Urbanisation, concentration and diversification as determinants of firm births and deaths

ABSTRACT This paper examines the impact of urbanisation, concentration and diversification on firm births and firm deaths across European regions while uniquely accounting for the role of firm interrelationships, regional factors and national fixed effects. A 3SLS model on firm births and deaths is estimated across 196 regions and 16 European countries from 2008 to 2017. We find that density positively influences firm births and negatively influences firm deaths. Related variety positively impacts firm deaths and negatively affects firm births. Significant national variations are also observed. Multiplier effects are identified within and across regions as firm births positively influence future firm births and negatively influence future firm deaths.


INTRODUCTION
Industrial structure impacts firm births and firm deaths (Corradini & Vanino, 2021;Power et al., 2020).Marshall (1890), Arrow (1971) and Romer (1986) (abbreviated as MAR) suggest that regions with high agglomerations of firms in similar industries may benefit from positive externalities like economies of scale and reduced transaction costs.These positive externalities can arise between similar firms located close to each other and may increase firm births (Capozza et al., 2018) and reduce firm deaths (Power et al., 2020;Basile et al., 2017).Conversely, Jacobs (1969) and Nielsen et al. (2021) hypothesise that diversification of industrial composition produces the innovations and knowledge spillovers that influence firm births due to different knowledge, skill-sets and capabilities.Diversification has been found to deter firm deaths, making regions more resilient (Basile et al., 2017;Boschma & Iammarino, 2009).Related and unrelated variety have also been recognised as a source of knowledge spillovers, leading to greater innovation and improvements in employment growth (Frenken et al., 2007;Delgado et al., 2010;Boschma, 2015).Moreover, urbanization externalities can play a role in influencing firm births and firm deaths by affecting local demand and access to greater arrays of services (Basile et al., 2017;Power et al., 2019).Additionally, industry concentration also influences firm births and deaths (Calá et al., 2016;Jacobs et al., 2014) by influencing barriers to entry and competitive pressures (Johan & Vania, 2022;Joffe, 2022).Thus, urbanisation, concentration and diversification are all important factors of the industrial structure of a region which can explain firm birth and death activity.
Our paper makes two contributions.Firstly, we analyse the determinants of firm births and firm deaths while also explicitly accounting for firm interrelationships (i.e., when firm births/ deaths influence future firm births/deaths).Existing literature focuses on the differentiated impacts of urbanisation (Power et al., 2019), concentration (Koo & Cho, 2011) and diversification (Howell et al., 2018).However, Arcuri et al. (2019) and Piacentino et al. (2017) emphasise the importance of considering factors like firm interrelationships in conjunction with industrial factors when analysing firm births and firm deaths.Despite the well-documented interrelatedness of firm births and deaths [see Gajewski and Kutan (2018) and Carree et al. (2011) for examples], many recent contributions to the literature do not account for them, e.g., Corradini and Vanino (2021), Demirdag and Eraydin (2020), Content et al. (2019) and Power et al. (2019).We build on existing research by specifically accounting for firm interrelationships in our analysis.
Secondly, previous studies on firm births and firm deaths have been either national (Audretsch & Belitski, 2017;Hundt & Sternberg, 2016) or regional studies (Arcuri et al., 2019;Power et al., 2019).Audretsch et al. (2019) recently discussed a 'knowledge gap on the impact of the country context on entrepreneurship in subnational units' (p.1149) which has not been explored in the literature.This distinction is critical as national factors have been shown to affect firm birth and death rates (Fernández-Serrano et al., 2018;Berdiev & James, 2018;Ayob, 2019) and regional studies often ignore the national context (Spigel, 2017(Spigel, , 2017)).Meanwhile, national level studies can fall victim to 'potential loss of nuance due to aggregation' (Audretsch et al., 2019).We contribute to the literature by controlling for both regional industrial structure and fixed country effects.
This paper uses business demography and employment share data from the OECD and Eurostat from 196 regions across 16 countries for the years 2008-2017 (Eurostat, 2019;OECD, 2020).A three-stage least squares estimation method is used to analyse firm birth and death activity while also controlling for endogeneity issues (Abdallah et al., 2015).Synthetic instrumental variables are generated through the Bartletts three-group method, in a similar manner to Bahlous-Boldi (2021) and Seya et al. (2016).The structure of this paper is as follows.Section 2 presents a review of literature.Sections 3 and 4 outline the data and methods of the estimation respectively.Section 5 presents and interprets the results of the analysis.Section 6 offers concluding remarks and recommendations for future research.

