Shoulders and shadows of giants: intra-regional distribution of the digital industry in Germany

ABSTRACT This paper investigates digital firm birth activity in municipalities in the urban hinterland of core cities in Germany. It conducts panel fixed-effect regressions for monocentric and polycentric urban labour market regions covering the years 1995–2017. The digital industry’s regional distribution is shaped significantly by the closest core cities: municipalities in monocentric urban regions (MURs) profit from urban population growth and universities’ general knowledge. Municipalities in polycentric urban regions (PURs), however, are affected by industry-specific externalities, that is, an above-average growth in the share of firm birth of their closest urban cores. Overall, agglomeration externalities experience spatial decay relative to the core size with all regions benefiting from their own industry-enhancing urbanization externalities as captured by population growth and universities.


INTRODUCTION
Entrepreneurial activity as pronounced in the birth of new, innovative firms is a predominantly urban phenomenon where firms derive agglomeration benefits.Because administrative borders do not cut off agglomeration externalities and spillovers, high levels of entrepreneurship can be advantageous for whole regions, resulting in regional persistency of firm birth patterns (Pijnen burg & Kholodilin, 2014;Fossen & Martin, 2018;Stuetzer et al., 2021).Nevertheless, it remains unclear whether benefits deriving from a city as the nucleus of regional development disperse homogenously in space.
This paper investigates digital firm birth patterns between 1995 and 2017 in the surrounding municipalities (LAU-2 regions, Gemeindeverbände) of German core cities. 1 It investigates firm birth in small communities serving their bigger neighbours' labour markets, and in return receiv ing income flows (Parr, 2014).Thereby, the analysis is not limited to high-rank first cities, but includes second-and third-tier cities as their impact on economic growth has been given atten tion in the literature (Dijkstra et al., 2013;Camagni et al., 2015).The analysis of the digital industry at the municipality level complements the analysis of NUTS-3 regions as predomi nantly used to assess regional development (Pijnenburg & Kholodilin, 2014;Fossen & Martin, 2018).The digital sector is particularly well suited to proxy entrepreneurship more generally because it has an inherent tendency towards geographical agglomeration (Moretti, 2012) and is a strong start-up sector.Further, this relatively new sector is characterized by strong growth rates and complements many other sectors.In addition, due to the knowledge-intensive nature of digital products and services, there are little natural advantages and relatively low sunk costs.At the same time, the sector depends on agglomeration externalities and thick labour markets in particular.Thus, firms' location choices are very sensitive to these externalities and largely dependent on the existing regional knowledge base.Due to these characteristics, the digital sector has been the target for many policy interventions seeking to foster regional growth.
This paper contributes to a deeper understanding of the spatial dimensions of agglomeration externalities, competition and dispersion effects within urban regions.It focuses on answering the following two main questions: First, how do local factors and core-city characteristics influ ence the intra-regional distribution of entrepreneurship capital?This questions covers two dimensions: (1) relevant location factors for smaller municipalities within core city-regions that contribute to the capitalization of entrepreneurship capital; and (2) the relation of the municipalities' firm birth dynamics vis-à-vis the dynamics within the respective core cities.This is especially relevant for policymakers in small and medium-sized cities that function as regional development engines outside metropolitan regions that have an outstanding signifi cance for a larger surrounding area, according to the Federal Ministry for Housing, Urban Development and Building (2022).Second, it investigates the industry's regional spatial distri bution in the long run by estimating whether the distribution of entrepreneurship capital differs between monocentric urban regions (MURs) and polycentric urban regions (PURs) (whose labour market regions host more than one core city) due to presumably overlapping agglomera tion effects of two core cities.
The political importance of supporting PURs is emphasized in key strategic documents of the European Union (2011), namely the European Spatial Development Perspective (European Commission, 1999), the EU Territorial Agenda 2020 (European Commission, 2011) and the 'Pact of Amsterdam' which established an EU Urban Agenda (ESPON, 2020).The mor phology of German city-regions offers unique patterns for analysing municipalities given their location in the vicinity of core cities: Cities are well connected due to short distances com pared with the United States and economic activity is less centralized than in other European countries, most notably France.
For the empirical analysis, I use panel fixed effects regressions for firm birth in German municipalities belonging to a core cities' labour market region from 1995 to 2017.The share of firm birth in a municipality relative to all firms born in the respective labour market region serves as the dependent variable.Hence, the results reflect relative advantages of small munici palities surrounding cities. Results show that municipalities' individual characteristicspopu lation growth and hosting universitieshave a positive effect on increasing the share of digital firm birth start-up activity by 0.38% and 0.95%, respectively.In line with the literature, the share of firm birth decays by approximately 0.01% with each additional kilometre of distance to the urban core.Further, firm birth activity is shaped by the morphology of the region: muni cipalities in MURs are exposed to strong competition against their cores in terms of industryenhancing factors.In contrast, municipalities in PURs gain advantages from a growing industry in the centre closest to them.
The remainder of the paper is structured as follows.Section 2 overviews the related literature on agglomeration effects, entrepreneurship capital, and the literature on MURs and PURs.Further, it presents the aim and hypothesis of the paper.Section 3 presents the data and the REGIONAL STUDIES, REGIONAL SCIENCE descriptive statistics.Section 4 describes the empirical strategy.Section 5 presents the results.Section 6 concludes and gives policy implications.

