Regional incidence and persistence of high-growth firms: Testing ideas from the entrepreneurial ecosystems literature

Coad, Alexander; Domnick, Clemens; Santoleri, Pietro; Srhoj, Stjepan Working Paper Regional incidence and persistence of high-growth firms: Testing ideas from the entrepreneurial ecosystems literature JRC Working Papers on Corporate R&D and Innovation, No. 02/2023 Provided in Cooperation with: Joint Research Centre (JRC), European Commission Suggested Citation: Coad, Alexander; Domnick, Clemens; Santoleri, Pietro; Srhoj, Stjepan (2023) : Regional incidence and persistence of high-growth firms: Testing ideas from the entrepreneurial ecosystems literature, JRC Working Papers on Corporate R&D and Innovation, No. 02/2023, European Commission, Joint Research Centre (JRC), Seville This Version is available at: https://hdl.handle.net/10419/283095 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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Srhoj, S. 1 Executive Summary High growth firms (HGFs) play a disproportionate role in contributing to aggregate economic outcomes. This has led policy-makers to implement initiatives to promote HGFs and such schemes are now embedded within national and regional entrepreneurship policies in many countries. Most academic literature in this field has taken advantage of the increased availability of firm-level data to provide evidence from a national perspective. While this offers a valuable characterization at the national-level, it provides little insight into the incidence of HGFs from a regional point of view, including the relationship of these businesses with local economic development. As a result, this has arguably hindered our understanding and the ability to produce useful evidence to inform the design and implementation of regional policy. Against this backdrop, this paper provides an in-depth empirical analysis of regional shares of HGFs. To that end, we leverage predictions regarding the dynamics of regional HGF shares stemming from the Entrepreneurial Ecosystems (EEs) literature. In line with what is commonly assumed by policy-makers and practitioners, the EE theory suggests that more developed regions have higher regional HGF shares, and that regional HGF shares are relatively persistent over time. We investigate empirically three broad hypotheses based on various operationalizations of these statements, using Eurostat data at the NUTS-3 level for up to 20 countries over the time span 2008-2020. The representative and cross-country nature of these data is particularly suitable to produce an accurate and rich account of regional dynamics of HGFs. Concerning the incidence of HGFs, our results suggest that the areas with the highest HGF shares – i.e. the Silicon Valleys of Europe with the highest levels of EE outputs – seem to be peripheral regions such as the Canary Islands (Spain), Sicily (Italy) and Algarve (Portugal). This represents a puzzle for the EE theory. Regression analysis further corroborates this result: regions with high levels of income per capita, innovative activity or EE quality are not those with the highest incidence of regional HGFs. We then investigate the presence of persistence in regional HGF shares. Results suggest that regional persistence of HGF shares is relatively high, which can potentially be reconciled with EE theoretical notions. However, we do not find evidence that i) persistence is stronger in regions with higher economic development, and that ii) regions at the top of the HGF shares distribution in the past are able to remain at the top of the distribution in the future. In other words, while evidence provides support for persistence, the nature of such persistence does not seem to be caused by path-dependence as put forward by the EE literature. Our results call for a more nuanced understanding of the meaning of the HGF shares both as an economic indicator as well as in terms of its operationalization within the current EEs framework. 2 Regional incidence and persistence of high-growth firms: Testing ideas from the Entrepreneurial Ecosystems literature Alex Coad, Clemens Domnick, Pietro Santoleri, Stjepan Srhoj 1 Abstract Policy-makers and scholars often assume that a higher incidence of high-growth firms (HGFs) is synonymous with vibrant regional economic dynamics, and that HGF shares are persistent over time as Entrepreneurial Ecosystems (EEs) have slowly-changing features. In this paper we test these hypotheses, which are deeply rooted in the EE literature. We draw upon Eurostat data for up to 20 countries over the period 2008-2020 and study HGF shares in NUTS-3 regions in Europe. Analysis of regional rankings yields the puzzling finding that the leading EEs in Europe, apparently, are in places such as southern Spain and southern Italy. These places would not normally be considered Europe’s foremost entrepreneurial hotspots. Additional results do not provide strong support for the hypothesis that more developed regions feature higher HGF shares. We do find evidence consistent with HGF shares displaying persistency over time. However, we show that more developed regions do not have higher persistence in their HGF shares, and that the strength in persistence does not increase across the HGFs distribution, which does not support pathdependency as the main mechanism behind the observed persistence. Overall, we call for a more nuanced interpretation of both regional HGF shares and the EEs literature. Keywords: Entrepreneurial Ecosystems, High-Growth Firms, Persistence, Firm Growth, Entrepreneurship Policy, Regional Policy 1 Authors listed alphabetically. Alex Coad ([email protected]), Waseda Business School, Waseda University, Japan. Clemens Domnick ([email protected]), Joint Research Centre, European Commission, Spain. Pietro Santoleri (pietro[email protected].eu), Joint Research Centre, European Commission, Spain. Stjepan Srhoj ([email protected]), Department of Economics, Faculty of Economics, Business and Tourism, University of Split, Croatia. Acknowledgements: We are grateful to Sara Amoroso, Werner Hölzl, Mike King-fai Fung, Alexander Lembcke, Carlo Menon, Simone Sasso, and participants at the Tokyo SIBR Conference, Joint Research Centre IID Seminar Series, and Metu-Tekpol for useful comments. We thank Sarmite Visocka for her clarifications on the Eurostat data. The opinions expressed herein are those of the authors and do not necessarily reflect those of the European Commission. The usual caveat applies. 