LITERATURE REVIEW
This paper examines firm demography activity which refers to changes in the business population as a result of firm births and deaths (Van Wissen, 2002).The birth and death of firms is generally viewed through three theoretical lenses, the resource-based view (Hart, 1995), the industrial view (Jovanovic, 1982) and the environmental/ecological view (Power et al., 2020).These lenses place a large emphasis on the accumulation and ownership of inimitable and non-tradable resources and market selection as key drivers of firm demographic activity (Esteve-Pérez & Mañez-Castillejo, 2008).During market selection, inefficient firms with inadequate resources, a cost disadvantage, or firms which face intense competition are weeded out, whereas more innovative, adaptive and efficient firms thrive and grow (Geroski, 1982).
Many empirical studies have considered why firms births occur (Armington & Acs, 2002) and why firms fail or disappear (Power et al., 2020).Reasons include the characteristics of entrepreneurs/founders (e.g., age, experience), the firms (e.g., access to finance, human capital), the market (e.g., concentration, capital intensity, new entry), and economic condition and location (e.g., rate of unemployment; skilled labour force, accessibility to human, social and financial capital) (Power et al., 2020;2019;Geroski, 1982;Westlund et al., 2014;Brixy & Grotz, 2007).This paper focuses on firm location.For example, the availability of key resources within regions can influence firm births (Sutaria and Hicks, 2004) and firm deaths (Barney, 1991) as well as the industrial structure of the region (e.g., Power et al. 2020;Basile et al., 2017;Müller 2016;Renski 2014;Fertala, 2008;van Dijk and Pellenbarg, 2000a) and firm interrelationships (Arcuri et al., 2019;Piacentino et al., 2017).The latter is also a key focus of this paper to which we now turn.
Firm interrelationships, whereby firm births/deaths at one point in time influence future firm births/deaths (Arcuri et al., 2019;Piacentino et al., 2017), can affect firm births and firm deaths via multiplier and/or competition effects (Johnson and Parker, 1994;Gajewski and Kutan, 2018).Multiplier effects occur when firm births induce future firm births and deter future firm deaths or if firm deaths induce future firm deaths and deter future firm births (Lu et al., 2008;Resende et al., 2015).Meanwhile, competition effects occur when firm births result in future firm deaths and deter future firm births or when firm deaths induce future firm births and deter future firm deaths (Carree et al., 2011;Pe'er and Vertinsky, 2008).The incorporation of firm interrelationships is important because the birth of new firms has the potential to positively or negatively affect the profits of incumbent firms through complementary or competitive effects, respectively; see Matsuyama (1995).Firm births and deaths can affect future firm births and deaths due to their ability to change competitive pressures and consumer demand (Carree et al., 2011;Gajewski and Kutan, 2018), available market room (Carree andDejardin, 2020), andnecessity-based entrepreneurship (O'Leary, 2022).Additionally, the availability of resources and factors like competition and multiplier effects provides insights into how firm births and firm deaths vary across regions (Sutaria and Hicks, 2004).Theoretically, these factors are important in determining firm births and deaths but have not been accurately captured in empirical works examining firm births and firm deaths (see Corradini and Vanino, 2021;Demirdag and Eraydin, 2020;Content et al., 2019;Power et al., 2019).The next subsection examines theoretical and empirical literature on the effect of the industrial structure of regions on firm births and deaths through examining externalities derived from urbanisation, concentration and diversification.

