Purchasing power parity in a transition country: the case of Croatia.
Tkalec, Marina ; Vizek, Maruska
INTRODUCTION
The purchasing power parity (PPP) determines the exchange rate that
equates domestic and foreign price levels, so that the purchasing power
of a unit of one currency would be the same in both economies (Sarno and
Taylor, 2001). PPP starts with the law of one price that says free trade
in goods ensures identical prices across countries when we abstract from
trade barriers and transportation costs (From and Rogoff, 1995). A
casual review of the empirical literature shows that PPP is probably one
of the most extensively tested theoretical propositions. The motivation
behind testing PPP is often a practical one; PPP can indicate the degree
of misalignment of the nominal exchange rate and the appropriate policy
response. Although PPP is simple and intuitively attractive, empirical
tests have often been unable to support conclusively this core principle
of international economics. Development of new econometric tools in the
last two decades, notably unit root tests, cointegration and nonlinear
models, gave rise to a new wave of empirical studies. Nonlinear
techniques in particular have performed somewhat better than their
linear counterparts, but still have not conclusively validated the PPP
hypothesis in developed and developing countries (Sarno and Taylor,
2001; Bahmani-Oskooee and Hegerty, 2009).
The aim of this paper is to test whether PPP holds in Croatia.
Debates about the possible overvaluation of the nominal HRK/EUR exchange
rate are quite common in Croatia, and thus we feel it is important to
establish whether the exchange rate is aligned with fundamentals
suggested by a particular theory. To do so, we use PPP to model the
long-run behaviour of the exchange rate in Croatia, although we are
aware of the limits of PPP theory and the relevance of other indicators
of currency misalignments including (a) persistent and large current
account deficits, (b) external debt, (c) high inflation, and (d) low
reserves. We use a multivariate approach to model the bilateral HRK/EUR
exchange rate as a function of Croatian and Eurozone price levels. In
order to test PPP, we use two cointegration methods. The first, Johansen
cointegration (Johansen, 1988), assumes that both the long- and the
short-run behaviour of the exchange rate and price levels are symmetric.
With this approach we also specify vector error correction models in
order to detect whether the exchange rate pass-through is present. The
second method, threshold cointegration, assumes symmetry in the long
run, but allows for nonlinear adjustment in the short run (Enders and
Siklos, 2001). We apply both linear and nonlinear methods because the
literature (Sarno and Taylor, 2001; Bahmani-Oskooee and Hegerty, 2009)
shows that nonlinear methods are more successful at detecting PPP. To
the best of our knowledge, this is the first paper that applies
nonlinear methodology to test PPP for the Croatian exchange rate.
The remainder of the paper is organized as follows. The next
section reviews the empirical literature on PPP, using both linear and
nonlinear methods. Special attention is then given to the results for
transition economies, particularly Croatia. The subsequent section
presents the methodology, data and results of the empirical analysis,
while the final section concludes.
LITERATURE REVIEW
Sarno and Taylor (2001) provide an extensive overview of PPP tests
for developed countries. The authors conclude that the consensus
concerning the validity of PPP between the currencies of the major
industrialized countries, in both the short and long run, has shifted
several times in the post-war period. In recent years the prevailing
view has been that the long-run PPP does have some validity, at least
for the major exchange rates, although a number of puzzles remain. Sarno
and Taylor also point out that investigating the role of nonlinearities
in the real exchange rate adjustment towards long-run equilibrium is a
promising strand of research that can reconcile the persistence of real
exchange rates with their observed high volatility. (1)
The results from empirical studies for transition countries are
less conclusive. Using a residual-based test, Thacker (1995) concluded
that PPP does not hold for two European transition economies, Poland and
Hungary. Choudhry (1999) reported mixed results using fractional
cointegration on Polish, Russian, Romanian and Slovenian exchange rates,
while Christev and Noorbakhsh (2000) showed there is little evidence of
PPP in Bulgaria, Czech Republic, Hungary, Poland, Romania and Slovakia
when Johansen cointegration is applied. Using the same technique, Barlow
(2003) got mixed results for Poland, Czech Republic and Romania.
