=Paper=
{{Paper
|id=Vol-2917/paper30
|storemode=property
|title=Innovation and Investment Factors in the State Strategic Management of Social and Economic Development of the Country: Modeling and Forecasting
|pdfUrl=https://ceur-ws.org/Vol-2917/paper30.pdf
|volume=Vol-2917
|authors=Rostyslav Yurynets,Zoryna Yurynets,Olena Budіakova,Lesia Gnylianska,Marianna Kokhan
|dblpUrl=https://dblp.org/rec/conf/momlet/YurynetsYBGK21
}}
==Innovation and Investment Factors in the State Strategic Management of Social and Economic Development of the Country: Modeling and Forecasting==
https://ceur-ws.org/Vol-2917/paper30.pdf
Innovation and Investment Factors in the State Strategic
Management of Social and Economic Development of the
Country: Modeling and Forecasting
Rostyslav Yurynetsa, Zoryna Yurynetsb , Olena Budіakovac, Lesia Gnylianskaa and
Marianna Kokhanb
a
Lviv Polytechnic National University, 12 Stepan Bandery str., Lviv, 79013, Ukraine
b
Ivan Franko Lviv national University, Svobody avenue 18, Lviv, 79000, Ukraine
c
Kyiv National University of Technologies and Design, 2 Nemyrovycha-Danchenka str., Kyiv, 01011, Ukraine
Abstract
The aim of the article is the modeling of impact of innovative and investment factors on the
social and economic development of Ukraine, and forecasting Ukraine's GDP growth in the
short term to improve the state strategic management. The model-based approach moves
away from classical regression analysis and instead uses combination of production functions
and regression analysis. The forecast was made for a short-term period by means of Box-
Jenkins method (ARIMA) with the use of Statistica. By means of the regression model, there
was established that forecast values of GDP volume over the long term will gradually
decrease. It was found out that the highest priority factors of a competitiveness according to
the innovative component of Ukraine are the amount of scientific and technological works, a
number of innovative technologies and technological processes introduced, fixed
investments, a number of innovative products sold. The effective investments in basic capital
and increase of sold innovative products volume will also cause GDP growth. All these
require the development and realization of the preventive measures, improvement of state
programs of social and economic development and implementation of state policy.
Keywords 1
Regression analysis, production function method, forecast, GDP, innovative and investment
factors, state programs of social and economic development
1. Introduction
Modern science uses many methods to assess the impact of factors on the level of social and
economic development of the country, but a special place is occupied by correlation regression
analysis. Multifactor correlation-regression analysis allows to estimate the degree of influence of the
factors that are included in the model on the performance indicator [1]. The use of machine learning
tools for economic decision-making remains important today.
The state strategic management is a functional system involved in the development and
implementation of the strategy of social and economic development of the state, regions, cities,
districts, municipalities. The mechanism of state strategic management is in the form of an integrated
system of measures conducted by the management subject on the basis of functions, principles,
predicates, social and economic development forecasts, in the direction of the control object
MoMLeT+DS 2021: 3rd International Workshop on Modern Machine Learning Technologies and Data Science, June 5, 2021, Lviv-Shatsk,
Ukraine
EMAIL: rostyslav.v.yurynets@lpnu.ua (R. Yurynets); zoryna_yur@ukr.net (Z. Yurynets); budyakova.oy@knutd.edu.ua (O. Budіakova);
lgnylianska@gmail.com (L. Gnylianska); marianna.kokhan@gmail.com (M. Kokhan)
ORCID: 0000-0003-3231-8059 (R. Yurynets); 0000-0001-9027-2349 (Z. Yurynets); 0000-0001-6028-2650 (O. Budіakova); 0000-0003-
2924-7165 (L. Gnylianska); 0000-0002-9358-2200 (M. Kokhan)
©️ 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
(economic quantifier) to ensure the effective functioning towards achieving social and economic
goals. The state strategic management based on organizational and legal principles. Organizational
principles include: planning and forecasting, innovation and investment dynamics, technological
progress, optimal engagement of human and intellectual capital in process of reproduction of material
goods and services [2]. Modeling and forecasting of innovation and investment dynamics give the
information that serves as a basis for social and economic development forecasts for the country. The
results of forecasting have an influence on action strategic plan in a state management, featuring the
economic and social programs. It can be said that the economic and social programs orientate towards
a strategy of social and economic development of the country.
Gross domestic product (GDP) is one of the most important indicators of social and economic
development of the country. Within a market economy, the innovations and investments are the
important factors for the production efficiency improvement and competitiveness. The world’s
experience shows that a country should, first of all, concentrate its efforts on innovations, forming of
the effective business environment that provides a sustainable social and economic development of
the country based on the use of investments and intellectual potential [3]. The considered and laid
GDP forecasting results of the country promote the definition and formation of the demand for
innovations and investments [4], building of potential needs and market condition forecasts, make the
consideration of the competitive advantages of the innovative goods and services important [5]. All
this is necessary for the adequate scientific ideas system building concerning formation of the state
programs of social and economic development of the country.
