The catching up process in Czech Republic, Hungary, and Poland is analyzed by investigating the integration properties of log-differences in per-capita GDP versus the EU15 and a Mediterranean country group. We account for structural changes by using unit root tests that allow for two endogenous breaks in the level and the trend. We find that Czech Republic and Hungary are stochastically converging towards the Mediterranean group, while only Czech Republic is stochastically converging towards EU15. Remaining per capita GDP differences are only reduced by deterministic trends. Extrapolating these trends we find that catching up will take about 20 years.Stochastic convergence, Catching up, Unit root tests, EU accession

Carsten Trenkler

Ralf Brüggemann

English

Research Papers in Economics

 
 
 
 
 
 
 
 
 
 
 
 
SFB 649 Discussion Paper 2005-014 
 
Are Eastern European 
Countries Catching Up? 
Time Series Evidence 
for Czech Republic, 
Hungary, and Poland 
 
Ralf Brüggemann* 
Carsten Trenkler* 
 
* Department of Economics, Humboldt-Universität zu Berlin, 
Germany 
 
This research was supported by the Deutsche 
Forschungsgemeinschaft through the SFB 649 "Economic Risk". 
 
http://sfb649.wiwi.hu-berlin.de 
ISSN 1860-5664 
 
SFB 649, Humboldt-Universität zu Berlin 
Spandauer Straße 1, D-10178 Berlin 
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 Are Eastern European Countries Catching Up?
Time Series Evidence for Czech Republic, Hungary,
and Poland¤
Ralf Br¨ uggemann
Humboldt-Universit¨ at zu Berlin
Carsten Trenkler
Humboldt-Universit¨ at zu Berlin
March 4, 2005
Abstract
The catching up process in Czech Republic, Hungary, and Poland is analyzed by inves-
tigating the integration properties of log-differences in per-capita GDP versus the EU15 and
a Mediterranean country group. We account for structural changes by using unit root tests
that allow for two endogenous breaks in the level and the trend. We ﬁnd that Czech Re-
public and Hungary are stochastically converging towards the Mediterranean group, while
only Czech Republic is stochastically converging towards EU15. Remaining per capita
GDP differences are only reduced by deterministic trends. Extrapolating these trends we
ﬁnd that catching up will take about 20 years.
Keywords: Stochastic convergence, Catching up, Unit root tests, EU accession
JEL classiﬁcation: C32, E24
1 Introduction
Czech Republic, Hungary, and Poland are the three largest economies among the group of eight
Central and Eastern European (CEE) countries that have entered the EU on May 1, 2004. The
CEE countries underwent major changes in their economic and political system during their
transition to market economies in the 1990s. Although, there was some catch-up of the transi-
tion countries in comparison to the old member states, economic differences, e.g. in per capita
GDP, still exists (see e.g. European Commission (2003)). However, economic integration of the
acceding countries is an integral part for the functioning of the EU. Furthermore, comparable
levels of economic activity are necessary for successfully enlarging the Euro currency area. Em-
pirical evidence regarding the state of convergence and the catching up progress will be helpful
for political decision makers. In this paper we therefore analyze the relative growth dynamics
of Czech Republic, Hungary, and Poland with respect to the former EU15 countries.
¤This research was supported by the Deutsche Forschungsgemeinschaft through the SFB 649 ‘Economic Risk’.
Corresponding author: Ralf Br¨ uggemann, Humboldt-Universit¨ at zu Berlin, Department of Economics, Spandauer
Str. 1, 10178 Berlin, Germany. E-mail: brueggem@wiwi.hu-berlin.de
1Speciﬁc evidence on the catching up progress of EU acceding countries is scarce. The few
existing studies include Koˇ cenda (2001), Boreiko (2003), and Holtem¨ oller (2005). The lack of
econometric studies may be explained by the difﬁculties involved modeling acceding country
data: only relatively few time series observations are available and structural changes have
occurred frequently. We account for structural breaks in our analysis by following Strazicich,
Lee & Day (2004) who have studied convergence among OECD countries. As Strazicich et al.
(2004) we analyze log-differences of real per capita GDP using LM unit root tests that allow
for two breaks in the trend and the level of a series at unknown time.