Bahmani-Oskooee and Hegerty (2009) list different explanations for the
apparent absence of PPP in transition economies. While some of the
reasons can be found in both developed and less-developed economies (eg
the choice of price indices or black-market exchange rates), others stem
from the characteristics of transition economies. The latter include
small number of observations available, administratively controlled
prices and exchange rates, Samuelson-Ballasa effects, and massive
increase in capital inflows and foreign investment during transition.
The reason for using nonlinear methods is that exchange rates can
exhibit nonlinear properties due to transaction costs, government policy
and price rigidity (Bahmani-Oskooee and Hegerty, 2009). Moreover, since
most the transition economies suffered large external and internal
shocks, government intervention, high inflation and/or major exchange
rate shifts, nonlinearity in the adjustment process is not surprising.
Transaction costs, for example, can promote nonlinear behaviour by
creating a threshold below which prices and exchange rates are
inflexible, while government policy is often more active once exchange
rates move farther away from their targets. The distinction between
upward and downward deviations from PPP is also important because prices
in general move in the upward direction. Thus, the exchange rate might
have to do more of the adjusting when exchange rates move up rather than
down and movements might thus not be symmetric.
After reviewing the literature for transition countries,
Bahmani-Oskooee and Hegerty (2009) concluded that nonlinear tests indeed
provide more support for PPP than linear tests do. Thus, Bahmani-Oskooee
et al. (2008) compared results with linear and nonlinear unit root tests
using the data for developing countries. They showed that nonlinear
tests are two times more successful in detecting PPP. Telatar and
Hasanov (2009a) tested for PPP across 12 Central and Eastern European
countries using linear and nonlinear unit root tests and found more
evidence in favour of PPP when applying nonlinear tests. Moreover, after
allowing for structural breaks and asymmetric adjustment they found that
PPP holds for all the 12 countries in the sample. Telatar and Hasanov
(2009b) reach the same conclusion using the same methods on data for
Commonwealth of Independent States countries.
The existing literature exploring the validity of PPP in Croatia
uses only the linear approach. Payne et al. (2005), using unit root
tests with two endogenous structural breaks, failed to find evidence of
PPP in Croatia. Pufnik (19961 and Egert (2005) find no evidence of
cointegration when testing PPP for Croatia. In his cointegration study
of 17 European transition economies, Sideris (2006), who used both
Johansen cointegration and panel cointegration, concluded that PPP does
not hold for a number of countries, including Croatia. Nevertheless,
there are results in favour of PPP in Croatia. Tica (2006) used a unit
root test on a 51-year-long data set and concluded that the bilateral
exchange rates are mean reverting. Further, Sonora and Tica (2010) used
panel unit root tests with structural breaks and showed that the real
exchange rates in Croatia are stationary. Moreover, their results imply
that the deviations from the long-run PPP are adjusted rather quickly.
EMPIRICAL ANALYSIS
Data and methodology
The data used here are monthly observations of the average nominal
HRK/ EUR exchange rate, the Croatian consumer price index and the
harmonized index of consumer prices for the European Monetary Union
(EMU). Although this choice of variables is common when testing for PPP,
we are aware that the consumption baskets for consumer price indices in
Croatia and in the EMU are not the same. Such differences imply that PPP
may not be perfectly measured and could lead to rejection of PPP. As for
the exchange rate, we use the bilateral HRK/EUR rate because this
exchange rate is of particular importance for the Croatian economy. In
addition to the fact that countries from the Eurozone account for about
half of Croatian exports and imports, (2) this exchange rate is an
implicit target of the Croatian National Bank, whose exchange rate
policy, though formally defined as a managed float, can also be
characterized as a 'quasi currency board' or 'floating
with a life jacket' (Billmeier and Bonato, 2004; Reinhart and
Rogoff, 2004). Further, since Croatia is a highly euroized economy whose
currency has not completely assumed store of value and unit of account
functions (Vizek, 2006), establishing whether the HRK/EUR exchange rate
is aligned with fundamentals is extremely relevant for policy
formulation. The sources for the exchange rate and the Croatian price
index data are the Croatian National Bank and the Croatian Bureau of
Statistics, while the EMU consumer prices are from Eurostat. The base
year for the consumer price indices is 2005. All series range from
January 1996 to October 2010, that is, 178 monthly observations, and
were seasonally adjusted and transformed to logarithms.
