1 Introduction

The debate on economic convergence or divergence—the process where countries with lower GDP per capita levels catch up with those having higher GDP per capita—has resurfaced in the economic community, as highlighted by Johnson and Papageorgiou (2020). In this context, Kremer et al. (2021) and Patel et al. (2021) revisited the debate on cross-country convergence over the last 6 decades, uncovering evidence of modest convergence, a finding that contradicts earlier assertions of non-convergence by researchers like Barro (1991) and Quah (1993). Kremer et al. (2021) was criticized by Acemoglu and Melina (2021), who found no convergence between the studied countries. While theoretically long run convergence should be expected, decades of absent economic convergence in Europe and globally has reborn the convergence debate (Diaz del Hoyo et al., 2017; Fedajev et al., 2022; Franks et al., 2018; Johnson & Papageorgiou, 2020).

While several studies investigate economic convergence in the form of GDP, there is a scarcity of research delving into the underlying long-term driver of economic development: technological change (Bernard & Jones, 1996; Churchill et al., 2020). The paper adds to the already existing recent additions to the scientific literature that examine regional level university patenting and technological specialization in European regions (Caviggioli et al., 2023; Colombelli et al., 2021).

The impact of technological change on economic growth has been a subject of extensive research in economics for many years. Robert Solow’s seminal economic growth model from the 1950s gave reason to believed that rich and poor countries in the long run would converge to steady rates of growth dependent on their technological development, savings rate (capital accumulation), and population (Solow, 1956). But will technology converge? Not necessarily according to Stiglitz (2016:138) “Contrary to the presumption in standard theory, countries do not necessarily naturally converge in technology (knowledge)”. Hence, if technology level diverge it is rather possible that the economic level will not manage to converge either (You et al., 2020).

The purpose of this paper is to analyze technological divergence or convergence among the member states of the European Union (EU) to determine if the pronounced EU-level goals for convergence are being met. This paper will investigate whether EU member states with lower levels of technological input and output in the year 2000 have caught up by 2018 with countries that initially had higher levels of technological input and output.

The European Union enacts specific policies aimed at promoting economic convergence among its member states. These policies decrease the chances of economic randomness and guide the economies towards a shared direction, in line with the objectives set out in the Treaty on the Functioning of the European Union, first signed in Rome in 1958. Antonelli and Fabrizio’s 2023 study reinforces this, suggesting that European integration is likely to reduce knowledge costs, thereby potentially aiding in further convergence.

The issue of European convergence is crucial, as divergence in the inventive capabilities and technological levels of EU Member States could lead to a broader economic divergence, potentially undermining the EU’s goal of fostering greater cohesion among its members (Archibugi & Filippetti, 2011). For EU integration to be successful, convergence in national inventive capabilities is essential. This is because, as Archibugi and Pianta (1994:19) argue, the convergence of national inventive capabilities is a key driver of the long-term convergence of per capita incomes and labor productivities:

“... similar economic performances might result from different combinations in the countries’ production and use of technology. But the question is to what extent economic convergence can be achieved and sustained without convergence also in innovative activities. We could expect that after some point further progress in economic convergence needs to be sustained by a parallel convergence in countries’ ability to carry out research and produce innovations”.

To fulfill the purpose of the paper, six key technological indicators are investigated: (a) Scientific journal publications, (b) total patents, (c) high-tech exports, (d) gross domestic expenditure on R&D, (e) government budget on R&D, and (f) human resources in science and technology as a share of the active population. These variables are intended to represent technological output and input. While the first three indicators are clear outputs of a research process, the latter three represent inputs.

We selected our output variables to capture three distinct stages in the technology production chain, as detailed in Grafström and Lindman's (2017) work, specifically covering invention, innovation, and diffusion. To elaborate, scientific journal articles generally represent foundational research conducted at universities, while patents are typically acquired by external firms and inventors. High-tech exports, in contrast, are indicators of technology transfer through diffusion into wider applications. Our choice of input variables aims to reflect the facilitators of technology transfer, who also function as inputs in knowledge production.

We utilized both a time-series approach and a longitudinal approach to analyze data spanning from 2000 to 2019, extending in some cases up to 2018, depending on the availability of data. Methodologically, our analysis is based on both traditional and recent strands of the convergence literature (Brännlund et al., 2015; Žižmond & Novak, 2007).

The remainder of the paper is organized as follows: Sect. 2 reviews the state of European research output and previous research on convergence. Section 3 presents the methodological approaches. In Sect. 4, the data used is presented, and the chosen variables as proxies for inventive capabilities are discussed. Section 5 synthesizes the empirical findings, while Sect. 6 discusses the results. Finally, Sect. 7 concludes the paper, highlighting key implications and offering suggestions for future research.