Agglomeration and entrepreneurship capital
Local start-up rates in knowledge-intensive industries such as information and communication technology (ICT) are higher in larger cities and surrounding areas (Bade & Nerlinger, 2000;van Oort & Atzema, 2004;Pijnenburg & Kholodilin, 2014).This is mainly due to advantages deriving from agglomeration externalities such as sharing infrastructure, matching the effects of thick labour markets and learning through knowledge spillovers (Duranton & Puga, 2001;Puga, 2010).
The learning channel is particularly important for digital companies as new knowledge created in both public and private knowledge institutions as well as industry competitors mani fests itself by additional firm birth (Audretsch et al., 2008).As stated in the 'Knowledge spillover theory of entrepreneurship', an individual will start a new business if the expected value of a piece of knowledge is higher for the individual than for a decision-maker within an incumbent firm or university (Audretsch & Keilbach, 2007;Acs et al., 2009).
Nevertheless, local and regional start-up rates have been shown to be very persistent over time despite major economic disruptions (Fritsch & Wyrwich, 2017;Stuetzer et al., 2021).The explanation of this phenomenon lies in the entrepreneurship capital, a deeply rooted social acceptance to encourage and support start-up activities through norms and values, strong formal and informal networks as well as high endowments of individuals willing to start a business (Audretsch et al., 2008).This is typically measured in firm birth rates.As the local culture drives entrepreneurial capital, it is tied to a region and locally bound (Audretsch & Keilbach, 2007;Fritsch & Wyrwich, 2017).
Further, Fossen and Martin (2018) find not only entrepreneurship capital manifesting itself in regional start-up rates, but also a spatial dependence to neighbouring regions in Germany.For the high-tech industry, a larger population nearby implies significantly higher start-up rates in the short term.This is best explained by employees leaving successful employ ers to start an own businesses near home where they have good knowledge of local networks (Klepper, 2002).Therefore, big cities within a short distance facilitate the exchange of indus try relevant knowledge and ideas as found in Fritsch and Wyrwich (2017), Fritsch andAamoucke (2013, 2017) as well as Pijnenburg and Kholodilin (2014).The latter find spatial entrepreneurship spillovers for German NUTS-3 to extend over a range of 50 km from the focus region.The reasons for spatial interactions are twofold.On the one hand, increased start-up rates enhance opportunities and lower the costs of starting a business, for example, by providing access to suppliers and customers (Delgado et al., 2010).These advantages are accessible for neighbours, especially at NUTS-3 levels.On the other hand, high start-up rates also increase the competition in neighbouring regions (e.g., capital investment), which would be a competitiveness-improving effect of entrepreneurship capital (Delgado et al., 2010;Pijnenburg & Kholodilin, 2014).
However, the above-mentioned authors mostly focus on regional growth mechanisms while paying little attention to the question of how these economic developments shape the studied regions in the long term.Theoretically, a region experiencing economic growth predominantly driven by externalities of a neighbouring region should become large enough in the long run to produce 'its own' agglomeration externalities, at least some scale externalities.Thus, we would either observe convergence resulting in a real expansion of externalities or even reach a point where competition between the players becomes very strong resulting in a dispersion of entre preneurship capital (as discussed by Delgado et al., 2010Delgado et al., , 2014)).
REGIONAL STUDIES, REGIONAL SCIENCE 2.2.The morphology of the region: MURs versus PURs Scholars studying agglomeration effects in a core-periphery dynamic usually focus on intra regional population distribution, that is, the sharing channel of agglomeration theory (Meijers et al., 2016;Volgmann & Rusche, 2020;Krehl & Siedentop, 2019).The difference to the lit erature presented above is that cities and places are assumed to interact, where 'performance', in terms of population or industry growth, is dependent on the position within the region.
The literature on urban systems reflects a discussion similar to competition versus dispersion by the concepts of 'borrowing size' and 'agglomeration shadows'.'Borrowing size' postulates smaller cities in larger urban areas inhabit more metropolitan functions (high-order economic, political and cultural features) than similar cities in less agglomerated areas.That is, a place bor rows size when holding more metropolitan functions than its own size could normally support (Volgmann & Rusche, 2020).For example, Phelps et al. (2001) show how small cities around London can 'borrow size' by avoiding costs of agglomeration but still access specialized labour and the informal external economies.
Borrowing size is somewhat akin to the concept of spillover effects.In contrast, 'agglomera tion shadows' predict limited growth near high-tier cities due to higher competition crowding out economic activity (Meijers et al., 2016).Interestingly for this paper, Volgmann and Rusche (2020) find both borrowing size and agglomeration shadows for population distributions of German city-regions, showing that both effects coexist in distinct regions.
Moreover, Volgmann and Münter (2022) compare differences in metropolitan growth of MURs with one dominant core with PURs having less spatial structural hierarchies.They argue that individual centres in PURs develop less agglomeration externalities due to lower con centration of population, cultural and political functions, but offer better quality of life due to lower negative externalities and congestion costs (Volgmann & Münter, 2022).In essence, it is assumed that agglomeration effects are distributed differently across MURs and PURs.
Empirical applications of these concepts focus on population distribution next to metropo litan functions rather than industry developments and labour market distributions (Meijers et al., 2016;Volgmann & Rusche, 2020;Volgmann & Münter, 2022).Ouwehand et al. (2022) investigate the impact of spatial structures on total factor productivity and conclude thatfor European regions with similar urban populationsthe urbanization externalities derived from multiple city cores do not substitute for those achieved with a structure relying on singular, larger cities.This paper contributes to the literature by putting the intellectual base line of 'borrowing size' and 'agglomeration shadows' to an industry context of entrepreneurship as the exposure to agglomeration externalities is a crucial input for digital, knowledge-intensive firms.