State programs of social and economic development for the strategic perspective are developed in
accordance with the country's GDP forecasts. It is important to forecast GDP based on innovation and
investment factors, which are the foundation of any developed economy. And in this way, the state
programs of social and economic development of Ukraine should be based on analytical results of
forecasting directions of innovative development of the country. This will allow the government to
concentrate investment and human resources for implementation competitive advantages and ensuring
progressive technological structural changes in economy. There is a certain demand for further study of
the investment and innovative factors effect on GDP of Ukraine with the application of the econometric
modeling. Based on the aforesaid, the development of the existing and building of the new dynamics
models is up-to-date and essential because of their theoretical value and applied meaning.
The aim of the article is the modeling of impact of innovation and investment factors on the social
and economic development of Ukraine, and Forecasting Ukraine's GDP growth in the short term to
improve the state strategic management. The model-based approach moves away from classical
regression analysis and instead uses combination of production functions and regression analysis.
2. Literature review
Representatives of classical economics [1; 6] offered lots of ideas, which are used in the present-
day theory of growth. On the basis of these models there are completed multiple parsing tasks and
forecasting of social and economic development.
Scientists considered different factors that influence social and economic development and GDP
growth, for example, foreign direct investments [7], public expenditure [8], various economic,
industrial, financial indicators [9] etc.
We wish to emphasize a research team [10; 11], who included such factors as innovative products,
technological processes into growth models. From those scientific papers there was identified that the
economic growth can result from research and development (R&D) sector work (through research and
development works increase) or innovations sector of the enterprises (through costs of the enterprises
introducing innovations increase). The higher is the rate of social and economic growth of the country
the more significant for the social and economic growth is the results of intellectual work of
personnel. The value of the innovation, science and technology spheres in the economy of the
developed countries continuously grows together with the growth of GDP.
Most countries with the developed economy have to stimulate the social and economic advance,
however, such growth requires innovations and investments. The innovative and investment issues
study is mostly concentrated on the study of the organization forms of innovative activity,
occupational groups, patent activity [12]. The scientific studies are mostly focused on the process of
innovations development and introduction, study of the specific elements of this process [13].
For many years there exists a trend to compare and analyze the innovative activity at the domestic
level [14] with due consideration of data bulks. The most popular for the innovative and investment
factors diagnostics and evaluation appear to be expert methods, simulation modeling, correlational
and regressive and factorial analysis, principal components method, fuzzy sets, index analysis, neural
networks, expert systems [15]. The complexity of the subject, data availability and mastered
mathematical tools exert an influence on model choice.
Economic and mathematical modeling and forecasting confer the possibility to use the results of
calculations in the planning of social and economic development of the country in order to provide
scientific validation and plans optimization. Based on econometric modeling there is defined the
dependence of GDP growth on a change of specific factors: the investment factors of reproduction
and renewal, the innovative growth results, number of people involved in the national economy in the
context of educational background [15], intramural expenditures for the research and development
(R&D), use of advanced technologies, created advanced manufacturing technologies [16]. The
received dependences give an opportunity to set GDP growth rate on the change of each model factor
and evaluate the structural changes influence level in separate indices on GDP growth rate.
The general economic equilibrium method is the best suited for the social-economic forecasting,
which allows creating complex, non-linear models with theoretical underpinning of non-linear links.
Among foreign models there may be distinguished the Norwegian MSG6 model [17], which considers
innovation development factor through the innovative economy sector, and GDP forecasting model
presented in the scientific work [18] is based on branch forecasts of the relevant ministries.
The author offers to use the production function method for the econometric modeling, to establish
the dependence of GDP growth of Ukraine on the innovation and investment factors, and make
forecast of social and economic development of the country for a short period of time.
3. Methodology
Using the production function method, there was carried out the modeling of GDP (Y) volume
with the consideration of the amount of introduced new technologies, technological processes, total
costs of the enterprises, introducing innovations and volume of financing of the research and
development works.
In the economic researches the production function is mostly used in the form of single equation,
where the output components are united into a single scalar value (y), and the amount of different
production resources (factors хі) is reduced to minimum that gives the opportunity to calculate the
functions parameters.
y = f(x1, x2 ,..., xn ). (1)
In scientific works [16, 19] the authors emphasize the importance of influence new technologies
and technological processes, total costs of the enterprises introducing innovations, financing of the
research and development works on economic growth and GDP.
In [17] the relationship between the number of completed research and development works,
research and development works volume and the number of the inventions used was studied.
Ramadani [20] found a relationship between the number of granted patents, the number of
organizations conducting the research studies and explorations and the number of inventions used.
Morris [21] found a relationship between research and development works volume, number of
completed research and development works and financing of research and development works.