2 Background literature

2.1 Convergence, or not?—Technological convergence from a theoretical standpoint

Technological convergence, or the concept of "catching up," refers to the idea that countries lagging in technological advancement can leverage a global backlog of existing knowledge to achieve accelerated productivity growth. In neoclassical economic theory, factors like competition and globalization are seen as catalysts for this convergence. Technological development is considered exogenous within the neoclassical growth model, leading to the long-term treatment of technology as a public good (Maurseth, 2001). As a result, long-run economic growth is also essentially viewed as exogenous. According to this perspective, convergence should result from exogenous technological changes that transcend national borders (Bernard & Durlauf, 1995). Specifically, increasing marginal revenues in technological development are thought to drive long-term convergence of technology across countries (Stiglitz, 2015). However, this view of technology as a public good has been challenged by the ‘technology gap’ approach, which sees technology as difficult to transfer (Fagerberg, 1994).

The debate on convergence was reignited by Baumol (1986), Romer (1986), and Lucas (1988), who questioned the neoclassical Solow growth model’s assumption of absolute convergence. As evidenced in recent decades, not all rich and poor countries have converged to the same income level, even though some poorer countries have been catching up (Johnson & Papageorgiou, 2020).

While the theoretical reasoning fit decently regarding GDP convergence, the reasoning does not necessarily translate to convergence in development, diffusion, and ability to make use of technologies. Development of technologies here refers to the ability to create but also make use of externally created technologies. Mulas-Granados and Sanz (2008) argued that long-term income convergence necessitates laggard countries investing more in R&D compared to their more competitive counterparts, as R&D investments are pivotal in driving innovation and new technologies that enhance economic competitiveness. Without substantial R&D investment, only a short-term catching-up process is feasible, due primarily to capital investments stemming from higher rates of return on capital and/or limited absorption of foreign technologies through foreign investments—but not—because of productivity improvements connected to R&D.

Several factors contribute to the absence of technological convergence, including the tendency for technological development to cluster in specific locations rather than disperse evenly. Technological cluster theory suggests a scenario where knowledge production diverges, and technology production clusters in certain geographical regions (Delgado et al., 2014). This clustering leads to increasing returns on investments in areas with robust research infrastructure. Despite costs potentially increasing tenfold in places like Silicon Valley or major European tech hubs, firms often opt to locate production in these high-cost areas. This decision goes against what baseline microeconomic theory would predict as profit-maximizing behavior.

If technology production clusters and researchers leave technologically lagging areas for better-paid opportunities in more advanced countries, the potential for convergence is undermined. As a result, technologically lagging countries may regress to specializing in low-technology industries that require minimal capital and less sophisticated technology (Rodriguez-Pose, 1999). This clustering scenario places technologically lagging countries in a "low-invention trap," where few inventions are produced, and frontier technology is difficult to diffuse. Conceptually, the low-invention trap is like the "low-level equilibrium trap" in economic prosperity, in which some poor countries are believed to be stuck (Desdoigts, 1999; Nelson, 1956).

Economic convergence is intricately linked to achieving convergence in a country’s inventive abilities and/or its capacity to diffuse external technological changes (Antonelli, 2008; Antonelli & Quatraro, 2010). Absorptive capacity refers to a country’s ability to assimilate foreign knowledge; the value of international technology flows hinges on the destination country’s ability to diffuse external knowledge effectively (Mancusi, 2008). The diffusion of knowledge is more likely when there is a high degree of technological proximity between the competencies and knowledge stocks of both the inventors and the adopters (Antonelli et al., 2011; Boschma & Iammarino, 2009).

Antonelli and Fabrizio (2023b) demonstrate that absorptive capacity is a significant issue and underscore the role of limited knowledge transferability in boosting total factor productivity, particularly emphasizing the variability in absorption costs among different entities (Antonelli & Fusillo, 2023a, 2023b). They suggest that European integration may reduce knowledge appropriability, thereby enhancing knowledge transfer. This hypothesis is supported by their empirical analysis of 12 European countries and 20 industries spanning from 1997 to 2018 (Antonelli & Fusillo, 2023a, 2023b).

Antonelli and Fabrizio (2023b) assert that a swift reduction in both knowledge appropriability and absorption costs accelerates the decline in overall knowledge costs, a concept also supported by (see also Antonelli & Gehringer, 2016; Antonelli & Fusillo, 2023a, 2023b), resulting in improved levels and growth rates of total factor productivity. This phenomenon presents a dual impact on economic convergence: while it provides an opportunity for lagging economies to catch up, assuming they remain relatively close to the technological frontier, it also poses a challenge as these advancements might widen the gap if they fall too far behind.

