“Is increasing a share of R&D expenditure in GDP a factor in strengthening the level of innovation development in Ukraine compared with GII’s top countries?”

The study aims to test whether increasing a share of R&D expenditure in GDP strengthens the level of innovation development in Ukraine compared with top countries in the Global Innovation Index. It models the impact of changing a share of R&D expenditure in GDP on the level of innovation development based on 10 countries-leaders in GII 2022 and Ukraine. Correlation analysis proved the existence of a relationship be-tween the levels of R&D expenditure (as percent of GDP) and innovation development (the overall score of GII); its strength and direction are characterized (for 2011–2020). The results show that in GII’s top countries, the relationship between innovation development and R&D expenditure is direct in 70% of the sample’s countries, mostly with high and very high relationship power without time lag or 1-2-year time lag. This relationship is inverse in Ukraine, with high relationship power and a 1-year time lag. The system dynamic linear panel-data model is built to determine and formalize the impact of changing a share of R&D expenditure in GDP on the level of innovation development for GII’s top countries and the linear regression model – for Ukraine. For GII’s top countries, it is confirmed that with an increase in R&D expenditures by 1%, innovation development potentially increases by an average of 2.71%, and in Ukraine – it decreases by an average of 4.8%. This discrepancy is explained by the need to improve state policy and regulatory framework in innovation development and its financing in Ukraine.


INTRODUCTION
Today, the critical role of innovations in economic development is beyond doubt, especially in the digital transformation era (Pakhnenko & Kuan, 2023;Chen et al., 2023).Building innovative potential plays a central role in the growth dynamics of prosperous countries (OECD, n.d.).Innovation is a key driver of economic growth, accelerates economic recovery, and puts countries on the path to sustainable development.Innovation development is associated with new opportunities and advantages, increasing the efficiency of economic and other activities, optimizing costs, and increasing income (V.Raghupathi & W. Raghupathi, 2017; Melnyk et al., 2022).Therefore, one of the critical objectives of the EU over the past few decades has been to encourage increased investment in research to boost competitiveness (Eurostat, 2023).
Research and development (R&D) expenditure is one of the indicators of innovation development, especially in the context of indices of innovation investments and global science within the Global Innovation Index (GII) on a row with venture capital deals, international patent filings, scientific publications, etc.It is also a key indicator of government and private sector efforts to gain a competitive advantage in science and technology.It includes both capital and current expenditures in four sectors: government, business enterprise, higher education, and private non-profit organization, covering fundamental and applied research and experimental development.
In 2022, R&D expenditure relative to the GDP of the EU stood at 2.23 %, lower than in 2021 (2.27 %) (Eurostat, 2023).This indicator differs from country to country.In Ukraine, this indicator is at the level of 0.29% of GDP (2021), which is lower than the value of 2020, when R&D expenditures reached 0.4% of GDP (World Bank, n.d.d).At the same time, these indicators are available and were calculated by the World Bank in the pre-war period in Ukraine.