3 1. Introduction High growth firms (HGFs) play a disproportionate role in contributing to aggregate economic outcomes (Haltiwanger, et al., 2016; Du and Vanino, 2021). This has led policy-makers to implement initiatives to promote HGFs and such schemes are now embedded within national and regional entrepreneurship policies in many countries (OECD, 2010; Brown et al., 2014; Stam and Bosma, 2015; Flachenecker et al., 2020; Coad et al., 2022). Most academic literature in this field has taken advantage of the increased availability of firm-level data to provide evidence from a national perspective (Friesenbichler and Hölzl, 2020). While this offers a valuable characterization at the national-level, it provides little insight into the incidence of HGFs from a regional point of view, including the relationship of these businesses with local economic development (Brown et al., 2014). As a result, this has arguably hindered our understanding and the ability to produce useful evidence to inform the design and implementation of regional policy. Against this backdrop, this paper provides an in-depth empirical analysis of regional shares of HGFs. To that end, we leverage predictions regarding the dynamics of regional HGF shares stemming from the Entrepreneurial Ecosystems (EEs) literature (Stam, 2015; Spigel, 2017; Leendertse et al., 2021). In line with what is commonly assumed by policy-makers and practitioners, the EE theory suggests that more developed regions have higher regional HGF shares, and that regional HGF shares are relatively persistent over time. We investigate empirically three broad hypotheses based on various operationalizations of these statements. We make use of Eurostat data at the NUTS-3 level for up to 20 countries over the time span 2008-2020. The representative and cross-country nature of these data is particularly suitable to produce an accurate and rich account of regional dynamics of HGFs. Concerning the incidence of HGFs, our results suggest that the areas with the highest HGF shares – i.e. the Silicon Valleys of Europe with the highest levels of EE outputs – seem to be peripheral regions such as the Canary Islands (Spain), Sicily (Italy) and Algarve (Portugal). This represents a puzzle for the EE theory. Regression analysis further corroborates this result: regions with high levels of income per capita, innovative activity or EE quality are not those with the highest indidence of regional HGFs. We then investigate the presence of persistence in regional HGF shares. Results suggest that regional persistence of HGF shares is relatively high, which can potentially be reconciled with EE theoretical notions. However, we do not find evidence that i) persistence is stronger in regions with higher economic development, and that ii) regions at the top of the HGF shares distribution in the past are able to remain at the top of the distribution in the future. In other words, while evidence provides support for persistence, the nature of such persistence does not seem to be caused by path-dependence as put forward by the EE literature. Our results call for a more nuanced understanding of the meaning of the HGF shares both as an economic indicator as well as in terms of its operationalization within the current EEs framework. Our study contributes to extant literature in several ways. First, it adds to the rich literature on HGF. As already pointed out, most studies in this field adopt a firm-level perspective (see, e.g. Coad et al,. 2014), whereas fewer have addressed this topic from a regional angle (e.g. Sleuwaegen and Ramboer, 2020; Friesenbichler and Hölzl, 2020, Fotopoulos, 2022). We add to this strand by leveraging official regional data encompassing up to 20 European economies. Second, the paper speaks to the literature addressing persistence in regional entrepreneurial dynamics (see, e.g. Fritsch and Mueller, 2007; Fritsch and Wyrwich, 2014). Similar to Friesenbichler and Hölzl (2020) and Coad and Srhoj (2023), we focus on regional HGF. Our results, based on a broader set of countries, suggest that persistence in regional HGF shares is generally stronger than found by these studies. Third, we also contribute to the strand that examines the mechanisms 4 behind persistence in entrepreneurial activities (see, e.g. Andersson and Koster, 2011). We show that persistence in regional HGFs cannot be attributed to path-dependency. Finally, we contribute to the literature on EEs (e.g., Stam, 2015; Spigel, 2017). Our empirical findings are not aligned with EE theoretical predictions and may be useful for its refinement. The remainder of the paper is organized as follows. Section 2 provides a background based on the theoretical literature and develops some hypotheses. Section 3 presents the methodology. Section 4 describes the data, and Section 5 contains the analysis. Section 6 contains a discussion of our results and their implications, and Section 7 concludes. 2. Background and hypotheses Economists and policy-makers have continually wondered how to replicate the Silicon Valley model in their own territories. Why is it that some regions seem to consistently outperform others in terms of their ability to produce innovative high-impact entrepreneurship? A number of theories have emerged in the literatures of economic geography and innovation studies to attempt to answer these questions, such as the frameworks of National Systems of Innovation (Lundvall, 1992; Freeman, 1995) and National Systems of Entrepreneurship (Acs et al., 2014), Regional Innovation Systems (Cooke et al., 1997; Fritsch, 2001), the cluster-based theory of competitive advantage (Delgado, Porter and Stern, 2010; Moretti, 2021), the Triplehelix approach (Etzkowitz and Leydesdorff, 2000), National Innovative Capacity (Furman et al. 2002), Competence Blocs (Henrekson et al., 2010), Environments for Entrepreneurship (Malecki, 2018), and more recently the EE approach (Isenberg, 2014; Stam, 2015; Spigel, 2017; Sternberg et al., 2019). Our empirical analysis of regional HGF shares is structured according to the theoretical intuitions of Entrepreneurship Ecosystems theory (Leendertse et al., 2021; Coad and Srhoj, 2023). This section draws on this stream of literature to develop 3 broad groups of hypotheses that can be tested using available data. 2.1 Regional development and incidence of HGF To begin with, we investigate suggestions that developed regions have higher rates of successful entrepreneurship in the form of regional HGF shares. A distinction between the EE approach and other similar ancestors (e.g. the Clusters approach) is that the EE approach emphasizes entrepreneurs as the main agents (Harima, 2020). Hundt and Sternberg (2016, p. 227) write that "we assume that regions with high levels of GDP per capita demonstrate a higher level of entrepreneurial activity than economically less prosperous regions." For example, stronger regional institutions may enhance firm growth and firm’s integration in supply chains (Cainelli et al., 2023). This idea of “higher level of entrepreneurial activity” is specifically linked to HGFs, which are the preferred indicator of entrepreneurial activity considering that they are put forward as the output of the EE. In this vein, Stam and Van de Ven (2021, p. 809) state that: “[…] the prevalence of high-growth firms in a region is strongly related to the quality of its entrepreneurial ecosystem.” Figure 1 visualizes the theoretical predictions of EE theory concerning the relationship between EEs and productive (high-growth) entrepreneurship. The success of EEs relies on the quality of their entrepreneurial inputs, which include elements such as physical infrastructure, demand, intermediate services, talent, new 5 knowledge, leadership, finance, formal institutions, culture, and networks (Stam, 2015, Stam and Van de Ven, 2021, Leendertse et al., 2021). Presumably the quality of these inputs increases with a region’s economic development. Given that more developed regions have better Ecosystem inputs, we would expect that regions that are more economically developed have higher HGF shares as output. Figure 1: the 10 inputs and the output of an Entrepreneurial Ecosystem. Source: Stam and Van de Ven (2021). In order to illustrate the positive relationship between the quality of the EE and the share of high-growth firms using a slightly different analogy, consider the fact that initial entrepreneurial talent may be uniformly distributed across geographical space. 