Trade Openness and Innovation Performance in the EU: An Analysis of Cluster Dynamics

Abstract

In the modern globalized context, innovation represents a key driver of economic growth, while international trade plays an important role in fostering it. This study examines the relationship between the degree of trade openness and innovation performance across 27 EU member states over the period 2018–2024. The period under review covers the COVID-19 pandemic. The data were analyzed using dynamic cluster analysis (K-means). In addition to simple linear regression, FE mixed-model analysis (REML) was also used to test the robustness of relationships. Dynamic cluster analysis from the perspective of trade openness and innovation identified three statistically significant and stable heterogeneous groups of countries—innovation leaders, emerging economies and countries with high economic openness. The mixed model included the variables trade-to-GDP, R&D expenditure, digitalization and GDP. The results confirmed a statistically significant positive relationship between trade openness and innovation performance in EU countries. The findings show a significant positive impact of Trade-to-GDP, digitalization and R&D expenditure (triple interaction) on innovation rates as a synergistic innovation effect. The findings highlight that the impact of trade openness on innovation is heterogeneous and conditioned by other specific factors, thus requiring differentiated innovation and trade policies within the European Union. Innovation policies should optimize all parameters influencing innovation and exploit their synergistic effect.

1. Introduction

In the modern economy, innovation is widely recognized as a key driver of long-term economic growth and competitiveness. In today’s globalized context, domestic R&D investments alone are not sufficient; international trade also plays a crucial role in fostering innovation (Rodil et al., 2015). Trade facilitates the free flow of technology across countries, benefiting both nations and enterprises, while simultaneously intensifying market competition and expanding the market size. This environment provides “innovative producers” with opportunities to enhance competitiveness through access to international markets, allowing firms to offset R&D costs and capture dynamic benefits unattainable in domestic markets alone (Zhao, 2021).

Current research highlights that a firm’s ability to innovate is closely linked to its external environment. In a globalized world, innovation correlates strongly with economic openness and the degree of participation in international trade (Sachs et al., 1995; Khan et al., 2023). Openness to trade is particularly crucial for developing and emerging economies, as it enables broader access to international markets, advanced technologies, essential raw materials, and fosters healthy competition. The trade-to-GDP ratio is a common measure of an economy’s openness, with higher values indicating stronger integration into global markets and greater reliance on imports and exports. Recent analyses show that EU countries with higher trade openness also demonstrate higher R&D intensity and superior outcomes in technological innovation (EIB, 2025; Eurostat, 2025c).

Two primary mechanisms underpin the relationship between trade and innovation. The first is the import channel, where the import of goods, components, and technologies introduces new knowledge and stimulates learning through adaptation, also known as learning-by-importing. The second is the export channel, which pressures firms to innovate in order to compete internationally, referred to as learning-by-exporting. Both channels support the emergence and dissemination of new technologies and knowledge, and empirical evidence confirms their relevance across EU economies (Silva et al., 2010; Štofkova et al., 2017; Juergensen et al., 2024; Chen et al., 2024).

Within the European Union, these dynamics take on particular significance. The single market, with its free movement of goods and services, reduces trade barriers and enhances the dynamism of innovation activities. However, substantial differences exist among member states in innovation performance and trade openness. According to the European Innovation Scoreboard 2024 (European Commission, 2025a) and preliminary results of the EIS 2025 (European Commission, 2025b), more than two-thirds of EU countries have improved their innovation performance. Top-performing states, including Sweden, Denmark, Germany, and the Netherlands, also maintain a high share of high-tech exports in GDP. Between 2018 and 2025, the EU’s overall innovation performance rose by 12.6 percentage points, with a slight decline of 0.4 percentage points between 2024 and 2025.

The trade balance—the difference between exports and imports—represents a key macroeconomic outcome of these processes. Innovation contributes indirectly through improved competitiveness, higher product quality, and greater technological sophistication of exports. Eurostat (2025a) reports that the EU’s trade balance improved to a surplus of €147 billion in 2024, with the most innovation-intensive sectors achieving the largest surpluses. Additionally, the High-tech Trade Report 2025 (Eurostat, 2025d) shows that EU exports of high-tech goods increased by 8.1% year-on-year, shifting the high-tech trade balance from a €15 billion deficit in 2023 to a €23 billion surplus in 2024.

These findings indicate that innovation and economic openness form a mutually reinforcing system. International trade openness puts pressure on firms to innovate, while innovation strengthens export performance and trade balances. Within the single European market, countries with greater technological potential benefit more from openness, whereas less developed economies remain reliant on technology imports (Gaál et al., 2023; Bauer et al., 2024).