A stationary log-difference of two per capita GDP series implies stochastic convergence in
the sense that stochastic shocks have only temporary effects. Output in the two countries is
then driven by a common stochastic long-run trend. In this case the catching up progress of the
poorer country is only determined by the deterministic components after the last break. Refer-
ring to a Solow model, Strazicich et al. (2004) interpret breaks in the deterministic components
as permanent changes in country-speciﬁc compensating differentials that have their origin in
e.g. different relative levels of technology. As we cover a much shorter time period, we inter-
pret the broken deterministic terms differently. In particular, we think of them as representing
e.g. changes in the political and economic environment in the CEE countries due to structural
reforms in the political and legal system, changes in the competition policy, and speciﬁc eco-
nomic policy programs. In this sense the broken deterministic terms refer to exogenous events.
In our empirical analysis for the acceding countries we use EU15 and a group of Mediter-
ranean countries (Spain, Portugal and Greece) as reference countries. If the log-difference of
per capita GDP (relative to the reference group) is stationary, we extrapolate the deterministic
trends and make rough projections for the timing of the catching up process. For comparison,
we also give results for the Mediterranean countries taking EU15 as a reference group.
The remainder of the paper is structured as follows: In Section 2 we brieﬂy describe the
econometric methods and our data before our main results are given in Section 3.
2 Methods and Data
We apply the LM unit root test of Lee & Strazicich (2003) that allows for two breaks in the trend
and the level of a time series at unknown time. We use this procedure for two main reasons.
First, it is the most ﬂexible unit root test in terms of the number of breaks at unknown time. This
is important because we do not have information on speciﬁc break points. Second, the test also
allows for structural changes under the unit root null hypothesis. Ignoring possible breaks in
connection with stochastic nonstationarity may lead to size distortions (see e.g. Strazicich et al.
(2004)).
The test works as follows. We deﬁne Zt = [1;t;D1t;D2t;DT1t;DT2t]0, where the dummy
variable Djt = 1 for t ¸ Tj+1 (j = 1;2) and zero otherwise, DTjt = t for t ¸ Tj+1 (j = 1;2)
and zero otherwise. Tj denotes the break point. Then, we have ¢Zt = [1;B1t;B2t;D1t;D2t]0
with Bjt = ¢Djt and Djt as above. The ﬁrst difference of the time series of interest, say
¢yt, is regressed on ¢Zt to obtain the estimated coefﬁcient vector ~ ±. The we compute ~ St =
yt ¡ (y1 ¡ Z1~ ±) ¡ Zt~ ± (t = 2;:::;T) and perform the unit root regression
¢yt = Á~ St¡1 + d
0¢Zt +
k X
j=1
°j¢~ St¡j + "t (2.1)
2to obtain the estimator ~ Á. Hence, the statistic for testing the unit root null hypothesis Á = 0 is
¿ = ~ Á=~ ¾Á; (2.2)
where ~ ¾Á is the estimated standard deviation of ~ Á. To endogenously determine the relative break
points ¸j = Tj=T (j = 1;2), a minimum LM unit root test is performed using a grid search
over ¸ = (¸1;¸2) in the time interval [0:1T;0:9T]. Hence, we apply the test statistic
LM¿ = inf
¸
¿(¸): (2.3)
The critical values depend moderately on the break dates. We use the ones given in Lee &
Strazicich (2003) for certain combinations of T1 and T2. The number of lags of ¢~ St in (2.1)
is determined by a general to speciﬁc procedure as suggested by Lee & Strazicich (2003) and
Strazicich et al. (2004). Thus, k is chosen according to the highest signiﬁcant number of lags of
a maximum of 8 lags. We employ the 10% critical value of 1.645 of the normal distribution for
the respective t-tests.1
For the empirical analysis we use monthly data of per capita real GDP of Czech Repub-
lic, Poland, Hungary, EU15 average, Spain, Greece, and Portugal in Euro purchasing power
standards (PPS), i.e. the GDP ﬁgures are adjusted for the purchasing power of the national
currencies. The sample covers the period 1991:01 - 2003:12 and the data are compiled from
databases of Eurostat, the IMF, the OECD, and the Czech Central Statistic Ofﬁce.2
Spain, Greece, and Portugal have been identiﬁed as a low income group among the EU
countries by Carvalho & Harvey (2005). Therefore, we consider the average per capita GDP
of these three Mediterranean countries as a second reference for the evaluation of the CEE
countries’ catching up progress.
