4. Empirical Analysis of Technological Convergence in the European Regional Area

The data necessary to compute TFP over 2008–2018 have been retrieved from the Annual Regional Database of the European Commission’s Directorate General for Regional and Urban Policy (ARDECO). We use GDP at constant prices as the output variable. The input variables include employment in thousand hours worked and the stock of physical capital. The former is calculated in line with the perpetual inventory method:where K stands for capital stock, 𝛿 stands for the depreciation rate, and 𝐺𝐹𝐶𝐹 stands for gross fixed capital formation. As with (Schatzer et al., 2019b) the depreciation rate is assumed to be 10 percent. The initial capital stock is calculated in accordance with Capello and Lenzi (2015) as the cumulative sum of 𝐺𝐹𝐶𝐹 over the preceding 10-year period from 1998 to 2007.

As regards the data on regional innovation, at the starting point of our analyses we have applied the database stem from Regional Innovation Scoreboard (RIS), which is a regional extension of the European Innovation Scoreboard (EIS). RIS tries to close a huge gap in the access to innovation data at the regional level and allows for comprehensive regional innovation benchmarks. Database includes data at regional level for 21 indicators. The data are normalized using the min-max procedure. Given the scope of our study, we use selected variables that relate to innovation framework characteristics, investments, activities, and impacts (Table 4.1). Moreover, regional data for R&D expenditures in the business sector per GDP and patent applications per GDP over 2008–2018 have been extracted from Eurostat’s regional database.

Our sample consists of 219 European regions. The regional coverage of this study is consistent with the Regional Innovation Scoreboard—RIS methodology. Depending on the differences in regional data availability, the sample covers 47 NUTS 1 regions and 172 NUTS 2 regions, including Austria (3 NUTS 1 regions), Belgium (3 NUTS 1 regions), Bulgaria (6 NUTS 2 regions), Croatia (1 NUTS 2 region), Czech Republic (8 NUTS 2 regions), Denmark (5 NUTS 2 regions), France (14 NUTS 1 regions), Finland (1 NUTS 1 region, 4 NUTS 2 regions), Germany (9 NUTS 1 regions, 29 NUTS 2 regions), Greece (1 NUTS 1 region, 12 NUTS 2 regions) Hungary (8 NUTS 2 regions), Italy (21 NUTS 2 regions), Ireland (3 NUTS 2 regions), Lithuania (2 NUTS 2 regions), the Netherlands (12 NUTS 2 regions), Poland (17 NUTS 2 regions), Portugal (2 NUTS 1 regions, 5 NUTS 2 regions), Romania (8 NUTS 2 regions), Spain (2 NUTS 1 regions, 17 NUTS 2 regions), Slovenia (2 NUTS 2 regions), Slovakia (4 NUTS 2 regions), Sweden (8 NUTS 2 regions), and the UK (12 NUTS 1 regions).

As mentioned previously, due to limited access to data on innovation at the regional level, the time period for the analysis ranges from 2008 to 2018. This period seems to be rather short but as argued by Islam (1995b) considering that process getting near to the steady state is essentially unchanged over the period as a whole, convergence-regressions for shorter time spans should reflect the same dynamics. Moreover, the period 2008–2018 appears to be appropriate as it includes the enlargement towards Central and Eastern European countries. Most importantly, it largely covers two programming periods of the EU regional policy: 2007–2013 and 2014–2020, which were geared at improving the economic well-being of regions and avoiding regional disparities.

To calculate TFP, we apply the Färe-Primont index, which meets all economically-relevant axioms and tests from the index number theory, hence it allows us to make both multi-lateral and multi-temporal comparisons. The output-input aggregator functions used for the Färe–Primont index calculation have the following forms (O’Donnell, 2011b):where x₀ and q₀ are vectors of representative input and output quantities, t₀ denotes a representative time period, and D₀(.) and D_I(.) are output and input distance functions.

The aggregator functions allow us to calculate the TFP of the region i in the period t:

In order to calculate the Färe-Primont index, we employ the DPIN programme. The programme makes use of data envelopment analysis (DEA) linear programmes (LPs) to estimate the production technology and the levels of TFP. DEA is underpinned by the assumption that the output and input distance functions reflecting the technology available in the period t have the following form, respectively:

DPIN estimates Färe-Primont aggregates by first solving the following variants of linear programmes (O’Donnell, 2011b):

Aggregate outputs and inputs are next estimated as:where α₀, β₀, γ₀, ф₀, δ₀, and η₀ solve (4.7) and (4.8).