Kovchuha [22] investigated the impact of fixed investment, volume of sold innovative products,
number of completed research and development works on the total costs of the enterprises introducing
innovations
We took into account the research of scientists and developed an original model. To build the
econometric model there was carried out the statistic information analysis of Ukraine within the
period from 2005 to 2019. In the result of the carried out analysis there was received the following
econometric dependence:
Y bx3 ln x 4 ln x9 , (2)
x4 a4 a5 x1 a6 x12 a7 x2 a8 x22 a9 x10 a10x10
2
,
x8 a16 a17 x5 a18x7 , x9 a1 a2 x6 a3 x10
x10 a11 a12x6 a13x62 a14x8 a15x82 ,
where Y – GDP volume; x1 – fixed investment, mln. UAH; x2 – volume of sold innovative products,
mln., UAH; x3 – applied new technologies, technological processes, units; x4 – total costs of the
enterprises introducing innovations, mln. UAH; x5 – number of granted patents in Ukraine, units; x6 –
research and development works volume, mln. UAH; x7 – number of organizations conducting the
research studies and explorations, units; x8 – number of the inventions used, units; x9 – financing of
the research and development works, mln. UAH; x10 – number of completed research and
development works, units.
Other multifactor model values (b,, and ) are the evaluating parameters. The model parameters
are determined according to the statistics data.
The forecast of the main innovation factors of Ukraine was made for a short-term period by means
of Box-Jenkins method (ARIMA) with the use of Statistica. In ARIMA model, the level of the time
series yt is defined as a calculated amount of its previous values and residual values ut – current and
previous. The applied modeling method let provide adequate representation of the object, significance
of the estimated models parameters and reliable results. All the built models are adequate, significant
and are characterized by high level of statistic performance.
4. Empirical results
Analyzing the behavior of autocorrelation and partial autocorrelation functions there may be drawn
a conclusion that ARIMA (0,0,1) is the best suited model for the range of fixed investments, for the
range of granted patents - ARIMA(1,0,0), for the range of sold innovative products - IMA(1,0,0), for
the range of implemented new technologies and technological processes - ARIMA(0,0,1), for the range
of scientific and technological work volume - ARIMA(1,0,0), for the range of number of organizations
completing the scientific researches and explorations - ARIMA(0,0,1).
The results of selected factors forecasts are shown in Tables 1-6.
Table 1
Forecast results and their confidential intervals for observations over fixed investments factor
Forecasts; Model:(0,0,1) Seasonal lag: 12
CaseNo. Input: X1
Start of origin: 1 End of origin: 15
Forecast Lower Upper
20 43083,53 23801,03 77987,82
21 42834,16 20960,38 87534,94
22 42834,16 20960,38 87534,94
Table 2
Forecast results and their confidential intervals for observations over volume of sold innovation
production factor
Forecasts; Model:(1,0,0) Seasonal lag: 12
CaseNo. Input: X2
Start of origin: 1 End of origin: 15
Forecast Lower Upper Std.Err.
20 5406,473 -1111,49 11924,44 3700,633
21 5173,311 -3847,91 14194,53 5121,878
22 4950,203 -5866,36 15766,77 6141,204
Table 3
Forecast results and their confidential intervals for observations over new technologies,
technological processes factor
Forecasts; Model:(0,0,1) Seasonal lag: 12
CaseNo. (Spreadsheet1)
Input: X3
Start of origin: 1 End of origin: 15
Forecast Lower Upper Std.Err.
20 1749,652 1171,701 2327,604 326,3540
21 1663,608 1012,549 2314,668 367,6361
22 1663,608 1012,549 2314,668 367,6361
Table 4
Forecast results and their confidential intervals for observations over research and development
works volume factor
Forecasts; Model:(1,0,0) Seasonal lag: 12
CaseNo. (Spreadsheet1)
Input: X6
Start of origin: 1 End of origin: 15
Forecast Lower Upper Std.Err.
20 2396,906 1850,795 2943,018 308,3750
21 2383,621 1617,635 3149,606 432,5319
22 2370,554 1440,068 3301,040 525,4214
Table 5
Forecast results and their confidential intervals for observations over number of granted patents
factor
Forecasts; Model:(1,0,0) Seasonal lag: 12
CaseNo. (Spreadsheet1)
Input: X5
Start of origin: 1 End of origin: 15
Forecast Lower Upper Std.Err.
20 2472,003 552,298 4391,707 1089,930
21 2360,293 -293,946 5014,531 1506,968
22 2253,631 -925,662 5432,924 1805,073
Table 6
Forecast results and their confidential intervals for observations over number of organizations
conducting the research studies and explorations factor
Forecasts; Model:(0,1,1) Seasonal lag: 12
CaseNo. (Spreadsheet1)
Input: X7
Start of origin: 1 End of origin: 15
Forecast Lower Upper Std.Err.
20 895,4 836,1745 954,6800 33,24536
21 860,9 738,2933 983,4896 68,78697
22 826,4 663,4148 989,2965 91,42231
The forecast made for 3- year period (2020-2022) is shown in Figures 1-3.
а) b)
Figure 1: Graph of variance of the fixed investments with the forecast made (а) and number of patents
granted in Ukraine (b)
а) b)
Figure 2: Graph of variance of the volume of sold innovation production with the forecast made (а) and
new technologies, technological processes (b)
а) b)
Figure 3: Graph of variance of the research and development works volume with the forecast made (а)
and number of organizations conducting the research studies and explorations (b)
In the course of investigation there was received an optimistic, a pessimistic, and an expected (the
most probable) forecast. According to the expected forecast:
The results obtained my means of ARIMA (0,0,1) model showed that the fixed investments in
2020 will be 43083,5 mln. UAH, in 2021-2122 the index will be 42834,2 mln. UAH.