Aim and hypothesis
The aim of this paper is to shed light on intra-regional distribution of entrepreneurship capital apart from core cities by identifying characteristics of municipalities being attractive to firm birth next to urban cores.
First, I consider the interplay of entrepreneurship within regions on the municipality level (LAU regions) while considering characteristics of the municipalities and their closest core city.Entrepreneurship is measured by firm birth, because new firms are not constrained by pre vious location decisions and sunk costs.Therefore, they provide better information on the role and magnitude of agglomeration effects than existing ones (Gómez-Antonio & Sweeney, 2021).To shed light on the intra-regional distribution, I use the share of firm birth (firm birth in municipalities divided by the total firm birth of the region).
Second, Germany offers a dense system of cities, where, for example in the Ruhr Area, sev eral core cities are located within one large labour market region.In this paper, this is referred to REGIONAL STUDIES, REGIONAL SCIENCE as PURs.In a European comparison, Meijers et al. (2018) show a large number of PURs in Germany with comparably large population size, although applying a different definition.Here, agglomeration effects and spillovers could be overlapping and causing different outcomes of competition and divergence compared with a MUR (e.g., Munich).Accordingly, the second aim of the paper is to identify differences in the distribution of entrepreneurship between monoand polycentric dynamics.Thereby, I also tackle questions on the spatial range of agglomeration externalities.In an extensive literature review on the spatial dynamics of agglomeration extern alities, Rosenthal and Strange (2020) point out that agglomeration effects operate at various spatial levelsdepending on the spatial reach of specific channels.While some tacit knowledge spillovers via face-to-face contacts seem to work on very small neighbourhood scales and beyond, effects arising from labour market pooling are likely to affect whole commuting areas.In this paper, I use municipalities within urban labour market regions as the unit of analy sis.This allows a coverage of several spatial scales that agglomeration effects work on.
Accordingly, the definition of the region is a fundamental determinant of the analysis' out come.The smallest spatial scale applied in studies on regional interactions of entrepreneurship is NUTS-3 (county level).For the German case in particular, this mostly benchmarks core cities against their (urban) periphery (kreisfreie Städte versus Kreise).This broad unit of analysis comes with certain disadvantages.Counties not being core cities can cover large areas and be hetero geneous within themselves, oftentimes hosting smaller, second-tier cities. LAU regions, as suggested by Volgmann and Münter (2022), who offer more in-depth results for urban regions.Moreover, the principle of subsidiarity in Germany allows self-governance of certain political and planning principles.Therefore, it is worthwhile investigating what relative advantages municipalities within the same labour market, i.e. similar locations within the system of cities, expose.
In general, I assume three major contributing factors.First, individual characteristics of municipalities creating small-scale agglomeration advantages for firms.Population size is used to proxy the 'sharing' channel (Duranton & Puga, 2004), as, for example, indivisible facili ties and varieties of input suppliers are subject to scale.A knowledge stock stemming from uni versities proxies the learning channel.Second, due to regional embeddedness, I assume the size of the next urban core and its knowledge stock to be a significant determinant of the spatial dis tribution.Third, as spillovers decay over distance (Rosenthal & Strange, 2003;Rice et al., 2006;Smit & De Groot, 2013), I expect advantages for municipalities located close to the core: Research question 1: How do local factors and core-city characteristics influence the intra-regional distribution of entrepreneurship capital?
Based on the empirical findings in the literature on 'agglomeration shadows' and 'borrowing size', it is likely that the impact of the core cities for the regional firm distribution differ in MURs and PURs.Therefore: Research question 2: Does the intra-regional distribution of entrepreneurship capital differ in MURs and PURs?
For MURs, I expect a stronger spatial concentration of the industry than for PURs.In turn, PURs are expected to be more dispersed with agglomeration externalities which probably are greater in scope.

DATA
The dataset employed in this paper consists of two major parts: First, I employ a tailor-made geocoded firm-level panel dataset that covers the development of the digital industry between 1995 and 2017.This dataset is aggregated on municipality level.Second, I use administrative data on these very municipalities being located in urban labour market regions.The (data-) innovation of the paper is that the literature on regional industry dynamics and spatial spillovers REGIONAL STUDIES, REGIONAL SCIENCE mostly focus on NUTS-3 levels (Pijnenburg & Kholodilin, 2014;Fossen & Martin, 2018).The spatial level of municipalities has been applied in the literature on borrowing size and agglom eration shadows (e.g., Volgmann & Münter, 2022), however with a focus on population distri bution rather than industry dynamics.