Building on this evidence, this study examines how trade openness and innovation performance interact across EU Member States, focusing on the role of technological intensity in shaping trade outcomes over the 2018 to 2024 time horizon. This period includes the critical phase when countries had to close down due to the COVID-19 pandemic. The findings highlight a mutually reinforcing relationship: trade openness drives innovation, while innovation strengthens export performance and trade balances. Understanding these dynamics is essential for designing effective innovation and trade policies that support sustainable growth across both highly developed and less advanced EU economies.

The relationship between economic openness and innovation performance is widely studied and generally accepted in economic theory. Traditional approaches, based primarily on the Schumpeterian approach, consider innovation as a key determinant of long-term economic growth and competitiveness (Bazhal, 2019). Economic openness and investment in science and research (R&D) are key elements in this context that enable the transfer of technology and knowledge leading to the support and development of innovations. Despite the extensive theoretical basis of this relationship in aggregate models, there is a need to examine its dynamics and validity in specific and heterogeneous economic blocs and the time of closure of individual countries. According to Pelikánová (2019), further and deeper research is needed, especially in connection with the persistent differences between EU Member States. During the pandemic, digitalization played an important role. To a large extent, digitalization acted as a critical moderating factor. The theoretical novelty of this study lies in examining the relationship between trade openness and innovation in the context of digital transformation, R&D expenditure, at a time when fundamental changes in the environment were implemented. How did these changes and the ways of interaction between countries affect the heterogeneity of groups of countries (clusters) from the perspective of the relationship under study. The period of pandemic restrictions supported and accelerated the development of digitalization, which also supported the growth of the knowledge economy (Untura, 2023). Therefore, this study offers insights into the impact of economic openness on innovation in EU countries. It takes into account parameters such as GDP, R&D expenditure, and digitalization. It examines not only the pandemic period but also the period before and after it, thereby trying to map the dynamics of development in the broader context of the variables under study.

Drawing on the preceding literature review, this paper aims to explore the relationship between economic openness and innovation levels across the European Union.

The remainder of the paper is structured as follows: Section 2 presents methodology in detail, describes the data as well as the measurement of the variables under study, and the economic approach including dynamic cluster analysis, and a robust specification of a FE mixed model (REML) specification. Section 3 analyzes the data under study, Section 4 discusses the results, and Section 5 offers the main conclusions and highlights the study’s limitations.

2. Methodology

The aim of this research is to analyze the relationship between economic openness and the level of innovation in the European Union member states. To verify this relationship, secondary data were used.

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Innovation performance was assessed using the Summary Innovation Index (SII), which reflects the innovation performance of individual countries as reported in the European Innovation Scoreboard (European Commission, 2025a).

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Exports of goods include changes in the economic ownership of goods from residents of the compiling economy to non-residents, irrespective of physical movement of goods across national borders. Exports of services include services provided by residents to non-residents. This indicator is expressed as a percentage of Gross Domestic Product (GDP) which is the total income earned through the production of goods and services in an economic territory during an accounting period—hereinafter referred to as exports/GDP (World Bank DataBank, 2025a).

➢

Imports of goods include change in the economic ownership of goods from non-residents to residents of the compiling economy, irrespective of the physical movement of goods across national borders. Imports of services include services provided by non-residents to residents. This indicator is expressed as a percentage of Gross Domestic Product (GDP), which is the total income earned through the production of goods and services in an economic territory during an accounting period—hereinafter referred to as imports/GDP (World Bank DataBank, 2025b).

The calculation of economic openness (Trade to GDP) for individual countries follows the approach of Rojíček (2010):

$$\mathbf{T}\mathbf{r}\mathbf{a}\mathbf{d}\mathbf{e} \mathbf{t}\mathbf{o} \mathbf{G}\mathbf{D}\mathbf{P}={\displaystyle \frac{\mathit{e}\mathit{x}\mathit{p}\mathit{o}\mathit{r}\mathit{t}+\mathit{i}\mathit{m}\mathit{p}\mathit{o}\mathit{r}\mathit{t}}{\mathit{H}\mathit{D}\mathit{P}}}=\mathit{e}\mathit{x}\mathit{p}\mathit{o}\mathit{r}\mathit{t}\mathit{s}/\mathit{G}\mathit{D}\mathit{P}+\mathit{i}\mathit{m}\mathit{p}\mathit{o}\mathit{r}\mathit{t}\mathit{s}/\mathit{G}\mathit{D}\mathit{P}$$

All examined parameters were evaluated for the period 2018–2024. This period was selected based on the maximum available coverage of the Summary Innovation Index (SII), whose data are only available from 2018 onwards. The aim was to empirically verify whether a higher degree of openness, represented by the Trade to GDP ratio, is associated with a higher level of innovation performance, measured through the Summary Innovation Index (SII) across EU countries. All data were standardized prior to analysis (Z-transformation) to allow for comparisons between variables measured on different scales. For each observation, a Z-transformation (Z-score) was applied, which converts the data into standard deviations from the mean (Hair et al., 2011; James et al., 2013).

$$\mathit{Z}\mathit{i}={\displaystyle \frac{\mathit{X}\mathit{i}-\mathit{X}}{\mathit{S}\mathit{D}}}$$

where Xi is the original value of the variable, X is its mean, and SD is the standard deviation. These transformed data were subsequently used for all statistical analyses.

