Economic Growth and Beta-Convergence Between EU and Ukraine

Abstract

This paper provides an analysis of the size and development of the shadow economy in Ukraine. The shadow economy is defined as a system of interconnected relationships that take place outside the existing laws and do not allow direct and regular statistical accounting and tax control. Insufficient quality of state institutions, ineffective regulatory policy, imperfection of the tax system, unformed competitive environment and corruption are the driving forces for the shadow economy. The paper identifies the socioeconomic consequences arising from the functioning of the shadow economy. Economic-mathematical model was constructed to identify patterns of shadow economy functioning. Economic-mathematical analysis allows formulating a list of proposals on ways and means of reducing the size of the shadow economy in Ukraine.

Full text

ISSN 1822-8011 (print)
ISSN 1822-8038 (online)
INTELEKTINĖ EKONOMIKA
INTELLECTUAL ECONOMICS
2014, Vol. 8, No. 1(19), p. 128–139
ECONOMIC GROWTH AND BETACONVERGENCE BETWEEN
EU AND UKRAINE
Andrii VERSTIAK
Chernivtsi National University
E-mail: a.verstyak@chnu.edu.ua
Oksana VERSTIAK
Institute of Trade and Economics
E-mail: oks1982@gmail.com
Svyatoslav ISHCHENKO
Chernivtsi National University
E-mail: isv.emm@gmail.com
Serhii ZIUKOV
Chernivtsi National University
E-mail: s.zyukov@chnu.edu.ua
doi:10.13165/IE-14-8-1-09
Abstract. e empiric analysis of convergence processes between Ukraine and EU coun-
tries showed that the most spreading method of convergence presence in the rate of economic
development is the reduction of the inequality of GDP per capita level among the countries
groups. e main characteristics of the convergence hypothesis are checked on the example
of EU and Ukraine. us, the economic dependence of emerging countries from developed
countries is primarily manifested in the fact that developed countries are net-exporters of
capital to developing countries, while developing countries are, in fact, their debtors. e hy-
pothesis of EU and Ukraine integration is checked on the base of convergence test.
JEL classication: F15, O47
Keywords: global crisis, economic convergence, b-convergence, s-convergence, diver-
gence, international integration, foreign (external) trade, integration processes, Ukraine.
Reikšminiai žodžiai: globali krizė, konvergencija, divergencija, ekonominė konvergen-
cija, tarptautinė integracija, užsienio prekyba, integracijos procesai Ukrainoje.
Introduction
e history of European integration shows that due to a set of objective reasons,
integration process was among the countries that have achieved relatively high levels of

129
Economic Growth and Beta-Convergence between EU and Ukraine
economic and political development. e basis of integration except the natural process of
increasing interdependence of national economies is a need for mutual adjustment and joint
regulation of economic processes across the entire economic complex. e eectiveness of
this regulation depends on the level of national economic, social and legal systems.
From the start, the entire EU mechanism was created to help less developed countries
and regions to achieve more advanced level, i.e. to ensure economic convergence. Creating
the conditions for economic convergence is crucial for an integrated association existence.
In theory of economic growth there is assumed that the initial dierentiation
of the development level is the result of exogenous shocks and imperfect adjustment
mechanism. In accordance with the hypothesis of convergence, if the country’s economy
at the initial time is further away from the position of stable equilibrium, its growth rate
will be higher than in the economy, which is closer to equilibrium. So, in the long term
dierentiation disappears. e most common hypothesis of convergence is used to study
the dynamics and dierences in the level of GDP.
1. e concepts of economic convergence
It should be noted that in the economic literature there is no single denition of
“convergence” and it is only mentioned several concepts of convergence hypothesis.
ere are two most widely used concepts of convergence - so-called beta and sigma
convergence concepts (Barro, Sala-i-Martin, 1991, 1992, 1995, 2004; Solow, 1957;
Bernard, 1996; Henin and Le Pen, 1995).
Concept of b-convergence denes convergence as a process of “building” in which
countries with lower levels of development have higher rates of economic growth. e
second type of convergence, i.e. s-convergence is dened as a reduction in the time
variance of the GDP per capita distribution or another income indicator.
Hypotheses of b-convergence and s-convergence are interdependent, but not
equivalent. In several papers (Barro, Sala-i-Martin, 1991, 1992, 1995, 2004) it was shown
that with absolute b-convergence s-convergence does not directly follow. (Henin and
Le Pen, 1995) proposed the relationship interpretation between absolute b-convergence
and s-convergence. Absolute b-convergence indicates the existence of the trend towards
reducing the gap in GDP per capita. At the same time, random shocks aects the
economy of countries (regions) may counteract this trend and temporarily increase the
distribution variance of the GDP per capita.
e starting point for the convergence analysis is the so-called unconditional model
of b-convergence, which is based on the neoclassical theory of growth (Solow, 1956,
1957). Within this model, the economic growth is positively correlated with the gap at
the initial time between initial per capita income for the country (region) and income
per capita in steady state equilibrium, which is the same for all regions. In steady state
equilibrium countries are on a stable growth path, characterised by constant growth rate
of per capita income. In accordance with the model, countries with lower development
level should grow at a faster rate than those with higher levels of development, so in the
long term regional levels of economic development should be aligning.

