Available via license: CC BY-NC-ND 4.0
Content may be subject to copyright.
Scientific Annals of Economics and Business
64 (4), 2017, 447-457
DOI: 10.1515/saeb-2017-0028
Regional Economic Growth Disparities in Ukraine:
Input-Output Analysis Approach
Vasyl Hryhorkiv*, Andrii Verstiak**, Oksana Verstiak***, Mariia Hryhorkiv§
*
Abstract
Regional inequalities in economic growth had been observed within many countries and regions. This
research emphasizes convergence/divergence technique for Ukrainian regions. As concepts of β- and
σ-convergence obtained from cross-country growth models has been subjected to a number of
criticisms and they do not embrace applied significance in studying regional inequalities in Ukraine,
we have built improved technique of investigating disparities across Ukrainian regions. The method is
based on the analysis of regional input-output tables and its aggregation. Adopted technique provides
weighted aggregation (by prices) of regional input-output tables that allows analyzing the structure of
total for each region across sectors (or kinds of economic activity). We showed that implementation of
aggregated regional input-output tables in analysis of regional convergence and the usage of
equilibrium (weighted) prices have many advantages. The main finding is that among regions of
Ukraine there are reduction of disparities in structures of different kinds of economic activities.
Keywords: regional disparities; regions of Ukraine; convergence; input-output.
JEL classification: B22; C67; C68; P52.
1. INTRODUCTION
Investigation of regional disparities and economic growth in Ukraine, as well as
regional convergence have always been and remain of great interest: this is evidenced by the
presence of a large number of scientific papers and publications on the subject issue. An
important contribution to solving the problems of regional convergence and development of
appropriate guidelines for effective regional policy had been made by well known Ukrainian
* Department of Economic Modelling, Faculty of Economics, Chernivtsi National University, Ukraine; e-mail:
v.hryhorkiv@chnu.edu.ua.
** Department of Economic Modelling, Faculty of Economics, Chernivtsi National University, Ukraine; e-mail:
a.verstyak@chnu.edu.ua (corresponding author).
*** Department of International Economics, Faculty of Economics, Chernivtsi Institute of Trade and Economics,
Ukraine; e-mail: oks1982@gmail.com.
§ Department of Economic Modelling, Faculty of Economics, Chernivtsi National University, Ukraine; e-mail:
m.hryhorkiv@chnu.edu.ua.
Unauthenticated
Download Date | 3/3/18 8:40 PM
448
Hryhorkiv, V., Verstiak, A., Verstiak, O., Hryhorkiv, M.
scientists and politicians. However, political and social crisis in Ukraine of 2013-2014, as
well as activation of decentralization process uncovered the existence of critical problems in
regional economic growth and its convergence. The importance of the above mentioned
issues had been argued by the adoption in 2015 the Law “About Principles of regional
policy”. The second article states that the purpose of national regional policy is to create
conditions for dynamic, balanced development of Ukraine and its regions, ensuring their
social and economic cohesion, raising living standards, adherence to state (Verkhovna Rada
of Ukraine, 2015).
We have conducted a critical analysis and found out “polarity” of empirical analysis
results obtained from well-known concepts of GRP (Gross Regional Product) convergence
among the regions in Ukraine. This statement leads us to a clear conclusion of the need to
develop new methodological approaches of assessment regional socio-economic
convergence, which should be the basis of effective regional economic development policy.
2. CRITICAL LITERATURE REVIEW
Vast majority of Ukrainian economists use two known concepts of β- and σ-
convergence as main methods discovering regional convergence/divergence; the methods
are based on neoclassical growth theory of Ramsey (1928), Solow (1956) and Cass (1965).
These concepts describe the tendency of the reduction in regional disparities of per capita
income between economies, i.e. countries, regions, provinces, states etc. Quah (1993) notes
that income in these models is a generalized dimension and as a convergence indicator it
might be used, as an example GDP or GRP per capita, return on assets, inflation, wages per
employee and even political attitudes. This concept is used in Abramowitz (1986) and
Baumol (1986), and it plays a central role in Barro (1991), Barro and Sala-i-Martin (1992)
and Mankiw et al. (1992).