The results obtained my means of ARIMA (1,0,0) model showed that the number of granted
patents in Ukraine will gradually decrease (in 2020 – 2472 patents, in 2021 – 2360 patents, and in 2022
– 2253 patents).
As for the amount of innovative products sold, the results obtained by means of ARIMA (1,0,0)
model showed that in 2020 this index will be 5406,5 mln. UAH, in 2021 – 5173,3 mln. UAH, and in
2022 – 4950,2 mln. UAH.
The results obtained my means of ARIMA (0,0,1) model showed that the number of the
implemented new technologies and technological processes in 2020 will be 1565,5 units, in 2021-2021 this
index will grow up to 1646,4 units.
The calculation results obtained my means ARIMA (1,0,0) model showed that volume of
scientific and technology works will gradually decrease (in 2020 – 2396,9 mln. UAH, in 2021 – 2383
mln. UAH, in 2022 – 2370 mln. UAH).
As for the amount of organizations, completing research activities and exploration then the results
obtained by means of ARIMA (0,0,1) model showed that index value will gradually decrease (in 2020 –
895 units, in 2021 – 860 units, in 2022 – 826 units).
Modeling of the following factors is the next exploration phase:
the financing volume of the research, scientific and technological works considering the influence
of the scientific and technological works volume and amount of completed research works and scientific
and technological works (Tables 7, 8 and Figure 4);
the total costs of the enterprises, introducing innovations considering the fixed investments
influence, amount of sold innovative products and amount of complete research, scientific and
technological works (Tables 9, 10 and Figure 5);
the amount of completed research, scientific and technological works considering the
influence of applied inventions amount and volume of scientific and technological works (Tables 11,
12 and Figure 6);
the amount of inventions applied considering the influence of number of patents granted in
Ukraine and number of organizations, which accomplish the research studies and explorations (Tables
13, 14 and Figure 7).
Using the statistical data, there was constructed a correlation matrix of the above-mentioned
factors (the financing volume of the research, scientific and technological works; total costs of the
enterprises, introducing innovations; the amount of completed research, scientific and technological
works; the number of applied inventions).
Table 7
Correlation matrix that characterizes the volume of financing factor of the research, scientific and
technological works
Correlations (Spreadsheet1)
Variable X6 X10 X9
X6 1,000000 0,568622 0,951451
X10 0,568622 1,000000 0,692699
X9 0,951451 0,692699 1,000000
Table 8
Conclusive results of the econometric model evaluation in regard to the volume of financing of the
research, scientific and technological works
Regression Summary for Dependent Variable: X9 (Spreadsheet1)
N=15 R= ,96915431 R?= ,93926008 Adjusted R?= ,92913676
F(2,12)=92,782 p<,00000 Std.Error of estimate: 110,53
Beta Std.Err. B Std.Err. t(12) p-level
Intercept 245,6791 180,0359 1,364612 0,197418
X6 0,823987 0,086488 0,6775 0,0711 9,527130 0,000001
X10 0,224163 0,086488 0,0096 0,0037 2,591820 0,023579
Analyzing the correlation matrix (Table 7), there was detected the influence of each factor on
volume of financing sources of the research, scientific and technological works. The previous analysis
of the statistical ensemble gave the opportunity to draw the conclusion concerning its uniformity and
closeness of the empiric distribution to the theoretical one, as well as, concerning absence of
multicollinearity. Thus, for finding factor model parameters there was used the least square method.
The results of the econometric model construction are shown in Table 8.
On the basis of the achieved parameters the factor model will appear as follows:
x9 245,7 0,6775x6 0,0096x10 (3)
The comparison of calculated value of Student’s test with the table one confirms the statistical
significance of the model coefficients. The value of the multiplying determination coefficients gives
the opportunity to draw a conclusion regarding the sufficient determination of the resultative feature
x9 in the model with factor features x6 and x10. The estimated value of the multiplying correlation
coefficient for the assumed model equals to R = 0,97 that shows a close connection between the factor
and resulting features. The calculated model residues are uncorrelated and approximately distributed
under the normal law that also proves the models adequacy. According to F- criteria (F = 92,8) with
about Р=0,95 reliability the econometric model may be considered adequate to the experimental data
and based on the assumed model there may be carried out an economic analysis and found a forecast
value.
The analysis of Beta coefficients and partial correlation coefficients shows that the volume of the
scientific and technological works has the greatest influence on the increase of sold innovative
products volume.
Based on the econometric model there was made a forecast of influence of scientific and
technological works volume and amount of completed research, scientific and technological works on
the volume of financing sources of the research, scientific and technological works (Figure 4).
Figure 4: Dynamics of the volume of financing of the research, scientific and technological works
The achieved results have showed that financing of the research, scientific and technological works will
gradually decrease in future. At present, the government financing of scientific and technological activity in
Ukraine is bound with the development of ІІІ and ІV technologic modes and promotes economic model
construction that does not need any innovations and does not form any impulses for the investments to
human capital assets development [23]. The increase of government financing of the scientific
researches will make no sense if the negative trends of the scientific and technological works self-
closing continue developing on the level of creation and improvement of technologies increasing their
disconnection from market demands.