Before exploring cointegration and asymmetric adjustment between
variables, one should always determine the order of integration of the
time series. Plots of the data on nominal exchange rate, domestic and
foreign prices suggest that all three series in levels do not revert to
their means (left-hand side of Figure 1). However, the series in first
differences seem to be mean reverting (right-hand side of Figure 1).
To detect the level of integration formally, we used an augmented
Dickey-Fuller (ADF) unit root test (Dickey and Fuller, 1981). In
addition to ADF, we also use the results of the Johansen cointegration
as an implicit unit root test.
After confirming that the series are integrated of the same order
we turn to modelling the long-run relationship between the HRK/EUR
exchange rate and domestic and EMU price levels. In order to test for
cointegration we use both Engle-Granger (Engle and Granger, 1987) and
Johansen cointegration frameworks (Johansen, 1988, 1991). We use the
Johansen results to capture the symmetric properties of PPP both in the
short and long run, while the estimates of Engle-Granger model are used
to test for threshold cointegration and asymmetric adjustment of PPP in
the short run.
Two test statistics, the Trace test and the Max test, are used to
detect the number of cointegrating vectors in the Johansen procedure.
The Trace statistic tests the hypothesis that the number of
cointegrating vectors is less than c, while the Max statistic tests that
the number of cointegrating vectors is equal to c against c + 1.
Johansen tests are biased when VAR residuals are not normal and when the
constant term is included in the model; the tests tend to detect
cointegration more often in finite samples when compared to asymptotic
cases (Cheung and Lai, 1993). Thus, we use finite sample corrections of
Trace and Max statistics proposed by Reimers (1992) that takes into
account the number of parameters and degrees of freedom. Adjusted test
statistics are denoted by Trace test (T-nm) and Max test (T-nm). If
these test statistics indicate the presence of more than one vector,
then one needs to restrict the cointegration space in order to identify
the long-run coefficients and adjustment parameters. After the long-run
coefficients are identified, they are used to formulate the vector error
correction model of the following generalized form:
[DRLTA][y.sub.t] = AB'[y.sub.t-1] +
[[GAMMA].sub.1][DELTA][y.sub.t-1] + [[GAMMA].sub.2][DELTA][y.sub.t-2] +
... + [[GAMMA].sub.p][DELTA][y.sub.t-p] + [[epsilon].sub.t] (1)
where [y.sub.t] is a vector of variables included in the
equilibrium relationship, B is a cointegration matrix containing
long-run parameters from cointegration vectors, A is a matrix of
adjustment parameters for each cointegration vector, and
[[epsilon].sub.t] is a vector of IID random variables with mean zero and
a constant variance.
[FIGURE 1 OMITTED]
As discussed in the literature review, PPP seems to exhibit
asymmetric properties when adjusting the deviations from the long-run
equilibrium. If the adjustment is indeed asymmetric, then Johansen test
or any other cointegration test that assumes symmetric adjustment and
corresponding error correction models are misspecified. Enders and
Chumrusphonlert (2004) suggest that nonlinearities are inherent to PPP
because of transaction costs, stickiness of national price levels, but
also due to asymmetric nominal exchange rate movements. In fact, in
managed float regime monetary authorities might be more willing to
tolerate currency appreciation than depreciation, which leads to an
asymmetric behaviour of the exchange rate. We would expect asymmetries
in the Croatian exchange rate (since it is managed by the central bank)
that provides a motivation for pursuing this kind of modelling strategy.
In order to detect nonlinearities of PPP in Croatia, we use a
threshold cointegration method developed by Enders and Siklos (2001). As
opposed to Engle-Granger or Johansen methods that assume symmetric
behaviour in the long and short run, this method allows for asymmetric
adjustment in the short run, while maintaining symmetry in the long run.