Geocoded firm-level panel dataset
The advantage of the firm data lies in the precision of individual birth firm locations over a long period.The analysis covers companies that entered the market between 1995 and 2017.The data provided by North Data (2019) originate from statutory publications of German corporations.
As there is no agreed-upon definition of the digital economy, a digital firm is defined as one that is information technology (IT) driven and internet based.I selected firms using NACE codes (similar to Weber et al., 2018) covering general programming activities, software devel opment, web portals, data processing and the development of web pages, processing, hosting and related activities and web portals. 2 Yet, standard industry classification systems have limit ations, especially industries that cross over traditional product categories, as it is the case for digital firms (Oakey et al., 2001).Since digital business models complement many other sectors, firms may be registered in other NACE codes despite running a digital business model.
To identify these firms, the description of the company's main business area is used. 3With the help of a word-search selection, firms not registered in the ICT sector but operating on a digital business model were added to the dataset.The resulting sample contains firms charac terized by the core knowledge on which their competitiveness ultimately draws (Martin & Moodysson, 2013).The resulting dataset comprises 144,230 individual firms born between 1995 and 2017 and is aggregated to municipality level for the analysis.

Spatial units of analysis and location characteristics
The region is defined by the labour market (following BBSR, 2022a) because knowledge spil lovers have shorter spatial ranges than labour market effects (Kerr & Kominers, 2015).The labour market defines the outer bounds of agglomeration externalities.Due to this strong theor etical foundation, the labour market was chosen over other regional definitions, such as 'func tional urban areas'.
Accordingly, the outer bounds of the labour market are where 25-50% of out-commuters commute to a centre/supplementary area (BBSR, 2022b).A PUR is a (labour market) region that hosts more than one centre, resulting in seven PURs. 4 A MUR hosts one centre, which are 42 regions in Germany. 5Within the regions, the unit of analysis is the municipality (Figure 1).Since the goal of this paper is to assess the regional distribution of entrepreneurship apart from the core cities, the latter are excluded from the final dataset.In total, the dataset contains 2023 municipalities, 6 resulting in 46,534 observations.The aggregate firm-data are merged with location characteristics of each municipality.First, I use population for 1995-2017 originating from the INKAR database (BBSR, 2022b).Locally available knowledge is proxied by the number of universities in the municipality.Locations pub lished in a public register of colleges and universities (Hochschulkompass, 2020) are used. 7The data are time variant, albeit with 27 additional higher education institutions (HEI) in 25 muni cipalities over the sample period.

Descriptive statistics
Table 1 shows the distribution of digital firm birth for core cities versus municipalities for the period from 1995 to 2017.There was an average of 53.1 firm births per core city, and 0.7 in municipalities.Berlin had most firm births in absolute terms in 2015.Neuss, a municipality close to Düsseldorf with the highest firm birth, registered 61 new firms in 2012.This pattern REGIONAL STUDIES, REGIONAL SCIENCE shows that digital firm birth is, in absolute terms, an urban phenomenonthe mean yields 0.05 per 1000 inhabitants for municipalities and 0.11 for centres.
Figure 1 displays the pooled share of digital firm birth in centres and municipalities for the sample period.Hamburg, Berlin, Erfurt, Leipzig and Dresden show a high concentration of firm birth, as 73-88% of all firms set up in the respective counties are in their respective core REGIONAL STUDIES, REGIONAL SCIENCE cities.West German regions, the Ruhr area in particular, show a more balanced distribution.This might be indicative of agglomeration benefits not decaying as strongly over distance.
Taken together, this indicates that the spatial range of agglomeration benefits decreases faster around bigger cores, seeing that Hamburg and Berlin are the biggest cities in Germany.
Further, these cities are more isolated in space that is they have very few neighbours that are big in size.
Table 2 shows summary statistics for the MURs and PURs (without the centres).The aver age MUR has 59 municipalities, while the average PUR has 127 municipalities.While some monocentric cores were able to absorb 100% of their entrepreneurship capital, the top city in a PUR absorbed 66% (Cologne in 2001).This indicates different distribution channels of entre preneurship capital for MURs and PURs.Presumably, municipalities in PURs can make use of a wider network of agglomeration externalities as laid out in Volgmann and Münter (2022).They argue that PURs have a lower mass to generate agglomeration externalities while cities serving as the single centre of their region are typically more oriented towards their central business districts.
Table A1 in Appendix A shows summary statistics of the control variables.Figure A1, also in Appendix A, shows the distribution of the share of firm birth (note that it is cut off at 15 for visual reasons, which covers the majority of observations).While there are relatively many zeros in total, there are only 44 out of 2026 municipalities that never registered a digital firm.Table A2 in Appendix A is a correlation table of the data.Notably, the share of firm birth in the next centre and the share of firm birth in municipalities have a correlation coefficient of only −0.003.However, the 'universities next centre' and the 'population in the next centre' show a rather high coefficient.Although multicollinearity between the variables should not be a major concern, additional regressions are presented in the robustness section.