130 Andrii VERSTIAK, Oksana VERSTIAK, Svyatoslav ISHCHENKO, Serhii ZIUKOV
Formally unconditional convergence model can be written as (Barro, Sala-i-Martin,
1992)
gy
NI
T=+ +
()
αβ εε
0
2
0
,,
,
σ
(1)
where gT - logarithm of the average growth rate for the period T; y0- logarithm of the
variable at initial level that is tested for convergence; a - parameter that contains the
norm of technological progress and the level of per capita income in the steady state
equilibrium; b - rate of convergence; e - random component.
e process of convergence is usually characterised by the speed of convergence and
time to overcome the half of distance that separates the economy of the country (region)
from its steady state. ese coecients can be calculated by evaluating the coecient
of convergence b as
( )
ˆ
ˆ
ln 1 /
b TT
β
=−−
and
( )
ˆ
ln 2 /hl b=. Rate of convergence is
determined by the sign and value of the coecient b. If b < 0, then the convergence is
observed, if b > 0, then the divergence is observed.
e hypothesis of a negative correlation between average growth rate and the initial
income per capita is veried in the model of unconditional convergence in line with
neoclassical growth theory (Barro, Sala-i-Martin, 2004). At the same time, the theory
assumes that countries (regions) tend to a single trajectory of proportional growth.
Countries (regions) studying in this model have rather uniform economic
structure and are characterised only by time disparities in economic development, which
are explained by dierences in initial levels of per capita income. It is logical to assume
that dierent countries (regions) have dierent trajectories of proportional growth and,
consequently, dierent long-term growth rates. In this case, the alignment of economic
development of countries (regions) cannot exist. e objective of regional policy in this
case is the adoption of such tools that can raise the growth level of underdeveloped areas.
e assumption that the countries (regions) have dierent stable path of growth
is formalised within the model of conditional b-Convergence as follows (Barro, Sala-i-
Martin, 1992):
gy
ZN
I
T=+ ++
()
αβ φε
εσ
0
2
0
,,
. (2)
where Z is matrix of regional growth factors that characterise the equilibrium.
us, the model of conditional convergence hypothesis is tested for the presence
of negative correlation between average growth rate and initial per capita income in the
presence of regulatory factors that characterise regional dierences in the levels of stable
equilibrium states.
In order to analyse the relationship between the two types of convergence, consider
the basic equation of the neoclassical growth model that links the growth rate of per
capita income (yi) for a certain period of time from the initial level of income (Barro,
Sala-i-Martin, 2004):
ln ln
,
,
,,
y
yae
yu
it
it
it it it
−
−−







=−−
()
()
+
1
1
1β. (3)