Enders and Siklos (2001) developed a test for threshold cointegration
based on generalized threshold autoregressive (TAR) and momentum-TAR
(M-TAR) tests for unit roots. (3)
After the Engle-Granger model of the long-run behaviour of PPP is
estimated, the disturbance term of that model ([[mu].sub.t]) is used to
formulate the threshold error-correction model with the following
specification:
[DELTA][[mu].sub.t] = [I.sub.jt][[rho].sub.1][[mu].sub.t-1] + (1 -
[I.sub.jt])[[rho].sub.2][[mu].sub.t-1] + [[epsilon].sub.t], j = 1,2 (2)
where [I.sub.1t] and [I.sub.2t] are the Heaviside indicator
functions for the TAR and the M-TAR models, respectively, such that:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
in the TAR case, and
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
in the M-TAR case. [[tau].sub.1] and [[tau].sub.2] are the values
of the threshold and [[epsilon].sub.t] is a sequence of liD random
variables with mean zero and a constant variance. We test for threshold
cointegration using both TAR and M-TAR, thereby setting the value of the
threshold r to zero and allowing the threshold to be determined
endogenously. In the latter case, the value of threshold r needs to be
estimated along with the parameters [[rho].sub.1] and [[rho].sub.2]
using the algorithm developed by Chan (1993). In each of the four cases,
depending on the type of asymmetry under consideration ([I.sub.1t] or
[I.sub.2t]), we estimated regression equation 2 and tested the null
hypotheses [[rho].sub.1]=0 and [[rho].sub.1]=[[rho].sub.2]=0, which are
direct tests of the existence of cointegration. (4) After this, we
compared the sample statistics with the critical values suggested by
Enders and Chumrusphonlert (2004). Eventually, if the test statistics
suggest the existence of cointegration, one uses the Wald test to detect
the existence of threshold adjustment. The null hypothesis of the Wald
test is symmetric adjustment (ie, [[rho].sub.1]=[[rho].sub.2]). (5)
Since the least squares estimates of [[rho].sub.1] and
[[rho].sub.2] have an asymptotic multivariate normal distribution (Tong,
1983, 1990) and given the existence of a single cointegration vector,
the error-correcting model for any variable [x.sub.it] can be written in
the form:
[DELTA][x.sub.it] = [[rho].sub.1,i][I.sub.jt][[mu].sub.t-1] +
[[rho].sub.2,i] (1 - [I.sub.jt])[[mu].sub.t-1] + ... + [v.sub.i,t], j =
1,2 (5)
where [[rho].sub.1,i] and [[rho].sub.1,i] are the speed of
adjustment coefficients of [[DELTA]x.sub.it], and [v.sub.i,t] is IID
random variables with mean zero and a constant variance. Note that model
2 is used only for testing for the existence of cointegration and
threshold adjustment, while model 5 is estimated in order to detect how
variables determining the long-run relationship react in the short run
to deviations from the equilibrium.
Results
The results of ADF unit root tests confirm our impressions from the
data plots (Tables 1 and 2). In levels, we cannot reject the null
hypotheses about the existence of a unit root. However, after
differencing the data, the ADF test suggests that all three series are
integrated of order one.
After confirming that our series are stationary in first
differences, we can continue with the cointegration analysis. The first
step of our modelling strategy is to estimate the Engle-Granger
cointegration equation with the exchange rate as the dependent variable
and domestic and EMU prices as the explanatory variables. The residuals
from this equation will later be used for the threshold cointegration
test of PPP. The estimates of the Engle-Granger cointegration equation
are displayed in Table 3. Coefficients for both the domestic and the EMU
price levels have incorrect signs, but are lesser than 1 in absolute
terms. In addition to wrongly signed coefficients, the ADE test of
residuals from the cointegration equation (when compared against
Davidson and MacKinnon (1993) critical values) suggests that the
residuals are not stationary. Therefore the Engle-Granger cointegration
test suggests that PPP does not hold for Croatia.
Given the fact that the Engle-Granger cointegration test has low
power in the presence of multiple cointegration vectors, we continue our
analysis with Johansen cointegration. Table 4 presents Trace and Max
test statistics along with their finite sample corrections. Corrected
Trace test (which is more robust in presence of non-normal VAR residuals
when compared to corrected Max test (Cheung and Lai, 1993)), along with
non-corrected test statistics, suggests the presence of two
cointegration relationships.
Long-run coefficients and adjustment parameters are reported in
Table 5. Since there are two cointegration vectors, we need at least
four restrictions to identify long-run coefficients and adjustment
parameters for both vectors. We assume that the first cointegration
vector reflects the absolute PPP condition, while the second vector
describes the long-run relationship between the exchange rate and
domestic price level. Hence, for the first vector we impose restrictions
derived from the absolute PPP condition:
* long-run coefficients for the exchange rate should be equal to 1,
* long-run coefficients for EMU prices should be equal to 1,
* long-run coefficient for domestic prices should be equal to -1,
* constant term should be equal to 0.