Urbanisation
Urbanisation externalities relate to the overall density of economic activity within a region (Basile et al., 2017).More urban regions can function as 'hotbeds' for entrepreneurial activity (Müller, 2016).The greater levels of density can provide superior access to services and higher levels of demand which could reduce firm deaths (Ciccone and Hall, 1996).The resource-based view of the firm emphasises the importance of firms possessing their own inimitable resources.Firms located in regions with higher levels of density are likely to have reduced costs associated with the concentration of production at a given location (Parr, 2002).Marshall (1890) asserted that knowledge is exchanged between firms with greater ease if firms and employees are located near to each other.Firms may also benefit from greater levels of economic activity (Badr et al., 2019;McCann and Folta, 2008).These benefits are referred to as urbanisation economies and exist because of the larger scale of economic activity.Conceptually, urbanisation economies are similar to the non-pecuniary benefits of being located in 'core' regions; for example, regions with greater pools of potential employees, superior access to information, and technological spillovers, as discussed by Krugman (1991).Additionally, the geographical concentration of firms in an area allows for firms to be closer to their customer and supplier base (Jofre-Monseny et al., 2011).Other work which discusses this includes Reilly (1931) who proposes Reilly's law of retail gravitation.This asserts that customers opt to travel to specific retail locations due to factors such as the size of the market and the location of competitors.Therefore, there is an incentive for entrepreneurs to found firms in urban locations with high population densities to be close to consumers.However, densely populated areas can also lead to increased levels of competition (Cainelli et al., 2014;Combes et al., 2012).New entrants can increase competition and reduce the profitability of incumbents.However, firm births can also attract more customers to an area and potentially increase the sales of incumbents (Matsuyama, 1995).The reductions in profits may also result in greater firm deaths due to the financial difficulties this may create (Musso and Schiavo, 2008).
Support for the existence of urbanisation economies and how they can influence firms are evident in the productive performances of firms in larger cities, where greater interactions and higher competition increases firm productivity (Combes et al., 2012).The benefits associated with densely populated areas can act as a stimulus which fuels further firm births and reduces firm deaths (Andersson et al., 2019;Motoyama and Malizia, 2017;Van Soest et al., 2006).Firms located in regions which are more urbanised with greater population density have been found to benefit from the greater levels of economic activity (Badr et al., 2019;McCann and Folta, 2008).Both van Dijk and Pellenbarg (2000) and Dijk and Pellenbarg (1999) point out that urban areas have relatively higher firm birth rates.Both Westlund et al. (2014), Renski (2014) and Brixy and Grotz (2007) find a positive relationship between population density and firm births.In terms of firm deaths, Fertala (2008) and Brixy and Grotz (2007) find that population density is associated with fewer firm deaths.Meanwhile some recent studies have found that urbanisation economies have no significant influence on firm deaths (Power et al., 2019;Basile et al., 2017).Potential reasons for this are alluded to by Basile et al. (2013).They observe non-linearities in the influence of urbanisation economies likely due to congestion effects like increased land prices and competition in more urban areas.Some empirical evidence even points towards these congestion effects leading to more firm deaths (Pe'er and Keil, 2013;Huiban, 2009) and less firm births (Nyström, 2007).The effects can manifest through competition effects whereby firm births create more competition which leads to more firm deaths (Carree et al., 2011;Pe'er and Vertinsky, 2008).This process is referred to by Audretsch (1995) and Cefis et al. (2020) as a displacement or revolving door effect.Arcuri et al. (2019) argues that the contrast between the positive effects of urbanisation and the negative effects of congestion is what makes the true relationship between density and firm deaths unclear.Considering the above, we propose the following hypotheses which examine evidence of a positive externality (H1a) or a negative externality (H1b) from urbanisation.
H1a: Higher levels of population density increase firm births and decrease firm deaths.H1b: Higher levels of population density increase firm deaths and decrease firm births.

Industrial concentration