EMPIRICAL STRATEGY
I use firm birth in the digital sector as a proxy for entrepreneurship capital as the variable reflects individuals capitalizing on their novel ideas in a relatively low sunk-cost environment.In order to set up a digital business, capital costs for physical inputs are typically low.Hence, the location of digital firm births reflects a spatial knowledge allocation as the profit-maxi mizing firm locates within a labour market where (agglomeration) benefits outweigh the costs.Thus, firms reveal their preferences in terms of labour, amenities and market access by choosing a suitable location.Note: Summary statistics on the share of firm births in mono-(MUR) and polycentric urban regions (PUR), including the centres, are shown.
REGIONAL STUDIES, REGIONAL SCIENCE

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The dependent variable is the share of regional firm births in non-core municipalities which is defined as: where profit maximizing firm k in year t is set up in municipality i.The sum of all digital firms set up in i in t relative to all digital firms set up in the same labour market region j reflects the municipalities' relative ability to foster firm birth.
The econometric analysis proceeds in two steps.First, I identify general determinants of local characteristics conducive to firm birth outside the administrative borders of the region's core city.Second, I use two subsets of the original dataset with individual estimations for MURs and PURs to determine differences in the distribution of entrepreneurship capital for each morphological type.
All estimations are panel fixed-effects models.With the inclusion of time-and region-fixed effects, I control for region-specific time-invariant characteristics and yearly increments such as general trends in the industry or the economy at large.Additionally, all observable and unob servable effects which might vary on region and time level are controlled for which reduces the threat of omitted variable bias.
The following model (1) will be estimated using ordinary least squares (OLS) with standard errors clustered at the municipality level: (2) The independent variables enter both models as follows: l i,t refers to locational character istics in location i at time t possibly creating agglomeration externalities (population size divided by 10,000 to proxy sharing; and institutions of higher education to proxy learning).l c,t refers to the same locational characteristics, but in the centre c that is closest to the municipality i as I assume the core to affect its labour markets' municipalities.FB j,t is the total firm birth in the region controlling for a general size effect.SFB c,t is the share of firm birth in the centre c, d ic is the physical distance between the geographic core of the centre in c the municipality i. T t is a year fixed-effect controlling for common trends, g i is the time-invariant region fixed-effect capturing unobservable (labour market) regionspecific and time-invariant factors which are potentially correlated with the number of new firms.1 i,t is the error term.
Examining differences between MURs and PURs, a second model will be estimated twice, one for each subset of the data (MURs and PURs separately).To specify the dynamics of agglomeration externalities more specifically, the baseline specification is modified as follows: The predictors remain the same as in the baseline model, but the share of firm birth in the next centre SFB c,t is interacted with distance.Distance quintiles are denoted as dq ic , being sensitive to the size of the individual labour market area.That is, for each municipality i, the distance to the next centre c within the labour market region is calculated.The municipality with the greatest distance, serves as benchmark for the fifth quintile in each labour market.For PURs, the quin tile is always defined in relation to its closest centre, that is, the next origin of agglomeration externalities.This measure was chosen over absolute distances (the greatest distance between all municipalities to the next centre) because it captures the relative size of each region.The share of firm birth is expected to vary with the next centre's share of firm birth in each quintile when agglomeration externalities diminish relative to the core's size.Further, it smoothens the REGIONAL STUDIES, REGIONAL SCIENCE distribution of the distance measure because the fifth quintile would only be covered by very large regions.

Local factors versus core-city characteristics
Table 3 presents the empirical results.Colum (1) presents the baseline model that is the pooled, full-sample regression estimated by equation ( 2).This captures Research Question 1: How do local factors and core-city characteristics influence the intra-regional distribution of entrepre neurship capital?The first ex-ante assumption was that general agglomeration externalities Table 3. Estimation results of baseline regressions.
( REGIONAL STUDIES, REGIONAL SCIENCE such as population (growth) and a local knowledge base create advantages over other municipa lities in the labour market region.Due to the usage of time and labour market (region) fixedeffects, the effect is identified by variation in the cross-section and over time.Therefore, the population size can be interpreted as change in population size that is growth.Results show that population growth and being a university town are significant factors for materializing entrepreneurship capital.That is, for a population growth of 10,000 inhabitants, the share of firm birth increases by an average of 0.38%.Additionally, hosting a university increases the share of firm birth by 0.95%.Note that this is a fixed-effect model and coefficients are interpreted as changes in the parameters.
Population growth in the next centre as well as an additional university do have a positive effect on the share of firm birth in municipalities.This indicates that firms in the regions' muni cipalities have access to additional agglomeration advantages provided by the respective core cities.This spillover effect may contribute to the general labour market.This finding provides evidence for a borrowing size effect, where the municipalities benefit from their core (Phelps et al., 2001).This result is in line with Meijers et al. (2016), who also find individual growth to be more important than growth in 'connected' areas.Consistent with theoretical expectations (Delgado et al., 2010;Pijnenburg & Kholodilin, 2014), the results clearly show municipalities' own characteristics, such as population growth and locally available knowledge, affecting the firm birth in a much stronger way than growth in the centre, as indicated by the significantly larger coefficients.
However, growth in the digital industry, captured by absolute firm birth in the region, as well as the share of firm birth in the next centre are negatively related to the share of firm birth in the municipality.These results show that non-core municipalities lose out in terms of relative attractiveness to the core's growing industry.Presumably, growth in the core lowers the costs of starting a business while simultaneously increasing learning effects within the indus try.These learning effects work on very small scales within few neighbourhood blocks (Arzaghi & Henderson, 2008) and contribute to outweighing agglomeration costs.
Altogether, 'borrowing size' effects and 'agglomeration shadows' seem to coexist along different channels: For generic population growth and institutional knowledge in HEI I find a borrowing size effect while specific industry-relevant factors such as within industry spillovers contribute to a stronger concentration of firms within core cities.Note that this finding does not necessarily contradict Pijnenburg and Kholodilin (2014) and Fossen and Martin (2018) findings that neighbours profit from core growth in absolute terms.
Lastly, the closer a municipality is located to the centre, the larger the share of firm birth that proxies entrepreneurship capital.The share of firm birth decays by approximately 0.01% with each additional kilometre of distance to the urban core.That confirms the hypothesis that agglomeration advantages decrease with distance and a significant advantage of small munici palities' lies in their geographical location, that is, their proximity to the next core.

