The study is devoted to solving the theoretical and applied problem of assessment of the investment and innovation security status of Ukraine based on the modeling of the Integral index of investment and innovation security and on identifying the interrelationships between different indicators characterizing innovation and investment spheres of Ukraine. The Integral (composite) index model was tested based on actual data from Ukraine for the period 2014-2022 using methods of data normalization and determination of characteristic values of the factor variables based on international experience and analysis of national regulatory restrictions for relevant indicators. Integration of factor variables into the Integral index estimates was carried out based on weighting coefficients calculated both based on expert evaluation method and alternative statistical methods: correlation analysis, pairwise correlation between GDP growth rates and every factor variable, as well as the principal component method. It has been proven that when identifying weak associations between indicators of innovative development and GDP dynamics, determining the weights of indicators based on their correlation with GDP growth rates leads to an overestimation of the Integral index of investment and innovation security. The proposed statistical methods for calculating the weighting coefficients of the variables in the model do not lead to distortion of trends in investment and innovation security, and therefore ensure obtaining consistent and, in contrast to the expert evaluation method, unbiased estimates of the status of investment and innovation security of the country. The results obtained are important in the context of solving strategic problems to prevent risks for the investment and innovation security of Ukraine and forming an innovative foundation for the revival of Ukraine's economy.
Russian aggressive war against Ukraine, complete with cyber-attacks and measles attacks on infrastructure, following the COVID19 pandemic, has dramatically changed the security situation and—consequently—the approaches to ensuring security in many countries [1]. The European Commission’s experts note that the new European strategy for economic security has to guarantee that economic interests and security interests will reinforce each other. In addition, ensuring the country’s economic security and improving its’ economic sustainability requires increased technological possibilities [2, 3].
NATO Heads of State and Government approved the new NATO strategic concept (in Madrid on June 29, 2022) [4], which is aimed at solving the tasks of state security, defense, crisis management, and crisis prevention. Within the framework of the main objectives of the concept, the universal importance of investment in technological innovation is policies and indicators. particularly highlighted, considering that new technologies are becoming key areas of both global competition and battlefield success. In OECD countries, national science, technology, and innovation strategies have become the main pillars of
post-crisis economic growth strategies [5].
Active use of modern economic growth factors, that ensure the formation of an innovative basis for long-term economic development, is an important prerequisite for the successful post-war recovery the economic security status to identify possible challenges and threats and to use the evaluation results to formulate the main directions and measures of economic policy.
Theoretical aspects of the formation of an institutional system as a factor of innovative development, as well as risk factors in the areas of innovation and investment activity and possible threats to economic recovery, are studied in the monograph by Iefymenko, T. [8]. The article by Iefymenko, T., Lovinska, L., & Kucheriava, М. [9] provides suggestions on the establishment of an information and analytical database for strategic decision-making under martial law. The work of K. Brown and coauthors of models for assessing economic security status and calculation of the relevant integral indices [11–15]. Freudenberg, M. [16] focuses on the peculiarities of the application of different methods to the construction of composite 3. Research Methodology The state of investment and innovation security is among the important prerequisites for economic growth and enhancing the international competitiveness of countries. This component of economic security acquires particular importance when solving the problems of eliminating the consequences of military aggression and forming an innovative foundation for the post-war economic recovery of Ukraine [17].
Analysis of investment and innovation security as a complex integrated sphere of economic activity requires the use of generalizing characteristics of its status in different periods. As evidenced by widespread international practice, quite often the solution to such problems for various spheres of the economy, society, or the environment is carried out using
complex indicators integral indices that serve as generalizing characteristics phenomena
of (for certain example, processes
Environmental Sustainability Index).
The Integral index of investment and innovation security, as well as indices for other areas of economic security, is calculated using formula (1) [18]:
= ∑ =1 , where I is an Integral index of investment and innovation security, coefficient, аj weighting coefficients determining the degree of contribution of the jth indicator of investment and innovation security to the Integral index, ∑aj = 1, n number of indicators of investment and innovation security, yj normalized value of the jth indicator of investment and innovation security, coefficient, 0≤ yj ≤1.