The concept of convergence obtained Cass from cross-country growth models has
been subjected to a number of criticisms. The most important was provided by Durlauf et
al. (2005). They argued that tests for β-convergence fail to distinguish between behavior
along a transition path to a steady-state and behavior in the steady-state, in the way
needed to allow reliable discrimination between neoclassical growth models and newer
alternatives. In spite of this criticism we have found more than 250 sources in scientific
databases (Vernadskii National Library of Ukraine) using concepts of β- and σ-
convergence for investigating disparities across Ukrainian regions. The works of
Benovs’ka (2013), Naumenko (2013), Hryha (2013) and Storonyans'ka (2014) seem to be
the most important in providing detailed analysis of convergence across Ukrainian regions
based on the mentioned concepts. But the analysis of β-convergence does not embrace
applied significance in studying inequalities of socio-economic development across
Ukrainian regions. This statement is associated with significant problem of neoclassical
growth model, associated with uncompetitive nature of the ideas laying in the root of
technology. We’ve found that Ukraine's economy as a set of regional economies is not
described by neoclassical Solow-Swan model of growth. Moreover, this concept implies
significant assumptions that must be taken into account by researchers. In addition,
regions in neoclassical model addressed as closed economies and this makes it impossible
to implement empirical analysis of beta β-convergence of Ukrainian regions among which
there is a redistribution of national income.
Unauthenticated
Download Date | 3/3/18 8:40 PM
Scientific Annals of Economics and Business, 2017, Volume 64, Issue 4, pp. 447-457
449
Despite of all these obstacles, we have provided estimates of β-convergence using a
neoclassical growth framework for Ukrainian regions and have received statistically
insignificant parameters.
There are a number of statistical techniques of variation that could be used to measure
regional disparities, and therefore σ-convergence. We have used coefficient of variation in
this paper to measure the level of regional disparities in Ukraine because it is easy to
understand, discuss and use to compare the level of variation of data sets.
Figure no. 1 shows the distribution of coefficient of variation in GRP per capita form
24 Ukrainian regions plus Kyiv city. Evidently, asymmetric development of Ukrainian
regions had a different character development at various period of time (Figure no. 1): in
periods 2004-2005 and 2007-2011 we observed a processes of σ-convergence, in 2005-2006
and 2011-2014 - a processes of σ-divergence.
However, examining trends toward or away from convergence across the Ukrainian
regions based on the methodology of σ-convergence (Figure no. 1) shows only the fact of
fluctuations (variability) of appropriate variable (in our case GRP per capita). This
technique does not allow examining structural changes and development trends in the
regions, the proportions between the various economic activities (industries or sectors) in
the region and, consequently, cannot be the basis for making recommendations in the field
of regional policy.
Source: author’s calculations based on State statistic services of Ukraine (2014)
Figure no. 1 – Distribution of coefficient of variation in GRP per capita in the regions of
Ukraine: σ-convergence/divergence
Critical analysis provided above brings up the task of developing improved method of
investigating disparities across Ukrainian regions. This technique should be based on the
values of gross regional product and gross value added created in each region through the
lens of different economic activities (industries, sectors), as well as through information on
the structure and dynamics of production of goods and services and gross value added of
regions (State statistic services of Ukraine, 2014). In other words, we propose to develop
regional “input-output” tables, which Ukrainian economists use relatively rarely, because of
the absence of national statistical data at the regional level.
Unauthenticated
Download Date | 3/3/18 8:40 PM
450
Hryhorkiv, V., Verstiak, A., Verstiak, O., Hryhorkiv, M.
3. METHODOLOGY AND DATA CONSTRUCTING
Input-output tables for various regions or countries have different dimensions and the
set of industries complicating its direct usage in comparative macroeconomic analysis of the
production and distribution processes. Due to this there is a need to aggregate these tables to
models of smaller dimension, including the one-dimensional equations. Note that problem
of aggregation comes down to a common scientific task overcoming the high dimensionality
of the original problem by a simple aggregates. Hatanaka (1952), Ara (1959), Malinvaud
(1954) and Cabrer et al. (1991) studied this problem by aggregating industries into sectors.
As it is mentioned in Cabrer et al. (1991) technic coefficients being defined on sectors, were
not affected by variations in the final demand vector.