Industrial concentration can have a significant impact on both firm births and deaths.The structure conduct and performance (SCP) paradigm developed by Bain (1956) argues that firm conduct and performance are a direct function of market structure (McWilliams and Smart, 1993;Bianchi, 2013).High levels of industrial concentration are indicative of a market characterised by high barriers to entry (Qualls, 1972;Joffe, 2022).Barriers to entry could include start-up costs as well as the cost of investment in new capital (Mann, 1966;Stringham et al., 2015).High barriers to entry would mean that firm births are unlikely to occur (Porter, 1980;Renski, 2014).Stearns et al. (1995) note that industrial factors can also play a role in determining firm deaths.Established firms may also enjoy an absolute cost advantage over new entrants as they are more likely to be operating at the optimal scale of production (or the minimum efficient scale) (Boulding, 1957).Thus, new firms at a cost disadvantage may struggle to avoid death as they attempt to overcome their 'liabilities of newness' (Gimenez-Fernandez et al., 2020;Stinchcombe, 1965) and Schumpeterian-type competition effects (Brixy, 2014).Additionally, markets characterised by high levels of industrial concentration may also reduce the likelihood of firm births due to what Ericson and Pakes (1995) refer to as the 'persistence-dominance' effect which occurs when a dominant, efficient firm disincentivises entrepreneurs from attempting to enter the market.Thus, industrial concentration traditionally was viewed as reducing firm births and increasing the deaths of new entrants.
However, industrial concentration may also produce positive externalities.For example, greater levels of industrial concentration are associated with low levels of competition (Johan and Vania, 2022).Low levels of competition could incentivise entrepreneurs to enter the market due to a perceived large share of available market room (Carree and Dejardin, 2007).Other incentives could include the advantages associated with 'early entry' like higher revenues per output (Jovanovic and Lach, 1989).Thus, a positive relationship between industrial concentration and firm births could be expected.Furthermore, regarding firm deaths, the low levels of competition would mean that firms are less likely to fall victim to creative destruction-type competitive pressures (Schumpeter, 1942) whereby new firms could lead to the death of firms unable to compete (Cefis et al., 2020).Fewer competitors could also mean that displacement effects have already occurred due to efficient firms displacing inefficient firms (Dejardin and Fritsch, 2011).Subsequently the remaining firms could be highly efficient firms selected by the market which would not be likely to die in accordance with the industrial or resource-based view of the firm (Esteve-Pérez and Mañez-Castillejo, 2008;Jovanovic, 1982).This implies that industrial concentration could reduce firm deaths.
Empirical research on the influence of industrial concentration on firm births and deaths does tend to find more evidence in support of positive externalities than negative externalities (Basile et al., 2017;Cainelli et al., 2014).Regarding positive externalities, industrial concentration has been found to increase firm births and the productivity and growth of firms (Van Soest et al., 2006;Andersson et al., 2019;Armington and Acs, 2002) and this in turn has been shown to minimise firm deaths relative to other regions (De Silva and McComb, 2012;Basile et al., 2017).The concentration of knowledge intensive business services can have a positive impact on firm births (Jacobs et al., 2014).Additionally, Calá et al. (2017) finds that industrial concentration is negatively associated with the death of small and medium sized firms.Zúñiga-Vicente and Vicente-Lorente ( 2006) also find a positive association between concentration and firm survival, implying fewer firm deaths.Similarly, the findings of Power et al. (2021), Ferragina and Mazzotta (2015) and Cainelli et al. (2014) provide evidence for industrial concentration reducing the likelihood of firm deaths.However, evidence for negative externalities can be found; for example, both O'Leary et al. ( 2022) and Audretsch et al. (2012) find a negative relationship between industrial concentration and firm births.Further to this, Strotmann ( 2007) and Mata and Portugal (1994) also observe that industrial concentration has no statistically significant influence over firm deaths.Considering the above, we propose the following two hypotheses to test for these externalities.
H2a: Higher levels of industrial concentration increase firm births and decrease firm deaths.H2b: Higher levels of industrial concentration increase firm deaths and decrease firm births.