LITERATURE REVIEW
A significant amount of scientific work has been created on innovation development issues, but given the dynamism of innovation development, new challenges, and achievements in this field, this scientific direction of research is constantly relevant.
One of the important questions that scientists ask themselves is the effectiveness of innovations, their role, and their impact.Innovation efficiency is considered an optimal combination of contribution and result (Triyonowati et al., 2023).
Within the organized innovation space, the chances of strengthening sustainable development are increasing, which is especially important in countries with a transition economy to accelerate and complete socioeconomic transformations.The direction of developing industrial, technological, and scientific parks in Ukraine is determined using the five-fold spiral model in the "knowledge-innovation" plane (Petrushenko et al., 2021).
The formation and development of the organizational and economic mechanism for the activation of innovation development is the key to the development of the economy, the formation of competitive production, and the assurance of sustainable development (Berezhnytska et al., 2022).In this regard, the relevance of the problem of forming a system of specialized innovation and investment banks, co-investment funds, etc., which would specialize in the field of investment support for innovation development, is not lost (Kozmenko & Vasylieva, 2008;Leonov et al., 2012).Mallinguh et al. (2022) analyzed the factors affecting R&D spending in developing countries.The results show that exports, skilled labor availability, and informal competition are positively and significantly correlated with R&D expenditures.In contrast, innovation strategy, financial constraints, and technological incompatibility have little effect on the outcome variable.Ildırar et al. (2016) assessed the impact of R&D spending on economic growth, taking into account the impact of various types of R&D spending on economic growth for selected OECD countries for 2003-2014.All R&D expenditures were found to positively and significantly impact economic growth in individual OECD countries, but the magnitudes varied.Goel et al. (2008), however, using the example of the USA for the 48 years from 1953 to 2000, found a similar influence.
Bozkurt (2014) also identified a relationship between R&D expenditures and economic growth and its assessment.The author concluded that there is a long-run relationship between R&D spending and economic growth based on Johansen's cointegration and vector error correction models; specifically, the GDP growth rate will increase by 0.2630% if the share of R&D in GDP increases by 1%.
Another assessment of the impact of investment in R&D (in particular, the share of investment in research and development in the high-tech sector) on long-term economic growth is presented by Falk (2007) 2019) investigated the relationship between innovation and R&D spending in the EU countries for 1995-2014.The results of the empirical analysis showed a relationship between innovation and research and development and a positive and significant impact of business, state, and higher education research and development on innovation.
The question of the connection and impact of business expenditures on research and development on innovation activity in the EU countries was studied by Hunady and Pisar (2020), who focused on research and development in the business sector as the most important part of the innovation system.At the same time, the study emphasizes that although R&D spending can be considered the main prerequisite for successful innovation, successful transformation of investments in research and development into an invention or innovation cannot be guaranteed.In the long term, a positive cause-and-effect effect of business expenditures on R&D on patenting has been determined.Relationships between R&D expenditures, patent activity, and intellectual property were also at the center of attention of Samoilikova and Artyukhov (2023) and Soumadi (2023).
In addition to business expenditures on R&D, scholars separately study the impact of education sector expenditures on R&D (Yu et al., 2023)  However, based on the above, it is worth noting that most scientists have studied the role of R&D spending in qualitative or quantitative terms, primarily on economic growth.The impact of R&D expenditures on strengthening innovation development was practically not assessed, especially for Ukraine compared to key countries, according to the Global Innovation Index.
The research purpose is to determine the impact of changing R&D expenditure in GDP on the level of innovation development based on 10 countries-leaders in GII 2022 and Ukraine.
The research hypothesis is formulated as follows: H1: Increasing a share of R&D expenditure in GDP strengthens the level of innovation development in Ukraine and top countries in the Global Innovation Index.

METHODS
The

RESULTS AND DISCUSSION
Before applying correlation analysis, the data for the factor variable should be checked for submission to the law of normal data distribution using the Shapiro-Wilk test (Table 1), which will allow deciding on the appropriate correlation analysis method in the following research stage.Note: * -the data do not follow a normal distribution (Prob > z is less than 0.05).
The results of the Shapiro-Wilk test mean that data for the factor variable of R&D expenditure do not follow a normal distribution in Switzerland and the Netherlands (Prob > z is less than 0.05).The Spearman correlation method is used for these countries, and for other countries, the Pearson correlation method is applied.The results of correlation analysis, including the calculation of the correlation coefficient without time lag and 1-3-year time lag, are given in Table 2 to confirm the existence of the relationship and to determine when the investigated relationship is the most statistically significant.
The results of correlation analysis show that in GII's top countries, the relationship between the level of innovation development and R&D expenditure is confirmed; it is direct in 7 from 10 countries (70% of the sample), mostly with high and very high relationship power without time lag or 1-2-year time lag.In the other 3 from 10 countries (30% of the sample), the relationship is inverse with moderate or very high relationship power without time lag or 2-3-year time lag.
In Ukraine, the relationship between the level of innovation development and R&D expenditure is confirmed as inverse with high relationship power and 1-year time lag.
Based on the identified relationship, to formalize the influence of the factor of R&D expenditures on the level of innovation development, a regression model was built for the assessment of panel data for GII's top countries (2011-2020) and time series data for Ukraine (2011-2020).
To increase the adequacy of the constructed models in addition to investigated indicators of the level of innovation development (as the value of general score of Global Innovation Index) (GII) and R&D expenditure (as a percent of GDP) (RD), the following additional indicators were added to the model: • net inflows of foreign direct investment (% of GDP) (FDI); • annual GDP per capita growth (%) (GDP); • the rate of labor force participation (% of total population ages 15-64) (L).
For panel data of GII's top countries, system dynamic linear panel-data model by Arellano-Bover/ Blundell-Bond was applied to estimate the impact of R&D expenditures on the level of innovation development.
This systemic dynamic linear model of panel data estimates assumes that panel-level unobserved effects correlate with the dependent variable's time lags.In addition, since this model is an extension of the Arellano-Bond estimator, which takes into account large parameters of autoregression and the ratio of the variance of the effect at the panel level to the variance of the idiosyncratic error, the influence of the values of the outcome variable of past periods is also taken into account.This method assumes no autocorrelation in the idiosyncratic errors and requires that the panel-level effects be uncorrelated with the first difference of the first observation of the dependent variable.
The following formula is used to construct the equation: where GII -the level of innovation development as a value of the general score of the Global Innovation Index; RD -research and development expenditure as a percent of GDP; FDI -net inflows of foreign direct investment; GDP -annual GDP per capita growth; L -labor force participation rate.
So, for the panel of GII's top countries, R&D expenditures positively impact the level of innovation development: with an increase in R&D expenditures (as a percentage of GDP) by 1%, the level of innovation development (as the overall score of the Global Innovation Index) potentially increases by an average of 2.71% with 90.5% of probability.
The results of regression modeling for Ukraine are given in Table 4.
According to Fisher's test, the model's significance level does not exceed 0.05 (Prob > F = 0.05), which indicates the adequacy of the constructed model.The determination coefficient is not very high where GII -the level of innovation development as a value of the general score of the Global Innovation Index; RD -research and development expenditure as a percentage of GDP.
So, for Ukraine, with a 94% probability, R&D expenditures do not positively impact the level of innovation development: with an increase in R&D expenditures (as a percentage of GDP) by 1%, the level of innovation development (as the overall score of the Global Innovation Index) potentially decreases by an average of 4.8%.
That is why the hypothesis that increasing a share of R&D expenditure in GDP strengthens the level of innovation development in Ukraine and the top countries in GII was confirmed partly, only for GII's top countries.
Based on international ratings, Lymonova and Mahdich (2020