With respect to aggregation of input-output tables, it should be noted that it a priori
would combine different products into the generalized products of manufactures, industries
of appropriate industry etc. It should be noted that aggregation matrix can be unweighted
(with elements 0 and 1) and weighted (Morimoto, 1971). The most rational method of such
weighting refers to the usage of dual price system. It is particularly important for carrying
out natural and financial analysis, as we can calculate various indicators based on the
aggregated balance sheets such as rates of financial stability, capital turnover, liquidity etc.
Following national input-output statistics, we need to build concrete regional aggregate
univariate models, reflecting the distribution of gross regional product at the intermediate
and final outputs specifying the value of the each component in the balance sheet. Common
aggregation algorithm does not exist. The aggregation of input-output models to one
equation could be provided through equilibrium prices as the aggregation operator as it was
adopted for EU countries in Grygorkiv et al. (2014). The authors used this methodology to
compare the aggregated shares of intermediate output and final demand for different
countries. In this paper we briefly remind the methodology of input-output aggregation as it
had been written in details in Grygorkiv et al. (2014). Let’s consider the classical input-
output Leontief model (Leontief, 1986):
x Ax y
(1)
where
1
( ,..., )T
n
x x x
and
1
( ,..., )T
n
y y y
- respectively vectors of total output and final
demand (
T
- transpose operation),
,1
n
ij ij
Aa
- matrix of coefficients of direct material
costs (technological matrix),
n
- the number of industries (sectors), the vector
1
( ,..., )T
n
p p p
(
i
p
- price of product i) is operator of aggregation, which allows to
aggregate model (1) to the one-dimensional equation.
* * *
x x y
(2)
where
*T
x p x
,
*T
y p y
,
- coefficient of direct production costs. Due to the (Kossov,
1972) the value of accurate aggregation is set by the so-called Hatanaka condition
TT
p A p
(Hatanaka, 1952). In the case of productive indecomposable matrix
A
and
positive
y
there is always accurate aggregation (2) (i.e. the Hatanaka condition), where
*
y
is a positive number,
1
A
- Eigen value, and
TT
A
pp
- left Frobenius vector of
matrix
A
(Onyshchenko, 2011).
Unauthenticated
Download Date | 3/3/18 8:40 PM
Scientific Annals of Economics and Business, 2017, Volume 64, Issue 4, pp. 447-457
451
Specified equation (2) enables assessing the activities of the country or region at
macroeconomic level, because it includes the value of GRP and final output, and thus
determines the proportion of gross regional product in the intermediate and final outputs.
This allows providing structure analysis of total output and comparing it with actual
statistics of input-output tables. Let us remark here that the aggregation operator is the
vector of equilibrium, not the real prices and these vectors are different from each other. The
vector of equilibrium prices is closely linked with the technological matrix
A
: the changes
in technological mode lead to changes in equilibrium price vector that can be used for
eliminating the effect of price fluctuations inherent in the real prices, the aggregate value
and productivity. The difference between GRP obtained from statistical analysis and
aggregated balance model indicates the limits of price changes for products, which in many
cases can improve the quality of aggregated indicators of economic system.
The most important issue of practical implementation of the above-described
techniques for investigation regional disparities in Ukraine consists in the absence of official
regional input-output tables. Official statistical review “Gross regional product” (State
statistic services of Ukraine, 2014) contains information on gross output and value added for
each kind of industry (sector). Therefore, there is an open problem of construction the
matrix of intermediate consumption for Ukrainian regions.
Accordingly, we offer to use location quotient as a simple measure for the
concentration of an industry (i) in a region (j) and as the mathematical basis for other related
indicators in regional economics. The essence of location quotient is that the coefficients of
direct material costs
R
ij
a
regionally consistent with their values at the national level
N
ij
a
:
RN
ij ij ij
a t a
. Coefficient
ij
t
in scientific literature describes “regional trade ratio” (Stevens
et al., 1983). There are several methods for estimating this indicator; we will focus on the
method bases on the localization of coefficient calculation
i
LQ
for each industry i and its
further usage as a proxy for
ij
t
. Logic of assessing location quotient in this paper will be as
follows. As far as we investigate the regions of Ukraine, we can assume the same level of
technology in all areas. This assumption is correct for the regional level as opposed to cross-
country analysis where developing countries have different access to investment goods,
technologies, information etc.