Modeling of the Integral index includes the following steps [18]: • Detection of a
set of indicators characterizing the status of investment and innovation security. or or (1) • Normalization of investment and innovation security indicators values (yj) based on the determination of their characteristic values. • Calculation of the indicators’ weighting coefficients (аj). • Assessment of the Integral index of investment and innovation security (I). 3.1. Detection of Initial Indicators and
Formation of a Set [x1, x2,..., xn] The first step of modeling involves detecting— based on theoretical, substantive considerations, the results of generalizing the experience of different countries and analyzing the multicollinearity of initial indicators—the most informative indicators for characterizing the investment and innovation sphere of Ukraine.
According to the Economic Security Strategy of Ukraine for the period up to 2025, the set of indicators of investment and innovation security includes 7 variables: • Net increase in foreign direct investment, percent of gross domestic product. • Gross fixed capital formation, percent of gross domestic product. • Industrial enterprises that introduced innovations (products and/or technological processes), in the total number of industrial enterprises, percent. • Innovative industrial products (goods, services) sold in the total amount of industrial products (goods, services) sold, percent. • Research and development costs (hereinafter referred to as R&D) are funded by the state budget, percent of gross domestic product. • R&D expenditures in gross domestic product, percent. • Ukraine’s rank in the Global Innovation
Index ranking.
At the same time, in our opinion, these indicators will not provide a comprehensive vision of the status and threats of the investment and innovation spheres. Based on the results of the analysis of international innovation indices, we consider it reasonable to supplement the set of investment and innovation security indicators with two variables: • Loans provided to other non-financial corporations as a share of gross domestic product; given that lending to enterprises is an important prerequisite for increasing their financial capacity and investment and, accordingly, strengthening the investment security of Ukraine. • The exports-to-imports ratio of the royalties, licensing services, computer and information services, D&D, and services in architectural, engineering, and other technical industries. This indicator characterizes the level of technological independence of the country. Technological dependence, especially on one or two countries of the world, is a serious risk for Ukraine since it leads to increased investment dependence on imports and inhibition of innovative development.
It should also be noted that the indicator “Ukraine’s rank in the Global Innovation Index ranking,” which is included in the set of indicators of investment and innovation security according to the Economic Security Strategy of Ukraine for the period up to 2025, describes not only the achievements or failures in Ukraine but also in other countries. Accordingly, Ukraine’s rank could be improved both due to the achievements in Ukraine and because of the worsening situation in other sample countries. Therefore, further analysis was carried out both with this indicator (i.e., for 9 indicators) and without it (for 8 indicators).
The full list of the set of indicators and their values is shown in Table 1. Notes: x1—R&D expenditures, % of GDP.
x2—R&D funded by the State budget, % of GDP.
x3—industrial enterprises that introduced innovations in the total number of industrial enterprises, %.
x4—innovative industrial products (goods, services) sold in the total amount of industrial products (goods, services) sold, %.
x5—the exports-to-imports ratio of the royalties, licensing services, computer and information services, D&D, and services in architectural, engineering, and other technical industries.
x6—gross fixed capital formation, % of GDP. x7—foreign direct investment to Ukraine, % of GDP.
x8—loans provided to other non-financial corporations, % of GDP.
x9—Ukraine’s rank in the Global Innovation Index ranking.