For the second vector, we impose the following restrictions:
* long-run coefficients for the EMU prices should be equal to 0,
* long-run coefficient for the exchange rate should be equal to 1.
(6)
Likelihood ration test results suggest that all restrictions are
jointly accepted (chi-squared test statistics is equal to 3.96,
corresponding p-value is 0.27). This indicates that the absolute version
of PPP hypothesis holds for the HRK/EUR exchange rate. This finding
suggests that the HRR/EUR exchange rate reflects the fundamentals and
that there is no need for depreciation. Moreover, the long-run
coefficients for the second vector suggest that there is a long-run
pass-trough between Croatian consumer prices and the exchange rate,
where a 1% increase in consumer inflation depreciates the exchange rate
by 0.12%.
After defining two cointegration vectors, we proceed by formulating
vector error correction equations for the HRK/EUR exchange rate,
domestic and EMU prices in the form of equation 1. All three error
correction equations include two error correction terms from two
restricted cointegrating vectors: one that represents the adjustment
from PPP deviations and the other that represents the pass-through
adjustment. Moreover, since the corresponding VAR included four lags,
the error correction equations have three lags. The estimation results
are presented in Table 6. As evident from the table, the three error
correction equations satisfy all diagnostic tests.
When analysing the results, one notices that error correction
equations of domestic and EMU prices have little explanatory power.
Moreover, both the exchange rate and EMU prices are weakly exogenous,
which means that only the domestic prices adjust to deviations from PPP
disequilibria in the short run. The adjustment coefficient is positive,
which is expected given the fact that long-run domestic prices enter the
error correction term with a negative coefficient. The speed of
adjustment coefficient suggests that it takes 22 months (ie almost 2
years) for domestic prices to cut in half the distance from the long-run
PPP. The error correction equation estimates for the HRK/EUR exchange
rate also suggest that the exchange rate is, in the short run,
responding to changes in EMU prices. Moreover, since lagged values of
the exchange rate are also significant for explaining the exchange rate,
one can conclude that there is a great deal of inertia in the behaviour
of the exchange rate, which precludes the adjustment from taking place.
The error correction equation for domestic prices indicates that there
is no pass-trough from nominal exchange rate to domestic prices in the
short run.
Although Johansen cointegration results provide evidence in support
of absolute PPP in Croatia, we wanted to verify whether there are any
asymmetries in the adjustment process. Namely, if the adjustment process
is characterized by threshold effects, then any cointegration test that
assumes symmetric adjustment (including Johansen cointegration) is
misspecified (Enders and Siklos, 2001). As suggested in the methodology
section, we first estimated the cointegration equation with the exchange
rate as a dependent variable and domestic and foreign prices as the
explanatory variables (Table 3). Residuals from the cointegration
equation were then used for testing threshold cointegration. We tested
for both TAR and M-TAR threshold cointegrations using two thresholds:
zero and a consistent estimate of the threshold as suggested in the
Chan's algorithm (1993).
Table 7 displays the results of TAR and M-TAR tests with the known
and unknown thresholds. All the four models satisfy diagnostic tests.
Comparing the test statistics for Tmax and [PHI], which are direct tests
of threshold cointegration, with the critical values tabulated in Enders
and Chumrusphonlert (2004), we conclude that there is no threshold
cointegration, that is, that the adjustment to deviations from PPP in
Croatia is not asymmetric. (7) The Wald test hypotheses are also
rejected, but since no threshold cointegration was found, the Wald test
has no real significance. This in turn suggests that the Johansen
cointegration tests and corresponding vector error correction model are
not misspecified. In other words, since no evidence of threshold
cointegration is found, we conclude that absolute PPP conditions hold
for Croatia.
CONCLUDING REMARKS
The aim of this paper was to test whether the PPP theory holds for
Croatia and to determine whether the adjustment of deviations from PPP
is symmetric or asymmetric. Using HRK/EUR exchange rate, domestic and
EMU prices, and applying Johansen cointegration we demonstrated that
there are two long-run relationships among the selected variables. Upon
imposing restrictions to the cointegration space, we conclude that one
long-run relationship is an absolute PPP condition, while the other
relationship suggests that the exchange rate is, in the long run, a
function of the domestic price level. Vector error correction models
indicate that exchange rate and EMU prices are weakly exogenous. Hence,
in the short run, only domestic prices adjust to deviations from the
long-run absolute PPP, with the half-life amounting to almost 2 years.