131
Economic Growth and Beta-Convergence between EU and Ukraine
Neoclassical growth theory shows that a free member ait is the sum of a variable
that reects the technological process, and the value factor which is the logarithm of
the equilibrium value of income in the country. is is the essence of the conditional
convergence concept, since income is taken into account that corresponds to a stable
equilibrium position.
Considering the countries (regions), it is assumed that free member ait is the same
for all regions. Moreover, if b > 0, then from equation (3) it follows that countries with
lower levels of development are characterised by higher rates of economic development.
Assuming that the random deviation ui,t has a distribution with parameters 02
,,
σ
ut
()
and
is distributed independent of log,
yit−
()
1 and uj,t , i ¹ j, we can obtain an expression that
allows following the connection between b and s-convergence:
σ
σσσ
ββ
β
t
uu
t
ee
e
2
2
20
2
2
2
2
11
=−+−
−








−−
−, (4)
where
σ
0
2
- variance ln ,
yi0
()
. It follows that
σ
t
2 tends to its equilibrium state
σβ
u
e
2
2
1
−−,
which increases with the
σ
u
2 but decreases with the increase of b. us, the positive
coecient b does not mean reducing
σ
t
2
i.e. the presence of convergence. However,
b-convergence is a necessary but insucient condition for the existence of s-convergence.
us, the s-convergence is observed in such cases where b-convergence reduces the
eect of random shocks. Lichtenberg distributed this conclusion on the conditional
b-convergence (Lichtenberg, 1994).
2. Economic convergence: empirical evidence in between the
EU and Ukraine
Current issue raised in foreign literature is to test the hypothesis of the convergence
presence/absence. In particular, Lichtenberg oers test convergence hypothesis,
which says that variation of performance between countries decreases over time
(Lichtenberg, 1994). If
yY
it it
=
()
ln (Where
Y
it a performance of the country i and
σ
tit
i
yy
N
22
=−
()
∑/ - variation
yit
between countries in time t), then Lichtenberg
argues that
σσ
1
22
/T has FN N
−−
()
22
,-distribution in the case when performance
between countries is not moving closer in time, where N is the number of countries and
T is the last year of the sample. us:
T
T
1
1
2
2
=σ
σ, (5)
(Carey and Klomp, 1997) conducted a critical analysis of the Lichtenberg convergence
hypothesis (Lichtenberg, 1994). Aer a model experiment scientists argue that test of
Lichtenberg hypotheses leads to a small probability of the hypothesis of convergence.
Instead, Carey and Klomp oer two alternative tests to verify presence/absence of
the convergence hypothesis. e authors receive the rst statistical test T2 using the

132 Andrii VERSTIAK, Oksana VERSTIAK, Svyatoslav ISHCHENKO, Serhii ZIUKOV
likelihood ratio test statistic and the second T3 adjusting the statistical test Lichtenberg
T4 (Lichtenberg, 1994). ese tests are formalised as follows (Carey and Klomp, 1997):
TN T
TT
d
2
0
22
2
0
22
0
2
2
25 1025 1=−
()
+−
()
−









