Models of Factors Driving the Czech Export

Abstract

This paper aims to analyze the cost factors that influence the export of the Czech Republic, and to estimate models suitable for quantitative analysis of export and its prediction. According to the macroeconomic theory, the fundamental export factors include foreign demand, domestic and foreign price level and exchange rate. Foreign demand reflects the business cycle of foreign economy, price levels and exchange rate characterize the competitiveness of the exported goods, and the exchange rate determines, among others, the production costs through the prices of imported crucial inputs. Several models are applied to set of these variables, and their impact on the export dynamics of the Czech Republic is evaluated.

Full text

PRAGUE ECONOMIC PAPERS, 3, 2011  195
MODELS OF FACTORS DRIVING THE CZECH EXPORT
David Havrlant, Roman Hušek*
Abstract
This paper aims to analyze the cost factors that infl uence the export of the Czech Republic, and
to estimate models suitable for quantitative analysis of export and its prediction. According to
the macroeconomic theory, the fundamental export factors include foreign demand, domestic
and foreign price level and exchange rate. Foreign demand refl ects the business cycle of foreign
economy, price levels and exchange rate characterize the competitiveness of the exported goods,
and the exchange rate determines, among others, the production costs through the prices of
imported crucial inputs. Several models are applied to set of these variables, and their impact on
the export dynamics of the Czech Republic is evaluated.
Keywords: export, exchange rate, import, producer and energy prices, VECM, cointegration
analysis
JEL Classifi cation: C22, C53, F47
1. Introduction
For a small and open economy the export represents not only an opportunity to join
the international market with all the well known benefi ts it brings, but it is indeed an
important economic stimulus, since it comprises a signifi cant component of the country‘s
gross domestic product (GDP). In case of the Czech Republic (CR) the volume of exports
is comparable with the total GDP of CR even in the long term, and its contribution to the
year-on-year GDP growth has come up to 30 % on average since 2006. All of these are
the typical features of an export oriented economy (Zweimüller, 2001).
This paper aims to analyze the cost factors that infl uence the export of the Czech
Republic, and to estimate models suitable for quantitative analysis of export and its
prediction. According to the macroeconomic theory, the fundamental export factors
Articles
* David Havrlant, Czech National Bank (david.havrlant@cnb.cz); Roman Hušek, University of
Economics, Prague (husek@vse.cz); this paper was written with the support of the GA 402/09/0273
Grant from the Czech Science Foundation.

196  PRAGUE ECONOMIC PAPERS, 3, 2011
include foreign demand, home and foreign price levels and exchange rate. Foreign
demand refl ects the business cycle of foreign economy, price levels and exchange
rate characterize the competitiveness of the goods to be exported, and the exchange
rate determines, among others, the production costs through the prices of imported
crucial inputs. Some papers concerning this topic have been already published; see for
example Pánková (2003), Nešvera (2006) or Rojíček (2010).
The analysis is carried out on the data set 1996Q1-2010Q2 on data with quarterly
frequency. Nevertheless in some cases the estimation range differs slightly. The series
are tested for stationarity, and the test outcomes indicate that the time series are mostly
integrated of order one (Greene, 2003), thus a cointegration approach is applied. When
necessary, the time series have been seasonally adjusted. The data used in this work were
obtained from the Czech Statistical Offi ce, the Czech National Bank and the Eurostat.
2. Foreign Demand
The most important factor for the development of export is foreign demand, because
if the consumer sentiment abroad weakens noticeably, the export production usually
cumulates in stocks, and that leads to output reductions as well as to the lowering of
production capacities in the long run. For example at the beginning of 2009 many
car producers had to store some part of their production on testing circuits, giving up
the possibility of testing, because they were forced by unexpectedly weak demand.
It is obvious that boom or recession is nowadays a globalized phenomenon which
infl uences all markets in a very short time. Regarding the main trade partners of
the Czech Republic the dynamics of foreign demand is approximated by the GDP
development of the European Union (EU). The following fi gure shows the quarter on
quarter dynamics of Czech export (X, on the left axis), foreign GDP (GDPEMU) and
home GDP (GDP) in the period 1996Q1-2010Q2.
Figure 1
Czech Export (X), Foreign GDP (GDPEMU) and Home GDP (GDP), q-o-q in %
It is obvious that Czech export and foreign GDP are closely related quantities.
This proves the positive correlation coeffi cient as well. The reaction of Czech export
comes shortly after changes in foreign demand. The correlation coeffi cient of export
-12
-8
-4
0
4
8
12
16
-6
-4
-2
0
2
4
6
8
1996 1998 2000 2002 2004 2006 2008 2010
X (left ax i s )
GDPEMU
GDP

PRAGUE ECONOMIC PAPERS, 3, 2011  197
and home GDP is positive as well - the net export makes up a substantial part of the
Czech GDP, and the relation is assumed to possess attributes of rather market driven
economy.
Table 1
Correlation Coeffi cient of Export (X), Foreign GDP (GDPEMU) and Home GDP (GDP), q-o-q in %
Correlation X GDPEMU GDP
X 1.0
GDPEMU 0.6 1.0
GDP 0.4 0.5 1.0
3. Cost Factors and Exchange Rate
Cost factors play a substantial role in the dynamics of export on the one hand and the
exchange rate on the other hand. The lower the price of exported goods is in comparison
with the price of similar product abroad, the more favourable are the arbitrage
opportunities. The price of exported goods in foreign currency is then determined
by the nominal exchange rate. The more the nominal exchange rate appreciates, the
higher is the price of the exported commodity in foreign currency, and that decreases
the profi t of arbitrage (Rogoff, 1996). It is necessary to investigate both – the infl uence
of the prices and the effect of the exchange rate. The fi gure bellow shows the quarter-
on-quarter growth rate of export (X, on the left axis), nominal exchange rate with one
quarter lag (EUR(-1)) and domestic producer prices with lag of two quarters (PPI(-2)).
Figure 2
Export (X), Producer Prices (PPI) and Exchange Rate (EUR), q-o-q in %
It is obvious that the exchange rate appreciation usually leads to decline in exports
and depreciation evokes export growth. This relation of export and exchange rate
corresponds with theoretical assumptions, while appreciation increases foreign prices
of exported products and dampens the advantage of arbitrage. The lag length in which
the exchange rate fl uctuations most infl uence the dynamics of export is one quarter.
-12
-8
-4
0
4
8
12
16
-3
-2
-1
0
1
2
3
4
1996 1998 2000 2002 2004 2006 2008 2010
X
EUR(-1)
PPI(-2) (right axis)