As one of the methods, dynamic cluster analysis was applied over the study period, allowing the observation of developmental changes in the grouping of countries and the identification of the stability of structural relationships between economic openness and innovation performance in EU countries. This analysis aimed to identify homogeneous groups of countries based on their characteristics of economic openness and innovation. The K-means clustering method was employed. K-means is used for clustering and minimizes within-cluster variance (Hastie et al., 2005). The optimal number of clusters for the K-means analysis was determined using silhouette analysis, which assesses the quality of clustering and the coherence within clusters (Rousseeuw, 1987; Kaufman & Rousseeuw, 2009).

In the second phase, the relationship between the degree of economic openness of EU countries and their level of innovation over the study period (2018–2024) was tested using correlation analysis. To verify the robustness of the relationship between Trade-to-GDP and innovation, GDP of EU countries (Eurostat, 2025b) was used as a control variable in the regression analysis. Correlation analysis is a fundamental statistical method used to quantify the relationship (association) or dependence between two or more variables. The key indicator is Pearson’s correlation coefficient, ranging from ⟨−1; +1⟩. A value close to ±1 indicates a strong relationship, whereas a value close to 0 suggests a weak or no relationship. A positive correlation (+) means that as the value of one variable increases, the value of the other also increases (direct relationship). Conversely, a negative correlation (−) indicates that as one variable increases, the other decreases (inverse relationship) (Selvamuthu & Das, 2024). To verify the robustness of the relationship between Trade_to_GDP and innovation, GDP of EU countries was used as a control variable in the regression analysis.

Subsequently, the relationship between the degree of economic openness and the level of innovation was tested using regression analysis. The regression was performed in two steps:

Model 1: This model examines innovation performance as a function of the economic openness of EU countries. The model was developed based on a literature review and formulated into the following hypotheses:

H0. 

There is no statistically significant positive relationship between the degree of trade openness and innovation performance.

H1. 

There is a statistically significant positive relationship between the degree of trade openness and innovation performance.

Model 2: This model extends the previous hypothesis to test its robustness using multiple linear regression, incorporating the standardized GDP of EU countries as a control variable.

Regression analysis and Pearson correlation analysis were conducted to verify the relationships defined in the hypotheses. The hypotheses were tested based on regression coefficients, the coefficient of determination (R²), and the overall model significance at a significance level of α = 0.05 (Christensen & Brockhoff, 2013; Wooldridge, 2016).

Model 3: This model extends the previous hypothesis to test its robustness using mixed model analysis, incorporating the GDP, research and development expenditure and digitalization as a control variable.

To address the limitations of simple linear regression (ignoring the structure of panel data), we used a comprehensive panel econometric method—a mixed model analysis with random effects (FE) with restricted maximum likelihood (REML) parameter estimation to model the complete analysis. This routine provides exactly the same estimates as the complete analysis. The advantages of this approach are that it allows testing the statistical significance of the complete analysis, modeling and testing the heterogeneity of the complete analysis and measurement error between samples, testing for non-zero directional asymmetry, and obtaining unbiased estimates of the individual levels of the complete analysis (Dongen et al., 1999). The determination variable is innovation, and the control variables are GDP, R&D expenditure (% GDP; World Bank, 2025) and digitalization. Digitalization is assessed using the DESI index. DESI is the Digital Economy and Society Index for Europe (DESI, 2025). Before checking the multicollinearity of the final model, the Variance Inflation Factor (VIF) will be used. This indicator measures how much the variance of the estimated regression coefficients increases when comparing situations where the predictors are considered to be independent of each other (Vittinghof et al., 2005). A rule of thumb is that VIF values > 4 may be problematic, values > 10 may seriously affect the modeling results (Katz, 2006).

Data were processed using IBM SPSS Statistics 20 (IBM, Armonk, NY, USA). For summarizing results and their presentation, MS Excel (Microsoft, Redmond, WA, USA), Colab and Google functionalities (Google LLC, Mountain View, CA, USA) were additionally used.