2 However, the appearance of high-performing EE regions comes about because some regions have better institutional frameworks, because some regions are better than others at nurturing and supporting the development of talented entrepreneurs, and also because of net migration. All regions may have “heroes”, but some regions direct their “heroes” into productive entrepreneurship, and support their ventures, spurring them on to success. Other regions may direct their “heroes” into unproductive entrepreneurship, and/or restrain their emerging ventures (through “blame” and “shame”) to stifle their chances of success. Our analysis is framed in the regional ecosystem as a supporting or suppressing context: hence our focus is not on comparing regions in terms of how many “heroes” they have, but instead we focus on comparing regions in terms of what they do with the “heroes” that they get (and how they attract the immigration of heroes from elsewhere). A strong supporting ecosystem could lower the threshold between “potential hero” and “probably non-hero” to help even individuals who start off as “semi-heroes” to achieve their full potential – therefore the total number of heroes that emerge depends on the strength of the supporting ecosystem. The stronger the supporting ecosystem (input), the higher the share of local “heroes” (output). Hypothesis 1: More developed regions will have higher regional HGF shares Regional development can be measured in various ways. The most common indicator of economic development is arguably GDP per capita. However, given that the EE approach is often linked to discussions of the knowledge economy, innovation systems, high-tech entrepreneurship, and so on, it seems also worth investigating regional development in terms of indicators of scientific and technical knowledge, i.e. patents 2 To assume otherwise could potentially lead to theories bordering on nationalism and racism, that are deeply problematic and best avoided. 6 per capita, and research and development (R&D) expenditures per capita. Finally, to better connect to previous empirical research on EEs, we take the index developed by Leendertse et al (2021, Appendix D) which is meant to directly capture the sophistication of a region’s EE. Hypothesis 1A: Regions with a higher GDP per capita will have higher regional HGF shares Hypothesis 1B: Regions with a more patents per capita will have higher regional HGF shares Hypothesis 1C: Regions with a more R&D investment per capita will have higher regional HGF shares Hypothesis 1D: Regions with a higher EE index will have higher regional HGF shares 2.2 Regional persistence of HGF shares Previous research has highlighted the persistence of entrepreneurial activity at the regional-level (Andersson and Koster, 2011; Fritsch and Wyrwich, 2014). Regarding regional HGF shares, our reasoning here proceeds along two lines: first, considering the persistence of EE inputs ; and second, considering the role of business accelerators. First, the standard view of an EE is that the outputs depend on a number of inputs (Figure 1) such as institutions, infrastructure, and culture. A key characteristic of these inputs, in statistical terms, is that they change little over time. Institutions, infrastructure, culture, and the factors in Figure 1 more generally, are highly persistent and often considered to be time-invariant (Coad and Srhoj, 2023). If the inputs are timeinvariant, then under most functional forms that map the inputs into outputs, we can also expect the outputs to be time-invariant (Figure 2). Figure 2: Persistence of EE inputs and outputs. Source: Coad and Srhoj (2023). We test the hypothesis of HGFs persistence represented by the thick red arrows. Second, an alternative line of reasoning relates to the empirical literature that has found rigorous evidence that effective institutions can boost the number of so-called “gazelles” (i.e. high-growth young firms). Evidence from Chile on the evaluation of Business Accelerators has identified a causal effect of business 13 4. Data Our analysis is based on Eurostat data (see Table 2 for the variables’ description). This is not microdata (unlike some previous work such as Friesenbichler and Hölzl (2020) and Coad and Srhoj (2023)) but it is micro-aggregated and publicly available. 9 These data provide two main advantages when studying HGF shares: i) they are based on representative data and avoid the tipycal pitfalls concerning selection bias attributable to e.g. commercial data sources 10 ; ii) they are available for a sizeable share of European countries, thus allowing for a cross-country analysis. Table 2: Description of variables Variable Description Available at: NUTS-3 NUTS-2 Dependent variable HGF shares Share of high growth enterprises measured in employment (in t): number of high growth enterprises divided by the number of active enterprises (in t) with at least 10 employees. Includes industry, construction and services except insurance activities of holding companies. Obtained from Eurostat (code: bd_hgnace2_r3). HGF shares capture three-year periods, which is why the variable is used only in years 2008, 2011, 2014, 2017, and 2020.   Independent variables GDP per capita Gross domestic product (GDP) in purchasing power parity (PPP, EU27 from 2020) per inhabitant. Obtained from Eurostat (code: nama_10r_3gdp). Constructed as predetermined variable capturing mean GDP per capita in the period 2000-2007.   Patents per capita Number of patent applications filed annually in a given region based on the address of applicants/inventors. Constructed as a predetermined variable capturing mean patents per capita in the period 1997-2007. Source: OECD, REGPAT database, August 2022. Mean patents in the period 1997-2007 is divided by the average annual population (obtained from Eurostat, code: nama_10r_3popgdp).   R&D investment per capita R&D expenditure purchasing power parity (PPP) per inhabitant at constant 2005 prices. Obtained directly from Eurostat (code: rd_e_gerdreg). Constructed as predetermined variable capturing mean R&D expenditure per inhabitant in the period 1997-2007.  Entrepreneur ial Ecosystem Index Quality of EEs, developed by Leendertse, Schrijvers and Stam (2021) (see Table D1). The EE index is a snapshot in time, and available in two different versions: the EE index additive and the EE index log.  The main dependent variable, HGF shares at the NUTS-3 and NUTS-2 levels, is not available for all EU countries, and regional coverage increases with time (Table 3). Our sample is an unbalanced panel covering up to 20 European countries throughout the period 2008-2020. In the results section we present NUTS 3 level results, however, in the robustness analysis we provide also NUTS-2 level results. In comparison to existing studies (e.g. Friesenbichler and Hölzl (2020) for Austria; Coad and Srhoj (2023) for Croatia and 9 Data available at this link: https://ec.europa.eu/eurostat/web/structural-business-statistics/business-demography [last accessed: 12th Jan 2023] 10 An example of this is the use of datasets such as ORBIS, which often do not provide exhaustive coverage of balance-sheet data for young and small firms thus introducing bias when it comes to computing HGF shares. 