Working Paper Identification of Sustainable Growth Regions Through Innovation on NUTS-3

Abstract

This study investigates the role of innovation in shaping economic growth across the heterogeneous landscape of the European Union (EU). Through a detailed analysis at the NUTS-3 level, it identifies regions characterized by sustained and above-average growth, thereby providing new insights into the mechanisms through which innovation contributes to regional economic resilience and long-term prosperity. Our methodology employs panel data from the EU27 Member States and the United Kingdom (UK), spanning the period from 2002 to 2022, allowing a more comprehensive understanding of the determinants of regional growth, including Gross Value Added (GVA) across various industries, the unemployment rate, and inflation. Furthermore, the role of innovation as a pivotal force driving economic progress is underscored. The analysis reveals significant differentiation within the cluster, supporting the assumption that innovation plays a crucial role in driving robust and, most notably, sustainable economic growth in a region. The findings further highlight that regions with an industry structure closely resembling the sample average are significantly influenced by innovation. From this, it can be deduced that innovation is a key driver of sustainable growth, especially in regions with the necessary infrastructure, skilled labour, and industry diversification to effectively harness innovative activities.

1. Introduction

Between 2010 and 2023, the gross domestic product (GDP) (measured in current US dollars) of the United States (US) grew significantly, rising by an impressive 81%. In stark contrast, the European Union (EU) (excluding the UK, as it is no longer part of the EU following Brexit) recorded a comparatively modest increase of just 26% over the same period (data source: World Bank national accounts data). This striking divergence prompts a closer examination of the underlying dynamics and driving forces behind the US’s remarkable economic expansion—especially considering that, back in 2010, the GDP gap between the two economies was only 3.4%.

A recent study by McKinsey (Reinventing our economy from within, published September 2023, https://www.mckinsey.de/publikationen/europe-startup-powerhose-2023-economic-value-creation-and-innovation accessed on 21 August 2024) provides a possible explanation for this pronounced growth disparity, attributing the United States’ lead primarily to a lack of innovation within the EU. Innovation, particularly in future-oriented sectors, plays a pivotal role in driving economic growth and sustaining prosperity. Innovations have the potential to create entirely new industries [1]. Recent developments in the US demonstrate how, within a short period, global market leaders like Apple, Microsoft, and most recently OpenAI have emerged.

Regarding the impact of innovation on GDP, studies demonstrate that innovation influences economic performance. An increase in innovation is related to an increase in the economic performance measured by GDP through increased productivity or even emerging new industries, and vice versa [2,3,4,5,6,7,8,9,10,11].

This paper advances the understanding of the relationship between innovation and economic growth by investigating how sustainable growth regions (while we refer to ‘regions’ in the context of this study, the term is used to denote individual markets. This is because conventional understanding of regions typically encompasses areas that exceed the scale of NUTS-3 units) can be identified based on innovation-related indicators. This approach provides a comprehensive framework for defining and measuring innovation, highlighting its critical role in driving economic progress. Furthermore, it emphasizes the importance of regulatory frameworks, particularly patenting regulations, as essential mechanisms for supporting innovation and promoting standardization across industries. The empirical approach explores the spatial distribution of patents across the EU at the NUTS-3 (Nomenclature des unités territoriales statistiques) (NUTS-3 regions generally have a population of 150,000 to 800,000 inhabitants. Every EU NUTS-region has a unique code. The length of the code depends on the hierarchical level of the NUTS-region) level and its influence on regional economic growth, shedding light on the geographical dimensions of innovation and their role in shaping localized economic outcomes.

The approach employed in this study seeks to accurately evaluate the impact of innovation by comparing the influence of patent application across different clusters within the EU using panel data. The methodology incorporates the Gross Value Added (GVA) by various industries along with a range of socioeconomic parameters to provide a more comprehensive understanding of the factors influencing economic growth. The analysis is carried out at the NUTS-3 level, encompassing a sample of 1303 regions during the period of 2002 to 2022, allowing a detailed examination of regional innovation dynamics.

The findings indicate that innovation has a significant long-term influence on economic growth and thus contributes to the sustainable development of regions. However, this effect is not uniform across all regions. Innovation exerts a particularly strong positive influence in non-rural regions and in areas that have exhibited above-average growth during the observation period. Interestingly, a positive effect is also observed in regions with lower growth rates. Upon closer examination of the sample, plausible explanations for this relation emerge. The findings also emphasize that the way innovation affects growth is strongly influenced by the region’s underlying economic structure.

This study provides a detailed analysis of patents as a key indicator of innovation within a regional context. It successfully highlights the impact of innovation across various clusters, demonstrating its role as a critical factor in fostering robust and sustainable economic growth within the EU.

The structure of the paper is as follows. It begins with a review of the relevant literature and is followed by an introduction of the model used. The subsequent section presents a detailed description of the data and descriptive statistics that serve as the foundation for the empirical analysis discussed in Section 5. The paper concludes with a summary of the findings and a brief outlook for future research.

2. Literature Review

With his theory of “creative destruction”, Ref. [12] was one of the first to emphasize the importance of innovation as a driving force for economic change and growth. Building on this, the theory of endogenous growth [13,14] further develops the idea that innovation is not just an external factor, but rather an internal one, generated by deliberate investment in research and development (R&D), human capital, and knowledge. According to this theory, innovation leads to sustained economic growth by increasing productivity and fostering technological advances from within the economy itself, rather than relying on external forces. Ever since, scholars have been studying the impact of innovation and innovative force [15,16]. However, research on innovation spans from firm-level to national. Scholars have almost consistently identified a positive relation between innovation and economic advancement at both the firm and national levels. At the firm level, innovation is reflected in enhanced productivity and improved quality of products and services [17,18,19]. At the national level, innovation-driven growth is often evidenced by metrics such as increases in GDP per capita [6,9,20]. Given that innovation at the firm level ultimately fuels national economic progress, this study does not draw a strict distinction between the two.

In line with this view, prior studies have defined innovation as the result of a diverse set of actions, including product, process, and technological advances. Several scholars have highlighted its critical role in driving long-term economic growth. Ref. [21] underscore the creation of new knowledge and ideas as key drivers of sustained growth, while [6] establish a clear link between increased innovation activity and economic expansion. Contributing to the finding of [22] who link innovation to the promotion of recruitment. Ref. [19] as well as [18] demonstrate that technological innovation serves as a strong predictor of productivity, further strengthening the central role of innovation in the promotion of economic growth.

However, a critical question arises regarding how innovation can be reliably measured, given the various parameters to which it can be linked. The literature presents multiple approaches, with the most commonly used methods focusing on venture capital investments, R&D expenditures, or patent applications as key indicators of innovation.