→
()
,ln,
σσ
σσ σχ
, (6)
T
N
N
Td
3
1
22
2
1
21
01
=−
()
−→
()
σσ
π
/
,, (7)
where T3 has a normal distribution with N – 1 degrees of freedom, N - number of
countries
σ
0T
- covariance of productivity in the rst and last periods,
p
- parameter of
regression
yyu
it
ii
=+
π
1 , a statistical test T2 has
χ
21
()
-distribution.
Carey and Klomp analysed hypotheses using the data on GDP per capita for 22
countries in OECD. All of the three statistical tests showed reduction in performance of
variation. However, when the authors used tests for the period from 1960 to 1985, the
statistic test of Lichtenberg T1 showed a lack of convergence in terms of GDP per capita,
while the other two tests T2 and T3 xed convergence. e authors also analysed the
convergence for short periods of time during 1950-1994 divided into 12 sub-periods. It
received a low hypothesis probability of the existence of convergence under Lichtenberg
test, which conrmed its low eciency.
We have got GDP per capita level for EU-27 and Ukraine for the period 2004-2012.
Distribution of GDP per capita (current US$) is shown in Fig. 1. Separate calculations
were made for the crisis point of 2008.
e concept of σ-convergence is valid in the case when a decrease in the dispersion
index of GDP per capita for the group of countries is observed. at is, if
σσ
tT t+
<
, where
σ
t
is a measure of dispersion, then s-convergence is observed. To prove this concept,
the most commonly used indicators are indicators of variance, standard deviation or
coecient of variation. As part of this work, s-convergence was calculated based on
the coecient of variation, weighted coecient of variation (taking into account the
proportion of the country’s population to the total) and the eil index. Values of
σ-convergence characteristics, which are calculated for GDP per capita for 2004-2012,
proved the existence of rapprochement between Ukraine and the EU. It was found that
the level of inequality indicated by the value of GDP per capita is not increasing, but
decreasing. is analysis of various inequality indicators yielded similar results. It should
be noted that for the intervals of 2004-2008 and 2008-2012, the presence of σ-divergence
was observed. During almost the entire study period (2004-2012) eil index was close
to zero (the lowest value of 0.0435 was recorded in 2004), i.e. a reduction of disparities
between the EU Member States and Ukraine in terms of GDP per capita was observed.
e increase in this inequality was observed only in the intervals of 2004-2008 and
2004-2012.

133
Economic Growth and Beta-Convergence between EU and Ukraine
Figure. 1. GDP per capita (current US$), EU27+Ukraine
Source: e World Bank (2013)
Aer receiving the data about the availability of σ-convergence between Member
States of the EU and Ukraine, we should conduct an analysis of statistical tests of
Lichtenberg (T1), Carey and Klomp (T2, T3) according to (5-7).
To check convergence availability, we need to verify two hypotheses:
1. H0 - no convergence hypothesis states that the variance of GDP per capita in the
period T is equal to the variance of that indicator in period 0, HT0
2
0
2
:
σσ
=;
2. H1 - hypothesis of convergence, HT1
2
0
2
:
σσ
<.
Test results of the above hypotheses are shown in Table 1. According to the results of
testing the hypothesis of presence/absence of s-convergence of GDP per capita between
the EU Member States and Ukraine, we can draw the following conclusions:
1) according to the test T1 we accepted the hypothesis HT0
2
0
2
:
σσ
= the lack of
convergence as false
σσ
T
2
0
2
>;
2) based on T2 test results the hypothesis of no convergence
H
T0
2
0
2
:
σσ
=was re-
jected and the hypothesis HT1
2
0
2
:
σσ
<. was accepted, which conrms earlier
ndings;
3) the results of T3 test also indicate rejection of the hypothesis H0. us, we
accepted the hypothesis HT1
2
0
2
:
σσ
<. the presence of convergence.

134 Andrii VERSTIAK, Oksana VERSTIAK, Svyatoslav ISHCHENKO, Serhii ZIUKOV
Table 1. Empirical test results of statistical tests of convergence
Statistical
test Received
value Critical
value Distribution Conclusion
T10.2501 1.9292
FN N
95
22
%
(, )−−
TT
1
*>
κρ
: No convergence
T225.8080 3.8415
χ
95
21
%
()
TT
1
*>
κρ
: e existing convergence
T31.3013 1.2816
N
90
01
%
,
()
TT
1
*>
κρ
: e existing convergence
Source: Author’s calculations
ese results prove a critical analysis of Carey and Klomp on inadequacy of the
Lichtenberg T1 test. e conrmation of tests T2 and T3 leads to the general conclusion
that σ-convergence of GDP per capita exists between the EU Member States and Ukraine.
Summarising the results, we can state that the concept of σ-convergence was
conrmed by the data on the EU and Ukraine. It was found that the level of inequality
indicated by the value of GDP per capita is not increasing, but decreasing. is analysis
of various indicators of inequality yielded similar results.
Availability of β-convergence reects a negative statistical correlation between the
growth rate of income per capita and its initial level during the cross-sectional analysis
of countries. is data regression model determines the kind β-convergence that should
be checked. In case of estimated regression steam dependence of the income growth
rate on a constant and the initial level of this index, we verify the existence of absolute
convergence. If the equation includes additional exogenous parameters that characterise
the dierences in the level of production technology, the savings rate, population growth
and other parameters, we test the hypothesis of conditional convergence.
Let us analyse the results of paired regression of the growth rate of GDP per capita
in 2012, relative to 2004 for equation (under 1):
1
00
Tyyab y
iT
ii
i