3. Results

The aim of the analysis was to verify whether a relationship exists between economic openness (measured by the Trade_to_GDP ratio) and the level of innovation (Summary Innovation Index—SII) in European Union countries during the period 2018–2024. For this purpose, dynamic cluster analysis was conducted, allowing the observation of the development of country groups within the EU over time, followed by correlation and regression analyses to examine their relationships, specifically innovation as a function of Trade-to-GDP.

The dynamic cluster analysis was performed using K-means clustering. To determine the optimal number of clusters for the K-means clustering, silhouette analysis was conducted (see Table 1).

Table 1. Silhouette analysis.

Number of Clusters	Silhouette Score
2	0.3510
3	0.4239
4	0.3962
5	0.3502
6	0.3695
7	0.3473
8	0.3452
9	0.3188

The optimal number of clusters, corresponding to the highest silhouette coefficient, is three, with the highest silhouette value being 0.4239. Based on this number of clusters, dynamic K-means cluster analysis was subsequently performed for the period 2018–2024, with the results summarized in Table 2.

Table 2. Results dynamics cluster analysis.

Years	Clusters		1	2	3	F	Sig.
2024	Countries		Austria, Belgium, Cyprus, Denmark, Estonia, Finland, France, Germany, Ireland, Malta, Netherlands, Slovenia, Sweden	Spain, Poland, Portugal, Romania, Slovakia, Italy, Latvia, Lithuania, Greece, Hungary, Czech Republic, Bulgaria, Croatia	Luxembourg
	Average	Innovation	129.85	80.16	123.88	21.906	0.000
		Trade to GDP	143.80	109.59	398.23	18.471	0.000
2023	Clusters		1	2	3	F	Sig.
	Countries		Austria, Belgium, Cyprus, Denmark, Estonia, Finland, France, Germany, Ireland, Malta, Netherlands, Slovenia, Sweden	Spain, Poland, Portugal, Romania, Slovakia, Italy, Latvia, Lithuania, Greece, Hungary, Czech Republic, Bulgaria, Croatia	Luxembourg
	Average	Innovation	129.32	78.45	125.39	22.202	0.000
		Trade to GDP	146.41	115.47	404.46	18.900	0.000
2022	Clusters		1	2	3	F	Sig.
	Countries		Austria, Belgium, Cyprus, Denmark, Estonia, Finland, France, Germany, Ireland, Netherlands, Slovenia, Sweden, Italy	Spain, Poland, Portugal, Romania, Slovakia, Latvia, Lithuania, Greece, Hungary, Czech Republic, Bulgaria, Croatia	Luxembourg, Malta
	Average	Innovation	128.84	72.03	113.78	33.159	0.000
		Trade to GDP	143.83	136.30	327.80	11.830	0.000
2021	Clusters		1	2	3	F	Sig.
	Countries		Austria, Belgium, Cyprus, Denmark, Estonia, Finland, France, Germany, Ireland, Malta, Netherlands, Slovenia, Sweden, Italy	Spain, Poland, Portugal, Romania, Slovakia, Latvia, Lithuania, Greece, Hungary, Czech Republic, Bulgaria, Croatia	Luxembourg
	Average	Innovation	121.94	68.52	127.93	30.585	0.000
		Trade to GDP	134.41	119.25	397.51	15.772	0.000
2020	Clusters		1	2	3	F	Sig.
	Countries		Austria, Belgium, Cyprus, Denmark, Estonia, Finland, France, Germany, Netherlands, Slovenia, Sweden, Italy	Spain, Poland, Portugal, Romania, Slovakia, Latvia, Lithuania, Greece, Hungary, Czech Republic, Bulgaria, Croatia	Luxembourg, Malta, Ireland
	Average	Innovation	118.96	65.74	115.53	29.477	0.000
		Trade to GDP	94.10	122.15	294.03	31.803	0.000
2019	Clusters		1	2	3	F	Sig.
	Countries		Austria, Belgium, Cyprus, Denmark, Estonia, Finland, France, Germany, Netherlands, Slovenia, Sweden, Italy	Spain, Poland, Portugal, Romania, Slovakia, Latvia, Lithuania, Greece, Hungary, Czech Republic, Bulgaria, Croatia	Luxembourg, Malta, Ireland
	Average	Innovation	118.96	65.74	115.53	29.477	0.000
		Trade to GDP	101.42	129.91	288.49	25.397	0.000
2018	Clusters		1	2	3	F	Sig.
	Countries		Austria, Belgium, Cyprus, Denmark, Finland, France, Germany, Netherlands, Slovenia, Sweden, Italy	Spain, Poland, Portugal, Romania, Slovakia, Latvia, Lithuania, Greece, Hungary, Czech Republic, Bulgaria, Croatia, Estonia	Luxembourg, Malta, Ireland
	Average	Innovation	118.13	65.62	114.54	28.258	0.000
		Trade to GDP	97.94	132.45	268.80	20.878	0.000

Table 2 presents the results of the cluster analysis, which divides selected European countries into three distinct groups.