Venture capital is typically invested in emerging companies or start-ups that, by their very nature, drive change and foster innovation. However, these companies are typically concentrated in regional agglomerations, with the most famous being Silicon Valley in the US, which is widely recognized as a hub for technology-driven innovations [23]. These agglomerations are often structured through a network in such a way that they attract further young companies within their industry and thus also support venture capital investments [24]. Furthermore, it is essential to keep in mind that the capital invested does not always necessarily lead to innovation. Venture capital investments are extremely volatile and, in some scenarios, lead to complete loss of the capital deployed and, therefore, not to lasting innovation [25]. Although venture capital transactions provide an indication of innovative activities, they seem to suffer from considerable deficits as a measure of innovation. Not only because of the insufficient informative value of the transactions with regard to the output of the invested capital, but also because of the strong regional agglomeration, which appears inappropriate for the objective of this work.

Since innovation is typically the result of investments in R&D, it seems reasonable to use R&D expenditure as a key metric to measure innovation. R&D activities, by definition, utilize existing resources and ideas to create new products, processes, or technologies, which is why R&D expenditures are usually regarded an input variable in the context of innovation [8]. R&D activities are often concentrated within research organizations, leading to the formation of agglomerations. These agglomerations have been observed to have positive effects on the immediate environment through knowledge spillovers [21,23]. However, the informative value of R&D expenditure remains controversial. A key shortcoming is that it is not possible to clearly quantify the amount of innovation which is generated by the expenditures on R&D. However, there is a dynamic relationship between the number of people employed in R&D and the number of patent applications [8]. This relation indicates that human resources in R&D have a significant influence on patent activity, which in turn allows conclusions to be drawn about innovation performance. However, it also shows that R&D expenditure alone does not provide sufficient information. Considering other factors such as the quality of research, corporate strategy and the legal framework could deepen the understanding of this relationship and improve the assessment of innovation capability. Thus, R&D expenditure can provide an indication as an input variable, but it remains questionable how efficiently the expenditure on R&D also leads to innovation [10].

Patent applications, as the so-called output variables, appear to be a more appropriate measure of innovation. According to the definition of [10], technological performance can be defined as the performance of companies in terms of the combination of their R&D input in the form of R&D expenditure, as an indicator of their research capacity, and their R&D output in the form of patents. Thus, the number of patent applications appears to be more meaningful than R&D expenditure, particularly in terms of the analysis of economic growth [26]. Patents provide a more clearly defined and measurable unit of innovation output, which emphasizes their suitability as an indicator of technological progress and economic development [27,28,29,30]. Patents are also suitable for taking into account previously omitted innovations [15]. Furthermore, they reflect the legal protection and economic exploitability of new technologies, making them a useful measure of the innovative capacity of a region or company [21].

The use of patent applications as a measure of innovation has become well established among scholars. In particular, it is becoming increasingly common to use statistics based on patent applications to analyze the relationship between economic growth and innovation [8,11,31,32,33]. For example, there has been shown to be a positive and significant relation between the number of patent applications filed with the European Patent Office (EPO) and economic growth [34]. However, there are major differences in the methodology of the various studies. Ref. [34] utilizes the number of patent applications per 1,000,000 inhabitants in his study as the basis for the analysis. Ref. [4] makes use of patents per 1000 inhabitants. Ref. [20] who analyses the deficits of the European Commission’s Catching Up Initiative within NUTS-3 regions in Europe, use the number of patent applications per 100,000 inhabitants as an indicator of innovation. Ref. [6] take an alternative approach using the number of patent applications as a proportion of one million dollars spent on R&D.

These differences in scaling and methodology illustrate the flexibility of patent applications as a measure of innovation. Despite the different approaches, the studies yield consistent results that underpin the importance of patent applications as a reliable indicator of innovation and its influence on economic growth. Patents offer a standardised, quantifiable measure that allows scholars to compare innovation activities across different regions and time periods (there is an extensive body of Literature on this topic; see, for example, [6,10,30,33,35]).

However, deficits of patents used as measure of innovation are recognized, particularly with regard to the informative value. There are significant differences in the quality of single patents regarding their “innovative capacity”, which cannot be corrected using the available data. This implies that not every patent can necessarily be assigned the same value or, respectively, explanatory value. Furthermore, not all companies pursue the same policy when it comes to patents. It can be assumed that there are a large number of innovations that are not patented in order to avoid disclosing the characteristics of the innovation. Regardless of this, there is no doubt that there are innovations that do not necessarily result in a patent. And finally, the legal framework for patent applications is not the same throughout the world [10]. With regard to this work, this is negligible, as the study is limited exclusively to the EU and the UK; therefore, harmonized competitive conditions apply in accordance with the European Patent Convention (EPC) [36] (nevertheless, there is extensive literature on the effects of the regulatory framework on intellectual property rights (IPRs). This is particularly relevant in respect of patents, as patents are a way of securing IPRs to an invention and thus protecting it [37] as well as [38] finding evidence that increased IPRs stimulate economic growth, since they indirectly attract R&D investments [39] finds a positive significant relation between IPR protection and economic growth in low-income and high-income countries).

The limitations above highlight the need to consider the granularity of the data at the regional level. Although the quality and policy of patenting may vary, a detailed analysis at the regional level provides valuable insight into the spatial distribution and regional dynamics of innovation. Looking at the granularity of the data, regional differences and specific innovation clusters can be identified that might otherwise be overlooked in the aggregated data, especially because innovation is considerably more geographically concentrated than traditional industries [40]. A regional analysis also enables the consideration of local factors and conditions that may impact economic growth, offering a more in-depth and nuanced understanding of the underlying dynamics.

Much of the existing literature focuses on the NUTS-1 or NUTS-2 level when examining regional economic growth. This approach neglects important factors, especially with regard to the distinctive spatial distribution within NUTS-1 or NUTS-2 clusters. Studies that have increased their geographical granularity by conducting analyses at the NUTS-3 level show that there is considerable heterogeneity in per capita income between NUTS-3 regions within the same NUTS-2 region [41,42].

Analysis at NUTS-3 level allows the focus to be clearly sharpened and the heterogeneity to be appropriately recognized [42]. It can be assumed that a significantly higher variation can be observed within the NUTS-3 regions [20]. This is not surprising, as the 2021 NUTS classification within the EU-27 distinguishes between 104 regions at NUTS-1 level, 283 regions at NUTS-2 level, and 1345 regions at NUTS-3 level (European Union, 2020).

Although there is a substantial body of literature that examines the impact of innovation on the economy, a notable gap exists in terms of the granularity of these analyses. Scholars have consistently emphasized the importance of this finer granularity, particularly given the concentration of innovation activities within agglomerations. This is especially pertinent when identifying regions that aim for sustainable growth through innovation. To address this gap in the literature, our research seeks to address the following question: how does innovation, when analyzed within distinct regional or sectoral clusters, influence sustainable economic growth? We focus on the influence of innovation on economic growth throughout the EU within NUTS-3 clusters, aiming to identify regions characterized by sustainable growth. This level of granularity allows for a more precise identification and analysis of regional innovation patterns and economic dynamics, mitigating the potential for regional differences to be obscured by aggregation effects. By employing the NUTS-3 level as the unit of analysis, this approach effectively captures the complexity and diversity of regional innovation processes and their corresponding impact on economic growth.