14 Slovenia; Fotopoulos (2022) for the UK) our persistency analysis of HGF shares has the broadest geographical scope and largest sample size. Importantly, two variables (R&D investment per capita, and Entrepreneurial Ecosystem Index - EEI) are measured at NUTS-2 level, but not at the NUTS-3 level. We still use these two variables in examining the heterogeneous persistency at the NUTS 3 level by merging their NUTS-2 level values to each NUTS 3 region within a NUTS-2 region. Table 4 presents some summary statistics for NUTS-3 regions. Table 3: Country coverage over time Year N # countries Countries added (cumulative) 2008 60 2 + Austria, Portugal 2009 60 2 2010 60 2 2011 470 13 + Bulgaria, Denmark, Spain, Finland, France, Hungary, Italy, Lithuania, Malta, Romania, Slovakia 2012 505 14 + Croatia 2013 559 16 + Czechia, Netherlands 2014 556 15 - Malta 2015 509 15 + Estonia ; - Spain 2016 644 18 + Spain, Latvia, Poland 2017 647 18 2018 668 19 + Sweden 2019 665 20 + Malta 2020 665 20 Notes: Malta has only two NUTS-3 regions. Due to changes in NUTS-3 regions in years 2019 and 2020 the number of observations has a small decrease although number of countries (due to Malta) increases. Table 4: Summary statistics at NUTS-3 level N Mean St. Dev. Min Median Max Panel A HGF shares (in %) 6,068 8.94 3.25 0.00 9.00 27.78 GDP per capita 6,066 17,530 8,415 979 17,763 68,900 Patents per capita 6,066 0.05 0.14 0.00 0.01 2.64 R&D investment per capita 5,478 261.60 280.45 7.03 161 1,791 EEI Additive 5,994 6.38 5.68 1.26 4.19 35.08 EEI Log 5,994 -9.07 6.90 -21.96 -9.82 10.58 Panel B HGF shares (in %) 2,398 8.64 3.14 0.00 8.65 27.78 GDP per capita 2,397 17,585 8,388 979 17,788 68,900 Patents per capita 2,397 0.05 0.14 0.00 0.01 2.64 R&D investment per capita 2,183 259.17 278.78 7.03 161 1,791 EEI Additive 2,369 6.34 5.63 1.26 4.21 35.08 EEI Log 2,369 -9.08 6.85 -21.96 -9.82 10.58 Notes: Panel A includes all years. Panel B includes years 2008, 2011, 2014, 2017, and 2020. Number of regions with HGF shares equal to zero in Panel A is 12 (out of 6068) and in Panel B is 5 (out of 2398). 15 5. Results 5.1. Hypothesis 1: More developed regions will have higher regional HGF shares Figure 3: Distribution of mean HGF shares over the period 2016-2020. This figure relates to H1 In this section we provide evidence to support or dispute Hypothesis 1, namely, whether more developed regions have higher regional HGF shares. We start by providing some basic descriptive statistics, in the form of a map (Figure 3) and Table 5 with top-15 performing regions. Figure 3 shows distribution of mean HGF shares over the period 2016-2020 (main dependent variable) across 20 EU Member States and their 643 NUTS 3 regions. The map below highlights the conundrum: less developed regions (e.g. south-eastern and insular Spain, southern and insular Italy, southern Portugal) seem to be the EE “hotspots” in terms of having higher HGF shares, which goes against common assumptions and EE theory. 11 11 For instance, according to the EE additive index developed by Leendertse et al. (2021), the top five entrepreneurial ecosystems at NUTS-2 level are: 1) Copenhagen (DK01), 2) West and East Inner London (UKI3&4); 3) Berkshire, 16 Table 5 shows the top-ranking regions in terms of HGF shares – i.e. the regions that EE theory considers as the top-performing entrepreneurial regions, that other regions should aspire towards. These regions are mainly in Spain, Italy, Portugal, and Finland. The top five EEs in Europe, apparently, are La Gomera and Lanzarote in the Canary Islands, Valencia in Spain, Pohjois-Pohjanmaa in Finland, and Medio Campidano in Sardinia, Italy. This does not match well with popular conceptions of Europe’s entrepreneurial hotspots. Table 5: Top-ranking regions in terms of average HGF shares during 2016-2020. Rank Top performing regions Regional HGF shares 1 La Gomera (Spain) 23.44 2 Medio Campidano (Italy) 17.08 3 Lanzarote (Spain) 15.95 4 Pohjois-Pohjanmaa (Finland) 15.82 5 Valencia (Spain) 15.47 6 Oeste (Portugal) 15.31 7 Potenza (Italy) 15.06 8 Caltanissetta (Italy) 15.04 9 Fuerteventura (Spain) 15.01 10 Lleida (Spain) 14.95 11 Toledo (Spain) 14.94 12 Castellón/Castelló (Spain) 14.93 13 Região de Leiria (Portugal) 14.80 14 Madrid (Spain) 14.73 15 Murcia (Spain) 14.73 The initial descriptive information does not seem to provide support for Hypothesis 1. The rest of this subsection conducts a more formal analysis, testing whether regions with higher GDP per capita, more patents per capita, more R&D investment per capita and higher EEI have higher regional HGF shares (Hypotheses 1A, 1B, 1C and 1D). We start the analysis with scatterplots of HGF shares and our four independent variables of interest. Figure 4 shows scatterplot of HGF shares and GDP per capita PPP. According to EE theory, we would expect a positive linear relationship. However, ourresults do not seem to show a positive correlation between HGF shares and GDP per capita PPP. Buckinghamshire and Oxfordshire (UKJ1); 4) Helsinki-Uusimaa (FI1B); 5) Stockholm (SE11). According to other popular metrics, such as the one published in the Global Startup Ecosystem Report, the top five entrepreneurial hotspots in Europe are 1) London; 2) Amsterdam; 3) Paris; 4) Berlin; 5) Stockholm. 17 Figure 4: HGF shares and regional development indicators. Notes: Results at NUTS-3 level. Loess function applied. In general, Figure 4 shows no clear relationship between HGF shares and any of the regional development indicators. We repeat this exercise for GDP per capita PPP, patents per capita and R&D investments per capita, but take logarithm of one plus the value (Figure A1). These results suggest a positive relationship between regional GDP per capita PPP and HGF shares among the regions with low HGF shares and low GDP, but after this initial positive relationship there seems to be no correlation. No clear relationship is visible for patents or R&D investments per capita. To test these relationships in a more formal manner, Table 6 provides Pearson correlation and Spearman’s rank correlation. There is no or very low magnitude of correlation between HGF shares and regional development indicators. 18 Table 6: Correlation: HGF shares and regional economic development indicators. This table relates to H1. Log (1 + GDP per capita PPP) Log (1 + Patents per capita) Log (1 + R&D investment per capita) EE Index Additive EE Index Log Pearson correlation 0.167 0.059 0.171 0.072 0.109 P-value 0.000 0.004 0.000 0.000 0.000 Spearman’s rank correlation 0.018 -0.023 0.016 -0.018 -0.018 P-value 0.374 0.252 0.444 0.390 0.382 N 2,398 2,398 2,398 2,398 2,398 Next, we move to the regression analysis and estimate Eq. (3). Table 7 shows that a change from the first (lowest) to the second GDP per capita tercile is associated with a statistically significant increase in HGF shares, at the NUTS-3 level. The first column of Table 7 suggests that regions in the lower range of the distribution of GDP per capita (countries such as Romania, with low GDP per capita) have lower HGF shares than regions with medium levels of GDP per capita. Being in the top tercile of GDP per capita does entail an increase in HGF shares relative to the lowest tercile. Yet, it does not result in any statistically significant increase in HGF shares with respect to countries located at the second tercile. This result provides only weak support for H1a. Moving from the first to the second tercile in patents per capita is associated with a strong increase in the HGF shares. However, surprisingly, moving from the first to the third tercile