Correlation analysis of a set of 9 indicators (Table 2) shows that the Pearson correlation coefficient exceeds 0.8, which indicates collinearity [20] only between such indicators: R&D expenditures, % of GDP (x1) and loans provided to other non-financial corporations, % of GDP (x8), R&D funded by the State budget, % of GDP (x2) and innovative industrial products (goods, services) sold in total amount of industrial products (goods, services) sold, % (x4). If a significant pairwise correlation is identified between indicators, that are important and without which the assessment of the security status would be incomplete, they are kept in the set of indicators of investment and innovation security, but further—in particular, on the stage of expert evaluation—they are given less weight (аj). 3.2. Determination of the Indicator's
Characteristic Values The detected indicators that characterize the investment and innovation sphere have different units of measurement: % of GDP (x1, x2, x6, x7, x8), specific weight or share of the total value (x3, x4), and the rank (x9) (Table 2). Therefore, their aggregation requires a transition to the unified measurement scale, that is, normalization, when a vector of detected indicators [x1, x2,..., xn] is replaced by a vector of normalized values [y1, y2,..., yn] in such a way as to bring them to common scale without distorting differences in value ranges and without loss of information. To normalize indicators for assessing investment and innovation security, characteristic values are used (optimal, satisfactory, unsatisfactory, dangerous, critical), since this makes it possible to identify situations that impede the normal functioning of the investment and innovation sector of the national economy and lead to the formation of negative or even destructive trends in its development. A high degree of security is achieved when all indicators have optimal values.
If an increase in the indicator value entails an increase in the Integral index, it is a stimulant, otherwise, it is a de-stimulant. For stimulating indicators, the designation “l(lower)” is used (for example, xoptl), for destimulating indicators, the designation “u(upper)” is used (for example, xoptu).
The justification of the characteristic values of the detected indicators that make up the set [x1, x2, ..., xn] was based on a synthesis of relevant international and domestic statistical information, in particular, regarding the smallest, average, and largest values of the corresponding indicators for EU countries (or OECD in case of lack in EU statistics); and also on determining the levels of criticality, optimality, and boundary limits for different indicators. To establish the optimal and critical values of the indicators, the dynamics of corresponding indicators in Ukraine as well as the legal regulation of their values were investigated. For example, The Law of Ukraine On Scientific and Scientific-Technical Activities (Article 48) stipulates that the state provides budgetary funding for scientific and scientifictechnical activities in the amount of at least values of indicators that have limited lower values (stimulant indicators) lie within the interval [хcritl, хoptl], and of indicators that have limited upper indicators)—within the interval [хoptu, xcritu].
The criticality/optimality intervals [хcritl, хoptl] and [хoptu, xcritu] were determined according to the scheme [18]: [xcrit, xdang), [xdang, xunsatisf), [xunsatisf, xsatisf), [xsatisf, xopt], where: • xcrit is a critical level of investment and innovation security equal to 0.2, or 20% of optimal value. • xdang is a dangerous level of investment investment and innovation security equal to 0.6, or 60% of optimal value. • xsatisf is a satisfactory level of investment and innovation security equal to 0.8, or 80% of optimal value. • xopt is an optimal level of investment and innovation security equal to 1.
An indicator’s value xj<xcrit characterizes the absolutely dangerous status lf x1 0.9 x2 0.5 x3 10 x4 7 x5 1 x6 12 x7 2 x8 12 • xunsatisf is an unsatisfactory level of normalized values included in the Integral index and Obtaining a Normalised Set [y1, y2,..., yn].
Normalization of indicators, that is, transition to the unified measurement scale where the best value of the indicator corresponds to 1, and the worst value—to 0, can be carried out by several methods. Though the minimax method is quite a common technique in this case, however, only the values of xmin and xmax obtained from statistical data are taken into account, but the characteristic values described above, which play a fundamentally important role in assessing the status of investment and innovation security, That is why the calculation of the indicators’ out by the provisions of the recommendations for was carried
specifically: calculating the level of economic security [18], where xj is the value of the jth indicator, yj is the normalized value of indicator xj.
If xj <xcritl, then yj = 0. • for the de-stimulant indicators: = {1, < 0,8 + 0,2 (
( 0,2 ( ( − ( − ) − − ) − ) , ) , − ) ( 0,2 ( &0,2 + 0,2 ( ≤ <
0,6 + ≤ <
0,4 + ) , − ) − ) , ≤ < ≤ < where xj is the value of the jth indicator, yj is the normalized value of indicator xj.
If xj >xcritu, then yj = 0.