Analyzing the correlation matrix (Table 9), there may be seen the influence of each factor on the total
costs of the enterprises, introducing innovations. The previous analysis of the specific statistical ensemble
gave the opportunity to conclude about its uniformity and closeness of the empiric distribution to the
theoretic one, as well as about its multicollinearity. Thus, to find the factor model parameters there was
used a ridge regression method.
Table 9
Correlation matrix that characterizes the factor of the total costs of the enterprises introducing
innovations
Correlations (Spreadsheet1)
Variable X1 X2 X10 X4
X1 1,000000 0,700105 0,614317 0,894897
X2 0,700105 1,000000 0,627604 0,873504
X10 0,614317 0,627604 1,000000 0,663062
X4 0,894897 0,873504 0,663062 1,000000
Ridge-value of the regression parameters vector
Aˆ ( X T X I ) 1 X T Y , (4)
where [ ; ] (usually, = 0,1; = 0,4).
Standard error of k ridge-value of the regression parameter equals to the square root of the
corresponding diagonal element of the covariance matrix vector value:
A u ( X T X I ) 1 , (5)
n
(Y Yˆ )
2
uT u
ˆ u2 i 1 .
n m 1 n m 1
The results of econometric model construction are shown in Table 10.
Table 10
Conclusive results of econometric model evaluation
Ridge Regression Summary for Dependent Variable: X4 (Spreadsheet1)
N=15 l=,30000 R= ,88986086 R?= ,79185234 Adjusted R?= ,73508480
F(3,11)=13,949 p<,00046 Std.Error of estimate: 495,25
Beta Std.Err. B Std.Err. t(11) p-level
Intercept 753,3908 677,0142 1,112814 0,289516
X10 0,154342 0,140927 0,0154 0,0141 1,095188 0,296835
x1^2 0,414703 0,163657 0,000000192 0,000000076 2,533979 0,027776
X2^2 0,343377 0,164433 0,00000526 0,0000025 2,088242 0,060825
Based on the achieved parameters the factor model will appear as follows:
x4 753,4 1,9 107 x12 5,26 106 x22 0,0154x10 . (6)
The comparison of calculated value of Student’s test with the table one confirms the statistical
significance of the model coefficients. The value of the multiplying determination coefficients gives
the opportunity to draw a conclusion regarding the sufficient determination of the resultative feature
x4 in the model with factor features x1, x2 and x10. The estimated value of the multiplying correlation
coefficient for the assumed model equals to R = 0,89 that shows a close connection between the factor
and resulting features. The calculated model residues are uncorrelated and approximately distributed
under the normal law that also proves the models adequacy. According to F-criteria (F = 13,95) with
about Р=0,95 reliability the econometric model may be considered adequate to the experimental data
and based on the assumed model there may be carried out an economic analysis and found a forecast
value. The analysis of Beta-coefficients and partial correlation coefficients shows that the fixed
investment factor has the greatest influence on the increase of total costs of the enterprises,
introducing innovations.
Based on the econometric model there will be made a forecast of influence of the fixed
investments, the volume of sold innovative products and amount of completed research, scientific and
technological works on the total costs of the enterprises, introducing innovations (Figure 5).
It is worthwhile noting that over the long-term the innovations financing that is mostly realized at
the sole cost and expense of the enterprise will decrease. At the same time, the existing financial
credit system is unable to provide the enterprises with the economic cost credit resources in sufficient
quantity. Besides, low ability to meet payments will have an influence over it as well.
Figure 5: Dynamics of the total costs of enterprises, introducing innovations
Analyzing the correlation matrix (Table 11), there may be seen the influence of each factor on the
amount of completed research, scientific and technological works.
Table 11
Correlation matrix that characterizes the factor of the amount of completed research, scientific and
technological works
Correlations (Spreadsheet1)
Variable X6 X8 X10
X6 1,000000 -0,109945 0,568622
X8 -0,109945 1,000000 0,654858
X10 0,568622 0,654858 1,000000
The previous analysis of the statistical ensemble allowed concluding about its uniformity and
closeness of the empiric distribution to the theoretical one as well as about absence of
multicolleniarity. Thus, to find the factor model parameters there is used the least square method.
The results of econometric model construction are shown in Table 12.
Table 12
Conclusive results of the econometric model evaluation
Regression Summary for Dependent Variable: X10
N=15 (Spreadsheet1)
R= ,90734404 R?= ,82327322 Adjusted R?= ,79381875
F(2,12)=27,951 p<,00003 Std.Error of estimate: 4379,7
Beta Std.Err. B Std.Err. t(12) p-level
Intercept 23772,61 4314,374 5,510094 0,000134
X8^2 0,753380 0,122803 0,0017 0,00028 6,134843 0,000051
X6^2 0,633986 0,122803 0,0025 0,00049 5,162609 0,000236
According to the received parameters the factor model will appear as follows:
x10 23772 0,0025x 62 0017x82 , (7)
The comparison of calculated value of Student’s test with the table one confirms the statistical
significance of the model coefficients. The value of the multiplying determination coefficients gives
the opportunity to draw a conclusion regarding the sufficient determination of the resultative feature
x10 in the model with factor features x6 and x8. The estimated value of the multiplying correlation
coefficient for the assumed model equals to R = 0,91 that shows a close connection between the factor
and resulting features. The calculated model residues are uncorrelated and approximately distributed
under the normal law that also proves the models adequacy. According to F-criteria (F = 28) with
about Р=0,95 reliability the econometric model may be considered adequate to the experimental data
and based on the assumed model there may be carried out an economic analysis and found a forecast
value. The analysis of Beta-coefficients and partial correlation coefficients shows that the number of the
inventions used factor and the research and development works volume factor has the greatest
influence on the increase of number of completed research and development works.