198  PRAGUE ECONOMIC PAPERS, 3, 2011
It is very likely that the producer prices infl uence the swings of export with a
lag, which is caused by the long-term character of contracts and to some extent by
the reserves of key materials. In that case the theoretical assumption would hold: the
drop of domestic prices would lead to an increase in the export activity, though with
lag of two quarters. The following chart shows correlation coeffi cients of export (X),
exchange rate with one quarter lag (EUR(-1)) and producer prices with a two quarters
lag (PPI(-2)). For more detail see
Frenkel (1981).
Table 2
Correlation Coeffi cient of Export (X), Exchange Rate (EUR) and Producer Prices (PPI), q-o-q in %
Correlation X EUR(-1) PPI(-2)
X, q-o-q 1.00
EUR(-1), q-o-q 0.3 1.00
PPI(-2), q-o-q -0.3 -0.2 1.00
3.1 Producer Prices
Producer prices in a small open economy (PPI) are strongly related to the prices of
imported semi-fi nished products and both energy and non-energy materials, which are
determined by the price development on the world markets. These are again adjusted
by the exchange rate. Some relations are pictured in the following fi gure. The world
prices of semi-fi nished products are represented by the producer prices in the European
Union (PPIEMU). Their high growth is usually moderated by the movements of
exchange rate (EUR). The data in following exploration are available for the period
1996Q1-2010Q2 on quarterly basis.
Figure 3
Domestic and Foreign Producer Prices and Exchange Rate, q-o-q in %
A brief analysis of logarithms of the data in levels indicates, that the original time
series possess a stochastic trend, i. e. they are non-stationary, as performed unit-root
tests suggest (
Elliott, 1996 or Enders, 2004). In the table below the results of
Augmented Dickey-Fuller test (ADF,
Dickey and Fuller, 1979) are summarized, and
-4
-3
-2
-1
0
1
2
3
-1
6
-12
-8
-4
0
4
8
12
1996 1998 2000 2002 2004 2006 2008 2010
PPI
PPIEMU
EUR (right axis)

PRAGUE ECONOMIC PAPERS, 3, 2011  199
provide suffi cient evidence, for it is not possible to reject the null hypothesis of unit
root on reasonable signifi cance level for all tested series. The ADF test is made under
assumption of individual intercept and trend for examined series, and the lag length
selection is based on modifi ed Schwartz information criterion (SC,
Davidson and
MacKinnon, 2004
). Nevertheless use of different lag length criteria (Akaike, 1969,
Hannan-Quinn, 1979) leads to similar outcome.
Particularly the time series are integrated of order one, i. e. I(1), as the ADF test
of fi rst differences in Table 3 proves, since it is possible to reject the null hypothesis of
unit root on reasonable signifi cance level for all examined series. The asterisk denotes
rejection of the null hypothesis at the 5% level of signifi cance. The ADF test is made
under precondition of individual intercept, while the trend is assumed to be eliminated
by differencing. The lag length selection is again based on modifi ed SC. Nevertheless
use of other lag length criteria leads to similar conclusion.
Table 3
Stationarity Test of the Logarithms of the Original Time Series and of the First Differences
Series Prob. Lag Series Prob. Lag
LOG(PPIPRO) 0.673 1 D(LOG(PPIPRO)) 0.002* 3
LOG(EUR) 0.349 0 D(LOG(EUR)) 0.000* 2
LOG(USD) 0.668 0 D(LOG(USD)) 0.000* 3
LOG(PPIEMU) 0.436 1 D(LOG(PPIEMU)) 0.004* 2
LOG(BRENT) 0.421 0 D(LOG(BRENT)) 0.000* 2
Consequently, the fi rst differences of logarithms of the original data can be
considered to be stationary, i. e. their mean and variance is expected to be constant
over time (Wooldridge, 2002). When a regression on this data is carried out, there is
no need to be afraid of spurious regression (
Granger and Newbold, 1974) or of the
heteroskedasticity problem.
Regarding the Granger causality (
Geweke, 1984) with emphasis on domestic
producer prices (PPIPRO), the signifi cance of relations among the variables is included
in the next table. It is obvious that the relations and their directions are in line with
economic intuition and with the later analysis (reject the null hypothesis on reasonable
level of signifi cance in Table 4), except the case of relation between the exchange rate
CZK/EUR and the domestic producer prices. This outcome would rather validate, that
the change in domestic prices precedes the change in exchange rate.

200  PRAGUE ECONOMIC PAPERS, 3, 2011
Table 4
Granger Causality regarding PPIPRO
Null Hypothesis: F-Statistic Prob.
LOG(EUR) does not Granger Cause LOG(PPIPRO) 0.582 0.628
LOG(PPIPRO) does not Granger Cause LOG(EUR) 6.046 0.001*
LOG(USD) does not Granger Cause LOG(PPIPRO) 2.514 0.041*
LOG(PPIPRO) does not Granger Cause LOG(USD) 1.143 0.334
LOG(PPIEMU) does not Granger Cause LOG(PPIPRO) 3.270 0.023*
LOG(PPIPRO) does not Granger Cause LOG(PPIEMU) 0.765 0.516
LOG(BRENT) does not Granger Cause LOG(PPIPRO) 10.495 0.000*
LOG(PPIPRO) does not Granger Cause LOG(BRENT) 0.168 0.918
The appropriate lag length used for Granger causality exploration was adjusted in
line with the Akaike information criterion (AIC, Akaike, 1969), Schwartz information
criterion (SC) and Hannan-Quinn criterion (HQ,
Hannan and Quinn, 1979), as it is
summarized in Table 5. The asterisk denotes the appropriate lag length.
Table 5
Appropriate Lag Length Selection
Lag AIC SC HQ
0 -13.4 -13.3 -13.4
1 -29.2 -28.6* -29.0
2 -29.5 -28.3 -29.0*
3 -29.4 -27.7 -28.7
4 -29.50* -27.3 -28.6
5 -29.5 -26.7 -28.3
6 -29.3 -26.0 -28.0
As all the series are of the same integration order, particularity I(1), the long-run
dynamics could be inspected within the vector error correction model (VECM, see
Greene, 2003), thus some prior exploration of cointegration is necessary, so the Johansen
cointegration test (
Johansen, 1988) is carried out onward. Under the condition of
intercept and trend the trace test as well as the maximum eigenvalue statistics gives the
same rank of cointegration (Johansen, Juselius, 1990), as shown in Table 6. The asterisk
denotes rejection of the null hypothesis at the 5% level of signifi cance.
Table 6
Cointegration Rank Test (Trace and Maximum Eigenvalue)
Number of hypothesized
cointegrating relations
Eigen-
value
Trace
Statistic
Critical
Value
Prob. Max-Eigen.
Statistic
Critical
Value
Prob.
None* 0.279 76.559 69.819 0.013* 47.339 33.877 0.001*
At most 1 0.096 29.220 47.856 0.758 14.685 27.584 0.773
At most 2 0.067 14.535 29.797 0.809 10.030 21.132 0.742
At most 3 0.024 4.505 15.495 0.859 3.473 14.265 0.910
At most 4 0.007 1.031 3.841 0.310 1.031 3.841 0.310