MURs versus PURs
Columns (2) and (3) in Table 3 provide estimation results for the second research question: Does the intra-regional distribution of entrepreneurship capital differ in MURs and PURs? Results show that MURs and PURs indeed differ in the distribution of entrepreneurship capital.
In MURs, 10,000 additional inhabitants increase the share of firm birth for municipalities by 0.89%.For PURs, there is only an increase of 0.21% for the same population growth.Results show positive effects if the municipalities host a university for both morphological types.How ever, a university within a MUR has a three times lager impact.Therefore, both population growthwhich can be interpreted as sharing externalitiesas well as institutionalized knowl edge boost relative advantages of municipalities in MURs four times as much as for REGIONAL STUDIES, REGIONAL SCIENCE municipalities in PURs.Concerning the interdependence of the municipalities' entrepreneur ship capital with the economic cores of the regions, MURs and PURs show significant differ ences.In MURs, population growth in the next centre increases the share of firm birth in its' surrounding areas.Similar population growth in centres within a PUR has no significant effect on its municipalities, that is, their shared labour market.Put differently, PURs do not create significant additional sharing externalities by means of population growth.Further, an additional university in a MURs' core city significantly increases the relative distribution of entrepreneurship capital in municipalities while there is no such effect in PURs.
These differences are also visible in general industry growth: A monocentric core absorbs absolute industry growth by lowering the municipalities' share of firm birth, but general industry growth does not impact the PUR's share.Overall, this shows that municipalities in MURs are more dependent on the core's general as well as industry-specific development than municipa lities in PURs, as the latter presumably access agglomeration externalities from several (at least two) cores.
Figures 2 and 3 visualize the relationship of distance and the next centre's share of firm birth on the share of firm birth in the municipality.Note that the y-axes differ and that the effects for MURs are significantly larger in size than for PURs as poly-centres are naturally more dis persed.The coefficient of the interaction term shows the effect of x 1 on y for a given quintile x 2 .That is, at certain distances the share of firm birth in the next centre has different effects on y.If the interaction coefficient is positive the effect of x 1 on y increases as x 2 increases, if negative it decreases.In other words, I expect the distribution of firm birth to wane with increas ing distance from the core.
For MURs, Figure 2 shows a steep negative slope of the interaction for the first distance quintile (municipalities located closest to the centre).The higher the share of firm birth in the centre, the lower the share of firm birth in the municipality with a mean distance of 13 km (see Tables A3 and A4 in Appendix A for summary statistics of the distance quintiles).For the second quintilemunicipalities not being located directly next to the centre (24 km mean distance)the slope is less steep than for the first quintile.The fifth quintile covering municipalities on the outer bounds of the labour market region are least dependent on the  dynamics in the inner core.Overall, the results show core cities in MURs are clearly the centres of economic activity and strongly interact with their direct neighbours, as the slope of the first quintile is the steepest.Nevertheless, this result does not provide an answer to whether there is an 'agglomeration shadow' or a 'borrowing size' effect; nonetheless the findings indicate that municipalities' dependence on the core is strongest for direct neighbours in the first quintile either way.
In PURs (Figure 3), the distribution of entrepreneurship capital is notably different from MURs.Note that the scale of the figures varies, as the share of firm birth is generally lower in PURs, as there are more centres to absorb higher firm birth rates.For the first distance quin tile, the effect is opposite to that for monocentric regions: An increase in the share of firm birth in the next centre also increases the share of firm birth in its direct neighbours.An increase in the relative advantage of the next core city therefore increases the relative advantages of its neighbours.Interestingly, this effect is detected for the first quintile so direct neighbours and municipalities very far away.Therefore, the spatial spillover of increasing industry concentration effects is limited to the first distance quintile around a core city in a PUR.For the second, third and fourth distance quintile there are very small negative effects when the entrepreneurship capital in the core city increases.Despite that, for regions in the fifth distance quintile, the effect turns positive again.However, this finding has to be taken with a grain of salt, as being located within the fifth distance quintile might imply a location between two core cities.Possibly, the outcome reflects an 'overlap' of agglomeration advantages in the outer-bounds of the labour market where costs of agglomeration are relatively high compared with the gains.
Overall, these results show that intra-regional distribution of entrepreneurship capital differ in MURs and PURs as the regional distribution of entrepreneurship capital is shaped by the urban core in MURs, but growing municipalities with better knowledge infrastructure have a relative advantage to their sparring partners.In sum, municipalities in MURs benefit from uni versities sharing general knowledge, more generally perhaps also from typical urbanization externalitiesthat is closeness to overall economic activity and diverse knowledge (Combes, 2000).Rosenthal and Strange (2003) argue that urbanization effects reflect the trade-off between benefits and dense areas and congestion costs.An increase in the industry density in the corethat is localization externalities, on average, results in the core throwing an REGIONAL STUDIES, REGIONAL SCIENCE agglomeration shadow.Ceteris paribus, an above average digital industry development in the core absorbs its small neighbours entrepreneurship capital.Thereby, increasing advantages from e.g., tacit knowledge exchange exceed congestion costs.This is in line with the literature, where localization externalities are usually found to decay more rapidly with distance than urbanization externalities (Rosenthal & Strange, 2003;Arzaghi & Henderson, 2008;Anders son et al., 2019).
Municipalities in PURs however are less affected by changes in urbanization externalities, specifically in the next core.PURs probably offer more evenly distributed agglomeration extern alities, as firms in municipalities can access several cores (Volgmann & Rusche, 2020).Thus, they are less dependent on urbanization externalities of one particular neighbouring centre.Nevertheless, for localization, the results show a reverse effect for municipalities being located closest to urban cores in terms of industry growth.This hints towards the existence of compe tition effects between urban cores in PURs.Thereby, more competition attracts rather than repels firms, which is in line Kim et al. (2022) who analyse the patterns of firm formation of 242 industries in 508 regions, over 15 years in Australia.While this seems at odds with the lit erature presented above, it still shows that digital firms gain advantages from being located in clusters (Delgado et al., 2010) and close to industry-specific knowledge, as the cores gain relative attractiveness over their competition cores within the labour market region.