Taking the above mentioned into consideration the location quotient has been
calculated as:
R
i
iN
i
IC
LQ IC
(3)
where
,
RN
ii
IC IC
- accordingly intermediate consumption by industry (sector) at regional
(R) and national (N) levels.
Thus, the rate of localization
i
LQ
could be compared with the value
ij
t
and used for
calculating the appropriate matrix of coefficients of direct material costs
,1
n
ij ij
Aa
. Further
mathematical calculations for the above-described models (1)-(3) have been provided in
MATLAB for period 2012-2014 as far as we’ve found out official statistical data.
Unauthenticated
Download Date | 3/3/18 8:40 PM
452
Hryhorkiv, V., Verstiak, A., Verstiak, O., Hryhorkiv, M.
4. EMPIRICAL RESULTS
Due to the conditions of Hatanaka, the aggregate ratio
of intermediate consumption
of products is Frobenius’ eigenvalues of technological Leointief’s matrix. Table no. 1 shows
the specific values of
for the Ukrainian regions, as well as Kyiv city found for their
technological matrix:
Table no. 1 – Aggregated values
of intermediate consumption, 2012-2014
Region
2012
2014
Change
Vinnitsa
0.6421
0.5876
-0.0545
Volyn
0.6244
0.5851
-0.0393
Dnipro
0.6483
0.6054
-0.0429
Donetsk
0.6597
0.606
-0.0537
Zhytomyr
0.6261
0.5901
-0.036
Zakarpattya
0.6051
0.5599
-0.0452
Zaporizhia
0.6308
0.5862
-0.0446
Ivano-Frankivsk
0.6277
0.5719
-0.0558
Kyiv region
0.6353
0.5824
-0.0529
Kirovohrad
0.6213
0.5813
-0.04
Lugansk
0.6523
0.6087
-0.0436
Lviv
0.6221
0.569
-0.0531
Mykolaiv
0.6286
0.578
-0.0506
Odessa
0.6238
0.5729
-0.0509
Poltava
0.6307
0.5736
-0.0571
Rivne
0.636
0.5808
-0.0552
Sumy
0.6275
0.5806
-0.0469
Ternopil
0.6273
0.5803
-0.047
Kharkov
0.6361
0.5819
-0.0542
Herson
0.6101
0.5851
-0.025
Khmelnytsky
0.6196
0.5889
-0.0307
Cherkassy
0.6429
0.588
-0.0549
Chernivtsi
0.6315
0.589
-0.0425
Chernihiv
0.6199
0.5809
-0.039
Kyiv city
0.6463
0.6084
-0.0379
Standard deviation
0.0126
0.01212
-0.0005
Coefficient of variation
1.9644
2.03149
0.06705
Source: authors’ calculations
The results obtained in the Table no. 1 allow assessing structural changes of the
economic system in each region including proportions and relationships between the
different spheres of production, the relationship of various elements of the regional
economics as opposed to the analysis of σ-convergence. Based on the economic structure of
Ukrainian regions (Table no. 1), the gap between them and the change in 2012-2014 are
modest. From this perspective, let us conduct detailed analysis of structural changes in the
regions, such as the characteristics of their reproductive processes of material and material
composition.