Error correction equations for the HRK/EUR exchange rate suggest that
inertia characterizes the short-run behaviour of the exchange rate.
Moreover, inflation in the Eurozone affects exchange rate movements in
the short run. The error correction equation for domestic prices
indicates that there is no pass-trough from nominal exchange rate to
domestic prices. Finally, we find no evidence of nonlinearities in PPP
in Croatia.
Our empirical results provide evidence for the validity of absolute
PPP in Croatia. In other words, the nominal exchange rate of the Kuna
against the Euro is aligned with the fundamentals, that is, in the long
run it is a function of domestic and EMU price levels. Given that Kuna
depreciation or devaluation is often perceived as a panacea for
Croatia's unsatisfactory growth performance and the lack of
competitiveness, results of this study suggest that efforts to increase
competitiveness and not exchange rate devaluation should be the
appropriate policy response. However, one must note that another
approach to studying exchange rate misalignment in Croatia might offer a
completely different result and policy recommendation. Namely, since
Croatia has been running relatively high and persistent current account
deficits for the last 15 years and since its external debt is projected
to surpass the 100% of GDP threshold by the end of 2011, other
indicators of currency misalignments might suggest that the exchange
rate is overvaluated, which in turn would mean that depreciation is an
appropriate tool in order to fight apparent structural problems.
Weak exogeneity of the exchange rate and EMU prices suggest that in
the short run only the domestic price level changes in order to restore
the fundamentals to equilibrium. This result should not come as a
surprise, since the HRK/EUR exchange rate is often perceived as almost
fixed with its movements contained within a relatively narrow implicit
band set by policy makers. Evidence from this exercise suggest that the
exchange rate is indeed not flexible enough to correct discrepancies in
prices, and in that sense it is not able to perform its basic economic
function. Moreover, its behaviour in the short run is characterized by
inertia, which might explain lack of responsiveness to disturbance in
the fundamentals.
Finally, since no evidence of short-run pass-trough from exchange
rate to domestic consumer price inflation was found, one might be
tempted once again to recommend that a monetary policy allows for more
nominal exchange rate variability. However, such a recommendation has to
be weighed against the fact that this study pursued a partial
equilibrium approach that did not control for the adverse impact of
nominal exchange rate changes on liability euroization and the import
dependence of Croatian economy. Taking these structural characteristics
into account might lead to different recommendations.
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Lecture Notes in Statistics 21, Heidelberg, Springer--Verlag.
Tong, H. 1990: Nonlinear time series: A dynamical system approach.
Claredon Press: Oxford.
Vizek, M. 2006: Ekonometrijska Analiza Kanala Monetarnog Prijenosa
u Hrvatskoj. Privredna Kretanja i Ekonomska Politika 109: 28-61.
MARINA TKALEC & MARUSKA VIZEK
Institute of Economics, Trg J.F. Kennedya 7, Zagreb 10000, Croatia.
E-mails: mtkalec@eizg.hr; mvizek@eizg.hr;
(1) Several other authors also concluded that nonlinear methods are
more appropriate for testing PPP in developed countries. Using a
theoretical model, Dumas (1992) showed that the speed of adjustment
towards the equilibrium varies with the magnitude of the deviation from
PPP. Accordingly, deviations then follow a nonlinear process. Taylor et
al. (2001) showed that four major real bilateral US dollar exchange
rates are characterized by a nonlinear mean reverting process. Thereby
the real exchange rates behave more like unit root processes the closer
they are to the long-run equilibrium. They become more mean reverting
the further they are from equilibrium.
(3) Details about TAR and M-TAR models can be found in Tong (1983),
Caner and Hansen (2001) and Enders and Siklos (2001).
(4) For the tests, we used the larger of the t values and F
statistics that were later denoted by Tmax and [PHI] both in the text
and in the corresponding tables.
(5) For the tests, we used F statistics that was denoted by W both
in the text and in the corresponding tables.
(6) Note that restrictions related to long-run coefficients are
written in vector notation.
(7) Tmax has to be equal to or less than -1.8, while the value of
[PHI] statistics has to be equal to or greater than 8.