Normalization of mixed-type indicators, when to a certain value it is a stimulant, and with a further increase it turns into a de-stimulant, requires a combination of calculations for stimulant indicators (for the left side, which interprets stimulation) and for de-stimulant indicators (for the right side, which interprets de-stimulation).
Within the interval of optimal values [xoptl, хoptu] the normalized value of a mixed-type indicator is equal to 1.
yj = 1 when xoptl≤xj≤xoptu.
Normalized indicators’ values necessary for the calculation of the Integral index of investment and innovation security (4) are are given in Table 4. 1) Based on correlation analysis [16] using the formula: =
∑ =1 ∑ =1
∑ =1 , where aj is the weighting coefficient, determining the degree of contribution of the jth indicator to investment and innovation security, rij is the correlation coefficient between the ith and jth indicators characterizing the status of investment and innovation security, j = (1, 2, 3, …, n). 2) Based on the
principal component method using the formula: =
∑ =1 ∗| |
∑ =1 ∑ =1 | | , where Сg is the contribution of the gth is component to the total variance of the set of investment and innovation security indicators that contains the jth indicator, Djg is factor loadings of the jth indicator in the gth component, l is the number of components that include the jth indicator. Their total variance must be at least 90%.
If multicollinearities exist, it is advisable to use the principal component method, which replaces significantly correlated indicators with the principal components, between which the correlation is much weaker.
3) Based on pairwise correlation between GDP growth rates and the values of investment and innovation indicators using the formula: =
∑ =1 , where kj is the correlation coefficient between the GDP growth rate and the jth indicator value.
This method was used because GDP growth increases the possibility of additional financing of scientific and innovative activities, and therefore improves investment and innovation security status.
4) Based on the expert evaluation method [18] using the formula: =
∑ =1 ∑ =1 ∑ =1 , (7) (8) where bjq is qth expert’s evaluation for the jth indicator, m is a number of experts.
The calculated weighting coefficients using different methods are given in Table 6. Weighting coefficients of the investment and innovation security indicators, calculated by different methods
For a set of 9 indicators Multiple
Pairwise correlation correlation to
GDP method
Principle component method
Expert evaluation method method evaluation method 3.5. Assessment of the Integral Index of Investment and Innovation Security (I) and Discussion of the Results The results of the assessment of the Integral index of investment and innovation security (formula (1)) using indicator weights calculated by different methods (formulas (5–8)) are presented in Fig. 1. (b) Figure 1: Dynamics of the Integral indexes of investment and innovation security of Ukraine assessed based on weighting coefficients calculated by different methods, for a set of 9 (a) and 8 (b) indicators, 2014–2022.
As the graphs show, the dynamic trends of the Integral index of investment and innovation security of Ukraine are close regardless of the calculating methods of indicators’ weighting coefficients. The estimates of the Integral index obtained from the results of the study reveal a significant deterioration in the investment and innovation security status of Ukraine in the period 2014–2022, and its rapid decline since 2018 regardless of the calculating methods of indicators’ weighting coefficients: 2.6 times for a set of 9 indicators (Fig. 1a) and 2.3–2.6 times for a set of 8 indicators (Fig. 1b).
Negative dynamics of the values of the Integral index of investment and innovation security are due to the deterioration in many of its components during 2014–2022. The most difficult situation was in the sphere of R&D financing in the economy as a whole (from various sources—x1) and from the State budget of Ukraine (x2). Since 2014, the values of these indicators have been at levels below critical (0.9% of GDP in terms of total relevant expenditures and 0.5% of GDP in terms of financing from the state budget). At the same time, total expenditure on R&D fell from 0.6% of GDP in 2014 to 0.4% in 2020, while the average for EU countries was 1.78% of GDP, and in Sweden exceeded 3.5% of GDP. In Ukraine’s neighboring EU countries, relevant expenditures ranged from 0.91% of GDP in Slovakia to 1.39% of GDP in Poland and about 2% of GDP in the Czech Republic and Slovenia [21].