Diversification
Diversification externalities are derived from the great variety of industries in a local economy (Jacobs, 1969).A diverse industry structure better facilitates the combination, interaction, modification and generation of ideas across different sectors (Basile et al., 2017).Related variety can be considered a balance of cognitive diversification and similarity between firms (Crowley et al., 2021).Frenken et al. (2007) distinguish between related and unrelated variety as potential inputs for economic growth and argue that higher levels of related variety would increase the amount of intersectoral knowledge spillovers, as knowledge from separate, but related, sectors get diffused between each other.For information to flow between firms, the firms need to be similar enough to understand the information being transmitted, but also different enough that the information is new (Boschma and Iammarino, 2009;Nooteboom, 2000).It would be assumed that greater levels of related variety could induce more knowledge spillovers as the knowledge being transferred is of greater relevance to most firms (Content and Frenken, 2016;Frenken et al., 2007).New knowledge then positively influences firm births when individuals identify entrepreneurial opportunities by linking knowledge from different domains (Content et al., 2019;Shane, 2000).The knowledge spillovers produced from greater levels of related variety therefore have a positive influence on firm births (Acs et al., 2013;Qian et al., 2013;Audretsch and Lehmann, 2005).Transfers of new knowledge could also lead to innovations (Hansen and Birkinshaw, 2007) which would, in accordance with resource-based theory, increase the competitiveness and value of firms (Barney, 2001;Teng, 2000); thus, better facilitating the survival of firms and reducing firm deaths.However, the similarity versus the diversification question remains debated within the literature (Beaudry and Schiffauerova, 2009;De Groot et al., 2016).Related variety is characterised by a balance of cognitive similarity and diversification (Frenken et al., 2007).This balance can produce potential negative externalities for firms.Large levels of relatedness or similarity may lead to cognitive lock-in issues (Crowley et al., 2021).Issues of cognitive lock-in occur when the information being transferred between firms is 'useless' because it is not new (Nooteboom, 2000).Cognitive lock-in can therefore act as a hindrance to innovation (Thrane et al., 2010), thus making the firm weaker in accordance with the resource-based theory, potentially leading to more firm deaths (Barney, 2001).Furthermore, large levels of relatedness may signal market saturation and disincentivise firm births due to the lower expected returns associated with late entrants into the market (Lambkin, 1988).Thus, it could be expected that greater levels of related variety may produce lower rates of firm births and higher rates of firm deaths.
The empirical findings relating to related variety show that related variety helps to lower firm deaths (Szakálné Kanó et al., 2019;Howell et al., 2018;Tavassoli and Jienwatcharamongkhol, 2016;Guo et al., 2018) and improve productivity (Boschma et al., 2009).However, some in the literature find that related variety has no influence on firm deaths (Ebert et al., 2019;Howell et al., 2018).Additionally, Ejdemo and Örtqvist (2020) and Content et al. (2019) find a positive relationship between related variety and firm births.Conversely, Corradini and Vanino (2021) finds some evidence of lock-in effects whereby related variety negatively affected the births of pioneering firms operating in industries which are new to the region.Additionally, the results of Cainelli and Iacobucci (2016) show how levels of related and unrelated variety influence future diversification patterns of business industries within Italian regions.They observe that the firm births in regions with high levels of related variety continue to produce an industrial structure which is characterised by related variety in the future.Considering the above, we propose the following hypotheses.
H3a: Higher levels of related variety increase firm births and decrease firm deaths.H3b: Higher levels of related variety increase firm deaths and decrease firm births.
Unrelated variety implies a greater degree of diversification between firms in different industries (Crowley et al., 2021).While the related variety hypothesis for knowledge transfer states that a certain degree of relatedness is required (Boschma and Iammarino, 2009;Nooteboom, 2000), some of the literature argues that that diversification of industry may better facilitate the transfer of different types of knowledge (Boschma et al., 2012).Regions characterised by greater levels of unrelated variety therefore could be expected to have higher firm birth rates given the positive role which new knowledge could play in idea generation (Boschma et al., 2012).Acs and Audretsch (1988) point out that one of Schumpeter's original hypotheses was that innovation came from outside the firm (Schumpeter, 1934), which would imply that diversification would be more optimal for innovation than relatedness (Scherer, 1965).The importance of diversification as a driver of innovation and consequently new firm births is similarly emphasised by Glaeser et al. (1992) and Duranton and Puga (2000).Additionally, greater diversification can insulate regions from economic shocks, reducing firm deaths (Basile et al., 2017;Boschma and Iammarino, 2009).This means that it may be unrelated variety which has the better propensity to increase firm births and lower firm deaths.While there is an argument for unrelated variety-type diversity producing positive externalities for firms (Jacobs, 1969), contradicting arguments set forth by Marshall (1890), Arrow (1971) and Romer (1986) would argue that similarity is what is needed to produce these positive externalities.Boschma and Iammarino (2009) and Nooteboom (2000) both specify the importance of cognitive proximity for the proper diffusion of knowledge between firms and could imply that that too great a level of diversity would impede on the transmission of knowledge.This issue is referred to as cognitive lockout.It is argued to impede on innovation and idea generation (Thrane et al., 2010;Cohen and Levinthal, 1990), thus reducing firm births.Similarly, the beneficial properties which are associated with new knowledge for firm productivity (Audretsch and Belitski, 2023) would be absent and as a result increased firm deaths may occur.
The results of Tavassoli and Jienwatcharamongkhol (2016) and Basile et al. (2017) find evidence of unrelated variety reducing firm deaths.Meanwhile the findings of Bishop (2012) and Colombelli (2016) show support for unrelated variety increasing firm births.Conversely, Guo et al. (2016) find evidence of a mostly negative relationship between unrelated variety on firm births.Furthermore, Cainelli and Iacobucci (2016) show how levels of unrelated variety influence future diversification patterns of business industries within Italian regions.They observe that the firm births of regions with high levels of unrelated variety continue to produce an industrial structure characterised by unrelated variety.This can be seen to relate to the multiplier effects (where firm births induce more firm births), which Nyström (2007) explains can occur due to demonstration effects.These may be less likely to manifest, given a greater level of unrelatedness, as the creation of a firm in one industry would only demonstrate the value of similar firms also in that industry.Meanwhile, the positive effects of diversification externalities have been found by Content et al. (2019) and Frenken et al. (2007).Considering the above, we propose the following hypotheses.
H3c: Higher levels of unrelated variety increase firm births and decrease firm deaths.H3d: Higher levels of unrelated variety increase firm deaths and decrease firm births.