in patents per capita leads to an increase that is considerably smaller in magnitude and barely statistically significant. We do not go as far as interpreting this finding as an inverted U-shape caused by diminishing returns for patents, but simply as a lack of systematic evidence of the expected positive relationship between regional patents per capita and HGF shares. We therefore reject H1b. Relatedly, moving from the first to the second tercile in R&D investment per capita is associated with higher HGF shares, though only marginally statistically significant. Moving from the first to the third tercile in R&D investments per capita is associated with higher HGF shares, however, the effect size is smaller and this association is only weakly statistically significant. This provides nuanced support for H1c. In the cases of H1a and H1c, we find weak support, although this relationship seems largely confined to some outliers at the low end of the distribution, as shown in Figure 4. Finally, we do not find any evidence of a statistically significant positive relationship between EEI and HGF shares. In other words, being a top performer in terms of the quality of the EE does not result in an increased incidence of HGFs in a region. 19 Table 7: Linear regression - HGF shares and regional economic development Dependent variable: HGF shares (1) (2) (3) (4) (5) GDP per capita PPP 2nd tercile 0.666** (0.271) GDP per capita PPP 3rd tercile 0.672*** (0.259) Patents per capita 2nd tercile 1.053*** (0.266) Patents per capita 3rd tercile 0.449* (0.261) R&D investment per capita 2nd tercile 0.514* (0.278) R&D investment per capita 3rd tercile 0.463* (0.272) EEI Additive 2nd tercile 0.142 (0.259) EEI Additive 3rd tercile 0.145 (0.264) EEI Log 2nd tercile 0.407 (0.264) EEI Log 3rd tercile 0.244 (0.269) Mean 8.64 8.64 8.64 8.64 8.64 Observations 2,397 2,397 2,183 2,369 2,369 R2 0.194 0.202 0.191 0.184 0.186 Adjusted R2 0.192 0.200 0.189 0.182 0.184 Notes: *p<0.1; **p<0.05; ***p<0.01. Reference category is always 1st (lowest) tercile. The linear regression is based on means, but there might be heterogeneity in the relationship between our dependent and independent variables. For this reason, we also estimate quantile regressions (see Figure 5 for a graphical representation of the results). An increase in GDP per capita is associated with a small increase in the HGF shares among those regions with low HGF shares (at the 10th and 20th percentile). However, GDP per capita is negatively associated among regions with HGF shares at the 60th or at the 70th percentile. Patents per capita are positively associated with the HGF shares only among regions with very low HGF shares (10th percentile), but less so for regions with higher HGF shares. 20 Quantile regression results for R&D investment per capita, and EEI show similar results, namely, an increase in R&D investments and EEI is associated with an increase in HGF shares only among regions with low HGF shares, but it is negatively associated or non-significant among regions with medium or higher HGF shares. The literature on HGFs and EEs often focuses on the upper quantiles, where one finds the above-average performing firms and regions. This is in contrast with the results in Figure 5, which highlight different behaviour that is confined exclusively to the lowest quantiles. It seems that economic development matters at the lowest quantiles, presumably for removing some of the most basic obstacles and constraints to economic dynamism (as proxied by HGF shares). For most regions however, there is a negligible relationship between economic development and (conditional) HGF shares. In sum, results presented in the subsection show negligible support for our Hypothesis 1 as more developed regions are not associated with higher regional HGF shares. Figure 5: Quantile regression plots. Notes: the plots report estimates from quantile regressions. All specifications include as dependent variable the HGF shares at the NUTS-3 level and control for year fixed effects. Standard errors are robust and clustered at the NUTS-3 level. Shaded areas represent 95% confidence intervals. 21 5.2. Hypothesis 2: Given the regional persistence of the inputs, there is regional persistence of HGF shares In this subsection we answer the question: how strong is regional persistence of HGF shares? We start by presenting pooled regional HGF shares for two consecutive three-year periods (Figure 6, left). In the Figure 6 (right) we also show regional persistence where points are colored based on the two three-year periods. There are two main clusters in Figure 6. Firstly, there is a smaller cluster of regions with low shares in both periods (left, bottom). More importantly, there is a large cluster in the middle of the figure indicating a variability in HGF shares between two periods, however, there seems to be some persistence between the regional HGF shares of two periods. The right graph shows that the magnitude of correlation might be affected by the time period, probably due to time-specific regional demand and macroeconomic conditions. Figure 6: Persistence of regional HGF shares. Notes: Left graph shows scatterplot of HGF shares in two consecutive three-year periods with smoothed conditional means using loess method. Right graph uses time variable to color the observations. Blue color for period 05/08 (t) and 08/11 (t+3); Red color for period 08/11 (t) and 11/14 (t+3); Black color for period 11/14 (t) and 14/17 (t+3). Color online. Persistence might be lower with a longer lag, which is why we also plot regional HGF shares with a longer time lag (Figure 7). The dependent variable (on Y-axis) is based on HGFs information 5 to 11 years ahead of the independent variable (lagged HGF shares, on X-axis). Scatterplots are similar to the main scatterplot in Figure 6. 22 Figure 7: Persistence of regional HGF shares with longer lags. Notes: All graphs use 2016-2019 as the last period (t-3 to t). At the x-axis, upper left graph shows 05/08, upper right 08/11, lower left 09/12, and lower right 11/14. In sum, Figures 6 and 7 show scatterplots for the persistence of regional HGF shares. Similar patterns are observed for the different years. However, HGF shares seem higher in some years than in others. The correlations generally look quite positive: more positive than what was observed previously for NUTS-3 regions in Croatia (Coad and Srhoj, 2023). There seems to be a separate cluster or regions that have low values of regional HGF shares. In other words, in the first graph, the distribution of regional HGF shares seems to be bimodal, with one mode at around 0.08 corresponding to the main group of datapoints, and then another mode at around 0.02 corresponding to a separate mini-cluster of observations corresponding to low HGF shares. Furthermore, there is a gap between these two groups, such that the regional HGF shares does not seem to be a continuous variable. Fortunately, there seems to be no problem of bunching at the lower bound (no bunching at HGF shares == 0.000), which is good news from a statistical perspective. Figure 8 presents a bivariate map of the persistence of HGF shares. The bivariate map is shown for two periods, although the results are similar for the left and right maps. Some regions (shown with dark brownpurple shading) appear to have above-average HGF shares in consecutive periods: parts of Spain, Finland, southern Italy, Slovakia, etc. Other regions (shown with light shading) have relatively low persistency of HGF shares: Austria, Romania, and parts of France. We continue with a more formal empirical exercise – Pearson correlation and Spearman’s rank correlation. Table 8 shows correlation statistics, both the usual Pearson correlations as well as Spearman’s rank correlations (that are more robust to the case of non-normally-distributed variables). The correlations are overall positive and reasonably large in magnitude; hence we conclude that they give reasonable support for H2. This is interesting considering that the corresponding relationship was weaker in the case of Croatian regions, but it is more similar to Slovenian (Coad and Srhoj, 2023) and Austrian regions (Friesenbichler and Hölzl, 2020). 