Cluster 1—“Innovation Leaders”: This is the largest and most consistent cluster. It includes highly innovative economies such as Austria, Belgium, Cyprus, Denmark, Estonia, Finland, France, Germany, Greece, Ireland, Malta, the Netherlands, Sweden, and Italy. Ireland and Malta occasionally move between clusters in some years. This cluster consistently exhibits the highest average innovation performance (SII) among all clusters throughout the observed period. The Trade_to_GDP values are also consistently high.

Cluster 2—“Emerging Economies”: This cluster represents a middle group, mainly including Central and Eastern European countries, as well as some Southern European countries: Spain, Poland, Portugal, Romania, Slovakia, Latvia, Lithuania, the Czech Republic, Hungary, Bulgaria, and Croatia. The cluster shows the lowest average innovation performance (SII), while the average Trade_to_GDP values are typically medium to high. Although their innovation performance is the lowest, some growth was observed during the study period.

Cluster 3—“High Economic Openness”: This cluster is the smallest and most heterogeneous. It consistently includes Luxembourg and, in the years 2018–2020, also Malta and Ireland. These countries are known for their highly open economies. This cluster shows medium to high innovation performance (SII) but extremely high Trade_to_GDP values.

For all observed years, the significance value (Sig.) is 0.000. These results indicate that the differences in the mean values of the observed variables (Innovation and Trade-to-GDP) between the clusters are highly statistically significant (p < 0.001) for each year, confirming the robustness and validity of the cluster grouping.

The cluster analysis confirms the persistent existence of three distinct groups of EU countries, which differ in innovation performance and the degree of economic openness. The cluster analysis supports theoretical assumptions about the dynamic relationship between innovation and economic openness.

The correlation analysis confirmed a relationship between innovation performance and economic openness as indicated in Table 3. The Pearson correlation coefficient between the variables is weak but statistically significant (r = 0.158, p < 0.05).

Table 3. Results of correlation analysis.

Correlations
		Innovation	Trade_to_GDP
Innovation	Pearson Correlation	1	0.158 *
	Sig. (2-tailed)		0.029
	N	189	189
Trade_to_GDP	Pearson Correlation	0.158 *	1
	Sig. (2-tailed)	0.029
	N	189	189

* Correlation is significant at the 0.05 level (2-tailed).

To assess the robustness of the relationship between Trade_to_GDP and innovation, the GDP of EU countries was included as a control variable in the regression analysis as shown in Table 4. The inclusion of GDP as a control variable confirmed the robustness of the relationship between Trade_to_GDP and innovation. The relationship remains positive and statistically significant (the original Pearson correlation coefficient of 0.158 increased to r = 0.163, p < 0.05, after controlling for GDP). These findings indicate that the effect of economic openness on innovation is not the only factor influencing innovation, and that both variables should be examined jointly within a multiple regression framework.

Table 4. Results of control correlation analysis—control Variables GDP.

Correlations
Control Variables			Innovation	Trade_to_GDP
GDP	Innovation	Correlation	1.000	0.163 *
		Significance (2-tailed)		0.026
		Df	0	186
	Trade_to_GDP	Correlation	0.163 *	1.000
		Significance (2-tailed)	0.026
		Df	186	0

* Correlation is significant at the 0.05 level (2-tailed).

Table 5 presents the results of the linear regression analysis, where innovation performance was modeled as the dependent variable and economic openness as the independent variable. The results of the simple linear regression confirm the statistical significance of the relationship between innovation performance and trade openness, albeit with an important limitation regarding its predictive power. The same value as in the Pearson correlation analysis (0.158) confirms a weak positive linear relationship between innovation and the economic openness of EU countries. The unstandardized regression coefficient (B) for the examined parameters is 0.158, indicating that an increase in economic openness by one unit leads to an increase in innovation performance by 0.158 units. Only 2.5% of the total variability in innovation performance is explained by the variability in trade openness across countries (R² = 0.025; p = 0.029). To test the robustness of the relationship and to isolate the effect of openness from the overall level of economic development, Model 2 was estimated, including GDP as a control variable. The overall model is also statistically significant (p = 0.008). The inclusion of GDP slightly increased the explained variance (R²) to 0.050, suggesting that both variables jointly explain 5.0% of the variability in innovation performance. The regression coefficient remains positive and statistically significant (B = 0.161, p = 0.026). The inclusion of GDP in the model only slightly strengthened the effect of Trade-to-GDP, confirming that the positive relationship between the openness of EU economies and innovation is robust and not merely a result of correlation with GDP. The coefficient for the control variable GDP is also statistically significant (p = 0.028). Since p = 0.029 for Model 1 and p = 0.008 < 0.05 for Model 2, both regression models are statistically significant. Therefore, the null hypothesis can be rejected, and hypothesis H1 is accepted: there is a statistically significant positive relationship between the degree of trade openness and innovation performance. To eliminate the limit of simple linear regression (ignoring the structure of panel data), which can explain even the very low value of R² = 0.025, we used the complex panel econometric method mixed model analysis FE with restricted maximum likelihood (REML) for Model 3, see Table 6.