Measuring firm births and firm deaths
The data used to measure firm births and firm deaths is derived from Eurostat and the OECD 1 (Eurostat, 2021b;OECD, 2021).The data used in the final estimation covers over 196 EU regions across 16 European countries over the years 2008 to 2017.The precise geographical regions and time periods for the regions used in this papers' analysis are displayed in Table 1, providing a total of 862 observations.Geographic variables measuring concentration, diversification and density are consistent with Power et al. (2019) and Corradini and Vanino (2021).Definitions and descriptions for the variables used in this study are presented in Appendix 2 in the online supplemental data.Using firm births, deaths, and stock variables in the data set, firm birth and death rates are constructed in the same manner to Carree et al. (2011).We divide the number of firm births or firm deaths in year t in region i by the stock of firms in the previous year t -1 in region i to capture change over the year period.
Table 2 presents the summary statistics and definitions of the variables included in this analysis and a more detailed discussion of the variables and their calculations can be seen in Appendix 2. 2

METHODOLOGY
This paper opts to estimate the effect of industrial factors on firm births and firm deaths across European regions utilising a three-stage least squares estimation (3SLS) of a two-equation system similar to Plummer and Acs (2014).The reason for this is because this method can mitigate against potential issues of endogeneity (Abdallah et al., 2015).Endogeneity occurs when an independent variable is correlated with a variable which is exogenous to the model (Gujarati, 2011).Our use of lagged dependent variables in each equation as explanatory variables to account for firm interrelationships raises potential issues of endogeneity whereby an independent variable may be influenced by the dependent variable 3 (Abdallah et al., 2015).
The 3SLS estimation allows for the estimation of a system of equations while accounting for potential issues of endogeneity by allowing for the use of instrumental variables (Abdallah et al., 2015).We use the Bartlett's (1949) three-group method to create instrumental variables and describe the use of them in depth in Appendix 4 in the online supplemental data.This technique was originally used to account for omitted variable bias (Hanushek et al., 1996), but has become a widely used method for dealing with endogeneity issues within the literature (e.g., Bahlous-Boldi, 2021;Doran and Fingleton, 2016;Angeriz et al., 2008).
The 3SLS regression estimation here is one which is executed in the manner described by Zellner and Theil (1962).A regression analysis is performed to estimate the predicted values of the variables suspected of being endogenous.Then, the residuals are used in order to estimate a cross-equation correlation matrix and then finally the 3SLS regression is performed where the coefficients in system equations are estimated jointly (Greene, 2003).The two equations to be estimated simultaneously are given by equations ( 1) and (2) below, where FB it is the firm birth Here, Density it is our measure of urbanisation (i.e., the natural logarithm of population density) in region i in time period t, Conc it is our measure of concentration (i.e., the Herfindahl index) in region i in time period t, RV it and UV it capture diversification and are the levels of related and unrelated variety in region i in time t respectively.Firm interrelationships are captured by FB it−1 , which is the firm birth rate in region i in time period t -1 and FD it−1 which is the firm death rate in region i in time period t -1.Additionally, X represents the control variables for log of income and education.m t and m c are a series of year and country dummy variables to capture time and national fixed effects. 1 it is the error term.The variables that are held endogenous are the FB it and FD it variables.Instrumental variables were created using the Bartlett's three-group method for these endogenous variables as described above.An analogous system of equations given by equations ( 3) and ( 4) include spatially weighted contiguity variables and are also estimated using 3SLS and are expressed as follows: Here, W * FB it−1 is the spatially weighted firm birth rate of region i in time period t -1 and W * FD it−1 is the spatially weighted firm death rate of region i in time period t -1.These spatially weighted lagged birth and death rates capture firm birth and death activity in bordering regions.They are treated as endogenous in the system and are instrumented using Bartlett's three-group method as discussed above.

RESULTS
Table 3 presents the 3SLS estimates of equations ( 1), ( 2), ( 3) and ( 4).In equations ( 1) and ( 2), we estimate the sole effect of urbanisation, concentration, diversification and the control variables on firm births and firm deaths while accounting for the influence of firm interrelationships. 4These estimates are presented in the first two columns of Table 3 and are labelled Eqn I and Eqn II.In equations ( 3) and ( 4) we use the same regressors but also include spatial contiguity variables which show the lagged firm birth and death variables in bordering regions.These are presented in columns labelled Eqn III and Eqn IV.

Firm interrelationships
Regarding firm interrelationships, the results of both systems of equations show dominance of the multiplier effect in determining firm births and firm deaths within regions. 5This means that firm births in year t -1 in region i increase firm births and decrease firm deaths in year t in region i.Similarly, firm deaths in year t -1 in region i increase firm deaths and reduce firm births in year t in region i.These results would support the findings of Lu et al. (2008) and Resende et al. (2015) who observe the multiplier effect in their examinations of Taiwan and Brazil respectively.Additionally, Carree et al. (2011) and Calá et al. (2016) also find evidence for the multiplier effect in the case of firm deaths in Italy and firm births in South America respectively.The multiplier effect is potentially explainable by the aforementioned demonstration effect (Nyström, 2007) or alternatively firm births increasing demand via increases in income which leads to further births to meet demand (Gajewski and Kutan, 2018).Across regions we also see evidence of the multiplier effect.The spatially weighted variables for lagged firm births and firm deaths in bordering regions show that firm deaths in year t -1 in bordering regions are positively associated with firm deaths and negatively associated with firm births within region i in year t.The spatially weighted variable for lagged firm births in bordering regions is positively related to firm births and negatively related to firm deaths, indicating that the multiplier effect also occurs across regional borders.Theoretically, the existence of the multiplier effects across regions could be explained by an 'urban-rural shift' in entrepreneurial activity due to incentives to relocate to other regions (Keeble and Tyler, 1995;Bürgin et al., 2022).Factors such as operating cost differences between urban and rural locations as well as urban space shortages lead to rural relocation.This could result in the reallocation of economic activity to neighbouring regions (Keeble and Tyler, 1995;Korsgaard et al., 2015).We now turn to the findings relating to industrial factors and national effects.