Table 1: ADF test--in levels
Name of the variable Chosen t-value (ADF) Beta Sigma
time lag
HRK/EUR exchange rate 9 -2.549 0.943 0.0065
Domestic prices 14 -1.869 0.994 0.0038
EMU prices 12 0.0379 1.000 0.0014
Name of the variable t-value (lag) AIC
HRK/EUR exchange rate 2.464 -10.01
Domestic prices 1.842 -11.03
EMU prices -3.943 -13.02
Note: ADF--Augmented Dickey-Fuller; constant included; Beta--lagged
dependent variable coefficient; Sigma--standard error of beta;
optimal time lag chosen according to AIC--Akaike Information
Criterion; all series are seasonally adjusted and in logarithms.
Table 2: ADF test--in first differences
Name of the variable Chosen t-value (ADF) Beta Sigma
time lag
HRK/EUR exchange rate 8 -3.472 * 0.178 0.006
Domestic prices 0 0.111 ** 0.16227 0.003
EMU prices 11 -3.974 ** 0.294 0.0014
Name of the variable t- value (lag) AIC
HRK/EUR exchange rate -2.29 -9.97
Domestic prices -0.66 -11.06
EMU prices 3.94 -13.02
Note: ADF--Augmented Dickey-Fuller; constant included; Beta--lagged
dependent variable coefficient; Sigma--standard error of beta;
optimal time lag chosen according to AIC--Akaike Information
Criterion; all series are seasonally adjusted and in logarithms.
* hypothesis about existence of unit root rejected at 5% level of
significance; ** null hypothesis about existence of unit root
rejected at 1% level of significance.
Table 3: Engle-Granger cointegration
Dependent variable: Coefficient Standard error
HRK/EUR exchange rate
Domestic prices -0.270 0.053
EMU prices 0.706 0.053
RSS=0.29234 AR test
LL=318.06 ARCH test
N=178 Normality test
Dependent variable: t-value and p-value
HRK/EUR exchange rate
Domestic prices -5.07 (0.00) **
EMU prices 13.3 (0.00) **
RSS=0.29234 F(7,169)=697.01
(0.00) **
LL=318.06 F(7,162)=267.62
(0.00) **
N=178 [chi square]
(2)=30.130
(0.00) nm **
Note: p-value is presented in parenthesis.
* null hypothesis rejected at 5% significance level; ** null
hypothesis rejected at 1% significance level.
Table 4: Johansen cointegration
Rank Eigenvalue Trace test Max test
0 -- 68.71 [0.001 ** 45.61 [0.00] **
1 0.231 23.10 [0.018] * 14.30 [0.088] *
2 0.079 8.81 [0.058] 8.81 [0.058]
3 0.049 -- --
Rank Trace test (T-nm) Max test (T-nm)
0 63.98 [0.000] ** 42.46 [0.00]
1 21.51 [0.032] ** 13.31 [0.124]
2 6.20 [0.131 6.20 [0.13]
3 -- --
Note: p-values presented in brackets; VAR includes four lags and a
restricted constant; Lag length chosen according to AIC--Akaike
Information Criterion; VAR residuals satisfy all diagnostic tests
except test for normality.
* null hypothesis rejected at 5% significance level; ** null
hypothesis rejected at 1% significance level.
Table 5: Johansen cointegration--restricted cointegrating space
Variables Long run Short-run Long run
(1. vector) (1. vector) (2. vector)
[beta] [alpha] [beta]
coefficients coefficients coefficients
Exchange rate 1.0 0.0215 1.0
(0.0) (0.011) (0.0)
Domestic prices -1.0 0.020 -0.12
(0.0) (0.007) (0.0033)
EMU prices 1.0 -0.0028 0
(0.0) (0.002) (0.0)
Constant 0 -- 0
Variables Short-run
(2. vector)
[alpha]
coefficients
Exchange rate -0.028
(0.016)
Domestic prices -0.0259
(0.0103)
EMU prices 0.0047
(0.004)
Constant
Note: [beta] coefficients are written in vector notation, which means
that all variables are placed on the left hand side of the long-run
equation; standard errors in parenthesis.