Table 5. Results models 1 and 2.

Model Summary
Model		R	R2		Adjusted R2			Std. Error of the Estimate
1		0.158 a	0.025		0.020			0.99000003
2		0.224 b	0.050		0.040			0.97980300
ANOVA c
Model				Sum of Squares		Df	Mean Square		F	Sig.
1	Regression			4.721		1	4.721		4.817	0.029 d
	Residual			183.279		187	0.980
	Total			188.000		188
2	Regression			9.437		2	4.719		4.915	0.008 e
	Residual			178.563		186	0.960
	Total			188.000		188
Coefficients f
Model				Unstandardized Coefficients			Standardized Coefficients		t	Sig.
				B		Std. Error	Beta
1	(Constant)			−4.176 × 10−16		0.072			0.000	1.000
	Trade_to_GDP			0.158		0.072	0.158		2.195	0.029
2	(Constant)			−4.384 × 10−16		0.071			0.000	1.000
	Trade_to_GDP			0.161		0.071	0.161		2.251	0.026
	GDP			−0.158		0.071	−0.158		−2.216	0.028

a. Predictors: (Constant), Trade_to_GDP; b. Predictors: (Constant), Trade_to_GDP, GDP; c. Dependent Variable: Innovation; d. Predictors: (Constant), Trade-to-GDP; e. Predictors: (Constant), Trade-to-GDP, GDP; f. Dependent Variable: innovation.

Table 6. Results model 3.

Estimates of Fixed Effects a
Parameters	Estimate	Std. Error	df	T	Sig.
Trade_to_GDP	0.944	0.266	100.742	3.546	0.001
DESI	1.053	0.492	98.083	2.142	0.035
R&D_expenditure	98.551	29.826	98.126	3.304	0.001
GDP	0.000	0.000	102.881	−0.200	0.842
Trade_to_GDP x DESI	−0.008	0.003	97.202	−2.394	0.019
Trade_to_GDP × R&D_expenditure	−0.712	0.238	103.368	−2.994	0.003
Trade_to_GDP × GDP	0.000	0.000	93.000	0.719	0.474
DESI × R&D_expenditure	−0.784	0.378	98.753	−2.077	0.040
DESI × GDP	0.000	0.000	108.213	0.498	0.620
R&D_expenditure × GDP	0.000	0.000	94.049	0.147	0.883
Trade_to_GDP × DESI × R&D_expenditure	0.008	0.003	102.791	2.593	0.011
Trade_to_GDP × DESI × GDP	0.000	0.000	94.354	−0.871	0.386
Trade_to_GDP × R&D_expenditure × GDP	0.000	0.000	89.636	−0.726	0.470
DESI × R&D_expenditure × GDP	0.000	0.000	95.746	−0.328	0.743
Trade_to_GDP × DESI × R&D_expenditure × GDP	0.000	0.000	88.291	0.750	0.455

^a. Dependent Variable: Innovation.

The interpretation of the FE mixed model with restricted maximum likelihood (REML) for the dependent variable Innovation revealed several statistically significant relationships (significance level α = 0.05). A significant positive impact on innovation was demonstrated for the key parameters Trade to GDP (p = 0.001), digitalization (p = 0.035) and R&D expenditure (p = 0.001). The impact of GDP was not demonstrated (0.842).

The openness of the countries’ economies (Trade_to_GDP) was significantly positive (Estimate = 0.944; t = 3.546; p = 0.001), indicating that with an increasing share of trade in GDP, the rate of innovation also increases. Digitalization (DESI) is also statistically significant (Estimate = 1.053; t = 2.142; p = 0.035). This confirms the importance of digital development for the support and development of innovations. Research and development expenditure (% of GDP) shows the strongest positive effect (Estimate = 98.551; t = 3.304; p = 0.001). This points to the need to allocate resources to research and development. Innovation financing is therefore a driving force for the development of innovations in EU countries. On the contrary, GDP in the mixed FE model did not show a statistically significant effect on innovations. The relationships (interactions) between the investigated variables in the mixed econometric FE model indicate the relationships Trade_to_GDP ad DESI (p = 0.019), Trade_to_GDP and R&D_expenditure (p = 0.003), DESI and R&D_expenditure (p = 0.040), Trade_to_GDP; DESI and R&D_expenditure (p = 0.011).