In our study, we use three approaches to test TFP convergence. The first one applies a unit root test framework and is related to the concept of stochastic convergence. Since the time dimension of our dataset is relatively small, we decided to use the Pesaran (2007) test, which works well also in very small samples (Moscone & Tosetti, 2009). Before carrying out the Pesaran (2007) test, we check the existence of cross-sectional dependencies (CD) in the calculated TFP scores. We use the Pesaran (2004) CD test and the Frees (1995) CD test. The first test is based on the pairwise correlation coefficients of residuals from Augmented Dickey-Fuller (ADF) regressions, where the optimal lag-order is found applying the general-to-specific procedure proposed by Ng and Perron (1995), and is given by:where \( {\hat{\rho}}_{ij} \) is the sample estimate of the pairwise correlation of the residuals.

It should be noted that the Pesaran (2004) CD test is likely to miss cases of cross-sectional dependence, when the signs of the correlations are alternating. In turn, the Frees (2004) CD test is not subject to this drawback, since it is based on the squared rank correlation coefficients and equals:where \( {\hat{r}}_{ij} \) is the sample estimate of the rank correlation coefficient of the residuals.

Pesaran (2007) unit root test augments the standard ADF specification with the cross-section average of lagged levels and first-differences of the individual series. This is done as follows:where Δy_it = y_it − y_{i, t − 1}, \( {\overline{y}}_{t-1}=\left(1/N\right){\sum}_{i=1}^N{y}_{it-1} \), \( {\overline{y}}_t=\left(1/N\right){\sum}_{i=1}^N{y}_{it} \), \( \Delta {\overline{y}}_t={\overline{y}}_t-{\overline{y}}_{t-1} \) a_i, b_i,c_i, d_i are the parameters and e_it is the error term.

The unit root hypothesis relies on the t-ratio of the estimate of \( {b}_i\left({\hat{b}}_i\right) \) in Eq. (3.​8). A truncated version of cross-sectionally augmented ADF t-statistics is also taken into account to correct for undue influence of extreme observations in short-T panels. Following the common practice in the time series convergence literature (Hernández-Salmerón & Romero-Ávila, 2015), our variable of interest for unit root and CD testing is relative TFP levels, i.e. \( {\mathrm{RTFP}}_{it}=\ln \left(\frac{{\mathrm{TFP}}_{it}}{{\overline{\mathrm{TFP}}}_t}\right) \).

The second approach is related to the β-convergence concept. Within this framework a starting-point for further analyses is the Barro-type growth model for panel data setting, which takes the following form:where β₀ is the constant, β₁ is the β-convergence parameter, ¹ γ_i addresses region-specific fixed effects, \( {x}_{it} \) is a vector of additional regressors, while β is a vector that shows their influence on the growth of y, and finally ε_it is the error term.

To estimate the parameters of Eq. (4.14), it is transformed into the following form:which allows to use efficient generalized method of moments (GMM) estimators. For datasets with many panels and few periods, like in our case, the system generalized method of moment (GMM-SYS) estimator proposed by Blundell and Bond (1998) is preferred. As shown by Bouayad-Agha-Hamouche and Védrine (2010), this estimator can be successfully incorporated into strategies to estimate dynamic panel models and spatial dynamic panel models used to study regional convergence. To addresses the spatial dimension of convergence processes, we consider the following general specification of the spatial dynamic panel model:where ρ represents the intensity of a contemporaneous spatial effect of y, θ captures space-time autoregressive dependence of y, ϕ is a vector that shows spatial effects of additional regressors on y, u_it is the sum of a spatially weighted average of the error components of neighbouring regions and the common error term, and W is a spatial weight matrix.

In the context of spatial effects of TFP we also calculate the Getis-Ord \( {G}_i^{\ast } \) local statistic, which is given as Ord and Getis (1995):where y_j is the level of y for region j, w_ij is the weight between feature i and j, \( \overline{y}=\sum \limits_{j=1}^N{y}_j \), and \( s=\sqrt{\frac{\sum \limits_{j=1}^N{y}_j^2}{N}-{\overline{y}}^2} \).

The \( {G}_i^{\ast } \) statistic is a z-score. A high positive z-score for a given region shows there is an apparent concentration of high y levels within its neighbourhood of a certain distance (hot spot), while a high negative z-score means the clustering of low y levels (cold spot).

Finally, our third approach to regional convergence considers the concept of club convergence. We conduct a twin-path analysis of this kind of convergence. Firstly, we apply the log t test proposed by Phillips and Sul (2007b). The test is based on time-varying factor representation of convergence variable:where μ_t is common factor and δ_it is time-varying idiosyncratic distance from the common factor. The time-varying element δ_it is modelled in semiparametric form as:where δ_i is time-invariant part of δ_it, σ_i is idiosyncratic scale parameter, ξ_it is iid(0, 1) across i and weakly dependent over t, and L(t) is a slowly varying function for which L(t)→∞ as t→∞.

The relative loading coefficient:measures the relation of loading coefficient δ_it to the panel average at time t. As the cross-sectional mean of h_it is unity, its variance is given by:

The convergence is present if H_t→∞ as t→∞.