29 3) weak support (mixed results) for more developed regions having higher persistence of HGF shares (H3). 6. Discussion Table 12 summarizes the results obtained so far by using them to evaluate whether the hypotheses are supported. Table 12: Revisiting the hypotheses Hypothesis Statement Indicator Supported? H1 More developed regions will have higher regional HGF shares H1a GDP per capita Weak support H1b Patents per capita Not supported H1c R&D investment per capita Weak support H1d EEI Not supported H2 Given the regional persistence of the inputs, there is regional persistence of HGF shares Supported H2a In two consecutive threeyear periods Supported H2b With longer lags Supported H3 Regional persistence of HGF shares is higher in more developed regions and in those with high shares in the past Not supported H3a GDP per capita Not supported H3b Patents per capita Not supported H3c R&D investment per capita Not supported H3d EEI Not supported H3e High HGF shares in the past Not supported Hypothesis 1 receives weak support in some cases, while in other cases it receives no support. Figure 4 showed that support for H1 seemed to be driven by the lower end of the distribution of economic development (e.g. regions with low GDP per capita PPP). There was some support for H1a and H1c in Table 7, which seemed to be driven by the lower end of the distribution of regional HGF shares (Figure 5). Support for H1a and H1c is weaker when focusing on the NUTS-2 level instead of the NUTS-3 level (Table C1). Overall, therefore, H1 is not supported. Hypothesis 2 receives the strongest support: there is persistence in regional HGF shares. Hypothesis 3 investigates whether the persistence of HGF shares is higher in more developed regions. H3 is generally not supported. The results actually appear to be significantly counter to expectations (i.e. significantly negative instead of positive) in our main specification for H3 (Table 10). Similarly, we do not find support for path-dependency in HGF shares as persistence is not stronger for regions with high levels of HGFs in the past. 30 7. Conclusion This paper investigated the phenomenon of regional shares of high-growth firms (HGFs), as well as their persistence. To that end, we derived some predictions from Entrepreneurial Ecosystem (EE) theory and tested three broad hypotheses using regional-level data (NUTS-3 and NUTS-2 level data) from several European countries. According to EE theory (Stam, 2015; Spigel, 2017; Leendertse et al., 2021; Coad and Srhoj, 2023), the output of ecosystems is measured in terms of regional HGF shares. Regions whose EE is built from a stronger set of inputs can expect higher levels of outputs, and the best-performing EEs are expected to produce more outputs in terms of having higher regional shares of HGFs. On this basis, analysis of regional rankings yields the puzzling finding that the leading EEs in Europe, apparently, are in regions such as the Canary Islands, Basilicata, and Algarve. These results cast doubt that regional HGF shares are truly capturing the performance of an EE. Additional analyses confirm that regions that are highly developed, innovative or with superior quality in terms of EEs do not feature the highest incidence of HGF. However, we do find evidence that is in line with EE theory, namely, the fact that HGF shares exhibit persistence over time. Yet, we show that this persistence is not stronger for regions with higher development, nor for those that experienced high levels of HGF shares in the past, something that is not consistent with pathdependency being the main mechanism behind persistence. These findings call for a more nuanced interpretation of regional HGF shares, including a better understanding of their nature and drivers. There is a widespread assumption among policy-makers and practitioners according to which a higher prevalence of HGFs in a given region is synonymous with vibrant regional economic dynamics. 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Entrepreneurship Theory and Practice, 1042258721998948. 35 Appendices This section contains the appendices to the paper “Regional incidence and persistence of high-growth firms: Testing ideas from the Entrepreneurial Ecosystems literature” by Alex Coad, Clemens Domnick, Pietro Santoleri and Stjepan Srhoj. The appendices contain the following information:  Appendix A: provides a summary of statements taken from the the EE literature concerning regional HGF shares incidence and persistence;  Appendix B: motivates the reason why growth periods should not be overlapping;  Appendix C: reports additional results and re-runs our main analysis using NUTS-2 regions instead of NUTS-3 regions;  Appendix D: reports results using as dependent variable the number of HGFs at time t divided by the number of active firms with ≥ 10 employees at time t-3;  Appendix E: reports results using as dependent variable the number of HGFs at time t divided by the number of all active firms at time t-3; 36 Appendix A: Statements by EE scholars regarding HGFs HGFs as the output of the Entrepreneurial Ecosystem Source Statement Harima (2020, p. 30) “The idea of entrepreneurial ecosystems, however, focuses on the entrepreneurial process within regional boundaries, with all entrepreneurs serving as the focal actors who drive the ecosystem evolution, and establishing high-growth firms as the primal output of entrepreneurial ecosystems (Spigel, 2017).” Spigel, Kitagawa and Mason (2020, p. 484) “we define entrepreneurial ecosystems here as the regional collection of actors (such as entrepreneurs, advisors, workers, mentors, and workers) and factors (cultural outlooks, policies, R&D systems, and networks) that all contribute to the creation and survival of high-growth ventures. We focus on high-growth entrepreneurship because it is seen as a major driver of job creation and economic growth in both advanced and emerging economies” Spigel, Kitagawa and Mason (2020, p. 485) “‘high-growth’ firms – the firms that ecosystems are, in principle, designed to support.” Sleuwaegen and Ramboer (2020, p. 2326) “we develop a conceptual model explaining the link between a virtuous entrepreneurial ecosystem and the emergence of HGFs” Stam and Van de Ven (2021 p. 817) “the envisaged output of the ecosystem: high-growth firms. … we have proxied productive entrepreneurship with the prevalence of high-growth firms … the share of high-growth firms of the regional business population” Stam and Van de Ven (2021, p. 809) “We find that the prevalence of high-growth firms in a region is strongly related to the quality of its entrepreneurial ecosystem.” Audretsch and Belitski (2021, p. 738) “Regions