3. Data

To obtain empirical evidence at the regional level, this study utilizes data on NUTS-3 regions from the EU27 Member States and the United Kingdom, spanning the period from 2002 to 2022 on an annual basis. The data utilized are based on the 2021 NUTS classification, comprising 1345 regions at the NUTS-3 level. The primary objective of this research is to analyze the determinants of regional growth, with a particular emphasis on innovation. Regional growth is defined as the annual increase in GDP.

This analysis targets several economic dimensions identified as critical growth drivers, including Gross Value Added (GVA) across various industries, unemployment rate, and inflation. These parameters are recognized as key factors that influence regional economic development. Furthermore, the role of innovation as a pivotal force driving economic progress is underscored. As in the prior literature, the number of patent applications within a given year is commonly used as the basis for measuring innovation. This metric serves as a widely accepted proxy for innovative activity, capturing both the inventive output and the capacity of a region or sector to generate new technologies and processes [6,26,30].

The data on NUTS-3 regions are sourced from various European statistical databases. Eurostat supplies data on industrial parameters such as GDP and sectoral GVA, as well as inflation and unemployment rates. Patent data are retrieved from the PATSTAT database, a comprehensive database maintained by the EPO. Given that the data are based on different NUTS-3 classification years, it is essential to harmonize the dataset to ensure consistency with a single NUTS-3 regional classification prior to analysis (The data from PATSTAT was issued based on the 2013 NUTS classification, whereas the other datasets were issued according to the 2021 NUTS classification. The NUTS classification has undergone significant changes in recent years, particularly at the NUTS-3 level. These changes include renaming regions, merging regions, and occasionally eliminating regions. Consequently, it is crucial to ensure that the data are harmonized with a consistent classification year to maintain precision and comparability in the analysis).

Initially, PATSTAT data adhered to the NUTS-2013 classification, which required an adaptation to the NUTS-2021 classification for consistency. Consequently, 42 regions were excluded due to the lack of available data for the period 2002 to 2022. This resulted in a dataset comprising 1303 NUTS regions, which represents 96.88% coverage of the EU27 and the UK, according to the 2021 classification. The NUTS-3 region with the largest area is Norrbottens län in Sweden, which covers 105,208 km², while the smallest area is Tower Hamlets in London, UK, which covers 20 km². In terms of population, Madrid in Spain is the largest region with 6.5 million inhabitants, whereas El Hierro in Spain is the smallest, with a population of 11,000. The pronounced variation in both territorial size and population among NUTS-3 regions reflects the substantial heterogeneity of the sample, highlighting the necessity of incorporating regional structural differences into any robust empirical analysis. The result of the cleaning procedure is presented in

Table 1. Regions.

Country	Code	Population	Sample	Percentage Covered
Austria	AT	35	35	100.00%
Belgium	BE	44	36	81.82%
Bulgaria	BG	28	28	100.00%
Cyprus	CY	1	1	100.00%
Czech Republic	CZ	14	14	100.00%
Germany	DE	401	401	100.00%
Denmark	DK	11	11	100.00%
Estonia	EE	5	3	60.00%
Greece	EL	52	52	100.00%
Spain	ES	59	59	100.00%
Finland	FI	19	19	100.00%
France	FR	101	101	100.00%
Croatia	HR	21	7	33.33%
Hungary	HU	20	20	100.00%
Ireland	IE	8	8	100.00%
Italy	ITC-I	107	102	95.33%
Lithuania	LT	10	10	100.00%
Luxembourg	LU	1	1	100.00%
Latvia	LV	6	6	100.00%
Malta	MT	2	2	100.00%
Netherlands	NL	40	40	100.00%
Poland	PL	73	72	98.63%
Portugal	PT	25	25	100.00%
Romania	RO	42	42	100.00%
Sweden	SE	21	21	100.00%
Slovenia	SIO	12	12	100.00%
Slovakia	SKO	8	8	100.00%
United Kingdom	UKc-g	179	167	93.30%
		1345	1303	96.88%

Note: This table summarizes the regional coverage of the dataset at the NUTS-3 level for selected European countries. For each country, the table reports the total number of regions, the number of regions included in the sample, and the resulting percentage coverage. While most countries are fully covered, some have partial coverage due to limitations in data availability, quality issues, or missing values for specific indicators. The final row provides the aggregated totals and the overall coverage rate across all listed countries.

.

Defining Regions

To account for regional heterogeneity within the sample, we build upon the classification framework provided in the Eurostat Regional Yearbook (The latest version is available under the following link: https://ec.europa.eu/eurostat/de/web/products-flagship-publications/w/ks-ha-23-001) accessed on 18 September 2024, which distinguishes between three categories as part of EU cohesion policy. In order to reflect the variation within and across the regions more precisely, we introduce a more fine-grained classification comprising four growth-related categories: high growth, moderate growth, transition, and low growth. This extended typology allows for a more nuanced analysis of regional dynamics beyond the original Eurostat framework.

In our sample, the growth level is based on the average annual GDP growth over the whole period under investigation, in the respective region (M). A region falls into the category of ‘high growth’ if the average GDP growth within the region during the period under review is ${\mathrm{GDP}}_M^{2002-2022}\ge 90\%$ of the sample average, ‘moderate growth’ if the average GDP growth is $50\%\le {\mathrm{GDP}}_M^{2002-2022}<90\%$, ‘transition’ if the average GDP growth is $25\%\le {\mathrm{GDP}}_M^{2002-2022}<50\%$, and ‘low growth’ if the average GDP growth is ${\mathrm{GDP}}_M^{2002-2022}<25\%$ of the sample average.

This approach allows for the heterogeneity of the sample to be recognized. Furthermore, growth is assessed over the entire period and not at specific points in time. This is particularly important with regard to the research question, which focuses on sustainable growth.

To better capture the sample’s heterogeneity, we introduce an additional distinction between rural and non-rural regions. In doing so, we focus on the work of [20] and draw on data from the European Commission, which has differentiated regions at NUTS-3 level into ‘predominantly urban’, ‘intermediate’ and ‘predominantly rural’. We also aggregate this dataset into the rural category, which represents ‘predominantly rural’ regions, and the non-rural category, which represents ‘predominantly urban’ and ‘intermediate’ regions. Thus, it is possible to take urbanization into account in the analysis.

The structure of the sample shown in

Table 2. Regions distribution by growth level and urbanisation.

Growth Level	Rural		Non-Rural		Total
	No.	%	No.	%	No.	%
High Growth	45	3.45%	86	6.60%	131	10.05%
Moderate Growth	155	11.90%	366	28.09%	521	39.98%
Transition	93	7.14%	232	17.81%	325	24.95%
Low Growth	116	8.90%	210	16.12%	326	25.02%
Total	409	31.39%	894	68.61%	1303	100.00%

Note: This table provides a cross-tabulation of regions by their assigned growth level and urbanisation classification. The categorisation distinguishes between rural and non-rural regions. Each cell shows both the number and percentage of regions within the respective group. The totals at the bottom of each column allow for an overview of the distribution across urbanisation types, while the rightmost column summarizes the share of each growth category across the entire dataset. The total number of regions in this table corresponds to the sample size used in the analysis (n = 1303).

illustrates the breakdown into the various categories. In view of the heterogeneity of the sample, it is of central importance to apply as detailed and differentiated an approach as possible. Otherwise, there is a risk that key observations will be overlooked or distorted.