Considering the approach of Phillips and Sul (2007b), the null hypothesis of convergence test is formulated as follows:

The testing procedure consists of the following steps:where r∈(0, 1). Following the results of their simulations, Phillips and Sul (2007b) recommend the use of r∈[0.2, 0.3]. When T is small, r = 0.2 is preferred, and if T is large, r = 0.3 is better choice.

Rejection of the null hypothesis means that there is no convergence in the group of all panel units. It does not imply, however, that there is no evidence of convergence in sub-groups of units (i.e. club convergence). Phillips and Sul (2009b) propose a specific procedure for testing club convergence. The algorithm includes four steps. First, the units are arranged in descending order with respect to the last period. Next, a core group is formed by adding regions one after another to a group of the two highest-TFP regions at the start and performing the log t test until the \( {t}_{\hat{b}} \) for this group is larger than −1.65. Then, the log t test is performed again for this group and all the other units (one after another), forming the sample to find if they converge. If they do not converge, the first three steps are performed for all the other units. In the case that no clubs are identified, it means that those units diverge.

To endogenize the process of clubs formation on the basis of the log t test procedure, an ordered logit model pioneered by McKelvey and Zavoina (1975) is used. This model can be written as:where \( {y}_i^{\ast } \) is a latent variable that relates to a region’s individual steady-state TFP level, X_i includes the explanatory variables (in the initial period) presented in Table 4.1 as well as a constant term, β is a vector that contains the structural coefficients, and ε_i is the error term that has a logistic distribution.

Secondly, we employ a two-step procedure for club convergence testing. Following the RIS methodology (European Commission, 2021), we create a composite indicator to evaluate regional innovation performance. For this purpose, we use Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). This method takes into account the distances to both the ideal and the negative-ideal solutions concurrently, given the relative closeness to the ideal solution (Hwang & Yoon, 1981). A TOPSIS algorithm includes the following steps: (1) construction of the normalized decision matrix, (2) construction of the weighted normalized decision matrix, (3) determination of the ideal and negative-ideal solutions, (4) calculation of the separation measure, (5) calculation of the relative closeness to the ideal solution, (6) preparation of the preference order ranking. Next, we employ the classification scheme used in the RIS (European Commission, 2021): innovation leaders (all regions with a relative performance more than 125% of the sample average), strong innovators (all regions with a relative performance between 100% and 125% of the sample average), moderate innovators (all regions with a relative performance between 70% and 100% of the sample average) and emerging innovators (all regions with a relative performance below 70% of the sample). Having identified four different sub-groups of regions, we perform the standard Barro-style convergence testing within the clusters.

Figure 4.1 presents the levels of TFP calculated using the Färe-Primont index for 219 European regions in 2008 and 2018. The average value of TFP levels for all the examined regions was equal to 0.242 in 2008 and increased only by 6% during the next 10 years reaching the level of 0.257 in 2018.

As Fig. 4.1 presents, the most productive regions in EU are located along the UK–Germany–Italy corridor both in 2008 and 2018. It is worth to point out that for decades, a banana-shaped metropolitan axis running from London to Milan—dubbed the ‘Blue Banana’—has been Europe’s major place abounding in innovation and growth (Hospers, 2003).

In 2008, the highest value of TFP occurred in the London region (0.441), and it was 80% higher than the average level for the analyzed NUTS 2 regions and nearly five times higher than the lowest level in the Bulgarian Southern Central region. The second-best score was achieved by the Dutch region of Groningen, and the third one by the German region of Düsseldorf, with the TFP levels equal 0.423 and 0.366, accordingly. What is worth to point, four out of the top ten most productive regions of examined sample were from Germany (besides Düsseldorf–Bremen, Darmstadt and Köln). The lowest levels of TFP were present in peripheral regions of Eastern and South-Eastern Europe. Six out of ten regions with the lowest levels of TFP ranging from 0.10 to 0.142 were Bulgarian and four of them, with the TFP levels ranging from 0.112 to 0.141, were Romanian. Similar findings are reported by Puškárová and Piribauer (2016). The extremely low TFP levels for these regions were also revealed by Beugelsdijk et al. (2018) who, contrary to our methodology, apply the technique of development accounting to find differences in total factor productivity (TFP) in the EU regions.

Although the advantage of the London region has decreased during the examined decade, it has managed to maintain the leading position of the most productive European region. Despite the decline in the TFP level in the London region to 0.440 in 2018, it was still considerably (70%) higher than medium level for the analyzed NUTS 2 regions and nearly 3.5 times higher than the lowest level in the Bulgarian Southern Central region. The second-best most productive was the Eastern and Midland Region of Ireland with TFP level equal 0.403 in 2018, with the 23% increase from 2010. Half of the top ten most productive European regions was German, as the Arnsberg region has joined the previous best four (Düsseldorf, Bremen, Darmstadt, and Köln). In 2018, the lowest levels of TFP were again observed in the peripheral regions of Eastern and South-Eastern Europe. However, besides the Bulgarian and Romanian regions, the Irish Northern and Western Region, the Polish Podlaskie Voivodship and Greek Western Macedonia appeared among the least productive regions.