Robustness
To analyse and establish robustness of the results, several tests have been conducted.Providing a more detailed picture of the importance of the distance, the empirical models were estimated again without the interaction term plus a continuous distance measure for MURs and PURs (see Table A5 in Appendix A). Results for the continuous measures show a stronger spatial decay of the share of firm birth in MURs compared with PURs (see columns 2 and 3 in Table A5 in Appendix A).Leaving out the interaction term as presented in the baseline model, results show the decay of the share of firm birth more precisely.Effects for the quintiles decay continuously, but the coefficient for the second quintile is larger than for the third quintile in MURs.This is indicative for agglomeration shadows diminishing over distance.That is, municipalities in the second quintile are overshadowed by the first quintile, but this shadow seems to fade out for the third and fourth quintile.Municipalities in the fifth quintile however are too far off to reach out to externalities provided by the respective core city.
The sensitivity of the results towards the chosen quintiles was tested by employing the absolute measure of quintiles.In contrast to the relative measure as described above, the quin tiles are benchmarked against the absolute distance of the largest labour market.The regressions (without interactions) have been repeated.Table A6 in Appendix A presents the results; Figure A2, also in Appendix A, illustrates the coefficients and the distribution of the standard errors.Figure A3 in Appendix A shows the coefficients of the relative distance quintiles for comparison.Note that the x-axis scales are different.To provide a better com parison, Figure A4, also in Appendix A, presents quintiles 2-4 separately.Results are strongly driven by the definition of the quintiles and relative measures produce less differences in MURs and PURs than the absolute measure.
The baseline regression including interaction effects was repeated with the absolute distance quintiles, that is, the largest absolute distance between a municipality and the centre determi nates the fifth quintile (instead of being individual for each labour market region).This is referred to as the alternative quintile measure in the following.Figure A5 and A6 in Appendix A show post-estimation plots similar the main section.The effects point to the same direction as the baseline model.However, especially for PURs, the results differ in the second to fourth quintile, as they show a positive slope.This underlines the overall picture, that municipalities in PURs are likely to gain advantages from 'borrowing size'.
REGIONAL STUDIES, REGIONAL SCIENCE Table A7 in Appendix A presents a variant of the baseline model, estimating the full sample while including a dummy variable for MURs.Results show that municipalities in MURs gen erate significantly more share of firm births as municipalities in PURs.This underlines the wider dispersion of the industry in PURs.
As multicollinearity might be a concern for the relations of the municipalities and the centres (as the correlation coefficient was high, see Table A8 in Appendix A), the regressions are con ducted with the municipality's characteristics only.Results presented in Table A8 show that the results for individual municipalities are robust.
Due to the count nature of the data and many zeros (see Figure A1 in Appendix A), results from an OLS estimation that excludes all zero observation as well as a pseudo-Poisson maxi mum likelihood (PPML) estimation are presented in Table A9 in Appendix A. Results are robust to the baseline estimation.
One limitation of using shares as the dependent variable is that it does not per se allow to distinguish whether a municipality is doing well, or the neighbour is performing badly.To over come this, the regressions are performed with the absolute firm birth as dependent variables (see Table A9 in Appendix A).Additionally, the table presents the baseline estimation excluding all zeros as well as a PPML estimation.Results show that the municipalities individual factors are less pronounced in absolute terms.That means, population and the presence of a university have similar effects in MURs and PURs.However, results show a similar pattern as for the relative measure for the characteristics in the next core cities: Municipalities in MURs take advantages of universities in the next core, for municipalities in PURs we see an opposite effect.Neverthe less, a general growth in the industry in the region has a stronger effect for MUR than PUR municipalities.