The impact of the openness of the EU countries’ economies in relation to digitalization has a negative impact on innovation (Trade_to_GDP, DESI—Estimate = −0.008; p = 0.019), as well as in relation to R&D expenditure Trade_to_GDP × R&D_expenditure —Estimate = −0.712). The relationship between digitalization (DESI) and R&D expenditure has a negative impact on innovation (estimate = −0.784) as does the relationship between economic openness (Trade to GDP) and digitalization, or economic openness (Trade to GDP) and R&D expenditure. However, the relationship of all three parameters together (trade to GDP; DESI and R&D expenditure) has a positive impact on innovation (estimate = 0.008; p = 0.011), i.e., all three parameters together form a positive cumulative effect on innovation-innovation synergy and mitigate the individual negative effect. All interactions involving GDP were statistically insignificant, further confirming that the measurement of innovation in this model is more sensitive to specific factors such as trade openness, digital development and research investment than to the general economic level measured by GDP. These results highlight that for maximizing innovation in EU countries, it is not only the amount of individual investments (e.g., in R&D) that is important, but also the context in which these factors interact (interactions with Trade_to_GDP; DESI; R&D expenditure). Based on Model 3, we can also reject the null hypothesis and accept hypothesis H1: there is a statistically significant positive relationship between the degree of trade openness and innovation performance. Although it should be noted that the impact of economic openness (trade to GDP) on innovation has a smaller impact than other variables, such as R&D expenditure. Before checking the multicollinearity of the final model, the variance inflation factor (VIF) was used. The VIF values of the individual parameters are in the range of 2, which is significantly below the average accepted limit (Trade to GDP—1.184, GDP—1.030, DESI—1.135, R&D expenditure—1.177). The model is chosen appropriately. and confirms the absence of problems with multicollinearity in our Model.

4. Discussion

The aim of this study was to verify the relationship between the openness of the EU economies and innovation, based on the assumption that international trade is an important factor in supporting innovation in the years 2018 to 2024. This period was marked by several significant events that could have influenced this fact, such as the COVID-19 pandemic and the military conflict in Ukraine, which continues to this day.

Based on the data for the monitored period, we identified three statistically significant groups of countries in the EU in terms of economic openness and innovation using dynamic cluster analysis. These groups of countries are different from each other and are internally similar. Countries such as Sweden, Finland, Denmark and others listed in cluster 1 represent innovation leaders, they show the highest degree of innovation activity. These countries try to gain dynamic advantages through the access of innovations to international markets to increase their competitiveness (Zhao, 2021). Countries such as Poland, the Czech Republic, Slovakia and others in cluster 2 show the lowest innovation performance on average among clusters. For this group of countries, the openness of economies to technology transfer and the absorption of external technologies serves as a catalyst for the economy’s openness to innovation and increases the efficiency of learning through imports (Chen et al., 2024). Their success is directly related to the ability to effectively use global knowledge flows. Luxembourg forms a separate cluster and is defined by an extremely high openness of the economy. Despite the strong impact of COVID-19 on the openness of economies in the studied period, the groupings of countries are more or less consistent throughout the studied period. More significant changes can be identified in clusters such as Malta and Ireland. These changes are especially during the COVID-19 period, when the economies of these countries had to respond to a decrease in the openness of the economy and minimize restrictions, because their economies were highly dependent on openness. Relationships within clusters confirm that there is a relationship between openness and innovation of individual EU countries.

To analyze the relationship between the openness of economies and innovation in EU countries, econometric models were subsequently tested. The analyses performed to test models 1 to 3 confirmed the existence of a statistically significant relationship between the variables, which led to the acceptance of the hypothesis H1—There is a statistically significant positive relationship between the degree of trade openness and innovation performance. This finding is in line with previous studies (Sachs et al., 1995; Khan et al., 2023), which emphasized the relationship between innovation and the openness of the economy in international trade. Despite its statistical significance in individual models, this relationship between the openness of the economies of individual EU countries and innovation has a low strength. This confirms the fact that economic openness itself represents only one component of the innovation performance of EU countries, while other factors also affect their innovation capacity (Gaál et al., 2023). The findings confirm that while economic openness acts as a catalyst for innovation, its actual effect depends on a number of other factors. For economic policy, this means that promoting openness and internationalization must be an integral part of innovation strategies, but should be differentiated and tailored to the specific needs of individual EU countries.