CONCLUSION
The purpose of the study was to determine the impact of changing a share of R&D expenditure in GDP on the level of innovation development in countries-leaders in GII-2022 and Ukraine.For the top 10 countries in GII rating and for Ukraine, correlation analysis allowed confirming that in GII's top countries, the relationship between the level of innovation development and R&D expenditure is direct in 7 from 10 countries (70%) mostly with high and very high relationship power without time lag or 1-2-year time lag.This relationship is inverse in Ukraine, with high relationship power and a 1-year time lag.A regression model was built to assess panel data for GII's top countries (system dynamic linear panel-data model by Arellano-Bover/Blundell-Bond) and time series data for Ukraine (linear regression model).In GII's top countries with an increase in R&D expenditures (as a percentage of GDP) by 1%, the level of innovation development (as the overall score of GII) potentially increases by an average of 2.71% with 90.5% probability.In Ukraine, with an increase in R&D expenditures (as a percentage of GDP) by 1%, the level of innovation development (as the overall score of the Global Innovation Index) potentially decreases by an average of 4.8% with a 94% probability.
The results show the different effectiveness of increasing R&D spending and their opposite effect in Ukraine and the top countries regarding the level of innovation development.In Ukraine, increasing a share of R&D expenditure in GDP is not a factor in strengthening the level of innovation development compared with GII's top countries.This discrepancy is explained by the need to improve state policy and regulatory framework in innovation development and its financing in Ukraine.At the same time, this study is limited by the sample of countries and time, which should be expanded in further studies to increase the quality of the obtained research results.Also, in further studies, it is advisable to analyze the structure of this indicator of R&D spending, distinguishing the components of financing by the state, business, education, etc.
Shkarupa et al. (2022) investigated innovation development in Ukraine compared to European countries and considered European development trends.The study emphasized that in countries with a developed economy, the acceleration of sci-entific and technological progress and the introduction of innovations differ and are related to the opportunities to develop the knowledge economy, commercialization of technologies, and innovation transfer networks.In the context of R&D expenditures, the emphasis on innovation financing and financial regulation is made by Strielkowski et al. (2022), who examined innovation development's tax, monetary, budgetary, and investment instruments.The issue of investing in innovation was considered by Iastremska et al. (2023), who studied the impact of investments in research and development as the basis of innovation development in modern conditions of economic development in real and virtual space.
in the context of university-company competition (Nahla, 2023; Kaya et al., 2023).Artyukhov et al. (2021) developed a model of transfer of innovations from the field of education to ensure innovation development.

Table 1 .
Checking the normal distribution of the data for R&D expenditure based on the Shapiro-

Table 2 .
Confirmation of the relationship between the level of innovation development and R&D expenditure based on Pearson and Spearman correlation analysis

Table 3 .
The results of the system dynamic linear panel-data model to formalize the influence of the factor of R&D expenditures on the level of innovation development in GII's top countries GII -the level of innovation development as a value of general score of Global Innovation Index; RD -research and development expenditure; FDI -net inflows of foreign direct investment; GDP -annual GDP per capita growth; L -labor force participation rate.

Table 4 .
The results of the linear regression model to formalize the influence of R&D expenditures on the level of innovation development in Ukraine GII -the level of innovation development as a value of the general score of the Global Innovation Index; RD -research and development expenditure as a percent of GDP. and based on other methodology, in particular, in the EU countries for the period 2007-2020, using causal analysis and the PVAR model to determine the relationship between research spending and innovation growth in the EU countries.The results show a long-term positive significant re-lationship between R&D expenditure and the Global Innovation Index, while the relationship is negative in the short run.At the same time, the results obtained in this paper show that the relationship between studied indicators is not positive (direct) in all EU countries.