Table 6: Vector error correction models
Dependent variable [DELTA] Exchange
[rate.sub.t]
Constant 0.0098 (0.669)
[A.sub.1](L) [DELTA] Exchange [rate.sub.t-i] 3.272 [0.022] *
[A.sub.2](L) [DELTA] Domestic [prices.sub.t-i] 0.609 [0.61]
[A.sub.3](L) [DELTA] EMU [prices.sub.t-i] 3.24 * [0.024]
ECT_[PPP.sub.t-1] 0.019 (0.12)
ECT_PASS_[THROUGH.sub.t-1] -0.032 (0.10)
Sigma 0.0062
[R.sup.2] 0.17
AR test 0.712 [0.66]
ARCH test 1.42 [0.11]
RESET test 2.523 [0.11]
Dependent variable [DELTA] Domestic
[prices.sub.t]
Constant -0.0163 (0.302)
[A.sub.1](L) [DELTA] Exchange [rate.sub.t-i] 1.025 [0.38]
[A.sub.2](L) [DELTA] Domestic [prices.sub.t-i] 0.242 [0.87]
[A.sub.3](L) [DELTA] EMU [prices.sub.t-i] 0.851 [0.47]
ECT_[PPP.sub.t-1] 0.023 ** (0.004)
ECT_PASS_[THROUGH.sub.t-1] -0.0189 (0.12)
Sigma 0.0038
[R.sup.2] 0.08
AR test 0.85 [0.54]
ARCH test 0.47 [0.85]
RESET test 0.67 [0.681
Dependent variable AEMU
[prices.sub.t]
Constant -0.007 (-0.203)
[A.sub.1](L) [DELTA] Exchange [rate.sub.t-i] 0.702 [0.55]
[A.sub.2](L) [DELTA] Domestic [prices.sub.t-i] 0.346 [0.79]
[A.sub.3](L) [DELTA] EMU [prices.sub.t-i] 1.029 [0.38]
ECT_[PPP.sub.t-1] -0.001 (-0.67)
ECT_PASS_[THROUGH.sub.t-1] 0.008 (-0.09)
Sigma 0.0015
[R.sup.2] 0.07
AR test 1.032 [0.41]
ARCH test 0.89 [0.59]
RESET test 1.85 [0.17]
Note: ECT-PPP--error correction term from the first restricted
cointegration vector; ECT_PASS_THROUGH--error correction term from
the second restricted cointegration vector; t-values in parenthesis,
p-values in brackets; statistics corresponding to [A.sub.i](L) refers
to F-statistics and associated p-value of block exclusion restriction
on all lags of an individual variable.
* null hypothesis rejected at 5% significance level; ** null
hypothesis rejected at 1% significance level.
Table 7: Threshold cointegration
TAR
Threshold=0
Parameters Values
and tests
[[rho].sub.1]= -0.015
[[rho].sub.2]= -0.016
Tmax -0.816
[PHI] ([[rho].sub.1]= 0.765
[[rho].sub.2]=0)
W([[rho].sub.1]= 0.0004 (0.98)
[[rho].sub.2])
AR test 1.94 (0.07)
M-TAR
Threshold=0
Parameters Values
and tests
[[rho].sub.1]= -0.014
[[rho].sub.2]= -0.020
Tmax -0.786
[PHI]([[rho].sub.1])= 0.861
[[rho].sub.2])=0)
W([[rho].sub.1]= 0.053 (0.82)
[[rho].sub.2])
AR test 1.98 (0.06)
TAR
Threshold=-0.0435
Parameters Values
and tests
[[rho].sub.1]= -0.013
[[rho].sub.2]= -0.034
Tmax -0.921
[PHI]([[rho].sub.1])= 1.355
[[rho].sub.2])=0)
W([[rho].sub.1]= 0.535 (0.46)
[[rho].sub.2])
AR test 1.05 (0.40)
M-TAR
Threshold=-0.0047
Parameters Values
and tests
[[rho].sub.1]= -0.009
[[rho].sub.2]= -0.067
Tmax -0.637
[PHI] ([[rho].sub.1]= 2.078
[[rho].sub.2]=0)
W([[rho].sub.1]= 2.464 (0.12)
[[rho].sub.2])
AR test 1.97 (0.06)
Note: [[rho].sub.1] and [[rho].sub.2] denote adjustment parameters;
W denotes Wald test; p-value in parenthesis.