2.2 Convergence research on technology in EU

For the EU, at least two potential scenarios exist regarding the future trajectory of inventive output. The first scenario aligns with the foundational principles of economic convergence theory (Barro, 1991; Quah, 1993). Theoretically, countries that are technologically lagging would experience faster growth (in percentage terms) compared to technology leaders, as higher growth rates enable these laggards to eventually catch up (Keefer & Knack, 1997). The alternative scenario suggests a concentration of technological output in a few countries. In empirical research, the evidence supporting either scenario is mixed.

In the EU, there is a noticeable gap in technological input and output among member states (e.g., Dobrinsky & Havlik, 2014; Lorenz & Lundvall, 2006). For instance, the diverging number of industrial robots in different countries indicates that some, being more industrially advanced, will become more productive, potentially leading to economic divergence (Jungmittag, 2021).

Fagerberg and Verspagen (1996) observed that the income and productivity convergence that prevailed in Europe post-World War II diminished and ceased in the 1980s, attributed to a decline in the ability to diffuse new knowledge. Jungmittag (2004), in a study on labor productivity convergence between 1969 and 1998 using beta- and sigma-convergence panel data models, found that capital accumulation and transferable technical knowledge facilitated the catching-up process for the EU’s laggard countries. Additionally, Filippetti and Peyrache (2013), examining labor productivity growth across Europe from 1993 to 2007, noted that the efficiency gap had reduced but cautioned that further narrowing would be challenging. They emphasized that improvements in labor productivity would depend on advancements in technological capabilities.

Martin et al. (2005) discovered that both patents granted and public R&D converged, contributing to the convergence of income per capita. Archibugi and Coco (2005) found that R&D investment within the EU was heterogeneous and predicted that the emergence of a homogeneous innovation system was unlikely. In their study, Archibugi and Filippetti (2011) examined the impact of the 2008 financial crisis on EU research and development (R&D) investment convergence, using the European Innovation Scoreboard (EIS) and a beta-convergence approach for the years 2004–2008. They observed slow convergence in terms of EIS indicators. Additionally, Žižmond and Novak (2007) investigated the EU15 Member States along with eight subsequent entrants and noted convergence in gross fixed capital formation.

Jungmittag (2006) conducted research on granted patents as a measure of convergence. The study focused on the EU15 countries from 1963 to 1998 and employed unit root tests for both time series and panel data. The results showed mixed support for the convergence of granted patents, indicating the presence of both beta-convergence and stochastic convergence, although this was not consistent across all countries in the sample.

Mulas-Granados and Sanz (2008) adopted a regional perspective to examine the relationship between technological and income convergence across EU regions from 1990 to 2002. They utilized R&D expenditure across all sectors as a percentage of GDP as the technology input indicator and patents per million people as the output indicator. Their findings indicated both technology output convergence and real income convergence. Izsak and Radošević (2017) noted that the 2008 financial crisis had significant repercussions for the convergence process, with R&D funding in several southern countries collapsing, leading to a North/South divergence. Blanco et al. (2020) investigated the evolution of R&D expenditure in the EU28 during the period 2004–2015, finding convergence in total expenditures but also identifying club convergence.

In their examination of the relationship between university patenting and regional industry specialization, Caviggioli et al. (2023) analyzed co-evolution patterns across European regions and found significant heterogeneity. Their empirical findings reveal that strong research universities in Europe are not uniformly distributed but are instead concentrated in key areas, predominantly in Western Europe. Colombelli et al. (2021) focused on Turin, Italy, to investigate the role of universities in regional technological development and proposed a taxonomy for the technological evolution processes of university-region interactions. Their research highlights the critical importance of absorptive capacity in facilitating knowledge transfer.

3 Method

Our analysis adopts a dual approach. In the first approach, a model for each technological indicator is constructed, where the observations are clustered based on specific EU groups, categorized by their year of entry into the EU. The objective is to identify convergence between these groups, resulting in three distinct time series for the EU15, EU13, and EU8. The countries included in each group are listed in Table 1 below.

Table 1 List of countries in EU groups.
Full size table

The countries in the EU15 are those that joined the EU before 30 April 2004, while the EU13 comprises countries that entered after 1 May 2004 (Eurostat, 2020). Although the UK ceased to be an EU member as of 1 February 2020, it is included in this analysis since the period investigated predates Brexit. The EU8 is a subset of the EU13, specifically consisting of Eastern European countries that share many similar characteristics.