The values of x3 indicator (innovative industrial products sold in total amount of industrial products sold, percent) were also below the critical level during 2014–2022, which did not exceed 2.5% (critical level is 7%), and in 2020 amounted to 1.9%, which is 6 times less than the average for EU countries (13%), and more than 20 times behind the corresponding figure for Ireland (42.4%) [22].
For many years now, the values of the x6 indicator (gross fixed capital formation) have been within the dangerous interval, and since 2017, the x8 indicator (loans provided to other non-financial corporations) has also joined the dangerous interval.
The only indicator of investment and innovation security, which even exceeded the optimal value during 2014–2022 was the exports-to-imports ratio of the royalties, licensing services, computer and information services, D&D, and services in architectural, engineering, and other technical industries.
The highest value of the Integral index of investment and innovation security of Ukraine, calculated on a set of 8 detected indicators, was achieved in 2016 regardless of the calculating methods of indicators’ weighting coefficients and ranged from 0.43 (using expert evaluation method) to 0.60 (using pairwise correlation method). The Integral index was also close to the maximum value in 2018 (using the multiple correlation method, slightly lower than in 2016).
The highest value of the Integral index of investment and innovation security of Ukraine, calculated on a set of 9 detected indicators, was achieved in 2018 regardless of the calculating methods of indicators’ weighting coefficients and ranged from 0.43 (using the multiple correlation method) to 0.63 (using the pairwise correlation method). The Integral index was close to the maximum value in 2016 (using the multiple correlation method, even slightly higher than in 2018).
It can be seen from the graphs above, that inclusion of the Ukraine’s rank in the Global Innovation Index ranking to the set of indicators when assessing the Integral index of investment and innovation security (that is, a set of 9 indicators) leads to overestimation of Integral index in certain years. Thus its exclusion from a set of indicators when assessing the Integral index is justified.
Fig. 1 shows that the maximum values of the Integral index were obtained in cases when investment and innovation indicators’ weighting coefficients were calculated using the method of pairwise correlation between the indicators and GDP. In 2014–2016 the values of the Integral index calculated using this weighting method exceeded the index values obtained using three other weighting methods (principal components, multiple correlation, experts evaluations) by 8–18%, and in 2017–2022—by 28–44%.
Such assessment results are because, in contrast to the results of theoretical analysis and the experience of many countries regarding the positive relationship between factors of innovative development of national economies and GDP dynamics, in the conditions of Ukraine, correlation analysis does not reveal a significant connection between the corresponding indicators. That is why, such basic indicators are important for the security of the investment and innovation sphere, in particular, x1 (R&D expenditures, % of GDP), x4 (innovative industrial products (goods, services) sold in the total amount of industrial products (goods, services) sold, %), x8 (loans provided to other non-financial corporations, % of GDP), received low weights according to this weighting method (Table 6). As a result, critically low or unsatisfactory values of initial indicators of the investment and innovation sphere in 2014–2022 did not have a negative impact on the value of the Integral index and has led to its overestimation. Consequently, when identifying weak relationships between indicators of innovative development and GDP dynamics, determining the weight of initial indicators using the method of their pairwise correlation with GDP leads to an overestimation of the Integral index of investment and innovation security, and therefore the use of this method is inappropriate.
The use of statistical weighting methods (principal components and multiple correlations) as well as the expert’s evaluations do not introduce a significant error in the assessment of the values and dynamics of the Integral index of investment and innovation security of Ukraine. Testing the robustness and sensitivity of the Integral index of investment and innovation security (according to 2014–2022 data) from the point of calculating methods of the detected indicators’ weighting coefficients indicates the reliability of calculations and aggregation of indicators in the Integral index of investment and innovation security using such methods.