PRAGUE ECONOMIC PAPERS, 3, 2011  201
Both tests reject the null hypothesis of none cointegration rank on reasonable level
of signifi cance, and do not reject the null hypothesis of at most one cointegration rank
at the same time, thus one cointegration relation that describes the long-run dynamics
of the system can be found. Since the time series are cointegrated, the Granger causality
can be tested on levels. It is assumed that the exogenity conditions hold. The lag length
used in VECM estimation is adjusted in line with SC (Table 5), and the numerical
results regarding domestic producer prices (PPIPRO) are shown below.
(1)
where the fi rst non differenced terms express the long-run relationship. Their statistical
attributes are in the following table, where the standard errors are in brackets and t-statistics
follow. The asterisk denotes rejection of the null hypothesis at the 10% level of signifi cance.
Table 7
Cointegrating Vector
LOG(PPIPRO(-1)) 1.000
LOG(PPIEMU(-1))
-0.724*
(0.061)
[-12.061]
LOG(EUR(-1))
-0.231*
(0.081)
[-2.856]
LOG(BRENT(-1)) -0.070*
(0.020)
[-3.473]
LOG(USD(-1))
-0.041
(0.031)
[-1.298]
The short-term dynamics, i. e. the error correction mechanism, is summarized in
Table 8 including standard errors and t-statistics.
The model proves a 47% correspondence with the data (R-squared = 0,471),
and is overall statistically signifi cant (F-statistic = 8,024). The next fi gure shows the
contributions of exogenous variables to the estimated year-on-year growth rates of
domestic producer prices.
ˆ
D(LOG(PPIPRO)) = - 0.148*( LOG(PPIPRO(-1)) - 0.724*LOG(PPIEMU(-1)) -
- 0.231*LOG(EUR(-1)) - 0.070*LOG(BRENT(-1)) - 0.041*LOG(USD(-1)) ) +
0.587*D(LOG(PPIPRO(-1))) - 0.113*D(LOG(PPIEMU(-1))) + 0.109* D(LOG(EUR(-1))) +
0.015*D(LOG(BRENT(-1))) - 0.039*D(LOG(USD(-1)))
Table 8
Error Correction Mechanism
CointEq1
-0.148*
(0.076)
[-1.949]
D(LOG(PPIPRO(-1)))
0.587*
(0.154)
[3.806]
D(LOG(PPIEMU(-1)))
-0.113
(0.187)
[-0.604]
D(LOG(EUR(-1)))
0.109*
(0.068)
[1.603]
D(LOG(BRENT(-1)))
0.015*
(0.008)
[1.875]
D(LOG(USD(-1)))
-0.039
(0.031)
[-1.248]

202  PRAGUE ECONOMIC PAPERS, 3, 2011
3.2 Import Prices
The prices of imported semi-fi nished products, i. e. the import prices excluding energy
and food prices (DCADJ), are on the one hand determined by the price development
on world markets and by exchange rate dynamics on the other hand. Moreover, they are
signifi cantly infl uenced through world energy prices, especially in times of their high
volatility. Consequently a curtail roll in the examination of import prices (excluding
energy and food) will play the world prices of semi-fi nished products in form of
producer prices in the European Union (PPIEMU), the world energy prices represented
by the prices of crude oil in USD/barrel (BRENT) and the exchange rate of the main
business partner CZK/EUR (EUR). The succeeding analysis of import prices is carried
out on data for the period 1998M1-2010M3 that is available in monthly frequency.
A quick view on the logarithms of the original time series indicates that all
mentioned series are non-stationary as the ADF test in next table proves. The ADF
test provides suffi cient evidence of non-stationarity, because it is not possible to reject
the null hypothesis of unit root on reasonable signifi cance level for all tested series.
The ADF test is carried out under assumption of individual intercept and trend for
examined series, and the appropriate lag length is selected line with modifi ed SC. Use
of different lag length criteria (AIC, HQ) leads to similar outcome.
As the ADF test of the fi rst differenced logarithms of mentioned time series shows, they
are integrated of order one, for it is possible to reject the null hypothesis of unit root on
reasonable signifi cance level (Table 9). The asterisk denotes rejection of the null hypothesis at
the 5% level of signifi cance. The ADF test is made under assumption of individual intercept,
for the trend is assumed to be eliminated by differencing. The lag length selection is again
based on modifi ed SC, nevertheless use of other lag length criteria leads to similar conclusion.
Table 9
Stationarity Test of the Logarithms of the Original Time Series and of the First Differences
Series Prob. Lag Series Prob. Lag
LOG(DCADJ) 0.553 1 D(LOG(DCADJ)) 0.001* 4
LOG(EUR) 0.349 0 D(LOG(EUR)) 0.000* 2
LOG(USD) 0.668 0 D(LOG(USD)) 0.000* 3
LOG(PPIEMU) 0.436 1 D(LOG(PPIEMU)) 0.004* 2
LOG(BRENT) 0.421 0 D(LOG(BRENT)) 0.000* 2
Thus the fi rst differences of logarithms of the original time series can be regarded
as stationary, i. e. their mean and variance are assumed to be constant over time. When
a regression on this data set is carried out, there is no jeopardy of spurious regression
or of the heteroskedasticity problem.
According to the Granger causality with emphasis on the import prices excluding
energy and food prices (DCADJ), the signifi cance and direction of relations among
variables is summarized in Table 10. The asterisk denotes rejection of the null
hypothesis at the 10 % level of signifi cance. Outlined relations and their directions
seem to be in line with economic intuition and with onward analysis as well (reject the
null hypothesis in the fi rst column on reasonable signifi cance level).