First, the EU groups are investigated, and time series of the mean values for each group and variable are created. This is done to determine whether the groups converge, diverge, or remain constant. The determination is made by testing for stationarity in the residuals according to the general formulas presented in Eqs. (1) and (2):

$${y}_{t}={\beta x}_{t}+{\varepsilon }_{t}$$
(1)
$${\varepsilon }_{t} ={y}_{t}-\upbeta {x}_{t},\dots \dots {\varepsilon }_{t}\left\{\begin{array}{c}I(1)\\ I(0)\end{array}\right.$$
(2)

where the residual (\({\varepsilon }_{t}\)) will be non-stationary (I (1)) if there is convergence or divergence between (yt) and (xt), and thus stationary (I (0)) if there is no convergence or divergence.

Given that the initial time-series tests indicated non-stationarity, we proceed to determine the direction of the effects using a longitudinal approach. Following the methodologies of Barro and Sala-i-Martin (1992) and Acemoglu and Melina (2021), our constructed model employs country-level panel data to investigate whether the value of the previous year can explain the growth of the following year. This is done by constructing the dependent variable according to Eq. (3).

$$\frac{{y}_{it}- {y}_{it-1}}{{y}_{it-1}}= {y}_{it}^{*}$$
(3)

The method will enable an analysis of whether the growth rate for each variable is accelerating or decelerating, thereby indicating whether there is a catching-up effect. The model can be described as follows:

$$y_{it}^{*} = \alpha + \beta_{1} (y_{it - 1} ) + \beta_{2 + ... + 4} {\text{log}}\left( {{\raisebox{0.0ex}{--}\kern-0.6em z}_{xit} } \right) + \phi_{1} \left[ {\left( {y_{it - 1} } \right){\text{log}}\left( {{\raisebox{0.0ex}{--}\kern-0.6em z} _{1it} } \right)} \right] + \phi_{2} \left[ {\left( {y_{it - 1} } \right){\text{log}}\left( {{\raisebox{0.0ex}{--}\kern-0.6em z}_{2it} } \right)} \right] + \eta_{t} + \mu_{it}$$
(4)

where i = 1,…, N = countries and t = 1,…,T = years, (\({y}_{it}\)) is the technological input or output and (\({y}_{it-1}\)) is the same variable lagged one period (in this case year). As seen in the in the left side of Eq. (3) the dependent variable is constructed as the growth rate of (\({y}_{it}\)).

Empirical literature and economic theory were analyzed to identify appropriate indicators of technological development in research. Data was sourced from the databases of Eurostat, the OECD, and the World Bank. This data was categorized under "Science and Technology" statistics. Six key variables were investigated to describe both technological input and output: (a) Scientific journal publications, (b) total patents, (c) high-tech exports, (d) gross domestic expenditure on R&D, (e) government budget for R&D, and (f) Human resources in science and technology as a percentage of the active population.

Three control variables (ƶit) are included to capture country-specific characteristics and not to over- or underestimate the predicted coefficient (\(\widehat{{\beta }_{1}}\)). The control variables in our study include population growth, GDP per capita, and a Democracy Index, allowing for heterogeneity among the countries in the model. For instance, the average Democracy Index score among the EU15 countries is 85.3, while for the EU13 countries, it is 73.7. In terms of GDP per capita growth, the control variable, when expressed in logarithmic form, shows a significantly higher average growth among the EU8 and EU13 countries compared to those in the EU15 group. To facilitate comparison of country-specific variables, all three control variables are used in their logarithmic form.

Two interaction variables are included. Where the variable for technological development has been multiplied by the first and second control variable to capture the effect of there likely being a correlation between the variable of interest the growth rate (\({y}_{it}\)) and the control variable (ƶit) . The first interaction term (denoted by \({int}_{1}\) in the results) is the product of (\({y}_{it}\)) times the GDP per capita (ƶ1it). And the second interaction term (denoted by \({int}_{2}\)) is the product of (\({y}_{it}\)) times the democracy index (ƶ2it).

Lastly, the variable (\({\eta }_{t})\) is included to hold constant for country specific effects meaning that the longitudinal approach will use a fixed-effects model as suggested in recent work by Acemoglu and Molina (2021).

4 Data sources and definitions

4.1 Technological indicators tested for convergence

Scientific journal publications: consists of the number of scientific articles published in journals per million inhabitants. The article counts are derived from the Institute for Scientific Information’s Science Citation Index (SCI) and Social Sciences Citation Index (SSCI) (World Bank, 2021a). In cases where there are multiple authors from different countries, the counts are fractionally divided between the countries.