Modeling of the Integral index of investment and innovation security of Ukraine is carried out using different approaches to calculating weighting coefficients of initial indicators that characterize the state of investment and innovation security. The use of various methods of weighting the indicators, in particular, the principle components method, the method of multiple correlation, and the method of expert evaluation, in the assessment of the Integral index of investment and innovation security provides consistent estimates of the state of investment and innovation security, which is an important component of economic security. The advantages of statistical methods over the method of expert evaluations are that they are available and unbiased. The proposed Integral indicator does not depend on the choice of the above-mentioned methods of weighing the initial indicators and is a fairly reliable tool for monitoring the state of investment and innovation security of Ukraine. https://eur-lex.europa.eu/legal-content Mark. Manag. Innov. 4 (2019). 364–372. /EN/TXT/?uri=CELEX%3A52023JC0020 doi: 10.21272/mmi.2019.4-28. [2] P. Anakhov, et al., Protecting Objects of [12] T. Kvasha, R. Voloshchuk, Approaches to Critical Information Infrastructure from the Integrated Assessment of the State of Wartime Cyber Attacks by Decentra- Economic Security as a Complex System, lizing the Telecommunications Network, Sci. Tech. Inf. (3) (2015) 31–41. in: Cybersecurity Providing in [13] J. Stiglitz, A. Sen, J.-P. Fitoussi, The Information and Telecommun. Systems, Measurement of Economic Performance vol. 3550 (2023) 240–245. and Social Progress Revisited: Reflec[3] H. Hulak, et al., Dynamic Model of tions and Overview, Commission on the Guarantee Capacity and Cyber Security Measurement of Economic Performance Management in the Critical Automated and Social Progress (2009). System, in: 2nd Int. Conf. on Conflict [14] L. Lipych, L. Savchuk Indicators of Management in Global Information Investment Security of the State, Networks, vol. 3530 (2023) 102–111. Economics forum 3 (2019) 26–30. [4] NATO 2022 Strategic Concept (SC), [15] L. Carrino, The Role of Normalisation in adopted by Heads of State and Building Composite Indicators. RationaGovernment at the NATO Summit in le and Consequences of Different StrateMadrid. URL: https://www.nato.int/ gies, Applied to Social Inclusion, Social nato_static_fl2014/assets/pdf/2022/6/ Indicators Research Series 70 (2017). pdf/290622-strategic-concept.pdf doi: 10.1007/978-3-319-60595-1_11. [5] OECD Science, Technology and [16] M. Freudenberg, Composite Indicators of Innovation Outlook 2016, Policy Profile, Country Performance: A Critical AssessNational Strategies for Science, ment, OECD Science, Technology and Technology and Innovation. doi: Industry Working Papers 2003/16 10.1787/sti_in_outlook-2016-en. (2003). doi: 10.1787/405566708255. [6] V. Grechaninov, et al., Formation of [17] V. Buriachok, et al., Invasion Detection Dependability and Cyber Protection Model using Two-Stage Criterion of Model in Information Systems of Situa- Detection of Network Anomalies, in: tional Center, in: Emerging Technology Cybersecur. Providing in Inf. and TeleTrends on Smart Industry and Internet commun. Syst., vol. 2746 (2020) 23–32. of Things 3149 (2022) 107–117. [18] On Approval of Methodological Recom[7] V. Grechaninov, et al., Decentralized mendations for Calculating the Level of Access Demarcation System Construc- Economic Security of Ukraine. Ministry tion in Situational Center Network, in: of Economic Development of Ukraine No. Workshop on Cybersecurity Providing in 1277 (2013). URL: https://zakon.rada. Information and Telecommun. Systems gov.ua/rada/show/v1277731-13#Text II, vol. 3188, no. 2 (2022) 197–206. [19] State Statistics Service data; National [8] T. Iefymenko, Fiscal and Monetary Bank of Ukraine. The Global Innovation Security of National Economy, The Aca- Index. URL: https://www.wipo.int/ demy of Financial Management (2016). global_innovation_index/en/ [9] T. Iefymenko, L. Lovinska, М. Kucheriava, [20] R. Gunst, J. Webster, Regression Analysis Reforming the Information Support of and Problems of Multicollinearity, Public Administration in the Wartime, Sci. Commun. Statistics-theory Methods 4 Innov. 18(4) (2022) 17–24. doi: (1975) 277–292.
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