During the analyzed period the largest increase in TFP performance (by more than 50%) was recorded in the Portuguese Autonomous Region of Madeira. What is worth to point out, although the Bulgarian regions are among those with the lowest levels of productivity, they achieved the highest increase of TFP levels (by more than 40%). This can be attributable to a low-base effect.

The TFP distribution is also interrelated with urban–rural distribution of specialization levels. Specialization in knowledge-intensive services is found to be the strongest in more densely inhabited areas, i.e. agglomerated regions (Capello & Lenzi, 2013). The observed disparities in TFP performance across the EU regions result, undoubtedly, from the EU enlargement to a set of 28 countries. As in the last decade, old member countries have experienced a six-time slower than the new member countries, which has induced them to delocalize part of their traditional industries to the new ones, they have developed specialization in knowledge-intensive services whereas the new ones in low-tech manufacturing (Marrocu et al., 2013).

As Fig. 4.1 shows, a high degree of dispersion in TFP can be noticed also within the examined countries. To assess the dispersion in TFP, we draw a box-plot showing the variation (i.e. interquartile range) in TFP within each country in 2008 and 2018 (Fig. 4.2).

The box-plot reveals that the degree of variation in TFP varies across countries. In countries like Belgium, Germany, Italy and the Netherlands, where TFP is on average high, there is also a considerable interregional dispersion in TFP. Interpreting the results for Belgium, it should be noted that there are only 3 regions. The low number of regions is also observed in Ireland, which is characterized by high interregional dispersion in TFP. On the other hand, there are examples of large countries, including France, characterized by relatively low levels of interregional dispersion of TFP. In the Eastern and South-Eastern European countries, where the TFP levels are on average low, the distribution of TFP variation is also polarized, with the highest interregional dispersion of TFP in Poland in 2008 and Romania in 2018. The observed considerable interregional dispersion in regional TFP within countries might arise from different efficiency of innovation and regional policies pursued at the national level aimed at reducing interregional disparities.

The spatial clusters of TFP (hot and cold spots) resulted from the local \( {G}_i^{\ast } \) statistics for the sample regions in the year 2008 and 2018 are shown in Fig. 4.3. The hot spots, (red colour) mean clusterings of regions with high TFP levels, and the cold spots (blue colour) represent clusterings of regions with low TFP levels. The results of local statistics obtained from the spatial autocorrelation analysis at the beginning of the study period confirm clear east-west and north-south divisions of TFP clustering. There are visible tendencies of the spatial clustering of regions with high TFP in both the west and the north and of low TFP in the east and the south. It is worth pointing out that among the regions concerned, the Spanish and Portuguese regions have less of a tendency to cluster. The same holds true for the regions from Sweden and Finland. As regards the degree of spots polarization, most of the top 10 hot spots are formed by the regions from the Benelux countries (the Netherlands and Belgium). In turn, most of top 10 cold spots are made up of regions belonging to the countries located in the Central and Eastern Europe (Romania and Hungary).

From 2008 to 2018, the pattern of TFP clustering was not significantly altered, but spatial segregation between hot and cold spots slightly increased. It should be noted that the hot spot narrows as spatial clustering is becoming more random in the central part and the northern part of European regional scope at the end of the analyzed period. In the case of cold spots, there is the opposite trend, reflected in the increase of spatial clustering of regions with low TFP levels. This tendency is particularly evident in the regions from Bulgaria and Romania. As regards the polarisations of the spots, the spatial distribution of top 10 hot spots and the top 10 cold spots in 2018 is similar to the distribution observed in 2008.

In line with the research procedure of our study, as outlined in subhead 4.1, we start with the analysis of stochastic TFP convergence. Since the assumption of cross-sectional independence seems to be unreasonable and is subject to severe critique (Breitung & Pesaran, 2008), we take into account the presence of cross-sectional dependence when carrying out a panel unit root test. In order to check cross-sectional dependence empirically in our panel of TFP for the 219 European regions over the period 2008–2018, we apply the CD statistics of Pesaran (2004) and Frees (1995).

Table 4.2 shows the results of CD tests. Both CD statistics reject the null hypothesis of cross-section independence at p < 0.000. These findings are not altered after including a linear trend into the specifications. Hence, a cross-sectional dependence in the analysis of stochastic and deterministic TFP convergence should be allowed.