A limitation of this approach is that the SCI and SSCI databases cover only a core set of scientific journals, potentially omitting some journals that are locally significant. Additionally, there may be a bias toward English-language journals. In the World Bank dataset, not all arts and sciences are represented; the data consists of scientific and engineering articles published in fields such as physics, biology, chemistry, mathematics, clinical medicine, biomedical research, engineering and technology, and earth and space sciences.

The number of scientific articles published per million inhabitants has risen in all European countries since the year 2000. The most significant percentage increase is observed in the countries that joined the EU after 2004, namely, the EU13. A visual examination reveals noticeable north/south and east/west divides (Fig. 1).

Fig. 1
figure 1

Source: Own calculations, data from Worldbank 2021a

Scientific articles. Note The number of scientific articles in scientific or technical areas per million of inhabitants in EU-countries. See variable explanation for further definition of what areas are included.

Full size image

Total patents: is defined as the total patent application per million inhabitants (OECD, 2021). The data is sourced from the EPO’s Worldwide Patent Statistical Database (PATSTAT Global). When two inventors are from different countries, each country gets a count of 0.5. The geographical location for the invention by the inventor instead of the applicant. Applications for "patents of invention" are considered (i.e., excluding utility models, petty patents, etc.).

Figure 2, highlighting patent applications per capita, reveals that some countries are inventive outliers, both in 2000 and 2018. Among the original EU15, eleven are clear leaders compared to the countries that joined later. Spain and Portugal, while having fewer patent applications than other early EU countries, surpass most of the later joiners. Latecomers such as Slovenia, Estonia, and Czechia had a similar number of patents per capita in 2018. Among the larger countries, there is a significant disparity: while the United Kingdom and France have comparable figures, Germany outpaces them by a factor of 2.5, placing it in the same league as the Nordic and Benelux countries. Finland, Luxembourg, and the UK are the only countries that have seen a decrease in their patent applications per capita to the European Patent Office.

Fig. 2
figure 2

Source: Own calculations, data from OECD (2021)

Total patent applications per million inhabitants to the EPO by country are displayed. All values are by priority date.

Full size image

High-tech exports: The data that is derived from Eurostat shows the share of a country’s exports of all high technology products in total exports. High technology products are based on Standard International Trade Classification, Revision 4 and consist of following products: Aerospace, Computers-office machines, Electronics-telecommunications, Pharmacy, Scientific instruments, Electrical machinery, Chemistry, Non-electrical machinery, Armament.

For high-tech exports in Fig. 3, a similar pattern of “leaders and followers” is not as clear as in Fig. 2. The export share level is more evenly distributed over the different EU-groups. Both Luxembourg and Malta had a relatively larger share of a high-tech exports compared to the other EU-countries in 2007 but their level dropped over the sample period. Luxembourg and Malta are likely outliers, attributable to their small size and high dependence on trade.

Fig. 3
figure 3

Source: Eurostat (2021a, 2021b, 2021c, 2021d)

High-tech exports as a share of total exports.

Full size image

Gross domestic expenditure on R&D (GERD): represents the total spending on R&D performed by a country during a specific reference period, measured in Euros per inhabitant. The data for this comes from Eurostat. As observed, the spending varies by more than a factor of ten between the leading and lagging countries. GERD (Euro per inhabitant) is illustrated in Fig. 4. Notably, the EU13/8 countries, on average, spend less than the EU15 countries, with a few exceptions. Additionally, there has been an overall increase in R&D expenditure, especially for the EU13/8 countries, which started with a lower nominal value in the sample but have experienced an average annual increase of just over 10%.

Fig. 4
figure 4

Source: Eurostat (2021d)

Gross domestic expenditure on R&D (GERD) measured as Euro per inhabitatnt.

Full size image

Government budget on R&D: represents the share of total government appropriations or outlays for research and development (Eurostat, 2021a). R&D spending as an input variable is commonly used to analyze a country’s inventive capacity (e.g., Romer, 1990). While it would have been both important and interesting to study private R&D, comprehensive data for this was not available. The share of the government budget on R&D has its limitations, notably that the earliest available data is from the midst of the 2007–2008 financial crisis, which likely impacted government spending and the relative allocation across different areas. Overall, the EU15 countries were spending a larger share (of a larger budget) on R&D, although in some cases the total budget was smaller. The values for 2008 and 2019, expressed as percentages of the government budget, show relatively small changes in most countries over this period (Fig. 5).

Fig. 5
figure 5

Source: Own calculations, data from Eurostat (2021a)

Government budget on R&D. Note The share of government budget on R&D per EU-country.