Unauthenticated
Download Date | 3/3/18 8:40 PM
Scientific Annals of Economics and Business, 2017, Volume 64, Issue 4, pp. 447-457
453
As a matter of convenience, aggregated factor
of intermediate consumption of
products is depicted in percentage terms, which will allow analyzing corresponding shares
of intermediate output and final demand (Table no. 2):
Table no. 2 – Structural changes of regional economic systems in
Ukraine in equilibrium prices: 2012-2014
Region (area)
The share of intermediate
consumption in total output
The share of final demand
in total output
2012
2014
2012
2014
Vinnitsa
64.21%
58.76%
35.79%
41.24%
Volyn
62.44%
58.51%
37.56%
41.49%
Dnipro
64.83%
60.54%
35.17%
39.46%
Donetsk
65.97%
60.60%
34.03%
39.40%
Zhytomyr
62.61%
59.01%
37.39%
40.99%
Zakarpattya
60.51%
55.99%
39.49%
44.01%
Zaporizhia
63.08%
58.62%
36.92%
41.38%
Ivano-Frankivsk
62.77%
57.19%
37.23%
42.81%
Kyiv region
63.53%
58.24%
36.47%
41.76%
Kirovohrad
62.13%
58.13%
37.87%
41.87%
Lugansk
65.23%
60.87%
34.77%
39.13%
Lviv
62.21%
56.90%
37.79%
43.10%
Mykolaiv
62.86%
57.80%
37.14%
42.20%
Odessa
62.38%
57.29%
37.62%
42.71%
Poltava
63.07%
57.36%
36.93%
42.64%
Rivne
63.60%
58.08%
36.40%
41.92%
Sumy
62.75%
58.06%
37.25%
41.94%
Ternopil
62.73%
58.03%
37.27%
41.97%
Kharkov
63.61%
58.19%
36.39%
41.81%
Herson
61.01%
58.51%
38.99%
41.49%
Khmelnytsky
61.96%
58.89%
38.04%
41.11%
Cherkassy
64.29%
58.80%
35.71%
41.20%
Chernivtsi
63.15%
58.90%
36.85%
41.10%
Chernihiv
61.99%
58.09%
38.01%
41.91%
Kyiv city
64.63%
60.84%
35.37%
39.16%
Standard deviation
0.0126
0.0121
The coefficient of variation
3.3595
2.8622
Source: authors’ calculations
The largest share of intermediate products in production 2012 is observed in (first 5
regions): Donetsk (65.97%), Dnipropetrovsk (64.83%), Luhansk (65.23%), Cherkasy
(64.29%) regions and Kyiv city (64.63%). This suggests that the economies of these regions
are the most material intensive. We would like to underline that this fact is extremely
negative, because in these regions there are the highest levels of GRP: this is due to the use
of outdated technologies of production requiring updates, modernization and going to cost
effective technologies. Accordingly, the smallest share of intermediate products in
production and therefore greater productivity of the production system is observed in
Zakarpattya (60.51%), Kherson (61.01%), Khmelnytsky (61.96%), Chernihiv (61.99%) and
Kirovohrad (62.13%) regions. Similar conclusions can be drawn for the year 2014: the list
Unauthenticated
Download Date | 3/3/18 8:40 PM
454
Hryhorkiv, V., Verstiak, A., Verstiak, O., Hryhorkiv, M.
of regions with the least capacity remained almost unchanged, but in some regions there
were a significant increase in productivity: Lviv (by 5.45%), Ivano-Frankivsk (5.85%),
Poltava (5.71%), Rivne (5.52%) and Cherkasy (5.49%) region.
To sum up, we must underline that among the regions of Ukraine there is a reduction of
disparities in structures of economic activities (industries or sectors): they have been converged
to their steady states, as in 2014 compared to 2012 in all regions we observe increasing of the
production system productivity. The regions have produced a larger share of final goods and
services (standard deviation and coefficient of variation for this indicator decreased,
respectively by 0.0005 and 0.4972 (Table no. 2). This conclusion differs from those based on
the analysis of σ-convergence of GRP per capita. Adopted technique is based on the analysis of
the structure of total output (that equals intermediate output plus final demand) for each region.