PRAGUE ECONOMIC PAPERS, 3, 2011  203
Table 10
Granger Causality regarding DCADJ
Null Hypothesis: F-Statistic Prob.
LOG(EUR) does not Granger Cause LOG(DCADJ) 3.156 0.004*
LOG(DCADJ) does not Granger Cause LOG(EUR) 2.828 0.009*
LOG(USD) does not Granger Cause LOG(DCADJ) 1.780 0.090*
LOG(DCADJ) does not Granger Cause LOG(USD) 1.105 0.364
LOG(PPIEMU) does not Granger Cause LOG(DCADJ) 4.109 0.000*
LOG(DCADJ) does not Granger Cause LOG(PPIEMU) 1.742 0.105
LOG(BRENT) does not Granger Cause LOG(DCADJ) 2.151 0.043*
LOG(DCADJ) does not Granger Cause LOG(BRENT) 1.143 0.341
The lag length used in computation of the Granger causality statistics was derived
from AIC, SC and HQ, but as it is shown in Table 11, the suggestions are quite distinct.
The asterisk denotes the appropriate lag length.
Table 11
Appropriate Lag Length Selection
Lag AIC SC HQ
0 -13.3 -13.2 -13.3
1 -29.1 -28.4* -28.8*
2 -29.1 -27.9 -28.6
3 -29.0 -27.3 -28.3
4 -29.1 -26.9 -28.2
5 -29.1* -26.4 -28.0
6 -28.9 -25.7 -27.6
As the examined time series are of the same integration order, particularity I(1),
the long-run relation could be again explored within the VECM. Consequently a prior
cointegration analysis follows, so the Johansen cointegration test is carried out further.
Under the condition of intercept and trend the trace test as well as the maximum eigenvalue
statistics concludes that there are two cointegration relations, as shown in Table 12. The
asterisk denotes rejection of the null hypothesis at the 5% level of signifi cance.
Table 12
Cointegration Rank Test (Trace and Maximum Eigenvalue)
Number of
hypothesized
cointegrating relations
Eigenvalue Trace
Statistic
Critical
Value
Prob. Max-Eigen.
Statistic
Critical
Value
Prob.
None * 0.268 112.172 88.804 0.000* 44.997 38.331 0.007*
At most 1 * 0.237 67.175 63.876 0.026* 38.901 32.118 0.006*
At most 2 0.087 28.274 42.915 0.606 13.107 25.823 0.795
At most 3 0.068 15.167 25.872 0.561 10.169 19.387 0.601
At most 4 0.034 4.997 12.518 0.597 4.997 12.518 0.597

204  PRAGUE ECONOMIC PAPERS, 3, 2011
Nevertheless, the trace test does not reject the null hypothesis that there is at
most one cointegrating relation at 1% signifi cance level. If the assumption of trend
occurrence in the original time series is left out – what could be a point of discussion
while dealing with price levels – then there remains only one cointegrating relation
among the variables as shown in the table below.
Table 13
Cointegration Rank Test (Trace and Maximum Eigenvalue)
Number of
hypothesized
cointegrating relations
Eigenvalue Trace
Statistic
Critical
Value
Prob. Max-Eigen.
Statistic
Critical
Value
Prob.
None * 0.245 81.600 69.819 0.004* 40.484 33.877 0.007*
At most 1 0.144 41.116 47.856 0.185 22.333 27.584 0.204
At most 2 0.072 18.783 29.797 0.509 10.762 21.132 0.671
At most 3 0.049 8.021 15.495 0.463 7.198 14.265 0.466
At most 4 0.006 0.823 3.841 0.364 0.823 3.841 0.364
It is important to emphasize that there is not such straightforward cointegrating
relation if any of the variables from the original data set is excluded, i. e. the whole
set of examined time series (DCADJ, EUR, USD, PPIEMU and BRENT) embodies
a comprehensible cointegrating relation, moreover in line with economic intuition.
Likewise an arbitrary pair of variables from the whole set does not seem to be
cointegrated. This information is summarized in the next table where the p-values of
the cointegration rank test (trace test) are shown. For selected subsets of variables it is
possible to judge their cointegration dispositions when the null hypothesis in the left
column is rejected accordingly to the relevant p-value. The outcome for the maximum
eigenvalue statistics is similar. The asterisk denotes rejection of the null hypothesis at
the 5% level of signifi cance.
Table 14
Cointegration Relations of Selected Subsets of Variables
Subset of variables and relevant p-values of trace test
Coint.
relations
DCADJ
EUR
USD
PPIEMU
DCADJ
EUR
USD
BRENT
DCADJ
EUR
PPIEMU
BRENT
DCADJ
USD
PPIEMU
BRENT
DCADJ
EUR
USD
DCADJ
EUR
PPIEMU
DCADJ
USD
PPIEMU
DCADJ
EUR
BRENT
DCADJ
USD
BRENT
None 0.424 0.000* 0.000* 0.000* 0.802 0.438 0.791 0.000* 0.663
At most 1 0.852 0.512 0.049* 0.480 0.802 0.875 0.652 0.242 0.915
At most 2 0.674 0.691 0.438 0.658 0.831 0.685 0.620 0.524 0.723
At most 3 0.647 0.494 0.777 0.468
To sum up, it can be assumed that there is one straightforward cointegration
relation among the whole set of considered time series, so the long-run dynamics of
the system can be estimated within a VECM. The time series are cointegrated so, the
Granger causality can be tested on levels. It is assumed that the exogenity conditions

PRAGUE ECONOMIC PAPERS, 3, 2011  205
are fulfi lled. The lag length used in VECM estimation is adjusted in line with the SC
(Table 11), and the numerical results regarding the import prices excluding food and
energy (DCADJ) are presented below.
(3)
The fi rst non differenced terms express the long-run dynamics. Their statistical
attributes are in the following table, where the standard errors are in brackets and
t-statistics follow.
Table 15
Cointegrating Vector
LOG(DCADJ(-1)) 1.000
LOG(PPIEMU(-1))
-0.521*
(0.079)
[-6.587]
LOG(EUR(-1))
-0.400*
(0.100)
[-3.972]
LOG(BRENT(-1))
-0.014
0.026
[-0.523]
LOG(USD(-1))
-0.228*
0.036
[-6.336]
The short term dynamics, i. e. the error correction mechanism, is summarized in
the next table including standard errors as well as t-statistics. The asterisk denotes
rejection of the null hypothesis at the 10% level of signifi cance.
Estimated model proves correspondence with the data of 45% (R-squared = 0,445),
and is overall statistically signifi cant (F-statistic = 6,728). The next fi gure shows the
contributions of exogenous variables to the estimated year-on-year growth rates of
domestic producer prices.
4. Models of Export
The variables analyzed in previous chapters can be used for the construction of several
models of export dynamics which are in line with economic intuition and comply with
statistical criteria. The models differ in particular in the exogenous variables standing
for domestic and foreign price level.
ˆ
D(LOG(DCADJ)) = - 0.032*( LOG(DCADJ(-1)) - 0.581*LOG(EUR(-1)) -
- 0.201*LOG(USD(-1)) 1.473*LOG(PPIEMU(-1)) - 0.335*LOG(BRENT(-1)) - 7.649 )
+ 0.287*D(LOG(DCADJ(-1))) 0.038*D(LOG(EUR(-1))) -
- 0.01