Full size image

Human resources in science and technology as a share of the active population (HRST): the individual must have a graduation from a tertiary level education or be employed in a science and technology sector and be between ages 25–64 and comes from Eurostat. The variable measures the labor intensity in the sector, which in our study serves as a proxy for human capital (Eurostat, 2021b; Prasetyo & Kistanti, 2020). As shown in Fig. 6, all countries have experienced an increase in HRST over the period. Notably, some countries with high levels of human capital in 2009 have seen a more significant increase than countries with lower levels of human capital in 2009, potentially indicating a trend towards divergence.

Fig. 6
figure 6

Source: Own calculations, data from Eurostat (2021b)

HRST. Human resources in science and technology as a share of the active population is displayed per EU country. Note Where the active population is defined as active individuals in the age group of 25–64.

Full size image

4.2 Control variables

Population growth: The data on population is sourced from the World Bank and represents a nominal population count (World Bank, 2021b). GDP per Capita: This variable includes data on GDP per capita for EU countries, expressed in current US dollars (as of 2021) (World Bank, 2021c).

Democracy index: The Democracy Index is an average score derived from five measurement indices: Electoral Pluralism, Government Index, Political Participation Index, Political Culture Index, and Civil Liberties Index. The index is calculated annually for each country by the Economist Intelligence Unit (EIU), and Gapminder has compiled all the reports into one dataset (Gapminder, 2021) (Table 2).

Table 2 Descriptive statistics
Full size table

5 Result and discussion

5.1 Time-series results

A visual presentation of the results, showing the development of the mean values for different technological proxy variables by EU groups, is displayed in Fig. 7. Following this visual inspection, an investigation into the stationarity of these processes and the stationarity in the residuals of these processes was conducted. The first observation is that none of the processes are stationary, as confirmed by the Dickey–Fuller test for unit root, where the test statistic did not surpass any of the conventional critical values. This test was conducted both with and without including a trend term, yielding the same outcome.

Fig. 7
figure 7

Histogram of mean values. Note Mean values for the three different EU groups. The x-axis spans over different time periods for the different variables as a results of data availability

Full size image

To test for potential convergence or divergence between the processes, the residuals between EU15 and EU13, as well as EU15 and EU8, were also tested for stationarity. Although the residuals in most cases appear to be stationary in Fig. 7, mathematical testing contradicts this initial intuition. By generating new processes based on these residuals, the same statistical tests for unit root, as previously conducted, can be applied. The results from these tests are displayed in Table 3 below. Subsequently, the residuals for each variable are graphed, similar to the treatment of the mean values above.

Table 3 Dickey fuller test for unit root
Full size table

As seen in Table 3, none of the values show a stationary process. This implicates that a cointegration between (\({y}_{t}\)) and (\({x}_{t}\)) exists, i.e., convergence or divergence is happening in the dataset. When testing for stationarity, the Engle-Granger test for cointegration yielded similar results. Therefore, the null hypothesis suggesting the presence of a unit root in the models cannot be rejected. It’s important to note that the low number of observations affects the critical values, making them relatively high. The short time period could explain why the graphs in Fig. 7 may give the impression of having stationary residuals, while the Dickey–Fuller test suggests otherwise. Below, these residuals are presented separately in Fig. 8.

Fig. 8
figure 8

Residuals of mean values for the EU15 and EU13 as well as EU15 and EU8. Note the x-axis spans over different time periods for the different variables as a results of data availability

Full size image

When displaying only the residuals, as done in Fig. 8, non-stationarity becomes evident, contrasting with the initial impression from Fig. 7. If the residuals for each EU group had shown stationarity for the variables, the histograms would have converged to zero. However, none of the graphs above exhibit such tendencies, as also confirmed by the Dickey–Fuller test. It should be noted that both Table 3 and Fig. 8 show a higher tendency for convergence among the input variables than the output variables. However, due to the short time frames, further conclusions cannot be drawn. To overcome this obstacle, panel data for the same period is analyzed.

5.2 Longitudinal results

The primary focus here is on the coefficient for the lagged value of the nominal proxy variable. A coefficient below zero would suggest that a higher nominal value last year would result in lower growth in the same variable the following year, ceteris paribus. In this analysis, the countries are no longer clustered into groups, and therefore, a fixed effects model is employed.

Four different models for each variable are presented to assess how the control variables, as well as the constructed interaction variables, affect the results. The primary results can be interpreted from Models 4, 8, 12, and 16 in Tables 4 and 5. It should be noted that the exact parameter values need to be interpreted with caution and are not our main focus due to the short period.