Detailed analysis of economic growth in the regions of Ukraine should be specified for
different sectors based on the calculated values of equilibrium income vectors for each
region. To do this, using values
we get the coordinates of aggregation vector
T
A
p
. It is
the vector of equilibrium prices for appropriate economic system up to a scalar factor, where
the price of production is proportional to the cost of its production:
Table no. 3 – Changes of equilibrium prices in the regions of
Ukraine in appropriate sector: 2012-20141
Region
Ukrainian economic activity (industries) classification system (2010)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
Vinnitsa
Volyn
Dnipro
Donetsk
Zhytomyr
Zakarpattya
Zaporizhia
Ivano-Frankivsk
Kyiv region
Kirovohrad
Lugansk
Lviv
Mykolaiv
Odessa
Poltava
Rivne
Sumy
Ternopil
Kharkov
Herson
Khmelnytsky
Cherkassy
Chernivtsi
Chernihiv
Kyiv city
Note: Sign ""Shows increasing equilibrium prices for the relevant period, and the sign"" shows decreasing
Source: authors’ calculations
Unauthenticated
Download Date | 3/3/18 8:40 PM
Scientific Annals of Economics and Business, 2017, Volume 64, Issue 4, pp. 447-457
455
Data in Table no. 3 make it possible to analyze the changes of equilibrium prices
across sectors thus to reduce convergence/divergence based on simultaneous changes of
these prices. Consequently, convergence of sectors is observed for:
1) agriculture, forestry and fisheries (A);
2) construction (B);
3) temporary accommodation and catering (I);
4) professional, scientific and technical activities (M);
Accordingly, the divergence is observed for the following industries:
1) information and telecommunications (J);
2) art, sport, entertainment and recreation (R);
Vector of equilibrium prices reflects balanced distribution of income between
industries in a particular region and their convergence. Beyond that, constructed regional
input-output tables allows to estimate predictive prices for each industry in the region. It is
the only type of models, which accumulates information on intersectional collaboration.
This makes it possible to track the impact of changes in economic indicators from one
industry to another.
We emphasize that the procedure of aggregation was based on the vector of
equilibrium prices, which generally differs from the actual vector of prices. Since the vector
equilibrium price is based on a technological matrix A, the obtained vector of prices could
be changed only in the case of changing technological way of production. Usage of the
vector of equilibrium prices eliminating the impact of price fluctuations, which are largely
inherent in vector of real prices.
5. CONCLUSIONS
Implementation of aggregated regional input-output tables in analysis of regional
convergence and usage of equilibrium prices have many advantages. First, input-output
tables consider the structure of economy in an aggregated nomenclature, were certain
positions sometimes include hundreds of names of specific products, estimated by the
relevant individual prices. Second, prices for the same uniform type of product may be
different for its specific customers. For example, it could be the set lower rates for electricity
consumption in rural areas compared to cities; enterprises can pay the electricity
consumption at different rates depending on the capacity of energy consuming facilities,
equipment and so on. Thirdly, the prices for the same type of products may vary due to the
differences in trade and transport margins for individual consumers.
Constructed regional input-output tables could be used as the main method in solving
other research problems of regional development, particularly in the analysis and forecasting
of the main branches of the national economy at various levels (regional, inter-product). It
could be applied in predicting the pace and nature of economic growth of the regions;
determining the characteristics of the main macroeconomic indicators to be the steady state
of economic growth of each region.
The results obtained from input-output tables allow assessing structural changes of the
economic system in each region including proportions and relationships between the different
spheres of production, the relationship of various elements of the regional economics as
opposed to the analysis of σ-convergence. We have found out the reduction of disparities in
structure of economic activity (industries, sectors) across the regions of Ukraine. This
conclusion differs from that based on the analysis of σ-convergence of GRP per capita. Thus,
Unauthenticated
Download Date | 3/3/18 8:40 PM
456
Hryhorkiv, V., Verstiak, A., Verstiak, O., Hryhorkiv, M.
adopted technique provides weighted aggregation (by prices) of regional input-output tables
that allows analyzing the structure of total output (that equals intermediate output plus final
demand) for each region across the sectors (or kinds of economic activity).
References
Abramowitz, M., 1986. Catching up, forging ahead and falling behind. The Journal of Economic
History, 46(02), 385-406. doi: http://dx.doi.org/10.1017/S0022050700046209
Ara, K., 1959. The Aggregation Problem in Input-Output Analysis. Econometrica, 27(2), 257-262.
doi: http://dx.doi.org/10.2307/1909446
Barro, R., 1991. Economic growth in a cross section of countries. The Quarterly Journal of
Economics, 106(2), 407-443. doi: http://dx.doi.org/10.2307/2937943
Barro, R., and Sala-i-Martin, X., 1992. Convergence. Journal of Political Economy, 100(2), 223-251.
doi: http://dx.doi.org/10.1086/261816
Baumol, W., 1986. Productivity growth, convergence, and welfare: What the long-run data show. The
American Economic Review, 76, 1072-1085.