Our results confirm that interregional cooperation creates the potential to access external knowledge and contributes to increase in the innovation capacity of regions. As innovation processes require the combination of different, although related, complementary pieces of knowledge to be most effective, the access to external knowledge allows to lower the risk of localism and lock-in processes (Arthur, 1989). Embedding in interregional networks of cooperation is in general a significant driver for exploitative and explorative modes of knowledge creation (Neuländtner & Scherngell, 2022). Moreover, as Fratesi and Senn (2009) reveal, regional economies that are capable to acquire external knowledge are likely to be more innovative.

Having found the existence of cross-sectional dependence in the panel of TFP, we proceed to study the existence of stochastic convergence by the application of the Pesaran (2007) test. The null hypothesis of this test assumes nonstationarity (i.e. no convergence), the alternative hypothesis assumes stationarity (i.e. convergence). As reported in Table 4.3, the results support the weaker notion of convergence given by stochastic convergence, which allows existence of consistent differences in TFP levels across regions due to the presence of a time trend (Li & Papell, 1999b). Our findings loosely correspond with a few empirical studies on regional stochastic TFP convergence in the European regional scope. For example Byrne et al. (2009) show a lack of stochastic convergence of TFP for Italian regions. Similar conclusions are drawn by D’Uva and De Siano (2011). Interpreting these results, it should be noted that both mentioned studies are limited in the spatial scope, which makes it difficult to formulate a general conclusion.

In the next step, we analyze the β-convergence. Table 4.4 contains the estimation results of two models. The former allows us to verify the existence of the absolute β-convergence of TFP for the period 2008–2018. The latter considers a possible difference in convergence processes in two time-periods (2008–2013 and 2014–2018). For this purpose, the model includes a dummy regressor—PP, which takes the value 0 for 2008–2013 and 1 for 2014–2018, and its interaction with the autoregressive term—TFP_i,t−1.

The revealed absolute β-convergence of TFP across European regions may result from the implementation of EU regional policy aimed at diminishing disparities among regions and member states, intended to pursue the goal of economic, social, and territorial cohesion. This is in line with findings of Celli et al. (2021), confirming that the EU regional policy played an important role in the economic recovery of the poorest regions in the aftermath of the Great Recession. However, the opposite results were demonstrated by Albanese et al. (2021) who did not find a positive effect of the European Regional Development Fund (ERDF) on local TFP growth in Southern Italy, the most backward regions of the country, between 2007 and 2015. Also Madeira et al. (2021) reveal that a poor Spanish region Extremadura, despite being eligible for EU funding as a convergence region by cohesion policy, diverged from the EU average between 2008 and 2014.

The obtained results indicating that convergence process across EU regions in 2014–2018 was more dynamic than in 2008–2013 may result from the fact that in the 2014–2020 programming period, EU regional policy changed significantly due to the implementation of the smart specialization strategies. Regional innovation policies, aiming at improving the capacity of regions to generate, transfer and acquire knowledge and innovation through implementation of smart specialization strategies, were assigned particular importance in the Innovation Union initiative of Europe 2020 strategy (Commission of the European Communities, 2010). As it was previously described, smart specialization strategies are place-based, focused on enhancing the capabilities and opportunities for technological development, taking into account the specific technological and human capital of the area. This profound shift in the directions of regional innovation policies enabled supporting the specific resources of regions increasing the effectiveness of public financing contributing to more dynamic development of lagging regions.

To address the issue of the spatial interdependencies of TFP regional convergence, we apply a spatial autoregressive model on panel data. The model uses three alternative spatial weights matrixes (i.e. W1—a first-order binary contiguity matrix, W2—a second-order binary contiguity matrix, W3—an inverse-distance matrix) to check the robustness of our results (Table 4.5). We introduce an interaction between the autoregressive term—TFP_i,t−1 and the spatially lagged TFP—wTFP_i,t. Hence, we allow the speed of convergence to vary according to the level of TFP in the neighbouring regions.

At the outset, it is worth noting that Model 3 provides results similar to those obtained in Model 4 and Model 5. As expected, TFP of the European regions are strongly affected by their spatial interdependence, which suggests that TFP convergence process has a spatial character. The spatially-lagged TFP coefficient indicates highly significant effects of TFP spillovers. Similar results are reported by Dettori et al. (2012). It should be noted that the coefficient associated with the autoregressive term drops sharply with the increase of TFP in neighbouring regions. For very low levels of TFP in neighbouring regions, there is a tendency to TFP divergence. However, after reaching a threshold, TFP in neighbouring regions positively affects the speed of TFP convergence. A possible explanation is that positive externalities of TFP appear in groups of regions in which the external knowledge base is already quite developed and rich.

Our results correspond with the assumption made by Basile et al. (2011) that growth rate of a region depends not only on its initial conditions and on its own structural characteristics but also on initial conditions, structural characteristics and growth rates in neighbouring regions. This confirms the important role of spatial proximity in knowledge diffusion across regions and reinforces the effects generated by geographical closeness thanks to synergies and increasing returns.