Figure 1 illustrates that the variability in average GDP growth is not only evident across countries, but also within them. While national averages remain relatively stable over time, considerable within-country disparities persist, with frequent outliers highlighting the heterogeneity of regional economic performance. These outliers are of significant interest within the scope of the analysis, as they represent regions that exhibit exceptionally strong growth. Understanding the factors driving this growth is crucial, as it may provide insight into underlying structural advantages that contribute to their economic performance.

The spatial distribution is visualized in Figure 2, which divides the average GDP growth into eight intervals. This map presents the average GDP growth of individual regions during the period under review, segmented into eight equal intervals, with interval 1 representing the lowest growth and interval 8 the highest, in ascending order. It becomes evident that regions in eastern Europe, as well as certain areas in Ireland, have experienced significant growth during the period, whereas many regions in Western and Southern Europe have shown relatively moderate growth. However, this should not be seen as a concern, as the initial economic conditions prior to the growth period play a substantial role in the observed results. Figure 2 further illustrates the spatial distribution of growth, highlighting both intra-country variability and differences between neighboring regions. This reinforces the importance of considering regional heterogeneity when analysing economic growth patterns. This is also confirmed by the descriptive statistics of the variables shown in

Table 3. Descriptive Statistics of the dataset.

Variable	Mean	Min	Max	Median	Std. Dev
$\Delta {\mathrm{GDP}}_{mt}$	0.01	−0.32	0.82	0.02	0.05
${\mathrm{GDP}\_\mathrm{real}}_{mt}$	8.71	4.88	12.40	8.68	1.04
${\mathrm{Unemployment}\_\mathrm{rate}}_{mt}$	1.88	−1.03	4.04	1.88	0.64
${\mathrm{Inflation}}_t$	0.02	0.00	0.04	0.02	0.01
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{agricul}\_\mathrm{fores}\_\mathrm{serv}}_{mt}\right)$	4.20	−9.21	7.90	4.47	1.70
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{construction}}_{mt}\right)$	5.77	−0.54	9.61	5.79	1.09
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{industry}}_{mt}\right)$	6.99	1.81	11.41	7.04	1.09
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{market}\_\mathrm{services}}_{mt}\right)$	7.54	3.41	11.39	7.49	1.10
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{non}\_\mathrm{market}\_\mathrm{services}}_{mt}\right)$	7.44	3.92	11.73	7.40	1.15
${\mathrm{Patent}\_\mathrm{pc}}_{mt}$	0.29	0.00	34.82	0.07	0.74

Note: This table provides descriptive statistics for the variables used in the empirical analysis, covering the full sample of NUTS-3 regions and years included in the dataset. For each variable, the table reports the mean, minimum, maximum, median, and standard deviation. Some variables, particularly the sectoral shares of gross value added (GVA), have been log-transformed to reduce skewness and improve comparability. Patent intensity is measured based on the number of patents per capita. The statistics show substantial variation across regions and time, especially for innovation indicators and sectoral composition, underlining the heterogeneity of regional economic structures in Europe.

, especially with regard to innovation.

The scatter plot (Figure 3) reveals that the majority of regions exhibit a low number of patents per capita, accompanied by a high degree of variability in GDP growth rates. As the patent intensity increases, the variability in growth rates appears to diminish; however, no clear linear relationship between the two variables is observable. Disaggregating the sample based on regional or structural characteristics could provide a more nuanced understanding of potential differentiated relations and improve the robustness of the analysis.

4. Methodology

In order to analyze the panel date, we utilize a fixed-effects model. This approach allows us to analyze the economic structure and the influence of innovation on growth. Due to the heterogeneity of the sample, the use of a fixed-effects model is suitable to ensure that the individual characteristics of the regions are sufficiently taken into account without reducing the explanatory power of the model. All models and analyses were performed using statistical software R, version 4.4.0 [43].

Fixed-effects models offer considerable advantages for analyzing regional economic growth, as they account for both temporal and spatial dimensions. A central strength of this approach lies in its ability to control for unobserved heterogeneity—both across regions and over time—which is particularly relevant given the structural differences inherent to regional economies [44,45]. Specifically, regional fixed effects control for time-invariant, unobservable characteristics unique to each region, while year fixed effects capture shocks or influences common to all regions in a given year. This framework mitigates biases arising from omitted variable problems and enhances the robustness of the analysis.

Moreover, fixed-effects regressions allow for the examination of dynamic relationships, such as the long-term impact of historical growth patterns on future development [46]. This is particularly valuable when assessing region-specific growth trajectories and identifying the underlying structural factors driving divergence [47].

The growth model of this study is as follows:

The dependent variable of the model is the annual GDP growth in each market m = 1, …, 1303 for each year t = 2002, …, 2022. The variable is defined as follows:

$$\Delta {\mathrm{GDP}}_{mt}={\displaystyle \frac{{\mathrm{GDP}}_{mt}}{{\mathrm{GDP}}_{mt-1}}}-1$$

(1)

The change in real GDP appears to be a suitable variable for analyzing regional growth dynamics in more detail considering the objective of this work. In particular, it is possible to quantify the impact of independent variables on economic growth. The simple growth model used to analyze the influence of innovation on the annual GDP growth is structured as follows:

$$\begin{array}{cc}\hfill \Delta {\mathrm{GDP}}_{mt}& ={\beta }_0+{\beta }_1\left({\mathrm{GDP}\_\mathrm{real}}_{mt-1}\right)+{\beta }_2\left({\mathrm{Unemployment}\_\mathrm{rate}}_{mt-1}\right)\hfill \\ \hfill & +{\beta }_3\left({\mathrm{Inflation}}_{t-1}\right)+{\beta }_{4}log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{agricul}\_\mathrm{fores}\_\mathrm{serv}}_{mt-1}\right)\hfill \\ \hfill & +{\beta }_{5}log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{construction}}_{mt-1}\right)+{\beta }_{6}log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{industry}}_{mt-1}\right)\hfill \\ \hfill & +{\beta }_{7}log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)+{\beta }_{8}log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{non}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)\hfill \\ \hfill & +{\beta }_9{\mathrm{Patent}\_\mathrm{pc}}_{mt-2}+{\gamma }_m+{\delta }_t+{\epsilon }_{mt}\hfill \end{array}$$

(2)

The right-hand side of Equation (2) includes three baseline controls. The control variables include GDP at the start of the growth process (${\mathrm{GDP}\_\mathrm{real}}_{mt-1}$). GDP in t − 1 is intended to capture the relative $\beta$-convergence in the model. The unemployment rate (${\mathrm{Unemployment}\_\mathrm{rate}}_{mt-1}$) is also taken into account in order to capture the effects of the labour market. This is particularly important, as labour has a notable influence on economic momentum. Furthermore, the inflation rate (${\mathrm{Inflation}\_\mathrm{rate}}_{t-1}$) is taken into account to allow for more precise predictions, as inflation is essential for economic growth. Due to the lack of data at the regional level, we use the inflation rate at EU level.