with a sizeable creative industry where the creative class works are more likely to display openness to diversity and new ideas generation that spillover into new marketable products leading to high-growth firms (Audretsch et al., 2019a).” Audretsch and Belitski (2021, p. 739) “In measuring productive entrepreneurship (Baumol, 1993), we used the share of high-growth firms in a region (Stam, 2018; Stam et al., 2011, 2012) (Table 1).” Wurth, Stam, & Spigel, (2021, p. 7) “one of the defining features of entrepreneurial ecosystems research has been a focus on productive entrepreneurship. ... It is often measured as high-growth entrepreneurship” Spigel (2022, p. 3) "Ecosystems differ from other territorial-based theories of economic development such as clusters and innovation systems due to their focus on the types of regional environment that impact high-growth entrepreneurs" High-performing Entrepreneurial Ecosystems should display persistence in HGF shares Spigel (2017, p. 49) “Entrepreneurial ecosystems have emerged as a popular concept to explain the persistence of high-growth entrepreneurship within regions.” Spigel and Harrison (2018, p. 155) “Cluster and RIS [Regional Innovation System] concepts provide wellresearched frameworks that help us understand why some places enjoy persistently higher rates of high-growth entrepreneurship than others.” Entrepreneurial Ecosystems are path-dependent Wurth, Stam, & Spigel, (2021, p. 764) “strong path dependence in the evolution of entrepreneurial ecosystems. EE should be treated as a system (strong path-dependency within its evolution), with overall quality positively related to entrepreneurial output, which in turn feeds back into the regional EE” (p. 764). Source: based on Coad and Srhoj (2023). 37 Appendix B: Why the growth periods must be non-overlapping This appendix is based on Coad and Srhoj (2023). The periods over which HGF shares are measured need to be non-overlapping, otherwise we will introduce severe positive bias in our estimates of persistence. Consider the regional share of HGFs, denoted by 𝑌𝑖𝑡 for region i and year t. 𝑌𝑖𝑡 refers to the three-year growth performance of firms, hence 𝑌𝑖𝑡 =𝑓(𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑗𝑡−1,𝑔𝑟𝑖𝑗𝑡−2), which shows that regional HGF shares depends on the growth of firm j over a three-year period (growth gr at time t, t-1, and t-2). For didactic purposes, we assume that annual growth of firm j, 𝑔𝑟𝑖𝑗𝑡 is a purely random variable (𝜇 =0,𝜎2=1) that is independent and identically distributed over years: 𝛾 =𝑐𝑜𝑟(𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑚𝑡)=1 𝑓𝑜𝑟 𝑗 =𝑚, and 𝛾 =𝑐𝑜𝑟(𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑚𝑡)=0 𝑓𝑜𝑟 𝑗 ≠𝑚, For non-overlapping periods, we have zero persistence (i.e. zero correlation of regional HGF shares). Considering the covariance: 𝛾 =𝑐𝑜𝑣(𝑌𝑖𝑡,𝑌𝑖𝑡−3)=𝑐𝑜𝑣[(𝑓(𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑗𝑡−1,𝑔𝑟𝑖𝑗𝑡−2),𝑓(𝑔𝑟𝑖𝑗𝑡−3,𝑔𝑟𝑖𝑗𝑡−4,𝑔𝑟𝑖𝑗𝑡−5))] =0, given that 𝛾 =𝑐𝑜𝑣(𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑚𝑡)=0 𝑓𝑜𝑟 𝑗 ≠𝑚, For overlapping periods, however, we introduce positive bias in the persistence: 𝛾 =𝑐𝑜𝑣(𝑌𝑖𝑡,𝑌𝑖𝑡−1)=𝑐𝑜𝑣[(𝑓(𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑗𝑡−1,𝑔𝑟𝑖𝑗𝑡−2),𝑓(𝑔𝑟𝑖𝑗𝑡−1,𝑔𝑟𝑖𝑗𝑡−2,𝑔𝑟𝑖𝑗𝑡−3))] This positive bias comes from the fact that the two terms 𝑓(𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑗𝑡−1,𝑔𝑟𝑖𝑗𝑡−2) and 𝑓(𝑔𝑟𝑖𝑗𝑡−1,𝑔𝑟𝑖𝑗𝑡−2,𝑔𝑟𝑖𝑗𝑡−3) are positively related because they include the same terms 𝑔𝑟𝑖𝑗𝑡−1 and 𝑔𝑟𝑖𝑗𝑡−2. The same growth events (i.e. 𝑔𝑟𝑖𝑗𝑡−1 and 𝑔𝑟𝑖𝑗𝑡−2) would be double-counted, because they are included in both three-year periods. Then the use of overlapping periods increases the value of 𝑐𝑜𝑟(𝑌𝑖𝑡,𝑌𝑖𝑡−3) towards 1 (i.e. positive bias that exaggerates persistence in regional HGF shares). Consider the special case where 𝑓(𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑗𝑡−1,𝑔𝑟𝑖𝑗𝑡−2)=𝑔𝑟𝑖𝑗𝑡 + 𝑔𝑟𝑖𝑗𝑡−1 +𝑔𝑟𝑖𝑗𝑡−2 In the case of non-overlapping periods, we have: 𝑐𝑜𝑣(𝑌𝑖𝑡,𝑌𝑖𝑡−3)=𝑐𝑜𝑣((𝑔𝑟𝑖𝑗𝑡 + 𝑔𝑟𝑖𝑗𝑡−1 +𝑔𝑟𝑖𝑗𝑡−2),(𝑔𝑟𝑖𝑗𝑡−3 + 𝑔𝑟𝑖𝑗𝑡−4 +𝑔𝑟𝑖𝑗𝑡−5))=0 38 given that 𝛾 =𝑐𝑜𝑣(𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑚𝑡)=0 𝑓𝑜𝑟 𝑗 ≠𝑚 However, in the case of overlapping periods (Cryer and Chan, 2008, Section 4.2), 𝑐𝑜𝑣(𝑌𝑖𝑡,𝑌𝑖𝑡−1)= 𝑐𝑜𝑣((𝑔𝑟𝑖𝑗𝑡 + 𝑔𝑟𝑖𝑗𝑡−1 +𝑔𝑟𝑖𝑗𝑡−2),(𝑔𝑟𝑖𝑗𝑡−1 + 𝑔𝑟𝑖𝑗𝑡−2 +𝑔𝑟𝑖𝑗𝑡−3)) =𝑐𝑜𝑣((𝑔𝑟𝑖𝑗𝑡,𝑔𝑟𝑖𝑗𝑡−3))+𝑐𝑜𝑣((𝑔𝑟𝑖𝑗𝑡−1,𝑔𝑟𝑖𝑗𝑡−1))+𝑐𝑜𝑣((𝑔𝑟𝑖𝑗𝑡−2,𝑔𝑟𝑖𝑗𝑡−2)) =0+1+1 The corresponding correlation coefficient can be calculated recalling that 𝜎2=1, to yield: 0+1+1 1+1+1 =0.6667 Use of overlapping periods therefore leads, in this case, to an estimated persistence of 66.7%, whereas in fact we know that it should be 0% (given that 𝑔𝑟𝑖𝑗𝑡 was set up to be independent from one year to the next). This might explain why some studies have found high persistence in regional HGF shares when using overlapping periods. For example, Fotopoulos (2022) uses a sample has 378 regions over a 6-year period (2012-2017), and N=2268 in Table 2. Considering that 2268/378 = 6, this suggests that the three-year periods are overlapping (e.g. the growth rates for the first time period overlap with those for the second time period), which would give a strong positive bias to the persistence of HGF shares because it is likely that the same growth events will be double-counted. 45 Notes: *p<0.1; **p<0.05; ***p<0.01. Reference category is always 1st (lowest) tercile. Results at the NUTS3-level. HGF shares definition computed from raw Eurostat data on the number of HGFs in a region, and on number of firms with 10 or more employees in a region, where lagged (t-3) number of firms in a region is used as a denominator. Time fixed effects included, standard errors are regionally clustered. Table D2: Regression results. Observations pooled across years. HGFs divided by lagged firms >= 10. Dependent variable: HGF shares (t) (1) (2) (3) N One lag model HGF shares t-3 0.516*** (0.020) 0.516*** (0.047) 0.667*** (0.021) 1507 R2 0.317 0.317 0.568 Two lag model HGF shares t-6 0.645*** (0.044) 0.645*** (0.058) 0.721*** (0.053) 948 R2 0.182 0.182 0.315 Three lag model HGF shares t-9 0.784*** (0.052) 0.784*** (0.055) 0.784*** (0.055) 448 R2 0.335 0.335 0.335 Time FE No No Yes Regionally clustered SE No Yes Yes Notes: *p<0.1; **p<0.05; ***p<0.01. Results at the NUTS3-level. HGF shares definition computed from raw Eurostat data on the number of HGFs in a region, and on number of firms with 10 or more employees in a region, where lagged (t-3) number of firms in a region is used as a denominator. Time fixed effects included, standard errors are regionally clustered. Table D3: Regression results. Observations pooled across years. Persistency with GDP, Patents and R&D investments interactions. Dependent variable: HGF shares (t) (1) (2) (3) HGF shares (t-3) 0.735*** (0.028) 0.703*** (0.023) 0.742*** (0.033) GDP per capita PPP 2nd tercile 0.022*** (0.004) GDP per capita PPP 3rd tercile 0.030*** (0.005) HGF shares (t-3) X GDP per capita PPP 2nd tercile -0.184*** (0.044) HGF shares (t-3) X GDP per capita PPP 3rd tercile -0.288*** (0.055) 46 Patents per capita 2nd tercile 0.026*** (0.005) Patents per capita 3rd tercile 0.005 (0.005) HGF shares (t-3) X Patents per capita 2nd tercile -0.213*** (0.042) HGF shares (t-3) X Patents per capita 3rd tercile -0.044 (0.053) R&D investment per capita 2nd tercile 0.027*** (0.006) R&D investment per capita 3rd tercile 0.002 (0.005) HGF shares (t-3) X R&D investment per capita 2nd tercile -0.240*** (0.057) HGF shares (t-3) X R&D investment per