Based on the econometric model there will be made a forecast of influence of the number of the
inventions used, the research and development works volume on the number of completed research
and development works (Figure 6). It is worth mentioning that the indices of effectiveness of the use
of scientific potential in Ukraine, which are manifested in the amount of completed research,
scientific and technological works are still low and actually are not going to be increased in the long
view. Not very positive dynamics of the total amount of completed research, scientific and
technological works is caused by decrease of quantitative indices related to the results of scientific
potential use, gradual decrease of relative share and the innovative work quality, enforcement of
“compilation” of the scientific and research works, absence of demand for them in the national
production, noncompliance with market demands and world trends.
Figure 6: Dynamics of the amount of completed research and development works
Besides, the issue of the research works commercialization is not always the major priority of the
scientists. The possibility of real implementation of the innovations is perceived as the remote and
unreal prospect that significantly decrease the practical application of the research, scientific and
technological works.
Table 13
Correlation matrix that characterizes the factor of the number of inventions used
Correlations (Spreadsheet1)
Variable X5 X7 X8
X5 1,000000 0,273433 0,541520
X7 0,273433 1,000000 0,699607
X8 0,541520 0,699607 1,000000
The results of the econometric model construction are shown in Table 14.
Analyzing the correlation matrix (Table 13), there may be seen the influence of each factor on the
amount of realized inventions. The previous analysis of the statistical ensemble provided with the
opportunity to conclude about its uniformity and closeness of the empiric distribution to the
theoretical one as well as about absence of multicollinearity. Thus, to find the factor model parameters
there is used the least square method.
Table 14
Conclusive results of the econometric model evaluation
Regression Summary for Dependent Variable: X8 (Spreadsheet1)
N=15 R= ,78868113 R?= ,62201792 Adjusted R?= ,55902091
F(2,12)=9,8738 p<,00292 Std.Error of estimate: 493,11
Beta Std.Err. B Std.Err. t(12) p-level
Intercept -2291,72 1183,086 -1,93707 0,076633
X5 0,378525 0,184510 0,35 0,172 2,05152 0,062704
X7 0,596105 0,184510 2,88 0,892 3,23075 0,007209
According to the received parameters the factor model will appear as follows:
x8 -2291,7 0,35x5 2,88x7 , (8)
The comparison of calculated value of Student’s test with the table one confirms the statistical
significance of the model coefficients. The value of the multiplying determination coefficients gives
the opportunity to draw a conclusion regarding the sufficient determination of the resultative feature
x8 in the model with factor features x5 and x7. The estimated value of the multiplying correlation
coefficient for the assumed model equals to R = 0,79 that shows a close connection between the factor
and resulting features. The calculated model residues are uncorrelated and approximately distributed
under the normal law that also proves the models adequacy. According to F-criteria (F = 9,9) with
about Р=0,95 reliability the econometric model may be considered adequate to the experimental data
and based on the assumed model there may be carried out an economic analysis and found a forecast
value. The analysis of Beta-coefficients and partial correlation coefficients shows the factor of the
number of organizations conducting scientific and research works has the greatest influence on the
increase of realized inventions amount.
On the basis of econometric model there was made a forecast of influence of the number of the
granted patents in Ukraine and number of organizations conducting the research works and
explorations on the amount of realized inventions (Figure 7).
Figure 7: Dynamics of the realized inventions amount
In Ukraine the amount of realized inventions decreases every year. As may be seen from the
Figure the number of the realized inventions will decrease year after year. According to the realized
inventions per 10 thousand people, Ukraine by 12 times remains short of the average level of EU,
however, at the same time by 1.7 times anticipates it in the number of scientists per 10 thousand
working people [23].
In spite of critical economy situation, the economic entities have to use and realize innovations,
inventions, however, the number of such organizations remains insignificant.
To forecast GDP, using the offered econometric model (2), it is necessary to make a forecast for all
the model factors that characterize the scientific and innovative activity of the country. The
production function (1) reduces to linearity by means of logarithmation:
y = lnb + ln x3 + ln ln x4 + ln ln x9, (9)
There was constructed the correlation matrix of the investigated factors. Having analyzed the
correlation matrix (Table 15) there may be seen the influence of each factor on GDP. The previous
analysis of the statistical ensemble gave the opportunity to conclude about its uniformity and
closeness of the empiric distribution to the theoretical one as well as about multicollinearity existence.