In order to capture the economic structure of the regions, we utilize the GVA of various sectors, since the economic structure is considered to be a key growth engine factor [48]. GVA enables us to better understand the economic contribution of various sectors to the regional economy. The variables are defined in terms of the sectoral share of GVA [20].

GVA in the agriculture and forestry sector is captured by the variable (${\mathrm{Share}\_\mathrm{GVA}\_\mathrm{agricul}\_\mathrm{fores}\_\mathrm{serv}}_{mt-1}$). Since agriculture and forestry are particularly important in rural regions, their contribution must be reflected to accurately depict the underlying economic structures [49]. GVA in the construction sector (${\mathrm{Share}\_\mathrm{GVA}\_\mathrm{construction}}_{mt-1}$) is also incorporated in the analysis, as increased activity in this sector can serve as an indicator of infrastructural development and economic progress. Construction is often regarded an early signal of economic recovery, particularly due to its labour-intensive nature [50]. Given its sensitivity to economic fluctuations, the construction industry can also provide valuable insight into a region’s resilience to varying economic cycles.

The GVA of the industrial sector (${\mathrm{Share}\_\mathrm{GVA}\_\mathrm{industry}}_{mt-1}$) is introduced into the analysis, encompassing the GVA of the mining, manufacturing and electricity and gas sectors. These three sectors constitute key industries that substantially contribute to total Economic Value Added. As such, they serve as important indicators of a region’s general economic health. In addition, due to their typically export-oriented nature, these industries also provide valuable insights into the international economic environment, reflecting broader global economic conditions and trends.

Market and non-market services are included to cover the service sector. In both cases, several related subsectors were aggregated under each variable.

Market services (${\mathrm{Share}\_\mathrm{GVA}\_\mathrm{market}\_\mathrm{services}}_{mt-1}$) encompass wholesale and retail services, transportation and storage services, real estate services, other services, financial and insurance services, as well as accommodation and food services. Non-market services (${\mathrm{Share}\_\mathrm{GVA}\_\mathrm{non}\_\mathrm{market}\_\mathrm{services}}_{mt-1}$), on the other hand, comprise services that are predominantly provided publicly or through government subsidies. These include information and communication services, health and social services, public administration services, scientific and technical services, education, art and entertainment services, and administrative and support services. These variables capture the service and non-market service sectors, which play a vital role in supporting the economic well-being of their respective regions.

The clustering of variables, such as the grouping of industries, market services, and non-market services, offers several notable advantages. By consolidating related variables into functional groups, it simplifies the analysis, reducing complexity, and enhancing interpretability. This approach facilitates a clearer identification of sectoral contributions to regional growth and improves the comparability of regions with differing economic structures. Moreover, it mitigates multicollinearity, thereby increasing the stability of estimates in econometric models. Clustering also allows for a more focused examination of functional relationships between sectors, enabling a more precise analysis of their combined effects on economic growth. This methodology draws on the work of [20], who employed similar clustering in his analysis.

Ultimately, the influence of innovation on economic growth is examined. As outlined above, this variable is based on the number of patent applications submitted within a one-year period in the respective region. The relevant literature highlights various approaches to incorporate patent data in empirical research, and in this analysis, we focus on patent applications per capita (${\mathrm{Patent}\_\mathrm{pc}}_{mt-2}$). This metric is an appropriate measure of innovation, as it directly reflects the output of technological progress. Patents protect novel and inventive ideas, making them a reliable indicator of the originality and economic value of innovation [35,36]. By relating patent counts to the population, this measure enables a more equitable comparison of innovative capacity across regions and countries of different sizes. Moreover, patent applications per capita serve as a proxy for the strength of the knowledge economy, since regions with high levels of patent activity often exhibit robust R&D infrastructures [4,51]. Furthermore, we lag the variable by two periods, accounting for the time it typically takes for a patent to progress from application to practical implementation. A patent can only fully exert its innovative impact once it is actively applied in practice. However, the primary reason for this lag is the 18-month period between the patent application and its official publication, during which the patent remains confidential (more on the patent application Process of the EPO and the disclosure document can be found via the following link: https://www.epo.org/en/new-to-patents/how-to-apply-for-a-patent) accessed on 18 September 2024. This delay in publication, through the EPO, ensures that the innovation remains undisclosed and its economic effects are not immediately observable. By incorporating this lag, the analysis more accurately reflects the timeline of a patent’s influence on economic growth.

Finally, ${\gamma }_m$ and ${\delta }_t$ represent vectors of region- and year-specific fixed-effects, while ${\epsilon }_{mt}$ denotes the error term.

5. Results

The comparison between the baseline and disaggregated models highlights that greater predictive accuracy in non-rural regions can be achieved by accounting for sample heterogeneity.

Table 4. Baseline regression vs. non-rural and rural.

	Baseline Regression	Non-Rural	Rural
${\mathrm{GDP}\_\mathrm{real}}_{mt-1}$	−0.126 ***	−0.129 ***	−0.137 ***
	(0.003)	(0.003)	(0.006)
${\mathrm{Unemployment}\_\mathrm{rate}}_{mt-1}$	−0.001 ***	−0.001 ***	−0.001 ***
	(0.001)	(0.0001)	(0.0002)
${\mathrm{Inflation}}_{t-1}$	−1.150 ***	−1.213 ***	−1.001 ***
	(0.024)	(0.028)	(0.045)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{agricul}\_\mathrm{fores}\_\mathrm{serv}}_{mt-1}\right)$	−0.001 ***	−0.001 ***	−0.011 ***
	(0.001)	(0.0005)	(0.003)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{construction}}_{mt-1}\right)$	0.013 ***	0.0017 ***	0.007 ***
	(0.001)	(0.002)	(0.003)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{industry}}_{mt-1}\right)$	0.029 ***	0.031 ***	0.029 ***
	(0.003)	(0.004)	(0.006)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)$	0.013	0.021 ***	0.001 ***
	(0.005)	(0.007)	(0.008)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{non}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)$	0.082 ***	0.104 ***	0.047 ***
	(0.005)	(0.0006)	(0.009)
${\mathrm{Patent}\_\mathrm{pc}}_{mt-2}$	0.001 ***	0.001 ***	0.0001
	(0.0005)	(0.0005)	(0.003)
Observations	27,363	18,774	8589
R2	0.148	0.165	0.122
Adjusted R2	0.105	0.123	0.077
F Statistic	501.026 ***	391.684 ***	126.021 ***
	(df = 9; 26,051)	(df = 9; 17,871)	(df = 9; 8171)

Note: *** p < 0.01.

presents these results, illustrating the differences in model performance and highlighting the importance of distinguishing between different regional contexts for a more precise analysis. This approach helps to capture region-specific dynamics that might otherwise be obscured in a more aggregated model, as outlined by [52].

When examining the entire sample, it becomes evident that the dependent variable is positively driven by construction, industry, market, and non-market services, as well as innovation. In contrast, agricultural services do not show a significant impact on GDP growth. Unsurprisingly, inflation exerts a negative influence on growth, as does the unemployment rate. Furthermore, there is evidence of a general convergence process across regions, as indicated by the negative coefficient of real GDP, consistent with the findings of [20]. This suggests that regions with lower initial GDP tend to grow faster, gradually catching up with wealthier regions over time.