5*D(LOG(USD(-1))) - 0.217*D(LOG(PPIEMU(-1))) - 0.013*D(LOG(BRENT(-1)))
Table 16
Error Correction Mechanism
CointEq1
-0.472*
(0.139)
[-3.380]
D(LOG(DCADJ(-1)))
0.759*
(0.254)
[2.978]
D(LOG(PPIEMU(-1)))
0.735*
(0.313)
[2.347]
D(LOG(EUR(-1)))
-0.155
(0.153)
[-1.013]
D(LOG(BRENT(-1)))
-0.041*
(0.018)
[-2.194]
D(LOG(USD(-1)))
-0.094
(0.074)
[-1.271]

206  PRAGUE ECONOMIC PAPERS, 3, 2011
4.1 Model with Producer Prices
First some analysis is carried out to get the idea about the characteristics of used time
series in subsequent regression.
In the table below the results of ADF test are summarized, and provide suffi cient
evidence, for it is not possible to reject the null hypothesis of unit root on reasonable
signifi cance level for all tested series. The ADF test is made under assumption of individual
intercept and trend for examined series, and the lag length selection is based on modifi ed
SC. Nevertheless use of different lag length criteria (AIC, HQ) leads to similar outcome.
The time series are integrated of order one, i. e. I(1), as the ADF test of fi rst
differences in Table 17 proves, since it is possible to reject the null hypothesis of unit
root on reasonable signifi cance level for all examined series. The ADF test is made
under precondition of individual intercept, while the trend is assumed to be eliminated
by differencing. The lag length selection is again based on modifi ed SC.
Table 17
Stationarity Test of the Logarithms of the Original Time Series and of the First Differences
Series Prob. Lag Series Prob. Lag
LOG(X) 0.826 1 D(LOG(X)) 0.005* 1
LOG(GDPEMU) 0.901 0 D(LOG(GDPEMU)) 0.029* 2
LOG(PPIEMU) 0.740 0 D(LOG(PPIEMU)) 0.018* 0
LOG(PPI) 0.888 0 D(LOG(PPI)) 0.031* 1
LOG(EUR) 0.255 0 D(LOG(EUR)) 0.000* 0
According to the Granger causality with emphasis on the export (X) the relations
among the variables and their signifi cance is included in the Table 18. It seems that
rather changes in export precede changes in other variables. Relations among the series
are not straightforward for purposes of the subsequent analysis, nevertheless in case of
export some more complex interconnections could be expected.
Table 18
Granger Causality regarding X
Null Hypothesis: F-Statistic Prob.
LOG(GDPEMU) does not Granger Cause LOG(X) 3.032 0.069
LOG(X) does not Granger Cause LOG(GDPEMU) 5.765 0.001*
LOG(PPIEMU) does not Granger Cause LOG(X) 4.922 0.051
LOG(X) does not Granger Cause LOG(PPIEMU) 13.529 0.000*
LOG(PPI) does not Granger Cause LOG(X) 3.226 0.052
LOG(X) does not Granger Cause LOG(PPI) 13.229 0.000*
LOG(EUR) does not Granger Cause LOG(X) 5.675 0.007*
LOG(X) does not Granger Cause LOG(EUR) 7.850 0.001*
The appropriate lag length used for Granger causality exploration was adjusted
in line with the AIC, SC and HQ as it is summarized in the next table. The asterisk
denotes the appropriate lag length.

PRAGUE ECONOMIC PAPERS, 3, 2011  207
Table 19
Appropriate Lag Length Selection
Lag AIC SC HQ
0 -20.6 -20.4 -20.5
1 -28.8 -27.6* -28.3
2 -29.4 -27.3 -28.6
3 -30.0 -26.9 -28.8*
4 -29.9 -25.8 -28.3
5 -29.7 -24.7 -27.8
6 -30.7* -24.7 -28.4
As all the time series are of the same integration order, particularity I(1), the
long-run dynamics can be inspected within the VECM, and some prior exploration of
cointegration is necessary. The Johansen cointegration test is carried out again. Under
the condition of intercept and trend the trace test as well as the maximum eigenvalue
statistics gives the same outcome, as shown in Table 20. Both tests reject the null
hypothesis of none cointegration rank on reasonable level of signifi cance, and do not
reject the null hypothesis of at most one cointegration rank at the same time. The
asterisk denotes rejection of the null hypothesis at the 5% level of signifi cance.
Table 20
Cointegration Rank Test (Trace and Maximum Eigenvalue)
Number of
hypothesized
cointegrating relations
Eigenvalue Trace
Statistic
Critical
Value
Prob. Max-Eigen.
Statistic
Critical
Value
Prob.
None * 0.612 86.167 69.819 0.001* 45.426 33.877 0.001*
At most 1 0.340 40.740 47.856 0.197 19.978 27.584 0.343
At most 2 0.246 20.762 29.797 0.373 13.555 21.132 0.403
At most 3 0.136 7.207 15.495 0.554 7.007 14.265 0.488
At most 4 0.004 0.201 3.841 0.654 0.201 3.841 0.654
So, one cointegration relation can be estimated within the VECM. Since the
variables are cointegrated, the Granger causality can be tested on levels, and it
is assumed that the exogenity conditions are met. The lag length used in VECM
estimation is set in line with the SC (Table 19). The numerical results regarding the
export (X) are shown below.
(6)
where the fi rst non differenced terms express the long run relationship. Their statistical
attributes are in the following table, where the standard errors are in brackets and
t-statistics follow. The asterisk denotes rejection of the null hypothesis at the 10% level
of signifi cance.
ˆ
D(LOG(X)) = 0.165*( LOG(X(-1)) + 1.278*LOG(GDPEMU(-1)) +3.167*LOG(PPIEMU(-1)) -
- 7.672*LOG(PPI(-1)) + 2.619*LOG(EUR(-1)) + 0.014*TREND - 1.429) -
- 0.722*D(LOG(X(-1))) 1.996*D(LOG(GDPEMU(-1))) - 0.2 11*D(LOG(PPIEMU(-1)))
+ 0.715*D(LOG(PPI(-1))) + 0.147*D(LOG(EUR(-1))) + 0.025