3 Results
The LM unit root test is applied to relative income with respect to the EU15 and the Mediter-
ranean group. Thus, we consider yit = log(Yrt)¡log(Yit), where Yit is the real per capita GDP
of country i under consideration and Yrt denotes the average real per capita GDP of the EU15
or the Mediterranean countries, respectively. Note that the two breaks allowed for are signif-
icant in all test situations at least at the 10% level. The analysis of Czech Republic indicates
the presence of three structural breaks. Consequently, we only use data after the ﬁrst break in
1992:05. In all other cases, we use data from 1991:01 onwards. Our results are summarized in
Table 1 and Figure 1.
For Czech Republic and Hungary we ﬁnd that relative income is stationary with respect
to the Mediterranean countries. Moreover, we ﬁnd relative income of Czech Republic to be
stationary with respect to EU15. In contrast, non-stationarity of per capita log-difference cannot
be rejected for Poland. In this case only the ﬁrst difference of relative incomes, i.e. the growth
rate differentials, are stationary (results not shown here). Thus, Czech Republic and Hungarian
1The statistic LM¿ has been computed by using a Gauss program provided by Junsoo Lee via the web page
http://www.cba.ua.edu/»jlee/gauss.
2All data are available from the authors upon request. The raw per capita real GDP series are of yearly fre-
quency. Therefore, wehaveinterpolatedtheyearlyseriesforeachcountryintoamonthlyseriesusingtherespective
monthly index of industrial production. This interpolation has been done with the help of the program ECOTRIM,
which is used by Eurostat to compute e.g. quarterly national accounts.
3real per capita GDP are stochastically converging towards the incomes of the Mediterranean
countries in the spirit of Strazicich et al. (2004). Moreover, Czech Republic is stochastically
converging towards EU15. Therefore, as pointed out in the introduction, only the exogenous
trend after the last break determines the catching up process.
Figure 1 shows the broken deterministic components obtained by regressing yit for each
country on segmented linear trends and constants for the corresponding subperiods together
with the relative income and the residuals after adjusting for the deterministic terms.3 Clearly,
the exogenous trend reduces the income differentials between Czech Republic and EU15 aver-
age. If that trend continues it will take about 21 years until Czech Republic ﬁnishes the catching
up process. However, regarding the Mediterranean countries the relative growth trend is practi-
cally zero. Hence, Czech Republic and the Mediterranean countries reduce income differentials
with respect to EU15 with the same speed. In contrast, the relative growth trends for Hungary
are much higher. Projecting the trends into future results in a 17 to 19 year catching up period
for Hungary with respect to former EU15 and the Mediterranean group.4 Note that the rela-
tive growth in Poland has stopped since the end of the 1990s. Since, in addition, the Polish
growth rate differentials regarding the former EU15 are stationary, one may not expect impor-
tant progress in reducing the income gap over the next decades. It will probably take much
longer for Poland to catch up than for Czech Republic or Hungary, not only because it is the
poorest of three countries.
Although we observe differences among the CEE countries, a further analysis has shown
that they all stochastically converge to their group mean in per capita GDP. Moreover, Czech
Republic and Poland are approaching the group mean deterministically from above and below,
respectively. In contrast, Hungary seems to diverge deterministically due to high growth rates
in the recent past.
As a benchmark for comparison, we also include some results for the Mediterranean coun-
tries (see Panel A in Table 1 and last row of Figure 1). We ﬁnd that the link to average EU15
GDP is much stronger than for the CEE countries. They all stochastically converge to EU15-
GDP and, with the exception of Portugal, the exogenous trends continue to reduce the income
differences. If these trends do not break, Spain will achieve average EU15-GDP in approxi-
mately 4 years and Greece in 8 years. These results suggest a much more optimistic view on
the economic development of these countries than presented in Carvalho & Harvey (2005).5
Overall, our results indicate that unless further exogenous breaks occur the catching up