Regarding the subdivision into rural and non–rural regions, it becomes immediately apparent that the non–rural category is based on a substantially larger number of observations. As shown in Table 2, non–rural regions account for approximately 68% of the total sample. Consequently, it is not surprising that the baseline estimates do not deviate much from those of the non-rural regions. In terms of innovation, a significant positive effect is observed in non-rural regions, whereas this effect is not evident in rural areas. This distinction implies that innovation may play a more prominent role in driving economic growth in non-rural regions. Alternatively, this finding suggests that innovative activities are highly clustered and predominantly concentrated in urban centers, which typically provide the necessary infrastructure to support such endeavors. Urban areas often offer stronger R&D networks, access to skilled labour, and better connectivity, all of which facilitate the generation and implementation of innovative ideas.

In the next step, the sample is divided according to growth levels, with the results presented in

Table 5. Regression results by growth level.

	High Growth	Transition	Moderate Growth	Low Growth
${\mathrm{GDP}\_\mathrm{real}}_{mt-1}$	0.067 ***	0.216 ***	0.112 ***	0.317 ***
	(0.007)	(0.008)	(0.004)	(0.008)
${\mathrm{Unemployment}\_\mathrm{rate}}_{mt-1}$	0.002 ***	0.002 ***	0.002 ***	0.003 ***
	(0.0003)	(0.0002)	(0.0001)	(0.0001)
${\mathrm{Inflation}}_{t-1}$	0.407 ***	0.341 ***	0.370 ***	0.429 ***
	(0.063)	(0.023)	(0.022)	(0.025)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{agricul}\_\mathrm{fores}\_\mathrm{serv}}_{mt-1}\right)$	0.007 ***	0.005 **	0.003 ***	0.011 ***
	(0.002)	(0.001)	(0.001)	(0.001)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{construction}}_{mt-1}\right)$	0.006	0.040 ***	0.057 ***	−0.015 ***
	(0.006)	(0.003)	(0.003)	(0.002)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{industry}}_{mt-1}\right)$	0.058 ***	0.033 ***	0.054 ***	0.003
	(0.011)	(0.006)	(0.005)	(0.006)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)$	0.082 ***	0.099 ***	0.117 ***	0.085 ***
	(0.014)	(0.012)	(0.008)	(0.011)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{non}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)$	0.164 ***	0.105 ***	0.196 ***	0.142 ***
	(0.014)	(0.011)	(0.009)	(0.010)
${\mathrm{Patent}\_\mathrm{pc}}_{mt-2}$	0.003 ***	0.002	0.0004	0.004 **
	(0.001)	(0.001)	(0.001)	(0.001)
Observations	2751	6825	10,941	6846
R2	0.105	0.156	0.127	0.235
Adjusted R2	0.057	0.113	0.083	0.196
F Statistic	33.952 ***	133.238 ***	168.923 ***	222.135 ***
	(df = 9; 2611)	(df = 9; 6491)	(df = 9; 10,411)	(df = 9; 6511)

Note: ** p < 0.05; *** p < 0.01.

. This subdivision offers deeper insights into the economic structure as it relates to growth. Notably, the smallest portion of the sample falls into the high-growth category. In this group, innovation is found to have a significantly positive impact on economic growth in both high-growth and low-growth regions. The results suggest that, on average, each patent per capita corresponds to an increase of approximately 30 basis points in GDP growth. In high-growth regions, this positive influence supports the assumption that innovation plays a crucial role in sustaining long-term economic growth, especially when considering the sample time span. In contrast, in low-growth regions, the results suggest that innovation can provide a competitive advantage, helping to stimulate growth where it may otherwise be limited. The findings highlight the importance of fostering innovation across diverse economic contexts. However, no significant influence of innovation has been noted among the transition and moderate-growth regions. This may be due to several factors, such as insufficient infrastructure, limited access to skilled labour, or a weaker research and development ecosystem in these regions. Furthermore, the innovation activities present in these areas may not yet have reached the scale necessary to generate a measurable economic impact, or there could be delays in the diffusion of technological advancements. Innovation in these regions may also not be effectively translated into practical applications that drive economic growth, reflecting challenges in converting innovative potential into tangible results. There are various differences in the wider economic structure of the regions, but these are less surprising. However, what is surprising is that the convergence effect has completely canceled out as a result of the clustering. This suggests that the regional subdivision into different growth categories may obscure the typical convergence pattern, where lower-growth regions tend to grow faster than wealthier ones. Clustering may reveal that within each group, regions exhibit more homogeneous growth dynamics, reducing the observable catch-up effect between regions.

To gain a deeper understanding of the relations, the sample is further disaggregated, with the results presented in

Table 6. Regression results by growth level and rural vs. non-rural.

	High Growth		Transition		Moderate Growth		Low Growth
	Non-Rural	Rural	Non-Rural	Rural	Non-Rural	Rural	Non-Rural	Rural
${\mathrm{GDP}\_\mathrm{real}}_{mt-1}$	0.050 ***	0.219 ***	0.219 ***	0.240 ***	0.111 ***	0.172 ***	0.341 ***	0.311 ***
	(0.008)	(0.017)	(0.009)	(0.015)	(0.005)	(0.009)	(0.011)	(0.014)
${\mathrm{Unemployment}\_\mathrm{rate}}_{mt-1}$	0.002 ***	0.002 ***	0.002 ***	0.001 ***	0.002 ***	0.002 ***	0.003 ***	0.002 ***
	(0.0004)	(0.001)	(0.0002)	(0.0003)	(0.0002)	(0.0003)	(0.0002)	(0.0002)
${\mathrm{Inflation}}_{t-1}$	0.502 ***	0.181 *	0.358 ***	0.285 ***	0.385 ***	0.319 ***	0.438 ***	0.389 ***
	(0.074)	(0.108)	(0.028)	(0.042)	(0.026)	(0.040)	(0.031)	(0.043)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{agricul}\_\mathrm{fores}\_\mathrm{serv}}_{mt-1}\right)$	0.006 ***	0.081 ***	0.002 *	0.017 ***	0.003 ***	0.029 ***	0.008 ***	0.044 ***
	(0.002)	(0.012)	(0.001)	(0.004)	(0.001)	(0.005)	(0.001)	(0.005)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{construction}}_{mt-1}\right)$	0.018 **	0.005	0.048 ***	0.025 ***	0.063 ***	0.050 ***	−0.015 ***	−0.014 ***
	(0.008)	(0.011)	(0.004)	(0.005)	(0.003)	(0.005)	(0.003)	(0.004)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{industry}}_{mt-1}\right)$	0.077 ***	−0.032	0.031 ***	0.032 ***	0.062 ***	0.020 *	−0.003	0.024 **
	(0.013)	(0.024)	(0.008)	(0.010)	(0.006)	(0.011)	(0.007)	(0.010)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)$	0.120 ***	0.051 **	0.082 ***	0.147 ***	0.132 ***	0.099 ***	0.103 ***	0.066 ***
	(0.020)	(0.022)	(0.015)	(0.022)	(0.011)	(0.014)	(0.014)	(0.018)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{non}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)$	0.166 ***	0.226 ***	0.087 ***	0.154 ***	0.175 ***	0.239 ***	0.130 ***	0.174 ***
	(0.018)	(0.023)	(0.015)	(0.017)	(0.011)	(0.015)	(0.014)	(0.016)
${\mathrm{Patent}\_\mathrm{pc}}_{mt-2}$	0.003 ***	−0.048	0.002	0.002	0.0002	0.001	0.004 ***	0.005
	(0.001)	(0.039)	(0.001)	(0.005)	(0.001)	(0.003)	(0.001)	(0.007)
Observations	1806	945	4872	1953	7686	3255	4410	2436
R2	0.111	0.220	0.160	0.175	0.127	0.167	0.249	0.238
Adjusted R2	0.063	0.174	0.116	0.130	0.082	0.123	0.210	0.197
F Statistic	23.854 ***	27.944 ***	98.002 ***	43.555 ***	118.176 ***	68.881 ***	154.402 ***	80.168 ***
	(df = 9; 1711)	(df = 9; 891)	(df = 9; 4631)	(df = 9; 1851)	(df = 9; 7311)	(df = 9; 3091)	(df = 9; 4191)	(df = 9; 2311)