208  PRAGUE ECONOMIC PAPERS, 3, 2011
Table 21
Cointegrating Vector
LOG(X(-1)) 1.000
LOG(GDPEMU(-1))
1.583
(1.316)
[ 1.203]
LOG(PPIEMU(-1))
3.668*
(0.911)
[ 4.024]
LOG(PPI(-1))
-8.705*
(1.183)
[-7.358]
LOG(EUR(-1))
3.093*
(0.535)
[ 5.776]
@TREND(95Q1)
0.020*
(0.004)
[ 4.089]
C -2.309
The short term dynamics, i. e. the error correction mechanism, is summarized in
Table 22 including standard errors and t-statistics.
The model proves a 46% correspondence with the data (R-squared = 0,463), and
is overall statistically signifi cant at 5% signifi cance level (F-statistic = 6,191). The
predictive ability of the model is shown in the following fi gure. Simulated ex-post
predictions (Hušek, 2007) are made in one quarter distances for three quarters ahead
from 2006Q1 onward.
Figure 4
Export ex-post Predictions
Table 22
Error Correction Mechanism
CointEq1
0.155*
(0.067)
[ 2.308]
D(LOG(X(-1)))
-0.724*
(0.140)
[-5.147]
D(LOG(GDPEMU(-1)))
1.961*
(1.153)
[ 1.703]
D(LOG(PPIEMU(-1)))
-0.090
(0.889)
[-0.100]
D(LOG(PPI(-1)))
0.661
(0.879)
[ 0.750]
D(LOG(EUR(-1)))
0.067
(0.403)
[ 0.16584]
500
600
700
800
900
2005 2006 2007 2008 2009 201
0
Forecasts of X
X

PRAGUE ECONOMIC PAPERS, 3, 2011  209
4.2 Model with Import and Export Prices
The cointegration analysis is carried out in a similar way as it was in the previous case. In
the table below the results of ADF test are summarized, and provide suffi cient evidence,
for it is not possible to reject the null hypothesis of unit root on reasonable signifi cance
level for all tested series. The ADF test is made under assumption of individual intercept
and trend for examined series, and the lag length selection is based on modifi ed SC.
The time series are integrated of order one, as the ADF test of fi rst differences
in Table 23 shows, since it is possible to reject the null hypothesis of unit root on
reasonable signifi cance level for all examined series. The ADF test is made under
precondition of individual intercept, while the trend is assumed to be eliminated by
differencing. The lag length selection is again based on modifi ed SC. Nevertheless use
of other lag length criteria leads to similar conclusion. The asterisk denotes rejection
of the null hypothesis at the 5% level of signifi cance.
Table 23
Stationarity Test of the Logarithms of the Original Time Series and of the First Differences
Series Prob. Lag Series Prob. Lag
LOG(X) 0.826 1 D(LOG(X)) 0.005* 1*
LOG(GDPEMU) 0.901 0 D(LOG(GDPEMU)) 0.029* 2*
LOG(DC) 0.895 0 D(LOG(DC)) 0.004* 0
LOG(VC) 0.614 0 D(LOG(VC)) 0.000* 0
LOG(EUR) 0.255 0 D(LOG(EUR)) 0.000* 0
The Granger causality outcome regarding the relation among variables with
emphasis on the export (X) is summarized in Table 24, and seems to be admissible,
even though some of the are not directly convincing.
Table 24
Granger Causality regarding X
Null Hypothesis: F-Statistic Prob.
LOG(GDPEMU) does not Granger Cause LOG(X) 3.032 0.059
LOG(X) does not Granger Cause LOG(GDPEMU) 5.765 0.006*
LOG(DC) does not Granger Cause LOG(X) 1.102 0.034*
LOG(X) does not Granger Cause LOG(DC) 0.804 0.454
LOG(VC) does not Granger Cause LOG(X) 1.105 0.141
LOG(X) does not Granger Cause LOG(VC) 0.536 0.589
LOG(EUR) does not Granger Cause LOG(X) 5.675 0.007*
LOG(X) does not Granger Cause LOG(EUR) 7.850 0.001*
The appropriate lag length used for Granger causality exploration was adjusted in
line with the AIC, SC and HQ as it is summarized in the next table.

210  PRAGUE ECONOMIC PAPERS, 3, 2011
Table 25
Appropriate Lag Length Selection
Lag AIC SC HQ
0 -18.9 -18.7 -18.9
1 -28.1 -26.9* -27.6*
2 -28.3 -26.2 -27.5
3 -28.2 -25.1 -27.0
4 -28.9 -24.8 -27.3
5 -28.9 -23.9 -27.0
6 -28.9* -23.0 -26.7
All the series are of the same integration order, particularity I(1), so the long-
-run dynamics could be inspected within the VECM. Some prior exploration of
cointegration is necessary, thus the Johansen cointegration test is carried out onward
and summarized in Table 26. At the 5% signifi cance level the trace test suggests that
there is at most one cointegrating relation, for it allows to reject the null hypothesis
of none cointegration rank, and does not reject the null hypothesis of at most one
cointegration rank at the same time. The maximum eigenvalue statistics suggests the
same outcome at 10 % level of signifi cance, so the VECM can be estimated under the
assumption of exogenity.
Table 26
Cointegration Rank Test (Trace and Maximum Eigenvalue)
Number of
hypothesized
cointegrating relations
Eigenvalue Trace
Statistic
Critical
Value
Prob. Max-Eigen.
Statistic
Critical
Value
Prob.
None * 0.493 71.373 69.819 0.037* 32.622 33.877 0.070*
At most 1 0.321 38.751 47.856 0.270 18.581 27.584 0.448
At most 2 0.221 20.170 29.797 0.411 12.002 21.132 0.547
At most 3 0.156 8.168 15.495 0.448 8.163 14.265 0.362
At most 4 0.000 0.005 3.841 0.941 0.005 3.841 0.941
The statistical attributes of the long-run dynamics are in the following table, where
the standard errors are in brackets and t-statistics follow. The asterisk denotes rejection
of the null hypothesis at the 10% level of signifi cance.
(8)
ˆ
D(LOG(X)) = 0.453*( LOG(X(-1)) - 1.851*LOG(GDPEMU(-1)) +
0.655*LOG(DC(-1)) - 1.627*LOG(VC(-1)) + 2.032*LOG(EUR(-1)) ) -
- 0.847*D(LOG(X(-1))) + 2.756*D(LOG(GDPEMU(-1))) -
- 0.085*D(LOG(DC(-1))) - 0.28