CONCLUSIONS
This paper analyses regional firm birth patterns of the digital industry apart from core cities to shed light on the spatial distribution of entrepreneurship capital that determines the general development of regions in the long run and the dependence of municipalities on their core cities.The municipalities provide labour inflows into the core, while the core itself provides agglom eration externalities that contribute to higher productivity and wages in the municipality.Nevertheless, it is in the interest of municipalities' political decision makers to attract some of the entrepreneurship capital of their regions as they gain attractiveness and income flows through business taxes by hosting businesses.
The paper considers a link between the intellectual baselines of 'agglomeration shadows' and 'borrowing size' and agglomeration economies.Therefore, the Research Question 1 is: How do local factors and core city characteristics influence the intra-regional distribution of entrepre neurship capital?
The empirical study shows that municipalities' digital industry development depends on individual characteristics as well as those from the next respective core city: for generic popu lation growth and institutional knowledge in HEI, I find a positive effect for individual charac teristics while specific industry-relevant factors such as within industry spillovers contribute to a stronger concentration of firms within core cities.Results further show that relative advantages of small municipalities next to 'giant neighbours' strongly depend on the distance between the dwarf and the giants.Research Question 2 is: Does the intra-regional distribution of entrepre neurship capital differ in MURs and PURs?The analysis shows that MURs and PURs differ in the general morphology of industry dynamics.This puts the results from the first research ques tion into perspective, as the industry development mechanisms differ.
Results show that MURs tend to absorb entrepreneurship capital from their direct neigh bours with growing industries, population growth and strong academic landscape.Thus, REGIONAL STUDIES, REGIONAL SCIENCE MURs with one successful digital centre lay an agglomeration shadow over their direct neigh bours in terms of digital start-ups.Successful cores in PURs, however, serve their neighbours by increasing their relative attractiveness over other municipalities and allow them to borrow industry-specific externalities.This gain in PURs is specific to the industry, as population growth and institutionalized knowledge in additional universities are not significant for PURs.On top of that, this indicates competition effects of the individual centres within PURs.
This result reveals important policy implications.The success of the same policy intervention in two similar municipalities may have different impacts depending on the relative location of the municipality in its specific labour market.This is why generic policy implication with a 'one size-fits-all' is probably not very fruitful.For municipalities in MURs, the development of an own, strong knowledge base (e.g., in the form of universities) can be a promising approach.However, they remain to be very dependent on their cores economic development and on the distance between the core and themselves.For municipalities in PURs however, a Smart Specialisation and an industry-focused business support would be a more promising approach.The EU states that the support of polycentric development can create a critical economic mass by combining efforts of urban centres.An understanding of joint competitive advantages can help cooperating cities to strengthen their competitive resourcing power in a greater regional context (ESPON, 2020).The results of the paper show that a specialization of individual cities in a PURs could be a promising approach.
In all, the results are likely to be transferable to other primarily European contexts.PURs also occur in other European countries, prominent examples being the Milan-Bergamo region or Randstad in the Netherlands, which includes Amsterdam, Rotterdam and The Hague.The German context primarily offers the advantage of sufficient sample size of both MURs and PURs.

ACKNOWLEDGEMENT
The author would like to thank Christiane Hellmanzik, Maren Kaliske and Felix Dorfseifer for excellent comments and suggestions within the research process.

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

NOTES
1 Core cities are cities with more than 100,000 inhabitants and a surplus of inbound commu ters.Additionally, the main commuter flow does not come from the neighbouring centre, as defined by BBSR (2022b).The terms 'core cites' and 'centres' are used interchangeably. 2NACE codes 62. 01.0, 62.01.1, 62.01.9, 62.02.0, 62.03.0, 62.09.0, 63.11.0 and 63.12.0.  3 First, the description of the identified ICT firms has been analysed and the most frequently used words related to information technology (IT) and software has been identified.These key words are then used to obtain those firms operating on digital business models with the help of several word combinations.Further, firms that only distribute their products via a webpage have been excluded.For those firms, keywords related to 'software development' needed to be included.As an example, a firm registered in 'Placement of workers' has been included in the sample because the objective of the company is 'the operation of a social networking platform for skills enhancement and marketing as well as the provision, brokerage and distribution of REGIONAL STUDIES, REGIONAL SCIENCE

Figure 3 .
Figure 3. Post-estimation interaction plot for polycentric urban regions (PURs).Note: All coefficients are significant in the estimation.

Table 1 .
Absolute firm birth in centres and municipalities.Summary statistics on absolute firm birth in municipalities and the centres are shown.

Table 2 .
Share of firm birth in regions including centres.