Table 4 Fixed effects OLS models for indicators 1 & 2
Full size table
Table 5 Fixed effects OLS models for indicators 3 & 4
Full size table

A negative value of the estimated parameter (\(\widehat{{\beta }_{1}}\)) indicate convergence and thus a positive (\(\widehat{{\beta }_{1}}\)) will indicate a divergence. Therefore, the main result of interests is if the estimated parameter \(\widehat{{\beta }_{1}} \ne 0\), and if the sign is positive or negative.

In addition to testing for beta-convergence absolute convergence is also of interest. An absolute convergence cannot be rejected if some of the control- and/or interaction variables are positive and statistically significant at a conventional level.

A fixed-effects OLS model is employed to control for country-specific effects. Table 4 offers additional insights into the non-stationarity observed in the time-series approach. The fixed-effects models for the output variables in Table 4 reveal beta-convergence at a 1% significance level. This implies that a catching-up effect in these variables can be anticipated.

As an example of interpretation, let’s examine Model 16. In this model, it suggests that if a country increases its total patent applications per million inhabitants, then it is expected that, on average, the growth in that variable will decrease in the following year, all other things being equal. The data thus indicates that countries with a lower nominal number of patent applications are likely to experience higher growth in the future.

Table 5 continues the longitudinal approach analysis by presenting two additional variables: one output variable, high-tech exports, and one input variable, gross domestic expenditure on R&D. Similar to Tables 4 and 5 also indicates beta-convergence in all models for the two technological indicators. It’s worth noting that while the lagged parameter for gross domestic expenditure may appear small, it cannot be directly compared to the other models in this table. In the case of this variable, it is multiplied by euros per inhabitant. The same concept applies to the parameter for scientific articles in Table 4 and Human resources in science and technology in Table 6. Additionally, gross domestic expenditure on R&D is the only technological indicator where the parameter is not statistically significant at the 1% level but is significant at the 5% level in models 22–24.

Table 6 Fixed effects OLS models for indicators 5 & 6
Full size table

In Table 6, both input variables demonstrate convergence at a 1% significance level in all models. This implies that a higher nominal value will, on average, lead to lower growth in the next year, assuming all other factors remain constant. Therefore, the expectation is that in the long run, there is a catching-up effect among the EU countries.

The longitudinal approach yields several key takeaways. Beta-convergence is significant at a 1% level for all parameters, except in the case of Gross domestic expenditure on R&D, where the models suggest beta-convergence at a 5% significance level. Additionally, the control and interaction variables indicate that absolute convergence in all variables can be rejected, except for total patents and government R&D expenditure. Beta-convergence remains significant, but absolute convergence cannot be rejected in these cases (Table 7).

Table 7 Convergence or divergence?
Full size table

6 Discussion

The overall findings of this analysis support the claim that there is convergence in the inventive abilities under investigation. Both the time-series analysis and the longitudinal analysis reject the hypothesis that the converging or diverging effects are zero. In the panel data analysis, statistically significant results of beta-convergence are found at a 1% significance level in all models, except for one where beta-convergence is found at a 5% level. Additionally, we can only reject absolute convergence for four out of the six variables. However, this does not imply the presence of absolute convergence, as beta-convergence could be influenced by other country-specific factors. Therefore, the results indicate that absolute convergence is not rejected for these two variables (Government budget on R&D and Total patents).

Over the last 2 decades, the analysed indicators do not show any evidence of technology clusters diverging from other countries within the EU. Furthermore, there is no evidence supporting the existence of a middle-innovation-trap; instead, a slow but steady convergence in all six indicators is observed. Based on these results, a catching-up effect in the inventive abilities within the EU is indicated. These convergence results align with what most of the literature has shown when analysing earlier data. As argued by Verspagen (1991), the catching-up phenomenon is present in the developed parts of the world when analysing inventive capabilities.

It should also be noted that in the models of total patents and government budget on R&D, absolute convergence could not be rejected. That is, the models cannot reject an unconditional convergence in these cases. It is important to distinguish this from evidence of unconditional convergence, as the latter would imply that all independent variables would exhibit statistically significant convergence.

A paper by Antonelli and Fusillo (2023a, 2023b) can likely shed some light on the slow phase of convergence. In their study, which covers determinants of patent costs in Europe between 1992 and 2012, they find that a larger stock of patents and a higher technological variety and coherence in its composition are associated with a sharper reduction in patent costs. This result suggests a competitive advantage for countries that already have a large research sector.