Note: * p < 0.1; ** p < 0.05; *** p < 0.01.

. In addition to growth groups, the sample is divided into non-rural and rural areas. However, this initial disaggregation does not yield any notable new findings. As expected, innovation has a significant impact in both high-growth and low-growth categories, but only in non-rural areas, confirming previous observations. This reinforces the notion of innovation tending to be more concentrated in urban centers.

So far, the analysis has demonstrated that innovation exerts a significant positive impact on economic growth, particularly in non-rural regions and in both high-growth and low-growth areas. This indicates that innovation not only drives significant growth in high-growth regions, but also fosters development in more low-growth regions, where growth may be more moderate due to already advanced economic structures. However, this prompts the question whether it is possible to further disaggregate the economic structures of the regions to draw even more precise conclusions.

To achieve this, we apply the Krugman concentration index, here referred to as the Krugman index [53]. This index is a measure of dissimilarity that quantifies the differences between two units of analysis, which, in our case, are the sectors within the regions. Following the approach of [54], we use the average of the entire sample as a reference, rather than comparing individual regions, and cluster the industries within growth groups based on whether they are above or below this average (see

Table 7. Regression results by growth level and Krugman index.

	High-Growth		Transition		Moderate-Growth		Low-Growth
	Above Avg.	Below Avg.	Above Avg.	Below Avg.	Above Avg.	Below Avg.	Above Avg.	Below Avg.
${\mathrm{GDP}\_\mathrm{real}}_{mt-1}$	0.095 ***	0.026 ***	0.245 ***	0.223 ***	0.134 ***	0.100 ***	0.327 ***	0.343 ***
	(0.010)	(0.009)	(0.014)	(0.010)	(0.007)	(0.006)	(0.014)	(0.011)
${\mathrm{Unemployment}\_\mathrm{rate}}_{mt-1}$	0.003 ***	0.001 ***	0.002 ***	0.002 ***	0.003 ***	0.002 ***	0.003 ***	0.003 ***
	(0.001)	(0.0004)	(0.0003)	(0.0002)	(0.0002)	(0.0002)	(0.0002)	(0.0002)
${\mathrm{Inflation}}_{t-1}$	0.409 ***	0.446 ***	0.380 ***	0.318 ***	0.399 ***	0.341 ***	0.484 ***	0.387 ***
	(0.001)	(0.014)	(0.046)	(0.026)	(0.002)	(0.026)	(0.002)	(0.002)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{agricul}\_\mathrm{fores}\_\mathrm{serv}}_{mt-1}\right)$	0.006 ***	0.016 ***	0.004 *	0.009 ***	0.003 ***	0.006 ***	0.028 ***	0.005 ***
	(0.002)	(0.005)	(0.002)	(0.002)	(0.001)	(0.002)	(0.004)	(0.001)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{construction}}_{mt-1}\right)$	0.017 *	−0.018 *	0.022 ***	0.063 ***	0.057 ***	0.054 ***	−0.017 ***	−0.026 ***
	(0.009)	(0.010)	(0.004)	(0.005)	(0.004)	(0.005)	(0.004)	(0.004)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{industry}}_{mt-1}\right)$	0.068 ***	0.038	0.057 ***	0.025 **	0.070 ***	0.018	0.024 ***	−0.070 ***
	(0.016)	(0.025)	(0.009)	(0.011)	(0.006)	(0.011)	(0.008)	(0.010)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)$	0.083 ***	0.056	0.123 ***	0.094 ***	0.135 ***	0.072 ***	0.131 ***	−0.031 *
	(0.018)	(0.039)	(0.019)	(0.019)	(0.011)	(0.019)	(0.016)	(0.018)
$log\left({\mathrm{Share}\_\mathrm{GVA}\_\mathrm{non}\_\mathrm{market}\_\mathrm{services}}_{mt-1}\right)$	0.206 ***	0.067 **	0.138 ***	0.095 ***	0.239 ***	0.109 ***	0.182 ***	0.016
	(0.019)	(0.033)	(0.016)	(0.019)	(0.011)	(0.018)	(0.015)	(0.018)
${\mathrm{Patent}\_\mathrm{pc}}_{mt-2}$	0.003 **	0.034 **	0.001	0.005 ***	−0.00003	0.0001	0.004 *	0.005 **
	(0.001)	(0.014)	(0.002)	(0.002)	(0.002)	(0.001)	(0.002)	(0.002)
Observations	1596	1155	2268	4557	5166	5775	2541	4305
R2	0.127	0.090	0.181	0.161	0.155	0.102	0.243	0.244
Adjusted R2	0.079	0.037	0.136	0.118	0.112	0.056	0.203	0.205
F Statistic	24.491 ***	11.946 ***	52.687 ***	92.538 ***	100.276 ***	69.183 ***	86.060 ***	146.890 ***
	(df = 9; 1511)	(df = 9; 1091)	(df = 9; 2151)	(df = 9; 4331)	(df = 9; 4911)	(df = 9; 5491)	(df = 9; 2411)	(df = 9; 4091)

Note: * p < 0.1; ** p < 0.05; *** p < 0.01.

). The resulting index values range between 0 and 2: a value of 0 indicates that the two regions have identical industry structures, while a value of 2 indicates that no industries are shared between the two regions. This index allows for a more nuanced understanding of the industrial composition of regions and how these structural differences may influence economic growth.

If a region’s Krugman index value is above the average, this indicates that its industry structure is relatively distinct from the overall sample average. Conversely, if the index value is below the average, it suggests that the region’s industry structure closely aligns with the sample average. Higher values indicate greater specialization or divergence from the common industry patterns, while lower values imply a more typical or balanced industry composition in line with broader regional economic structures. The Krugman index gives only a general overview of sectoral specialization or diversification. In our case, the index was calculated using the sectoral GVA.