−
()
=+
()
+ln ln ln ,
ε
(8)
where yi0 and yiT - GDP per capita in the initial and nal periods, be
T
T
=−−
1β
- rate of
convergence (shows how the value of economic growth will decrease in percentage terms
by increasing the initial per capita GDP by 1%)
β
=− −
()
ln /1
Tb T
- rate of convergence
(shows how the gap is shrinking every year), T - length of time interval, a - constant,
ε
i
- random error,
in
=1, .
According to (8), on the basis of calculations, pair regression equation is:
10 163 0 0126
00
Tyy y
iT
ii




−
()
=−
()
ln ln ,,ln ,, (9)
i.e. the rate of convergence
b=−0 0126,
. Speed of convergence b is 0.0049. e annual
gap will be 0.49% per year, which is a relatively low rate in these calculations (in works
of Barrow and Sala-i-Martin, the rate of convergence constituted 2 to 3% per year). In

135
Economic Growth and Beta-Convergence between EU and Ukraine
other words, poorer countries in 2004 grew at a rate that was 0.49% and was higher
than the growth rate of countries with GDP per capita in 2004. Based on that b < 0 and
b < 0 we can conclude that the entire study period conrmed the concept of absolute
b-convergence for the EU members and Ukraine.
A more accurate conclusion can be drawn by conducting an econometric analysis
of convergence rate. e correlation coecient r = –0,5291, connection between these
factors is moderate and back. e index of correlation (empirical correlation ratio) is
h= 0,5833. e resulting value indicates that GDP per capita in 2004 had moderate
impact on growth rate of GDP per capita in 2012.
Coecient of determination R2 = 0,2795, i.e. 27.9489% of change in GDP per capita
in 2004 lead to changes of the growth rate of GDP per capita in 2012. e accuracy of
regression selection was low. Checking of hypotheses on the coecients of the linear
regression equation allowed obtaining tb = 4,39, statistically signicant regression
coecient b was conrmed. F = 10,111, Fcr = 4.23. Because F > Fcr, the coecient of
determination is statistically signicant.
e results of evaluations conrm the existence of absolute b-convergence for the
EU members and Ukraine for the period 2004-2012 and 2004-2008 with 95% condence
level. Figure 2 shows the dispersion of the logarithm values of average growth for the
period from 2004 to 2008 (and 2012), depending on the logarithm of per capita in 2004.
e chart clearly shows one separate result – Ukraine (before and aer the crisis
period). Indeed Ukraine has had the lowest growth rate (log) GDP per capita in 2004-
2012. Calculations for the data excluding Ukraine (only the 27 EU Member States) gave
the following results. Rate of convergence b = –0,0173. Speed of convergence b is 0.0065.
is means that the annual gap will be 0.65% per year, which is also a relatively low rate
in such calculations. In other words, the poorer countries in 2004 grew at a rate of 0.74%
that was higher than the growth rate of countries with GDP per capita in 2004. Based on
that, b < 0 and b < 0, we can conclude that the entire study period conrmed the concept
of absolute b-convergence for the EU Member States.
e correlation coecient r = –0,7858, relationship between these factors is strong
and opposite. e index of correlation (empirical correlation ratio) is h = 0,7211. e
resulting value indicates that GDP per capita in 2004 signicantly aected growth rate of
GDP per capita in 2012.
Coecient of determination R2 = 0,62 62% of the change GDP per capita in 2004
led to changes of the growth rate of GDP per capita in 2012. e accuracy of selection
regression was high. Testing hypotheses about the coecients of the linear regression
equation allowed obtaining tb = 8,15, i.e. statistically signicant regression coecient b
was conrmed. F = 40,3508, Fcr = 4,26. Because F > Fcr, the coecient of determination
is statistically signicant.
e results of evaluations conrm the existence of absolute b-convergence for the
EU Member States for the period 2004-2012 with 95% condence level. e inclusion of
Ukraine in the sample did not signicantly aect the rate and pace of convergence, thus
we can draw a general conclusion about the convergence of the EU Member States and
Ukraine.