These findings are consistent with Schumpeter’s theories (Bazhal, 2019) that consider technological progress and innovation as an intrinsic factor of economic development. Likewise, the openness of economies supports the transfer of technology and knowledge, which are also essential for supporting the innovation process (Rodil et al., 2015). The openness of economies facilitates the international flow of innovation and knowledge, thereby increasing competitive pressures and forcing firms to invest in R&D (Bakari, 2024; Bakari et al., 2022). As stated by de Lucas Ancillo and Gavrila (2023) and others, the fundamental driving force of innovation performance and economic growth is R&D expenditure. This fact is also confirmed by our results, as the relationship between innovation and R&D expenditure has been demonstrated. Therefore, the EU’s innovation-focused objectives, which set a threshold of 3% of GDP for R&D investment (Pelikánová, 2019), can be considered correct, as this relationship is the most significant. This finding supports the objectives of the Europe 2020 strategy.

During the pandemic, digitalization played a very important role. The relationship between the openness of economies and digitalization has shown that during the pandemic, the “invisible hand” effect of digitalization can ensure the intensive development of digital economy sectors against the background of a significant slowdown in traditional sectors (Karpunin et al., 2020; Kang, 2023). ICT and digital transformation towards a knowledge economy play an important role for economic development and innovation (DESI and innovation relationship) and reduce barriers to international trade and increase competitiveness (Audi et al., 2025; Benazzouz & Sadok, 2024; Kang, 2023). This finding is one of the key ones and points to the fact that investing in innovation is essential even during exceptional situations, such as the COVID-19 pandemic.

However, the double interactions between the variables under study indicate a negative impact. This can be interpreted as saturation or mutual substitution of the combination of these parameters. This means that, for example, high R&D expenditure may not increase the openness of the economy to a sufficient extent to increase the expected increase in innovation. Innovation capacity may already reach or exceed the limits of the capabilities of a given country (Pelikánová, 2019). Therefore, as de Lucas Ancillo and Gavrila (2023) state, it is necessary to focus on the effectiveness of R&D expenditure rather than just the volume.

However, the triple interaction between the variables negates this phenomenon, as their joint interaction creates a significant positive impact. This fact confirms the holistic approach of innovation management. The synergy of several parameters creates a synergistic effect of innovations. The mutual complementarity of individual parameters and their strategic integration increases innovation performance through a cumulative effect. For management in the knowledge economy and digital transformation, this fact represents a systemic approach to supporting and developing innovations (Untura, 2023).

Another key finding is that there is no statistically significant impact of GDP on innovation. This supports the theory of Untura (2023), who argues that in the era of knowledge economy and digitalization, GDP is no longer a traditional macroeconomic aggregate and predictor of innovation. Therefore, it is necessary to focus on systemic actions in the field of digitalization, science and education (Untura, 2023). Innovation in EU countries is therefore primarily R&D expenditure, digitalization and, last but not least, openness of economies. What is important is their quality, structure and strategic objectives of their implementation in economic development, and not only gross domestic product (Trade to GDP, DESI and R&D expenditure).

The future EU innovation policy should therefore focus on an individual approach to increasing resources for R&D and optimizing interactions and synergies between trade openness, digitalization and research investments in order to achieve sustainable innovation growth.

5. Conclusions

This paper aims to assess the openness of EU economies to innovation. It assesses it from the perspective of specific interactions of dynamics in the period from 2018 to 2024 (including the COVID-19 pandemic). Based on the results, we can conclude that the closure of economies due to the pandemic did not significantly affect the rearrangement of countries within the dynamic cluster analysis.

The results consistently confirmed the importance of the openness of economies to innovation. However, it should be noted that their combination with other parameters has a more significant impact. These are mainly digital and global connectivity of economies as well as investments in science and research for the development of innovations. The synergistic effect of several parameters on the development of innovations confirms growth theories even during the pandemic. GDP does not have a significant impact on the development of innovations in the context of the synergistic effect of other parameters, which, however, can be partially influenced by GDP. Based on the presented findings, we recommend the following:

The policy on the framework supporting and developing innovations should take into account the specificities of each country so as to structurally and systematically support the synergistic innovation effect. Within the framework of the innovation policy of EU countries, it is appropriate to focus not only on the volume of expenditures on science and research but also on their optimization with a focus on efficiency and quality. The transfer of innovations to the commercial environment should be supported, especially in the digital environment. It is necessary to focus on countries with low digitalization as a priority so that they can effectively absorb know-how from international trade and develop a knowledge economy.

The limitations of this study are in the data range and their annual frequency. This data frequency may not capture all the impacts of innovation policies. While the FE mixed model provides robust estimates for fixed effects, future studies could use dynamic panel models, such as GMM and others. These models could also be enriched with other research parameters, such as human capital (education) and governance efficiency, which can influence the absorption capacity of innovations.