process in Czech Republic and Hungary will take about 20 years, while it will take much longer
in Poland.
References
Boreiko, D. (2003). EMU and accession countries: Fuzzy cluster analysis of membership,
International Journal of Finance and Economics 8: 309–325.
3Formulating an ARMA model for the stationary series gives very similar estimates of the deterministic terms.
4One has to be careful in interpreting the trend with respect to the EU15, since Hungarian relative income
vs. EU15 is not stationary. However, the ﬁrst difference of the relative income series is stationary. Hence, the trend
slope after the last break approximately equals the growth rate differential between Hungary and EU15.
5The difference could be explained by the different sample periods covered. Carvalho & Harvey (2005) stop
their analysis in 1997, after which the Mediterranean countries have experienced a large relative growth (compare
Figure 1).
4Carvalho, V. M. & Harvey, A. C. (2005). Convergence in the trends and cycles of euro-zone
income, Journal of Applied Econometrics, forthcoming.
European Commission (2003). Towards an enlarged European Union: Key indicators on mem-
ber states and candidate countries, Booklet, Brussels.
Holtem¨ oller, O. (2005). Uncovered intrest rate parity and monetary convergence of potenial
EMU accession countries, International Economics and Economic Policy, forthcoming.
Koˇ cenda, E. (2001). Macroeconomic convergence in transition countries, Journal of Compara-
tive Economics 29: 1–23.
Lee, J. & Strazicich, M. C. (2003). Minimum lagrange multiplier unit root test with two struc-
tural breaks, The Review of Economics and Statistics 85: 1082–1089.
Strazicich, M. C., Lee, J. & Day, E. (2004). Are incomes converging among OECD countries?
Time series evidence with two structural breaks, Journal of Macroeconomics 26: 131–145.
5Table 1: Unit Root Test Results
Panel A: EU15 Average
Country ~ k ~ T1, ~ T2 Test statistic LM¿ Critical value
relative break points ¸
Czech Republic 0 1995:10, 2000:04 ¡8:25¤¤ 0.2, 0.6
Hungary 3 1993:01, 1995:12 ¡4:42 0.2, 0.4
Poland 7 1992:05, 1997:06 ¡4:25 0.2, 0.4
Greece 6 1998:08, 2001:09 ¡9:65¤¤ 0.6, 0.8
Portugal 0 1994:11, 2002:06 ¡12:24¤¤ 0.2, 0.8
Spain 6 1997:03, 2001:09 ¡6:00¤ 0.4, 0.8
Panel B: Mediterranean Group Mean
Country ~ k ~ T1, ~ T2 Test statistic LM¿ Critical value
relative break points ¸
Czech Republic 3 1995:08, 1998:11 ¡7:04¤¤ 0.2, 0.6
Hungary 4 1992:07, 1995:11 ¡6:56¤¤ 0.2, 0.4
Poland 7 1992:05, 1996:10 ¡4:68 0.2, 0.4
Note: Panel A: The LM unit root test is applied to the log-difference between real per capita GDP of the
respective country and the real per capita GDP of EU15 average. Panel B: Results for unit root test for
the log-difference between real per capita GDP of the respective country and the average real per capita
GDP of the Mediterranean countries Spain, Greece, and Portugal. The data period is 1991:01-2003:12
except for Czech Republic, for which the sample 1992:05-2003:12 is considered. Critical values can
be found in Table 2 of Lee & Strazicich (2003). ¤ and ¤¤ refer to the 5% and 10% signiﬁcance levels,
respectively.
6-.08
-.04
.00
.04
.08
.35
.40
.45
.50
.55
.60
92 93 94 95 96 97 98 99 00 01 02 03
Czech Republic vs. EU 15
-.12
-.08
-.04
.00
.04
.08
.5
.6
.7
.8
.9
91 92 93 94 95 96 97 98 99 00 01 02 03
Hungary vs. EU 15
-.12
-.08
-.04
.00
.04
.08
0.8
0.9
1.0
1.1
1.2
1.3
1.4
91 92 93 94 95 96 97 98 99 00 01 02 03
Poland vs. EU 15
-.08
-.04
.00
.04
.08
.00
.05
.10
.15
.20
.25
.30
92 93 94 95 96 97 98 99 00 01 02 03
Czech Republic vs. Mediterranean Group
-.08
-.04
.00
.04
.08
.12
.25
.30
.35
.40
.45
.50
.55
91 92 93 94 95 96 97 98 99 00 01 02 03
Hungary vs. Mediterranean Group
-.10
-.05
.00
.05
.10
.15
0.5
0.6
0.7
0.8
0.9
1.0
1.1
91 92 93 94 95 96 97 98 99 00 01 02 03
Poland vs. Mediterranean Group
-.15
-.10
-.05
.00
.05
.10
.15
.1
.2
.3
.4
.5
.6
91 92 93 94 95 96 97 98 99 00 01 02 03
Greece vs. EU 15
-.10
-.05
.00
.05
.10
.15
.28
.32
.36
.40
.44
.48
.52
.56
91 92 93 94 95 96 97 98 99 00 01 02 03
Portugal vs. EU 15
-.08
-.04
.00
.04
.08
.05
.10
.15
.20
.25
.30
91 92 93 94 95 96 97 98 99 00 01 02 03
Spain vs. EU 15
Figure 1: Log-differences in real per-capita GDP (measured in Euro PPS) together with broken deter-
ministic trends and corresponding residuals. Sample: January 1991 to December 2003. (May 1992 to
Dec. 2003 for Czech Republic.)
7 
SFB 649 Discussion Paper Series 
 