7*D(LOG(VC(-1))) + 0.532*D(LOG(EUR(-1))),

PRAGUE ECONOMIC PAPERS, 3, 2011  211
Table 27
Cointegrating Vector
LOG(X(-1)) 1.000
LOG(GDPEMU(-1))
-7.195*
(3.765)
[-1.910]
LOG(DC(-1))
-4.405*
(2.742)
[-1.606]
LOG(VC(-1))
11.295*
(5.483)
[2.060]
LOG(EUR(-1))
-13.174*
(2.958)
[-4.453]
@TREND(95Q1)
-0.098*
(0.017)
[-5.483]
C 44.556
The short term dynamics, i. e. the error correction mechanism, is summarized in
Table 28 including standard errors and t-statistics.
The model proves a 60% correspondence with the data (R-squared = 0,596), and
is overall statistically signifi cant (F-statistic = 10,093). The predictive ability of the
model is illustrated in the next fi gure of simulated ex-post predictions, which are made
in one quarter distances for three quarters ahead.
Figure 5
Export ex-post Predictions
Table 28
Error Correction Mechanism
CointEq1
-0.106*
(0.023)
[-4.591]
D(LOG(X(-1)))
-0.654*
(0.109)
[-5.974]
D(LOG(GDPEMU(-1)))
2.346*
(0.98813)
[ 2.374]
D(LOG(DC(-1)))
-0.573
(0.528)
[-1.085]
D(LOG(VC(-1)))
0.457
(0.883)
[0.517]
D(LOG(EUR(-1)))
-0.192
(0.445)
[-0.430]
500
600
700
800
900
2005 2006 2007 2008 2009 201
0
Forecasts of X
X

212  PRAGUE ECONOMIC PAPERS, 3, 2011
4.3 Model with Consumer Prices
If the foreign as well as the domestic prices are represented by consumer price levels,
the directions of infl uences of exogenous variables remain unchanged; the lag of
interactions is nevertheless shorter (Abdelhak and Montenegro, 1999).
The results of VECM are in this case unfortunately not intuitive, and the main
reason can be seen in defi cient cointegration dispositions of the data set. The domestic
price level (CPI) seems to be integrated of order two, i. e. I(2) as the next table
summarizes. The asterisk denotes rejection of the null hypothesis of unit root at the
5% level of signifi cance.
Table 29
Stationarity Test of the Logarithms of the Original Time Series and of the First Differences
Series Prob. Lag Series Prob. Lag
LOG(X) 0.826 1 D(LOG(X)) 0.000* 2
LOG(GDPEMU) 0.901 0 D(LOG(GDPEMU)) 0.000* 0
LOG(CPIEMU) 0.968 0 D(LOG(CPIEMU)) 0.000* 0
LOG(CPI) 0.062 0 D(LOG(CPI)) 0.084 7
LOG(EUR) 0.255 0 D(LOG(EUR)) 0.000* 1
That makes the cointegration uneasy as the Johansen cointegration test in Table 30
shows. Under the assumption of intercept and trend the trace test as well as the
maximum eigenvalue statistics give the same outcome, i. e. both tests suggest at most
three cointegration ranks on reasonable level of signifi cance.
Table 30
Cointegration Rank Test (Trace and Maximum Eigenvalue)
Number of
hypothesized
cointegrating relations
Eigenvalue Trace
Statistic
Critical
Value
Prob. Max-Eigen.
Statistic
Critical
Value
Prob.
None * 0.555 115.545 76.973 0.000* 38.899 34.806 0.015*
At most 1 * 0.496 76.646 54.079 0.000* 32.919 28.588 0.013*
At most 2 * 0.415 43.727 35.193 0.005* 25.762 22.300 0.016*
At most 3 0.207 17.965 20.262 0.100 11.133 15.892 0.242
At most 4 0.133 6.832 9.165 0.136 6.832 9.165 0.136
Nevertheless for purposes of the short-term analysis the CPI can be considered for
I(1), while rejecting the null hypothesis of a unit root for the fi rst difference of logarithms
at 10 % level of signifi cance (Table 26), and en equation can be estimated onward.
In the next equation the role of foreign price level is taken by consumer prices in
the European Union (CPIEMU), and domestic prices are represented by consumer
prices in the Czech Republic (CPI). There is again the foreign demand as foreign
GDP (GDPEMU) and exchange rate (EUR). The equation is estimated on data with
quarterly frequency for the period 1995Q3-2010Q2. The estimation is again carried

PRAGUE ECONOMIC PAPERS, 3, 2011  213
out on differences of logarithms. The fi rst differences of logarithms can be considered
for stationary, even in case of the CPI. Consequently no problem of spurious regression
as well as heteroskedasticity is expected.
(6)
and after the parameters are estimated
The table bellow displays basic statistic. The asterisk denotes rejection of the null
hypothesis at the 5% level of signifi cance.
Table 31
Basic Statistics of the Export Equation
C1 C2 C3 C4 C5 C6
-0.011
(0.013)
[-0.872]
-0.595*
(0.095)
[-6.214]
3.939*
(0.707)
[5.568]
7.332*
(2.202)
[3.328]
-1.509*
(0.532)
[-2.834]
0.586*
(0.211)
[2.769]
Modelling export dynamics with the consumer prices improves the congruence
of the estimate to 63% (R-squared = 0,627). The estimate has an overall statistical
signifi cance (F-statistic = 18,159), and individual parameters are statistically signifi cant
at least at 5% level of signifi cance. The economic assumptions are satisfi ed.
The forecasting performance of the model is shown in the following fi gure.
Simulated ex-post predictions are again carried out in one quarter distances for three
quarters ahead. It is obvious that the model with consumer prices has got the best
forecasting performance.
Figure 6
Export ex-post Predictions
DLOG(X) = C(1) + C(2)*DLOG(X(-1)) + C(3)*DLOG(GDPEMU) +
C(4)*DLOG(CPIEMU) + C(5)*DLOG(CPI) + C(6)*DLOG(EUR(-1)) + u,
ˆ
DLOG(X) = -0.011 - 0.595*DLOG(X(-1)) + 3.939*DLOG(GDPEMU)
+ 7.332*DLOG(CPIEMU) - 1.509*DLOG(CPI) + 0.586*DLOG(EUR(-1)).