The convergence coefficient is, in most cases, small, indicating that the half-time for reaching convergence between the countries is substantial. Not catching up soon is not a promising prospect, and as seen in other convergence literature, the poorer European countries have been thrown off their growth track during crisis times (Bolea et al., 2018). The 2008 global financial and economic crisis led Northwest Europe to increase support for research and investment activities, while Southern Europe witnessed a collapse of its national public support for research and investment (Izsak & Radošević, 2017).

The findings of this paper are interesting in relation to the findings of Antonelli and Fabrizio (2023b), along with Antonelli’s earlier works (2013) and Antonelli and Gehringer (2016), offer a lens through which to view the EU’s convergence efforts by highlighting the critical role of knowledge costs and their transferability in influencing total factor productivity. In the context of the EU, there are varying levels of knowledge absorption and transferability across member states which could either facilitate or hinder the convergence process. While the EU’s structural and cohesion funds aim to foster economic convergence, the disparities in knowledge transferability and the pace of technological change could present a challenge. If regions closer to the technological frontier benefit more from reduced knowledge costs, potentially leading to a growing productivity gap between more and less advanced areas. Country disparities within the EU might therefore widen, challenging the union’s cohesion and long-term stability.

The last thing to note is that the interpretation of the specific magnitude of the parameter estimates should be approached with caution. Using the models to forecast the effect on the growth rate is likely to be misleading due to the choice of the model and the influence of exogenous factors on future outcomes.

For potential EU candidate countries, a primary attraction of the EU has been the prospect of catching up to EU living standards. Within the EU, differences in GDP across regions and countries have always been seen as undesirable, and many significant EU policies have focused on reducing income disparities. If the Union does not deliver on this promise, there is reason to believe that its ability to attract new members or retain old ones will be in jeopardy. Fortunately, there is evidence of technological catch-up, albeit small, among the countries. If technology levels can converge, there is good hope for long-term economic convergence.

7 Conclusion and implications for policy

As President Lincoln once concluded, "A house divided against itself cannot stand" (speech, Springfield, Illinois, June 16, 1858). The same analogy is appropriate for the EU. A significant amount of EU funding is directed towards structural and cohesion funds aimed at achieving economic convergence and cohesion. Following Brexit, the EU faces questions, and in the long run, citizens might challenge a monetary transfer union. It is, therefore, highly relevant to determine if convergence exists within the EU. Our empirical findings suggest a converging pattern since the millennium in all six inventive capabilities analyzed.

Will Europe be able to sustain this slow convergence? With more frequent crises and what appears to be a growing productivity gap between countries and regions, there is a risk of a new wave of divergence. Europe’s convergence efforts might need an upgrade to accommodate accelerating technological change. Accelerating technological change offers increasingly rich opportunities for well-skilled employees and frontier companies, while low-skilled employees and less productive companies risk falling behind, especially in low-productivity regions.

t was not initially clear whether the inventive capabilities analyzed were converging or diverging within the EU. Even with trends of convergence, we cannot dismiss the concept of "leaders and followers" and the existence of technology clusters that could be influential in the event of accelerated technological change. Both when analyzing countries as members of EU-groups as well as single entities of a panel dataset the theory of a diverging pattern could be rejected. The last few decades of European regional policies might have yielded results, as a convergence process is evident. Although disparities in most indicators are still significant across EU countries, the observed technological convergence process provides some evidence of success.

A weakness of this study is its level of aggregation when comparing countries. When comparing countries, it is easy to overlook the fact that large parts of countries could be lagging behind, while most of the economic prosperity is concentrated and developed in specific economic areas geographically.

There are several ways to improve the analysis carried out here, for one, the choice of indicators (scientific journal publications, total patents, high-tech exports, R&D expenditure, government budget on R&D, and human resources in science and technology) to define a country’s technological level might not fully capture the complexity of technological capabilities. These indicators may overlook qualitative aspects of technological development and innovation. The time frame (2000–2019) might affect the comprehensiveness and the current relevance of the findings, particularly for rapidly evolving technological fields. Furthermore, the use of time-series and longitudinal approaches, while robust, may not fully account for non-linear dynamics and regional disparities within individual EU countries. These methods may also struggle to capture the intricate causal relationships between technological development and economic growth. The focus on EU member states might limit the applicability of the findings to other regions or global contexts. Differences in political, economic, and social structures across regions could mean that the study’s conclusions are specific to the European context.

Given the theoretical and empirical rationale presented, future research on convergence should meticulously concentrate on technology. Currently, there is a profound level of analysis and comprehension regarding technology gaps and convergence. Understanding this issue is vital to guide EU policies effectively in addressing the uneven economic conditions within the union.