policy on the economy as a whole and not just
the trade balance. It is possible to observe the trade balance improve as a result of real
depreciation at the same time register a decline in gross national product. The net effect
is zero because the improvement in the trade balance is offset by the decline in the gross
44
national product. To eliminate this shortcoming, we recommend a multi-dimensional
approach in studying the effect of a real devaluation on the trade balance. This may
include understanding the behavior of interest rate, inflation rate, GDP and other macro
economic variables under devaluationary policies. Such approach is beneficial for the
economy at large other than just a small sector of the economy. One needs to bear in
mind that devaluation has its own contractionary effects on the economy. Devaluation
raises the cost of imported intermediate inputs and this affects supply side of the
economy. In situations where devaluation is accompanied by inflation in the domestic
market, it erodes purchasing power of money (real balance effect) resulting in a decline
in aggregate demand.
One limitation of this study is the use of aggregated data. The effective
exchange rate does not provide much information about the relative competitiveness of
the trading countries. It is possible for a country’s currency to be depreciating against
one country while appreciating against another. In this situation, the direction of the
trade balance is undetermined. Future research should try to use bilateral trade data (if
available) to investigate the J-curve to capture the competitive aspect of the real
exchange rate compared to real effective exchange rate. Researchers interested in
extending this study should try to investigate the response of other variables in the
model to a real depreciation. This will help understand the net effect of a real
depreciation on the economy as a whole.
45
Finally, countries planning to implement policies targeted at the exchange rate
need to do that with caution because countries experience varying macroeconomic
environments and respond differently to currency depreciation.
46
APPENDIX A
SUMMARY STATISTICS
47
Table A.1 Variable Description
Variable
Definition
X/M
Log of ratio of export to import
REER
Log of real effective exchange rate
Y
Log of real domestic income
Y*
Log of real foreign income
CPIUS
Average consumer price index in the United States for all items in urban
areas, in the year 2000.
CPISA
Average consumer price index in South Africa for all items in urban
areas, for the year 2000
E$R
Average exchange rate between the U.S. dollar the South African rand
for the year 2000
48
Table A.2 Descriptive Statistics of Data for Malawi
Variable
X/M
Mean
Std.Dev
Min
Max
-0.3512
0.1870
-0.6574
0.1504
4.897
0.2213
4.3142
5.0916
Y
13.9160
0.3242
13.1958
14.4016
Y*
22.5800
0.3136
22.0508
23.0987
Exports
302.9669
140.1892
59.64
541.16
Imports
433.3911
216.1886
99.1
932.52
REER
Number of observations = 35
Notes: Imports and exports are denominated in millions of U.S dollars.
49
Table A.3 Descriptive Statistics of Data for South Africa
Variable
Mean
Std.Dev
Min
Max
X/M
0.1461
0.2189
-0.2104
0.7861
REER
4.8390
0.2073
4.2495
5.2234
Y
17.8694
1.1430
15.7600
15.7996
Y*
22.6560
0.2500
22.2266
23.0749
Exports
5668.332
1594.717
1979
9533.4
Imports
5115.709
2044.22
1527
10215
E$R
0.1446
0.0105
0.1301
0.1631
CPISA
99.9917
2.135
96.4
102.4
CPIUS
179.8583
1.3311
177.7
181.7
Number of observations = 112
Notes: Imports and exports are in millions of U.S dollars.
50
APPENDIX B
GRAPHICAL REPRESENTATION OF RESIDUALS
51
Figure B.1 Graphs of residuals from the real effective exchange rate equation for South
Africa.
52
Figure B.2 Graphs of residuals from the domestic income equation for South Africa.
53
Figure B.3 Graphs of residuals from the foreign income equation for South Africa.
54
Figure B.4 Graphs of residuals from the trade ratio equation for South Africa.
55
Figure B.5 Graphs of residuals from the real effective exchange rate equation for
Malawi.
56
Figure B.6 Graphs of residuals from the domestic income equation for Malawi.
57
Figure B.7 Graphs of residuals from the foreign income equation for Malawi
58
Figure B.8 Graphs of residuals from the trade ratio equation for Malawi.
59
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BIOGRAPHICAL INFORMATION
The author received his Bachelor of Science in Agricultural Economics at
University of Malawi in 2002. In fall 2004 he joined the masters program in Economics
at University of Texas at Arlington. This paper is part of the requirements for the degree
of Master of Arts in Economics at UTA to be obtained in May 2006.
64