500
600
700
800
900
2005 2006 2007 2008 2009 201
0
Forecasts of X
X

214  PRAGUE ECONOMIC PAPERS, 3, 2011
5. Conclusion
All of the above-mentioned export models confi rm macroeconomic relations between
export dynamics, development of foreign demand, domestic and foreign price levels
and exchange rate. The model with consumer prices is the most appropriate for
prediction, while the models with producer prices and import and export prices have
higher analytical value.
The exchange rate appreciation leads to a decrease in import prices, which lowers
the costs of domestic producers. On the other hand, the export model shows that the
increase of import prices leads to the increase of export, probably because the import
prices are mainly driven by world prices of crude materials and semi-fi nished products
- this cost factors can be considered for almost the same in both foreign and domestic
economy. It seems that the Czech exporters cope better with price increase of crucial
inputs on world markets. Furthermore, the rise of import prices reduces the import
dynamics, and the net export consequently increases. This is, nevertheless, not that
straightforward in the case of the Czech Republic, where the export is signifi cantly
import-intensive, and exports are highly correlated with imports.
At the same time export dynamics decreases with exchange rate appreciation.
Exchange rate movement therefore works as a stabilizer of producer costs as well
as of export dynamics. Thus in case of noticeably growing prices of crude materials
and semi-fi nished products in the world markets, exchange rate appreciation usually
buffers the growth of domestic producer cost factors on the one hand, and reduces
export growth directly through higher prices of exported goods in foreign currency on
the other hand. While the domestic producer costs lower, the exports prices increase.
This leads to stabilization of export dynamics through exchange rate movements.
The importance of this buffering effect rises as the volatility of world prices of crude
materials increases.
References
Abdelhak Senhadji, A. S., Montenegro, C. (1999), “Time Series Analysis of Export Demand Equations:
A Cross-Country Analysis.” IMF Working Paper.
Akaike, H. (1969), “Fitting Autoregressions for Prediction.” Annals of the Institute of Statistical
Mathematics, 21 (2), pp. 243-247.
Čihák M., Holub, T. (2000), “Cenová konvergence k Evropské unii – problém relativních cen.” Politická
ekonomie, Vol. 48, No.5, pp. 214-226.
Davidson, R., MacKinnon, J. G. (2004), Econometric Theory and Methods. Oxford University Press.
Dickey, D. A., Fuller, W. A. (1979), “Distribution of Estimators for Autoregressive Time Series with a
Unit Root.” Journal of American Statistical Association, Vol. 74, No. 366, pp. 427-431.
Elliott, G., Rothenberg, T. J., Stock, J. H. (1996), “Effi cient Tests for an Autoregressive Unit Root.”
Econometrica, 64 (4), pp. 813–836.
Enders, W. (2004), Applied Econometric Time Series, 2nd Ed. John Wiley & Sons, Inc.
Engle, R. F., Granger,C. W. J. (1987), “Cointegration and Error Correction: Representation, Estimation
and Testing.“ Econometrica, Vol. 55, No. 2, pp. 251-276.
Frenkel, J. A. (1981), “Flexible Exchange Rates, Prices and the Role of News: Lessons from the
1970s.” Journal of Political Economy, Vol. 89, No. 4, pp. 665-705.

PRAGUE ECONOMIC PAPERS, 3, 2011  215
Greene, W. H. (2003), Econometric Analysis, 5th Ed. New Jersey: Prentice Hall.
Geweke, J. (1984), Inference and Causality in Economic Time Series Models. Handbook of
Econometrics. Elsevier Science Publishers BV.
Granger, C. W. J., Newbold, P. (1974), “Spurious Regressions in Econometrics.” Journal of
Econometrics, Vol. 2, No. 2, pp. 111-120.
Hamilton, J. D. (1994), Time Series Analysis. New Jersey: Princeton University Press.
Hannan, E. J., Quinn, B. G. (1979), “The Determination of the Order of an Autoregression.” Journal of
the Royal Statistical Society B, Vol. 41, No. 2, pp. 190–95.
Hušek, R. (2007), Ekonometrická analýza. Praha: Oeconomica.
Johansen, S., Juselius, K. (1990), “Maximum Likelihood Estimation and Inference on Cointegration
– With Application on Demand for Money.“ Oxford Bulletin of Economics and Statistics, 52, pp.
169-210.
Johansen, S. (1988), “Statistical Analysis of Cointegrating Vectors.” Journal of Economic Dynamics
and Control, 12, pp. 231-254.
Nešvera, V. (2006), “Ceny v obchodě České republiky se zeměmi Evropské unie.” Politická ekonomie,
Vol. 54, No. 2, pp. 214-226
Norman, D. (2006), “Modelling Manufactured Exports: Evidence from Australian States.” Reserve
Bank of Australia.
Pánková, V. (2003), “Analýza vlivu cenových relací na objem exportu v České republice.“ Politická
ekonomie, Vol. 51, No. 4, pp. 533-515
Rogoff, K. (1996), “The Purchasing Power Parity Puzzle.” Journal of Economic Literature, 34 (2),
pp. 647-668.
Rojíček, M. (2010), “Konkurenceschopnost obchodu ČR v procesu globalizace.” Politická ekonomie,
Vol. 58, No. 2, pp. 147-105
Tichý, F. (2007), “Impact of Accession to EMU on International Trade – Case of the Czech Republic.”
Prague Economic Papers, Vol. 16, No. 4, pp. 336-346
Williams, J. C., Wright, B. D. (1991), Storage and Commodity Markets. Cambridge: Cambridge
University Press.
Wooldridge, J. M. (2002), Introductory Econometrics, 2nd Ed. South-Western College Publishing.
Xu, Z. (1999), “The Exchange Rate and Long-Run Price Movements in the US and Japan.” Applied
Economics Letters, 6 (4), pp. 227-230.
Zweimüller, J. (2001), Open Economy Macroeconomics. Zurich: University of Zurich.