Urbanisation, concentration and diversification
Density is found to increase firm births and reduce firm deaths, though the reduction in firm deaths is only evident when the effect of deaths in neighbouring regions is unaccounted for.These results provide tentative support for hypothesis H1a.The positive effect which density has on firm births in this analysis is compatible with the findings of Jacobs et al. (2014) who observe that dense agglomerations can have a positive impact on firm births.This can be due to areas with high population density providing greater ease of access to consumers and input factors required for firms (Reynolds et al., 1994;Wagner and Sternberg, 2004;Guo et al., 2016).Supporting literature shows that density can increase firm births and improve firm growth (Van Soest et al., 2006;Andersson et al., 2019).The Herfindahl index, capturing industrial concentration, has a positive association with firm births and a negative association with firm deaths in columns labelled Eqn I and Eqn II.Thus, we find support for industrial concentration producing positive externalities which supports hypothesis H2a.These findings are similar to those of Calá et al. (2017) who find that industrial concentration is negatively associated with the death of small and medium sized firms, respectively.However, we note that concentration is not statistically significant in the columns labelled Eqn III and Eqn IV when spatial weighted firm births and firm deaths are added to the model.Potentially this is attributable to characteristics relating to industrial concentration, like low levels of competition (Johan and Vania, 2022), being influenced by firm birth/death activity in bordering regions.For example, low levels of competition may indicate that there is a large market share available, which could positively influence firm births (Carree and Dejardin, 2007).However, when spatial weights are added it could be possible that the lagged firm births or deaths in bordering regions also to some extent capture available market share and as a result industrial concentration becomes insignificant.We find that related variety has a significant influence on both firm deaths and firm births.Higher related variety reduces firm births and increases firm deaths, providing support for the H3b hypothesis, and there is evidence that related variety, contrary to expectations, has a negative externality on firm birth and death activity when accounting for firm interrelationships and activity in neighbouring regions.The lower rate of firm births may be attributable to potential issues of cognitive lock-in impeding on innovation and idea generation (Thrane et al., 2010).Alternatively, firm births may be being negatively impacted due to the greater levels of relatedness indicative of a highly saturated market which is unattractive to new entrants (Lambkin, 1988).The higher firm death rates are mostly likely attributable to greater competitive pressure which high degrees of relatedness can bring (Huiban, 2009;Pe'er and Keil, 2013).
Unrelated variety is not significantly related to firm births or deaths in the columns labelled Eqn I and Eqn II.However, in columns labelled Eqn III and Eqn IV when the spatial weights are added, we see that higher unrelated variety increases firm births and decreases firm deaths.Thus, increased unrelated variety is found to induce a positive externality supporting hypothesis H3c.The positive influence of unrelated variety on firm births could be attributable to greater diversity leading to greater knowledge diffusion (Boschma and Iammarino, 2009;Frenken et al., 2007).Subsequently the greater knowledge diffusion could positively influence idea generation and firm births (Boschma et al., 2012;Bosma and Sternberg, 2014).The reduction in firm deaths could result from more diversified regions being less exposed to economic shocks (Basile et al., 2017;Boschma and Iammarino, 2009).

National effects
All the country-specific results are relevant to the reference country, namely Austria.In general, the coefficients for fixed country effects associated with firm births and firm deaths are insignificant save for Bulgaria, Italy and Norway.Norway and Italy have significantly lower firm birth rates and significantly higher firm death rates relative to Austria and other countries except for Bulgaria when the spatially weighted lagged birth and deaths are added to the model.Italy's lower firm birth rate and higher firm death rate could be attributable to it being a lower performing economy which is arguably having a negative impact on its entrepreneurial ecosystem (Audretsch and Belitski, 2017;Spigel, 2016).Norway's significantly lower firm birth rate and higher firm death rate is likely to be attributable to its relatively high rates of income tax and generous social welfare payment system (Eurostat, 2022;OECD, 2022).Higher income taxes may affect the potential revenues of firms given the lower spending power of their consumers.This in conjunction with generous social welfare payments may disincentivise business births (Baptista and Thurik, 2007).The effects of higher income taxes on consumer demand may increase Norway's firm death rate also.
In contrast, Bulgaria has a significantly higher firm birth rate and a significantly lower firm death rate relative to Austria and other countries.The exact reasoning for Bulgaria's higher firm birth rate and lower firm death rate is difficult to pinpoint.Bulgaria was a significantly lower performing economy compared to the reference country, Austria, between 2008 and 2017, the period for which we analyse the data (WB, 2023b).However, the Bulgarian government also had one of the lowest mean spends on social protection spending in Europe during this period (Eurostat, 2022).Dissolving a business in Bulgaria was perhaps a less attractive proposition as a result (Baptista and Thurik, 2007).Furthermore, Bulgaria had a significantly lower mean total tax and contribution rate (% of profit) for the 2008-2017 time period compared to OECD average (28.24< 43.24) (WB, 2023a).The lower cost imposed upon profits may act as a financial incentive for entrepreneurship and increase firm births.Institutional quality or differences could also potentially be a factor in explaining this finding.Henrekson and Sanandaji (2011) have previously emphasised the influence of institutional quality on entrepreneurship and new firm creation.Nevertheless, evidence of variations in firm birth and death rates across nations emphasises the need to account for national effects in firm dynamic research as emphasised by Audretsch et al. (2019).