For a complete list of Discussion Papers published by the SFB 649, 
please visit http://sfb649.wiwi.hu-berlin.de. 
 
001  "Nonparametric Risk Management with Generalized 
Hyperbolic  Distributions"  by Ying Chen, Wolfgang Härdle 
and Seok-Oh Jeong, January 2005. 
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Detlefsen and Giacomo Scandolo, February 2005. 
007 "Implied Trinomial Trees" by Pavel Čížek and Karel 
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008 "Stable  Distributions"  by Szymon Borak, Wolfgang Härdle 
and Rafal Weron, February 2005. 
009  "Predicting Bankruptcy with Support Vector Machines" by 
Wolfgang Härdle, Rouslan A. Moro and Dorothea Schäfer, 
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012  "Common Functional Implied Volatility Analysis" by Michal 
Benko and Wolfgang Härdle, February 2005. 
013  "Nonparametric Productivity Analysis"  by Wolfgang Härdle 
and Seok-Oh Jeong, March 2005. 
014  "Are Eastern European Countries Catching Up? Time Series 
Evidence for Czech Republic, Hungary, and Poland" by Ralf 
Brüggemann and Carsten Trenkler, March 2005. 
 
 
 
 
 
 
 
 
SFB 649, Spandauer Straße 1, D-10178 Berlin 
http://sfb649.wiwi.hu-berlin.de 
 
This research was supported by the Deutsche 
Forschungsgemeinschaft through the SFB 649 "Economic Risk". 

5The difference could be explained by the different sample periods covered. Carvalho & Harvey

Are Eastern European Countries Catching Up? Time Series Evidence for Czech Republic, Hungary, and Poland

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