Our findings indicate the existence of knowledge spillovers provided the determined level of productivity is achieved in regions. They are in line with evolutionary approach, assuming that the spatial processes of knowledge creation and distribution are cumulative, path-dependent, and interactive and that new knowledge is expected to be based on related, former sources of knowledge (Balland, 2016) and that the region’s current resources impact its further capacity to produce knowledge (Heimeriks & Boschma, 2014). Due to the cumulative nature of knowledge, the convergence processes depend not only on the initial innovative potential of the regions and their capacity to absorb knowledge spillovers generated in other regions (Roper & Love, 2006; Verspagen, 2010).

To extend the β-convergence framework, we employ the log t test proposed by Phillips and Sul (2007b). This approach allows us to identify local convergence clubs. The log t test applied to the group of all panel units indicates that the null hypothesis of overall convergence is rejected at the 1% significance level (−2.326). It means that PS club clustering procedure may be used. Table 4.6 shows the final results for the club clustering and merging algorithms.

The \( \hat{b} \) value for Club 1 is significantly positive, but less than 2. It provides a strong evidence of conditional convergence, i.e. growth rates of TFP converge over time, but little evidence of level convergence within this club. The \( \hat{b} \) value for Club 1 is also positive, but not statistically different from zero. In turn, the \( \hat{b} \) value for Club 2 is negative, but not statistically different from zero. The lack of statistical significance of the \( \hat{b} \) values for Club 1 and Club 2 implies that these clubs are weaker convergence clubs than Club 3. The convergence speed \( \hat{\alpha} \) for Club 3 is 15%, whereas the values of \( \hat{\alpha} \) for Club 1 and Club 2 lack interpretations.

The spatial distribution of clubs is presented in Fig. 4.4. Club 1 consists of the regions with the lowest level of TFP (0.1611 on average in 2008). The regions that converge in this club are located mostly in the Central-Eastern European countries (Poland—14 regions, Czech Republic—8 regions, Hungary—8 regions, Bulgaria—6 regions, Romania—5 regions) and Greece (5 regions). Club 2, with an average of TFP equal to 0.2643 in 2008, is spatially heterogeneous and contains about 50% of all regions. This club is dominated by the regions from Germany, France, and Spain. It also includes a large number of regions from the UK and the Netherlands. As regards Club 3 with the highest level of TFP (0.2998 on average in 2008), it is the least numerous and its core group is formed by the regions from Germany and Italy.

Figure 4.5 presents the relative transition paths for regions within a particular club. The transition path is determined by the transition coefficient \( {\hat{h}}_{it} \) (Eq. 4.20), which is calculated as the ratio of the individual region’s log of TFP over time to the average of the log of TFP for panel units over time. As can be seen in graphs, the bundles of transition paths for all clubs take a form of a funnel. This tendency is most evident for Club 2 and Club 3. Furthermore, the transition seems to be uniform in the whole period.

Summing up, we find that both the stochastic technological convergence and the absolute β type of technological convergence took place in the European regional space in the period 2008–2018. Moreover, the analysis of the β-convergence in the spatial context underscores the importance of technological interdependence among regions, which is reflected in the fact that a region’s speed of convergence depends on the TFP levels of neighbouring regions.

Our results correspond with catching-up approach, as regions that are not capable to innovate and lag behind could benefit from the adoption of technological improvements developed by technologically leading regions. In consequence, they achieve a relatively faster rate of growth, ceteris paribus, that should lead to convergence process, provided they developed absorptive capacities (Alexiadis, 2012). We demonstrate that interregional connections and knowledge flows are shaped by spatial patterns and convergence is enhanced by spatial proximity. This is in line with the empirical results indicating that knowledge externalities across regional space have an impact on innovation performance (Bottazzi & Peri, 2003; Moreno et al., 2005; Roper et al., 2017). This finding supports the approach to technological externalities presented in the spatially augmented Solow models (Yu & Lee, 2012). The extension of our analysis to the multiple equilibria framework by applying the log t test suggests the existence of conditional convergence in the clubs of regions. Interpreting this result it should be noted that regions which belong to different clubs in the short run may be slowly converging towards each other in the long run.

To study the impact of innovation on TFP convergence in the European regions, two proxies for innovation activities are included as additional regressors in the Barro regression for panel data. This results in extending our research to the concept of conditional convergence, which assumes that each region possesses its own steady-state TFP growth rate that is conditional on innovation. As mentioned previously, comparable data on regional innovation are rather scarce. Similar to other previous works, we use R&D investments and patents as indicators of regional innovation (e.g. Acs et al., 2002; Baptista & Swann, 1998; Bode, 2004; Di Cagno et al., 2016; German-Soto & Flores, 2013; Jaffe, 1989). The former reflects regional innovation input and the latter relates to regional innovation output (Hauser et al., 2018). Although both indicators have several shortcomings (Acs et al., 2002; Guellec & van Pottelsberghe de la Potterie, 2001), they are still considered to be the most reliable single measures of cross-regional differences in innovation.