136 Andrii VERSTIAK, Oksana VERSTIAK, Svyatoslav ISHCHENKO, Serhii ZIUKOV
Figure 2. Scatter Chart average GDP growth per capita for the 2004-2008 (2012) relative to the logarithm of initial GDP per capita in
2004, 28 countries






137
Economic Growth and Beta-Convergence between EU and Ukraine





Source: Author’s calculations

138 Andrii VERSTIAK, Oksana VERSTIAK, Svyatoslav ISHCHENKO, Serhii ZIUKOV
Conclusion
e study of the convergence problem showed the following results:
1. e estimation of the convergence rate for countries participating in the EU
and Ukraine was made using international experience of econometric modelling. e
results can be used to determine the eciency of integration policy and to generate
recommendations for its improvement.
2. e classication of convergence mechanisms was suggested, which allows
determining the level of economic policy that reduces disparities between the EU
Member States and Ukraine: promotion of technological progress, development of
international cooperation.
3. A system of models of economic growth, and forecasts at a theoretical level on
the presence/absence of convergence were suggested.
4. e calculations show that s-convergence was conrmed by the data for the EU
and Ukraine. e conclusion was reached that the level of inequality indicated by the
value of GDP per capita was not increasing, but was decreasing. is analysis of various
indicators of inequality yielded similar results. It should be noted that for the intervals
2004-2008 and 2008-2012, the presence of s-divergence was observed.
5. Statistical hypothesis tests were held for presence/absence of s-convergence of
GDP per capita between the EU and Ukraine. e results conrmed the conclusions of
the study of foreign scientists Lichtenberg, Cary and Klomp on statistics T1, T2, T3. ese
tests also showed the presence of s-convergence for the investigated variable.
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EKONOMIKOS AUGIMAS IR BETA KONVERGENCIJA
TARP ES IR UKRAINOS
Santrauka. Empirinis konvergencijos procesų tarp Ukrainos ir ES šalių tyrimas parodė, kad
labiausiai pastebima konvergencijos pagal BVP vienam gyventojui tarp šalių grupių. Pagrindinė
konvergencijos hipotezė yra tikrinama tarp ES ir Ukrainos. Taigi, ekonominė priklausomybė nuo
sparčiai augančios ekonomikos šalių iš išsivysčiusių šalių visų pirma pasireiškia tuo, kad išsivysčiu-
sios šalys yra grynosios kapitalo eksportuotojos į besivystančias šalis, o besivystančios šalys iš tiesų
yra jų skolininkės. ES ir Ukrainos integracijos hipotezė tikrinama konvergencijos testu.
Andrii VERSTIAK – Chernivtsi National University, Ukraine.
Andrii VERSTIAK – Chernivtsi nacionalinis universitetas, Ukraina.
Oksana VERSTIAK – Institute of Trade and Economics, Ukraine.
Oksana VERSTIAK – Prekybos ir ekonomikos institutas, Ukraina.
Svyatoslav ISHCHENKO – Chernivtsi National University, Ukraine.
Svyatoslav ISHCHENKO – Chernivtsi nacionalinis universitetas, Ukraina.
Serhii ZIUKOV – Chernivtsi National University, Ukraine.
Serhii ZIUKOV – Chernivtsi nacionalinis universitetas, Ukraina.