capita 3rd tercile -0.009 (0.054) Observations 1,499 1,499 1,377 R2 0.588 0.583 0.531 Adjusted R2 0.586 0.581 0.529 Notes: *p<0.1; **p<0.05; ***p<0.01. Reference category is always 1st (lowest) tercile. Results at the NUTS3level. HGF shares definition computed from raw Eurostat data on the number of HGFs in a region, and on number of firms with 10 or more employees in a region, where lagged (t-3) number of firms in a region is used as a denominator. Time fixed effects included, standard errors are regionally clustered. Table D4: Regression results. Observations pooled across years. Persistency with EEI interactions. Dependent variable: HGF shares (t) (1) (2) HGF shares (t-3) 0.742*** 0.739*** (0.044) (0.044) EEI Additive 2nd tercile 0.025*** (0.005) EEI Additive 3rd tercile 0.008*** (0.006) HGF shares (t-3) X EEI Additive 2nd tercile -0.252*** (0.057) HGF shares (t-3) X EEI Additive 3rd tercile -0.099 (0.062) EEI Log 2nd tercile 0.026*** 47 (0.016) EEI Log 3rd tercile 0.006 (0.006) HGF shares (t-3) X EEI Log 2nd tercile -0.249*** (0.057) HGF shares (t-3) X EEI Log 3rd tercile -0.087 (0.063) Observations 1,486 1,486 R2 0.509 0.511 Adjusted R2 0.506 0.508 Notes: *p<0.1; **p<0.05; ***p<0.01. Reference category is always 1st (lowest) tercile. Results at the NUTS3level. HGF shares definition computed from raw Eurostat data on the number of HGFs in a region, and on number of firms with 10 or more employees in a region, where lagged (t-3) number of firms in a region is used as a denominator. Time fixed effects included, standard errors are regionally clustered. 48 Appendix E. HGF shares denominator: all firms in the region at time t-3 A potential drawback of the baseline HGFs indicator is that firms with fewer than 10 employees are not taken into consideration. An alternative indicator could therefore be the following: 𝐻𝐺𝐹𝑠 𝐹𝑖𝑟𝑚𝑠=𝐹𝑖𝑟𝑚𝑠 𝑤𝑖𝑡ℎ ≥10 𝑒𝑚𝑝𝑙 𝐹𝑖𝑟𝑚𝑠 ∙𝐻𝐺𝐹𝑠 𝐹𝑖𝑟𝑚𝑠 𝑤𝑖𝑡ℎ ≥10 𝑒𝑚𝑝𝑙 (4) This indicator arguably seeks to describe the overall dynamism of an economy, by showing the frequency of HGFs as a proportion of all firms. However, the inclusion of the first right-hand-side component, i.e. 𝐹𝑖𝑟𝑚𝑠 𝑤𝑖𝑡ℎ ≥10 𝑒𝑚𝑝𝑙 𝐹𝑖𝑟𝑚𝑠 is potentially problematic because firms with fewer than 10 employees cannot possibly become HGFs and therefore should not be taken into consideration as the sample from which HGFs emerge. This indicator penalizes regions with lots of firms with <10 employees. Also, it could be considered to be “unfair”, because we are looking at the ratio of HGFs with firms that could not possibly become HGFs even if they wanted to. Compared to the indicator in 3.1.2.1, this indicator would be akin to the following ratio: 𝑙𝑜𝑡𝑡𝑒𝑟𝑦 𝑤𝑖𝑛𝑛𝑒𝑟𝑠 𝐸𝑣𝑒𝑟𝑦𝑜𝑛𝑒 𝑖𝑛𝑐𝑙𝑢𝑑𝑖𝑛𝑔 𝑡ℎ𝑜𝑠𝑒 𝑡ℎ𝑎𝑡 𝑑𝑖𝑑 𝑛𝑜𝑡 𝑏𝑢𝑦 𝑎𝑛𝑑 𝑤𝑒𝑟𝑒 𝑛𝑜𝑡 𝑒𝑣𝑒𝑛 𝑒𝑙𝑖𝑔𝑖𝑏𝑙𝑒 𝑡𝑜 𝑏𝑢𝑦 𝑎 𝑙𝑜𝑡𝑡𝑒𝑟𝑦 𝑡𝑖𝑐𝑘𝑒𝑡 A potential problem here is the denominator is not such a relevant source group for the numerator. Nevertheless, in what follows, we re-run our analysis using this HGF shares definition. Table E1. Linear regression - HGFs (divided by lagged all firms) and regional economic development Dependent variable: HGF shares (t) (1) (2) (3) (4) (5) GDP per capita PPP 2nd tercile -0.001*** (0.0003) GDP per capita PPP 3rd tercile -0.001*** (0.0003) Patents per capita 2nd tercile -0.001*** (0.0003) Patents per capita 3rd tercile -0.0002 49 (0.0003) R&D investment per capita 2nd tercile -0.0004** (0.0002) R&D investment per capita 3rd tercile 0.0004* (0.0002) EEI Additive 2nd tercile -0.001** (0.0003) EEI Additive 3rd tercile 0.0002 (0.0002) EEI Log 2nd tercile -0.001*** (0.0003) EEI Log 3rd tercile 0.0001 (0.0003) Mean 0.004 0.004 0.004 0.004 0.004 Observations 2,156 2,156 1,966 2,133 2,133 R2 0.077 0.068 0.086 0.061 0.065 Adjusted R2 0.075 0.066 0.084 0.059 0.063 Residual Std. Error 0.003 (df = 2150) 0.003 (df = 2150) 0.002 (df = 1960) 0.003 (df = 2127) 0.003 (df = 2127) Notes: *p<0.1; **p<0.05; ***p<0.01. Reference category is always 1st (lowest) tercile. Results at the NUTS3-level. HGF shares definition computed from raw Eurostat data on the number of HGFs in a region as numerator, and on lagged number of all firms in a region as a denominator. Time fixed effects included, standard errors are regionally clustered. Table E2: Regression results. HGFs divided by all firms. Dependent variable: HGF shares (t) (1) (2) (3) N One lag model HGF shares t-3 0.684*** (0.015) 0.684*** (0.032) 0.716*** (0.039) 1509 R2 0.588 0.588 0.687 Two lag model HGF shares t-6 0.434*** (0.022) 0.434*** (0.068) 0.446*** (0.067) 950 R2 0.287 0.287 0.310 Three lag model HGF shares t-9 0.494*** (0.033) 0.494*** (0.038) 0.494*** (0.038) 448 R2 0.333 0.333 0.333 Time FE No No Yes Regionally clustered SE No Yes Yes 50 Notes: *p<0.1; **p<0.05; ***p<0.01. Results at the NUTS3-level. HGF shares definition computed from raw Eurostat data on the number of HGFs in a region as numerator, and on lagged number of all firms in a region as a denominator. Time fixed effects included, standard errors are regionally clustered. Table E3: Persistency with GDP, Patents and R&D investments interactions. Dependent variable: HGF shares (t) (1) (2) (3) HGF shares (t-3) 0.696*** (0.046) 0.671*** (0.043) 0.762*** (0.019) GDP per capita PPP 2nd tercile -0.0004 (0.0003) GDP per capita PPP 3rd tercile -0.0003 (0.0003) HGF shares (t-3) X GDP per capita PPP 2nd tercile 0.054 (0.065) HGF shares (t-3) X GDP per capita PPP 3rd tercile 0.086 (0.062) Patents per capita 2nd tercile -0.001*** (0.0002) Patents per capita 3rd tercile -0.001*** (0.0002) HGF shares (t-3) X Patents per capita 2nd tercile 0.170*** (0.062) HGF shares (t-3) X Patents per capita 3rd tercile 0.165*** (0.055) R&D investment per capita 2nd tercile 0.0003** (0.0002) R&D investment per capita 3rd tercile -0.0003* (0.0002) HGF shares (t-3) X R&D investment per capita 2nd tercile -0.046 (0.043) HGF shares (t-3) X R&D investment per capita 3rd tercile 0.103** (0.043) Observations 1,501 1,501 1,377 R2 0.689 0.694 0.704 Adjusted R2 0.688 0.693 0.702 Notes: *p<0.1; **p<0.05; ***p<0.01. Reference category is always 1st (lowest) tercile. Results at the NUTS3-level. HGF shares definition computed from raw Eurostat data on the number of HGFs in a region as numerator, and on lagged number of all firms in a region as a denominator. Time fixed effects included, standard errors are regionally clustered. 51 Table E4: Persistency with EEI interactions. Dependent variable: HGF shares (t) (1) (2) HGF shares (t-3) 0.930*** 0.929*** (0.022) (0.022) EEI Additive 2nd tercile 0.001*** (0.0001) EEI Additive 3rd tercile 0.0004* (0.0002) HGF shares (t-3) X EEI Additive 2nd tercile -0.428*** (0.031) HGF shares (t-3) X EEI Additive 3rd tercile -0.114** (0.046) EEI Log 2nd tercile 0.001*** (0.0001) EEI Log 3rd tercile 0.0003 (0.0002) HGF shares (t-3) X EEI Log 2nd tercile -0.427*** (0.031) HGF shares (t-3) X EEI Log 3rd tercile -0.096** (0.047) Observations 1,486 1,486 R2 0.743 0.742 Adjusted R2 0.741 0.740 Notes: *p<0.1; **p<0.05; ***p<0.01. Reference category is always 1st (lowest) tercile. Results at the NUTS3level. HGF shares definition computed from raw Eurostat data on the number of HGFs in a region as numerator, and on lagged number of all firms in a region as a denominator. Time fixed effects included, standard errors are regionally clustered. https://europa.eu/european-union/contact_en https://europa.eu/european-union/contact_en https://europa.eu/european-union/index_en https://publications.europa.eu/en/publications https://europa.eu/european-union/contact_en