Table 4.7 contains the empirical results for the conditional β-convergence model. We include interactions between the autoregressive term—TFP_i,t−1 and innovation-related variables, i.e. RD_it and PAT_it . In this way, we can observe how innovations affect the speed of convergence. The findings show that both R&D and patents stimulate convergence processes after exceeding certain thresholds. One explanation for this fact is that there is a critical scale of innovation activities required to trigger convergence processes. Moreover, as the empirical evidence provided by Foray (2014) indicates there are substantial indivisibilities in knowledge production and the existence of economies of scale, economies of scope and spillovers is an essential determinant of the productivity of innovation activities. The positive impact of innovation on TFP convergence comes from decreasing effects of R&D investments and patenting activities. In other words, the higher the level of regional knowledge base, measured by TFP level, is, the less effective innovation activities are. Similarly, Burda and Severgnini (2018b), following the ‘distance to the frontier’ approach of Griffith et al. (2004), find that R&D investment acts as a source of TFP convergence, since for theGerman regions that are closer to the technological frontier additional R&D spending reduces TFP growth. These results are generally consistent with the conclusions of the semi-endogenous growth models of Jones (1995) and Kortum (1997b).

The results of estimation of the conditional β-convergence model with spatial effects are summarized in Table 4.8. By convention, the results are presented for the first-order contiguity matrix (Model 7), for the second-order contiguity matrix (Model 8), as well as for the inverse-distance matrix (Model 9). Our estimates indicate the relevance of knowledge externalities across regional economies in the process of TFP convergence. Interestingly, spatial spillovers due to R&D activity performed in other regions strongly affect the convergence process of a particular region. It is important that this finding is robust to the alternative weight matrices. The evidence corroborates the previous findings, which reveal the existence of R&D spillovers among the European regions. For example Abdelmoula and Legros (2009) prove that R&D spending of neighbouring regions affects positively a region’s total factor productivity. With regard to patenting activity, the situation seems less obvious. For Model 8 with the second-order contiguity matrix, the increase of patenting activity of neighbouring regions impedes TFP convergence process of a particular region. In the case of two other models (Model 7 and Model 9) the interaction effect appears to be insignificant. One possible explanation for this finding is that the protection function of patent outweighs its information-sharing function, which facilitates knowledge spillovers by disclosing the specification of inventions. For example Song et al. (2022) report that patent lifetime affects the technological knowledge diffusion growth rate negatively. Another more plausible explanation is that a patent novelty requirement may hinder knowledge flows, since too much novelty of invention brings large cost of its absorption (Gilsing et al., 2008). As mentioned by Benoliel and Gishboliner (2022), novelty traps intensify in developing regions, where technology diffusion is costlier due to lower absorptive capacity.

In the next step, we consider initial conditions related to regional innovation systems (Table 4.1) that can explain the emergence of multiple steady-state equilibria across the European regions, which are identified by the log t test. For this reason, we use the ordered logit model, where the variable to be explained represents the club to which a given region belongs. In Table 4.9 we report the results of the ordered logit model estimation and the marginal effects, calculated as a mean of marginal effects at each value of explanatory variables. These effects provide a direct and easily interpretable answer to the question of how changes in covariates affect the change in the probability of outcomes (club membership). To reduce the multicollinearity problem, we apply the backward stepwise approach, which leads to a reduced model that best explains the club formation process.

We can conclude that an increase in the number of innovative SMEs collaborating with others in the population of SMEs leads to convergence processes that take place in regions from Club 1. The inclusion of a given region in networks of collaboration and knowledge transfer structures significantly increases innovative potential as it allows to access to external knowledge that they are not able to create on their own (Mahroum, 2008; Matras-Bolibok et al., 2017). However, the benefits to a great extent depend on the abilities of individual institutions and areas, and are achieved by those that are best connected (in terms of the number and quality of networks to which they have access) and equipped with adequate human and technical resources necessary to absorb and use knowledge obtained from outside effectively. Regions with weaker innovation potential are forced to bear not only the higher costs of instant access to network structures but also of reducing the innovation gap to the leaders. Thus, cooperation in innovation activities in regions with a low innovation potential may be difficult and ineffective initially and bring results only in the long run, provided the improvement of their innovation capabilities.