Thus, to find the factor model parameters there is used a ridge regression method.
Table 15
GDP volume correlation matrix
Correlations (Spreadsheet2)
Variable x3* lnx4* lnx9* y*
x3* 1,000000 0,277653 0,448384 0,581033
lnx4* 0,277653 1,000000 0,784670 0,636863
lnx9* 0,448384 0,784670 1,000000 0,808032
y* 0,581033 0,636863 0,808032 1,000000
The results of econometric model construction are shown in Table 16.
According to the received parameters, the GDP determination factor model will appear as follows:
Y 0,0036x30,4 ln x4 1,4 ln x9 5,9 . (10)
Table 16
GDP volume correlation matrix
Ridge Regression Summary for Dependent Variable: y*
N=15 (Spreadsheet2)
l=,40000 R= ,76272197 R?= ,58174480 Adjusted R?= ,46767519
F(3,11)=5,0999 p<,01876 Std.Error of estimate: ,25975
Beta Std.Err. B Std.Err. t(11) p-level
Intercept -5,63098 5,123869 -1,09897 0,295252
x3* 0,252609 0,174015 0,40605 0,279715 1,45165 0,174516
lnx4* 0,184673 0,199052 1,42546 1,536451 0,92776 0,373441
lnx9* 0,392756 0,205946 5,91796 3,103152 1,90708 0,082950
The comparison of calculated value of Student’s test with the table one confirms the statistical
significance of the model coefficients. The value of the multiplying determination coefficients gives
the opportunity to draw a conclusion regarding the sufficient determination of the resultative feature y
in the model with factor features x3, x4 and x9. The estimated value of the multiplying correlation
coefficient for the assumed model equals to R = 0,76 that shows a close connection between the factor
and resulting features. The calculated model residues are uncorrelated and approximately distributed
under the normal law that also proves the models adequacy. According to F-criteria (F = 5,1) with
about Р=0,95 reliability the econometric model may be considered adequate to the experimental data
and based on the assumed model there may be carried out an economic analysis and found a forecast
value.
The derived estimates allow using the model for GDP forecast (Figure 8). The primary task of the
model for GDP forecast is to provide with the basic material for further researches, to serve as a tool
for the effective state strategic management and formation of the strategies and programs of social
and economic development at different levels of national economy. As is seen from the above-
mentioned, GDP forecast value will gradually decrease over the long term. It should be mentioned
that the developed countries pay much attention to the development of technological and innovative
activity. Unfortunately, in Ukraine the factors that influence GDP growth are neglected.
The increase of investment factor in basic capital by 1% will lead to 0,1% GDP growth. The same
result can be achieved with the increase of the sold innovative products volume. Growth of the
introduced new technologies and technological processes amount up to 1% will cause 0,4 % GDP
gross. At the same time, the increase of research and technological works scope will lead to 0,7 %
GDP gross. In the course of the calculation process there has been found that GDP growth of Ukraine
can be achieved with the support for research, technological and innovative activities, in particular,
with the growth of research and technological works scope, introduction of progressive technical
processes, creation of the new technologies and putting them into production.
Figure 8: Ukrainian GDP forecast value
All these requires the development and realization of the preventive measures, and improvement of
state programs of social and economic development. The effective investments in basic capital and
increase of sold innovative products volume will also cause GDP growth.
The result of this study consistently with [24] where the investment, research and development
costs has a positive impact on the GDP but this study covers more innovation factors and uses the
combined method of modeling for forecasting GDP.
Ukraine realizes opportunities in innovative development at a low level. This is especially true for
the commercialization of innovations in the field of protection of intellectual property rights. The
innovative way of development of Ukraine's economy turned out to be rather declarative. In fact,
Ukraine is still implementing a partially resource model without high-tech production and an
intellectual-donor model, from which the production stage has been removed.
These models have a low level of efficiency in the strategic perspective, lead to depletion of the
country's resources, leakage of factors of production of the national economy abroad and make it
impossible to ensure adequate indicators of the level of population welfare. The consequence of the
implementation of such models is an economic downturn.
The most effective for Ukraine is the innovation model, which provides for the transformation of
money for research into knowledge, the transformation of knowledge into the skills of employees and
innovation, the transformation of innovation into a commodity and the receipt of money.
5. Conclusion
These findings may provide some insight as to which innovation and investment factors are
involved with social and economic development of the country and formation of GDP. All the more
significant is the studies which are reflect the innovation and investment changes, analyses and
forecasts of the public management, economic and social policies of Ukraine. By means of the
econometric model, there was established that forecast values of GDP volume over the long term will
gradually decrease. It was found out that the highest priority factors of a competitiveness according to
the innovative component of Ukraine are the amount of scientific and technological works, a number
of innovative technologies and technological processes introduced, fixed investments, a number of
innovative products sold. These are the key factors the possibility of social and economic
development of Ukraine depends on. The obtained forecast values of GDP volume give the
opportunity to form the corresponding programs of social and economic development of the country
for the short-term period and can help the public authorities to develop a well-balanced and effective
policy of social and economic development. As long as on such grounds there should be taken
management decisions of the corresponding administrative bodies regarding the development of the
innovative activity in the country.