Benovs’ka, L., 2013. Assessment of regional convergence in Ukraine. Regional economics. Working
papers of Lutsk National University, 10(39), 5-11.
Cabrer, B., Contreras, D., and Miravete, E. J., 1991. Aggregation in input-output tables: How to select
the best cluster linkage. Economic Systems Research, 3(2), 99-110. doi:
http://dx.doi.org/10.1080/09535319100000011
Cass, D., 1965. Optimum Growth in an Aggregative Model of Capital Accumulation. The Review of
Economic Studies, 32(3), 233-240. doi: http://dx.doi.org/10.2307/2295827
Durlauf, S., Johnson, P., and Temple, J., 2005. Growth econometrics. Handbook of Economic Growth.
Amsterdam: North-Holland.
Grygorkiv, V., Verstiak, A., and Grygorkiv, M., 2014. Cross-country comparative analysis for the
national economies based on aggregated input-output models. Intellectual Ecomomics:
International scientific research journal of Mykolas Romeris University, 8(19), 178-186.
Hatanaka, M., 1952. Note on Consolidation within a Leontief System. Econometrica, 20(2), 301-303.
doi: http://dx.doi.org/10.2307/1907853
Hryha, V., 2013. Economic dynamics of regional development in Ukraine. Working papers of
Uzhorod National University, 4(41), 134-139.
Kossov, V., 1972. The Theory of Aggregation in Input–Output Models. In A. P. Carter and A. Brody
(Eds.), Contributions to Input-Output Analysis: North-Holland Publishing.
Leontief, W. W., 1986. Input-Output Economics (2nd ed. ed.). New York: Oxford University Press.
Malinvaud, E., 1954. Aggregation Problems in Input–Output Models. In T. Barna (Ed.), The
Structural Interdependence of the Economy: John Wiley and Sons.
Mankiw, N., Romer, D., and Weil, D., 1992. A contribution to the empirics of economic growth. The
Quarterly Journal of Economics, 107(2), 407-437. doi: http://dx.doi.org/10.2307/2118477
Morimoto, Y., 1971. A Note on Weighted Aggregation in Input-Output Analysis. International
Economic Review, 12(1), 138-143. doi: http://dx.doi.org/10.2307/2525502
Naumenko, Z., 2013. Convergence and divergence in regional economics. Economic Innovations, 52,
255-261.
Onyshchenko, A., 2011. Modeling of environmental and economic interaction in the enforcement of
the Kyoto Protocol. Poltava: Poltava literator.
Quah, D., 1993. Empirical cross-section dynamics in economic growth. European Economic Review,
37(2-3), 426-434. doi: http://dx.doi.org/10.1016/0014-2921(93)90031-5
Ramsey, F. P., 1928. A Mathematical Theory of Saving. Economic Journal (London), 38(152), 543-
559. doi: http://dx.doi.org/10.2307/2224098
Solow, R. M., 1956. A Contribution to the Theory of Economic Growth. The Quarterly Journal of
Economics, 70(1), 65-94. doi: http://dx.doi.org/10.2307/1884513
Unauthenticated
Download Date | 3/3/18 8:40 PM
Scientific Annals of Economics and Business, 2017, Volume 64, Issue 4, pp. 447-457
457
State statistic services of Ukraine, 2014. Gross regional product 2014. Statistical summary. from
http://ukrstat.gov.ua/druk/publicat/kat_u/2016/zb/04/Zb_VRP_2014.pdf.zip
Stevens, B. H., Treyz, G. I., Ehrlich, D. J., and Bower, J. R., 1983. A new technique for the
construction of non-survey regional input-output models. International Regional Science
Review, 8(3), 271-286. doi: http://dx.doi.org/10.1177/016001768300800306
Storonyans'ka, I. Z., 2014. Financial mechanisms of convergent model of regional development. Lviv:
Institute of Regional Research.
Verkhovna Rada of Ukraine, 2015. About Principles of State Regional Policy. from
http://zakon0.rada.gov.ua/laws/show/156-19
Copyright
This article is an open access article distributed under the terms and conditions of the
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Unauthenticated
Download Date | 3/3/18 8:40 PM