CONCLUSION
This paper provides a comprehensive analysis of the impact of the industrial structure on firm births and firm deaths across European regions and countries.A key contribution of this paper is that it controls for firm interrelationships which are frequently not accounted for within the literature (e.g., Gajewski and Kutan, 2018;Carree et al., 2011).When controlling for these we find that population density increases firm births and reduces firm deaths, though the reduction in firm deaths is only evident when the effect of neighbouring regions is unaccounted for.This is not the case in other contributions which do not control for firm interrelationships and thus find that population density has either no significant impact (Basile et al., 2017;Power et al., 2019) or a mixed impact (Sato et al., 2012) on firm birth and death activity.Furthermore, we observe and discuss the significant variations in firm birth and death rates which exist between countries.These are not observed in many modern studies as they do not conduct cross regional and crosscountry analyses (e.g., Arcuri et al., 2019;Audretsch and Belitski, 2017).We also find that related variety increases firm deaths and reduces births, which is contrary to the findings in the literature (e.g., Ejdemo and Örtqvist, 2020;Content et al., 2019).This negative externality persists when the effect of neighbouring regions is accounted for.Positive externalities are observed based on increased concentration and increased unrelated variety.While increased concentration increases firm births and lowers firm deaths this effect is not significant when spatially weighted lagged birth and death rates are added to the model.The opposite is the case for unrelated variety.Unrelated variety increases firm births and lowers firm deaths when the effect of neighbouring regions is controlled for.
Our findings are of clear relevance to the policy makers behind the 'Smart Specialisation' plan which intends to focus investment into a region's 'relative strengths' and 'emerging trends' to improve economic growth (EC, 2014).The EC has stated it plans to pursue an investment policy catered towards the diversification of a region's economic base (EC, 2017), and some have noted that their policies clearly favour fostering a related variety type of diversification (Foray, 2015).The findings of this paper suggest that related variety would increase firm deaths and reduce firm births in European regions.Policies keen to preserve entrepreneurial activity within European regions should note that density and unrelated variety appear to have a positive effect on firm births within regions when firm interrelationships and firm birth and death activity in neighbouring regions are accounted for.In addition, unrelated variety also reduces firm deaths within regions in these circumstances.
While this paper makes for a welcome contribution to the literature, it also raises questions which future research could seek to answer.Firstly, while we observe national variations in the rates of firm births and deaths, we cannot identify these causes exactly.Future examinations of this area could seek to include additional variables to capture institutional quality.This would help better pinpoint which national factors are leading to the country variations in firm births and deaths.Secondly, we expand on a lot of firm birth and death studies by controlling for firm interrelationships, but a more micro-level examination of firm births and deaths would enhance our understanding of the potential causes of multiplier and competition effects.Here, the multiplier effect is attributed to either income or signalling effects like other recent macro investigations into firm interrelationships; e.g., Gajewski and Kutan (2018), Calá et al. (2016), andResende et al. (2015).A more micro-level study which can identify the exact motivations of entrepreneurs who set up firms would help to identify whether those motivations were attributable to income or signalling effects.

DISCLOSURE STATEMENT
No potential conflict of interest was reported by the author(s).

NOTES
1 For examples of other studies concerning entrepreneurship which have used Eurostat and OECD data in their papers see Doran et al., (2016), Davidavičienė and Lolat (2016) and Angulo-Guerrero et al., (2017). 2 The geographical span and discussion of the data for firm births and firm deaths can be seen in Appendix 1 in the online supplemental data or on Fig Share at the following link: https://doi.org/10.6084/m9.figshare.21262956. 3See Appendix 3 for Durbin-Wu-Hausman tests for endogeneity. 4LR tests performed on the difference between the reduced and complete models produced an LR Chi-square of 11.17 (p<0.01) between equations (1) and (3) and 13.43 (p<0.01) in the case of equations ( 2) and (4). 5Support is still found for the multiplier effect in Appendix 5 where models are estimated with increased lag lengths of up to 3 years.

FUNDING
This work was supported by Irish Research Council [grant number GOIPG/2021/809].

Table 1 .
Regional Data by Country rate in region i in time period t and FD it is the firm death rate in region i in time period t.

Table 2 .
Variable Definitions and Statistics Note: y ij is the level of employment in region i in industry j, y i is the level of employment in region i, y Nj is total employment in all regions in industry j, and y N is total employment in all regions, where the two-digit NACE classification h fall exclusively under a one-digit NACE classification j and where P ji = h[( ji) P hi indicates the one-digit shares.Higher values of these indices indicate higher levels of unrelated variety or higher levels of related variety.

Table 3 .
Three Stage Least Squares Estimates

Table 3 .
Continued.Eqn refer to equation.A correlation matrix of the variables used in this estimation is provided in Appendix 5 in the online supplemental data.