On the other hand, a rise in human capital measured as the share of the population aged 25–64 enrolled in education or training aimed at improving knowledge, skills, and competences, stimulates convergence processes peculiar to regions with the highest TFP level (Club 3). As expected, in line with the empirical evidence and theoretical considerations, human capital is a crucial factor that determines the productivity and innovation performance of a given economy (Diebolt & Hippe, 2022), as there are several channels through which human capital may affect technological progress (Acemoglu & Autor, 2012). According to Nelson and Phelps (1966b), human capital not only determines the ability to create innovation, but also contributes to diminishing the technological gap between more and less developed economies through imitation and absorption of innovation. Most importantly, the same conclusions as for human capital can be drawn on the impact of product and process innovations on convergence processes in regions with the highest TFP level. In line with our expectations, implementation of innovation contributes to a better TFP performance (Mohnen & Hall, 2013). It is worth to indicate that the impact of innovation performance on productivity level depends on the type of innovation, however the evidence is ambiguous. This could result from the fact that product and process innovations often appear together and their individual contribution is hard to assess (Jaumandreu & Mairesse, 2017). For example empirical evidence presented by Hall (2011) indicates that product innovations have an economic impact on productivity, while the impact of process innovations is more ambiguous. Peters et al. (2017) report that in German high-tech industries product innovation increases productivity, whereas in low-tech industries—process innovation. Moreover, as Demmel et al. (2017) demonstrate, the level of development is also a mediating factor in the innovation–productivity link.

As regards intellectual property rights in the form of designs, they also generate convergence processes peculiar to regions from Club 3. This is in line with previous evidence in the literature indicating that intellectual property rights have a great impact on productivity and innovativeness (Chang et al., 2018; Habib et al., 2019). As Su et al. (2022) demonstrate, the linkage of IPR protection to TFP is negative in least-developed countries that offer the weakest protection and inverted U-shaped in developing and developed countries with the strongest IPR protection. Moreover, the optimal IPR protection level for TFP is greater in developed than in developing countries. What is worth to point out, as Chen et al. (2013) reveal, patent-oriented R&D productivity growth serves as the main source of national R&D productivity growth than the journal article-oriented one. However, we finally find that the increase in the share of the most cited scientific publications in the total number of scientific publications has the positive influence on the probability of belonging to Club 3. Publications are considered as a strong proxy for the real amount of science-driven (Pasteur-type) research, given the requirement to publish the results of scientific R&D. The higher quality of publications, on average, is, the greater impact on innovation performance in terms of citations in subsequent publications (Varga et al., 2014). It is worth to point out that knowledge production processes are becoming ever more interregional as a growing number of cross-regional collaboration in scientific publications is observed (Barrios et al., 2019b). Scientific collaboration makes the knowledge production more efficient and shortens the time for obtaining research results due to division of labour (Coccia & Bozeman, 2016). Moreover it leads to an increase in scientific productivity and a higher impact of publications (Bozeman et al., 2013).

In the last step of our analysis, we endogenously determine clubs of regions on the basis of a full set of conditioning variables associated with regional innovation systems (Table 4.1). Following RIS (European Commission, 2021) methodology and applying the TOPSIS method we identify four regional innovation clubs: Emerging Innovators, Moderate Innovators, Strong Innovators, and Innovation Leaders. The most innovative regions, on average, lead in most of the indicators. They score particularly well in the field of patent applications and public-private co-publications. The best performance of Strong Innovators is observed in the fields of trademark and individual design applications and lifelong learning. Moderate Innovators obtain the highest results in the level of sales of new-to-market and new-to-enterprise product innovations as a percentage of total turnover. The group of the least innovative regions outperforms the innovation performance of the other groups in the level of non-R&D innovation expenditures. The relatively high performance of Emerging Innovators in this field may mean that in less innovative regions enterprises innovate by purchasing external knowledge embedded mainly in advanced machinery and equipment.

Figure 4.6 presents the spatial distribution of the regional innovation club members. As can be seen, the group of the most innovative regions in EU, belonging to the Innovation Leaders club, is the most numerous and consists of 54 regions that are located along the UK–Germany–Switzerland corridor and in Scandinavian countries—Finland and Sweden. The lowest levels of innovation performance are present in peripheral regions of Eastern and South-Eastern Europe, mainly in Romania, Bulgaria, Poland, and Greece. It can be observed, that the innovation performance distribution across European regions is interrelated with TFP distribution.

Table 4.10 shows the results of the absolute β-convergence model for individual regional innovation clubs.

Basing on the data presented in Table 4.10, the main conclusion that can be derived is that innovations accelerate TFP convergence. More precisely, the group of Emerging Innovators converges very slowly with TFP levels. This group is also characterized by the lowest average level of TFP in the whole period. The convergence speed and the average level of TFP rise gradually moving across the two middle groups to the group of Innovation Leaders, which experiences the highest speed of TFP convergence and the highest average level of TFP over the analyzed period. It is worth noting that the results received from both our approaches to club convergence testing prove to be qualitatively similar.