The results of the regression analysis clearly indicate that innovation positively influences economic growth, particularly in regions with an industry structure that is below average. These regions tend to exhibit an economic structure that closely resembles the sample average, without a strong dominance of any specific sector. The most pronounced effect is observed in high-growth regions. The emergence of a significant innovation effect in transition regions further illustrates the heterogeneous nature of regional development pathways. These findings suggest that while innovation is a crucial driver of growth across all regions—except for moderate-growth regions—its effect is more pronounced in areas experiencing sustained strong economic expansion.

Building on these insights, it is equally important to reflect on the policy implications that emerge as a result of such a granular approach to regional innovation. By understanding how innovation contributes to sustainable economic growth at the NUTS-3 level, policymakers can develop more targeted strategies that align with the specific needs and strengths of individual regions. At the core of EU budgetary planning, the Multiannual Financial Framework (MFF) defines the overall financial architecture from which all major funding instruments are derived. Several contributions to the literature have critically examined the evolution of EU innovation policy in this context. While Horizon Europe remains the main framework programme for research and innovation, structured around three pillars, scholars have pointed out that its emphasis on research-intensive models may not fully account for the diverse innovation capacities across EU regions. The European Innovation Council (EIC), which became fully operational in 2021, represents a significant policy shift toward supporting high-risk, high-impact innovations, often through instruments similar to venture capital. However, EU-backed venture capital has thus far mobilized limited private investment, especially in less developed regions [55]. As [56] argue, longstanding strategies such as the Lisbon Agenda and the Europe 2020 3% GDP target for R&D spending among other strategies overlook the heterogeneous nature of innovation systems in Europe. Particularly among small- and medium-sized enterprises (SMEs)—which represent about 99% of all firms in the EU, Norway, Switzerland, and the UK (see the European Commission data on small and medium-sized enterprises (SMEs). Available online: https://single-market-economy.ec.europa.eu/smes_en (accessed on 4 April 2025)), —R&D investments alone have proven insufficient in driving innovation, especially in less innovative regions. These findings underscore the need for more nuanced, regionally embedded innovation policies that move beyond linear, research-driven models and recognize the importance of practice-based forms of innovation. While these policy aspects provide valuable context, the primary focus of this paper remains in the empirical identification of regional patterns of sustainable growth through innovation.

6. Conclusions

Innovation has a significant impact on the economy and plays a crucial role in maintaining competitiveness. Research shows that innovation effectively enhances productivity and thus fosters the long-term sustainable growth of regions. Yet it remains uncertain whether this assumption persists over longer time horizons and among varying regional structures.

This study applies a parametric panel data model with year and regional fixed-effects to analyze the impact of innovation on economic growth at the NUTS-3 level within the EU and the UK over the period 2002 to 2022.

Our analysis confirms the positive influence of innovation on economic growth within the sample. However, this effect is not uniform across all regions—in rural areas, no significant influence of innovation on growth is observed. This finding suggests that the relationship between innovation and economic performance is context-dependent, with factors such as infrastructure, access to resources, and regional economic structures influencing the extent to which innovation drives growth.

To gain a more precise understanding of the growth trajectories, we decided to further subdivide the sample. The growth cluster reveals that the influence of innovation is particularly pronounced in regions that experienced strong growth during the observation period (falling within the 90th percentile of the sample). In contrast, regions with moderate growth appear to remain largely unaffected by innovation. Interestingly, a significant causality between innovation and growth is also observed in low-growth regions, which is somewhat unexpected. In a subsequent step, we further divide the cluster into rural and non-rural regions; however, this subdivision does not yield any additional significant findings. These results initially align with the findings in the existing literature, particularly regarding strong growth. The analysis reveals significant differentiation within the cluster, supporting the assumption that innovation plays a crucial role in driving robust and, most notably, sustainable economic growth in a region. However, for regions with low growth, the underlying causes must be examined before definitive conclusions can be drawn. An explanation could be that lower growth rates are due to an already strong economic foundation at the beginning of the observation period. For instance, Stuttgart (NUTS code DE111) is positioned in interval 2 (see Figure 2), despite being a highly economically developed region with a significant number of patents issued. However, it cannot be ruled out that low growth in some regions is due to genuinely weak economic performance, highlighting the need for further investigation.

Clustering based on the Krugman index provides valuable insights into the predominant economic structure of each region. The analysis reveals that regions with an economic structure closely resembling the sample average are significantly influenced by innovation. This influence is particularly pronounced in regions characterized by strong growth, suggesting that innovation plays a pivotal role in driving economic performance, especially in areas where the industrial composition aligns with broader regional patterns.

Furthermore, the observed disappearance of the convergence effect after clustering regions suggests a considerable degree of regional heterogeneity in the underlying growth dynamics. While the baseline regression indicates a negative relationship between initial GDP levels and subsequent growth—consistent with the notion of $\beta$-convergence—this pattern does not hold uniformly across all regions once they are grouped by similar growth performance. This finding suggests that structural differences among regions—such as industrial composition, innovation capacity, and demographic dynamics—play a decisive role in shaping regional growth trajectories. As a result, spatial convergence cannot be assumed to occur uniformly.

In conclusion, the study provides clear evidence of a strong and positive connection between innovation and above-average economic growth across a wide range of regions over the two decades from 2002 to 2022. This is particularly evident in non-rural regions and those whose economic structure closely aligns with the sample average. From this, it can be deduced that innovation serves as a key driver of sustainable economic growth, especially in regions with the necessary infrastructure, skilled labour, and industry diversification to effectively harness innovative activities. Innovation not only fosters short-term growth but also long-term economic resilience by promoting technological advancements and productivity improvements, which are essential for maintaining competitiveness in a rapidly evolving global economy, as seen in low-growth regions. This highlights the critical role of innovation in ensuring that economic growth is not only robust but also sustainable over time, allowing regions to adapt to changing market conditions and continue to thrive in the face of external economic challenges.

Drawing on these insights, it becomes evident that innovation can significantly influence the economic condition of individual regions. In connection with the policy implications discussed above, this highlights the importance of accounting for regional heterogeneity in any meaningful analysis of innovation dynamics. Particularly in economically lagging regions, innovation may serve as a crucial lever to stimulate growth and help reduce long-standing structural disparities [57].

Future research could involve a more detailed examination of industry structures and their mediating role in the relationship between innovation and regional growth by further disaggregating the sample. Expanding the geographical scope to include non-EU regions may also yield comparative insights and offer a broader perspective on regional innovation dynamics. In terms of policy relevance, it would be worthwhile to analyze the allocation patterns of EU funding and assess the extent to which investment schemes effectively support innovation across diverse regional contexts. Moreover, examining how the observed $\beta$-convergence process has been shaped by previous MFFs, and considering the potential implications of the 2028–2034 MFF, could provide valuable input for future cohesion policy design. Finally, a more nuanced understanding of regional growth trajectories may be achieved by accounting for region-specific characteristics and exploring potential non-linearities in the underlying economic mechanisms.