6. References
[1] J. Kleinberg, J. Ludwig, S. Mullainathan, Z. Obermeyer, Prediction Policy Problems, in:
American Economic Review, 105(5), 491-95 (2015).
[2] N. Yukhneva, O. Mokerova, P. Kukhtin, The regulatory role of the state strategic management in
the development of the regional entrepreneurial sphere, in: International Science Conference
SPbWOSCE-2016 “SMART City”, MATEC Web of Conferences, 106, 08089. URL:
https://doi.org/doi:10.1051/matecconf/201710608089 (2017).
[3] J. Edler, J. Fagerberg, Innovation policy: what, why, and how, in: Oxford Review of Economic
Policy, 33(1), 2-23 (2017).
[4] G. Martín-de Castro, M. Delgado-Verde, J. E. Navas-López, J. Cruz-González, The moderating
role of innovation culture in the relationship between knowledge assets and product innovation,
in: Technological Forecasting and Social Change, 80(2), 351-363 (2013).
[5] K. Łobacz, P. Głodek, Development of Competitive Advantage of Small Innovative Firm – How
to Model Business Advice Influence within the Process, in: Procedia Economics and Finance, 23,
487-494 (2015).
[6] R. Ciegis, A. Dilius, K. Andriuskevicius, An Assessment of Impact of Income Inequality on
Sustainable Economic Growth in the Context of Saving, in: Engineering Economics, 28(3), 232-239
(2017).
[7] P. Hlavacek, B. Bal-Domanska, Impact of Foreign Direct Investment on Economic Growth in
Central European Countries, in: Engineering Economics, 27(3), 294-303 (2016).
[8] Sh. Y. Wu, J. H. Tang, E. S. Lin, The impact of government expenditure on economic growth:
How sensitive to the level of development, in: Journal of Policy Modeling, 32(6), 804-817
(2010).
[9] A. Stundziene, V. Barkauskas, V. Giziene, The Leading Indicators of the Economic Cycles in
Lithuania, in: Engineering Economics, 28(3), 280-289 (2017).
[10] G. Grossman, E. Helpman, Innovation and Growth in the Global Economy. Cambridge MA:
MIT Press (1991).
[11] A. Bucci, On scale effects, market power and growth when human and technological capital are
complements, in: International Review of Economics and Business, 48(1), 21-47 (2001).
[12] J. Koo, How to analyze the regional economy with occupation data, in: Economic Development
Quarterly, 19(4), 356-372 (2005).
[13] А. Kacprzyk, W. Doryń, Innovation and economic growth in old and new member states of the
European Union, in: Engineering Economics, 30(1), 1724-1742 (2017).
[14] T. K. Das, Cross-Sectional Views of GDP Growth in the Light of Innovations, in: SSRN
Electronic Journal, December 13. URL: http://dx.doi.org/10.2139/ssrn.3503386 (2019).
[15] G. M. P. Swann, M. Prevezer, K. D. Stout, The Dynamics of Industrial Clustering: International
Comparisons in Computing and Biotechnology. Oxford: Oxford University Press (1998).
[16] L. Ding, F. Hou, X. Zhang, G. Li, S. Wang, W. Sun, The Factors Affecting GDP Growth, in:
Learning and education, 9(3), 61-64 (2020).
[17] S. Sokolov-Mladenović, S. Cvetanović, I. Mladenović, R&D expenditure and economic growth:
EU28 evidence for the period 2002–2012, in: Economic Research-Ekonomska Istraživanja,
29(1), 1005-1020 (2016).
[18] H. Lofgren, R. L. Harris, S. Robinson, A standard computable general equilibrium (CGE) model
in GAMS. Microcomputers in policy research. Washington: International Food Policy Research
Institute (2002).
[19] B. Krstić, T. Stanišić, V. Radivojević, Uticaj faktora inovativnosti na konkurentnost zemalja, in:
EUIndustrija, 44(2), 101-116 (2016).
[20] V. Ramadani, et al, Product Innovation and Firm Performance in Transition Economies: A Multi-
Stage Estimation Approach, in: Technological Forecasting and Social Change, 140, 271-280.
URL: https://doi.org/10.1016/j.techfore.2018.12.010 (2019).
[21] D. M. Morris, Innovation and Productivity among Heterogeneous Firms, in: Research Policy,
47(10), 1918-1932. URL: https://doi.org/10.1016/j.respol.2018.07.003 (2018).
[22] L. Kovchuha, Evaluating the Relationship between Investment in Innovation and the Volume of
Sold Innovative Products in the Industry of Ukraine, in: Virtual Economics, 3(3), 67-79. URL:
https://doi.org/10.34021/ve.2020.03.03(4) (2020).
[23] Z. Yurynets, R. Yurynets, T. Gutor, Game theory model for the development of optimal strategy
towards innovative products manufacturing at the enterprise, in: Problems and Perspectives in
Management, 15(3), 285-294 (2017).
[24] Z. Yurynets, Forecasting model and assessment of the innovative and scientific-technical policy
of Ukraine in the sphere of innovative economy formation, in: Investment Management and
Financial Innovations, 13(2), 16-23 (2016).