Measure Twice, Cut Once

An entrepreneurial ecosystem comprises a set of interdependent actors and factors that are governed in such a way that they enable productive entrepreneurship within a particular territory. While the entrepreneurial ecosystem approach is useful to think about regional economies, it currently lacks full‐fledged metrics to enable policy. In this paper, we bridge this gap by quantifying and qualifying regional economies using the entrepreneurial ecosystem approach. We operationalize ten elements of entrepreneurial ecosystems for 274 regions in the 28 countries of the European Union. The ecosystem elements show strong and positive correlations between them, confirming the systemic nature of entrepreneurial economies, and the need for a complex systems perspective. Our results show that formal institutions and physical infrastructure take a central position in the interdependence web, providing a first indication of these elements as fundamental conditions of entrepreneurial ecosystems. We then use the elements to calculate an index that measures the quality of entrepreneurial ecosystems. This index is robust and performs well in regressions to predict entrepreneurial output, which we measure using novel data on productive entrepreneurship.


Introduction
An entrepreneurial ecosystem comprises a set of interdependent actors and factors that are governed in such a way that they enable productive entrepreneurship within a particular territory (Stam, 2015;Stam and Spigel, 2018). The entrepreneurial ecosystem approach has become popular in economic policy because of the recent shift from managerial economies to entrepreneurial economies (Thurik et al., 2013). In these entrepreneurial economies entrepreneurship is a key driver of economic change (Schumpeter, 1911). For scientific research on the entrepreneurial economy to be relevant for economic policy, it needs to provide a sound understanding of how the economy works and provide an actionable framework that guides policymaking. The entrepreneurial ecosystem approach has the promise of providing such an actionable framework.
It offers a lens to empirically trace the systemness of entrepreneurial economies and the degree to which economic systems produce entrepreneurship, as an emergent property of the system (Brown and Mason, 2014;Isenberg, 2010;Stam, 2015). It is especially useful to synthesize and integrate a large variety and quantity of data to measure the (changing) nature, outputs and outcomes of (regional) economies (Stam, 2015).
Economic policy often fails to achieve its objectives. One cause of this failure is a lack of diagnosis and monitoring in the policy cycle. We develop entrepreneurial ecosystem metrics to better measure entrepreneurial economies. These metrics enable adequate diagnosis of entrepreneurial economies and monitoring of economic change affected by policy and other dynamics. This paper takes heed of the old carpenter's adage "measure twice, cut once", reducing policy failures with better measurement tools. Even though the academic literature on entrepreneurial ecosystems has been flourishing recently, it does not yet provide an actionable framework for economic policy.
In this paper we address this gap in the literature by developing and extending the entrepreneurial ecosystem framework as a tool to analyse and improve entrepreneurial economies. The objective final section concludes, reflects on the findings, policy implications, and sets out an agenda for further research.

Entrepreneurship and economic development
The empirical literature on entrepreneurship and (regional) economic development can be divided in the entrepreneurship growth literature, focusing on the aggregate economic effects of entrepreneurship, and the geography of entrepreneurship literature, focusing on the causes of the spatial heterogeneity of entrepreneurship. In the next two sections we summarize the insights from these two literatures.

Entrepreneurship and economic growth
The role of entrepreneurship in economic development has been studied for a long time, going back to Schumpeter (1934), Leibenstein (1968) and Baumol (1990). The entrepreneurship growth literature is mainly concerned with the question how and to what extent entrepreneurship affects economic growth. Even though the entrepreneurship and economic growth literatures do not provide full consensus on the positive effects of entrepreneurship, there seems to be more evidence in favour of than against positive (causal) effects of entrepreneurship on economic growth (Audretsch et al., 2006;Bosma et al., 2018;Carree and Thurik, 2010;Fritsch, 2013). Key causal mechanisms being the creation and diffusion of innovations, and competition created by entrepreneurs (Bosma et al., 2018). The direction and strength of the effect of entrepreneurship on economic growth depends on the type of context and type of entrepreneurship: ambitious, opportunity and growth oriented types of entrepreneurship are more likely to lead to economic growth than self-employed, necessity based entrepreneurship (Bosma et al., 2018(Bosma et al., , 2011Fritsch, 2013;. In addition, entrepreneurship is most productive in conditions of inclusive and growth enhancing institutions (Bosma et al., 2018;Sobel, 2008).
Entrepreneurship does not occur in a vacuum, but is very much a local event (Feldman, 2001).
There is also substantial regional variation in the prevalence of entrepreneurship, with underlying causes being very much spatially bound.

The geography of entrepreneurship
The geography of entrepreneurship literature has provided numerous insights into the role of different factors enhancing the prevalence of entrepreneurship in regions (Bosma et al., 2011;Stam, 2010;Stam and Spigel, 2018;Sternberg, 2009). We summarize the empirical geography of entrepreneurship literature with ten elements affecting the prevalence of entrepreneurship (cf. Stam and Van de Ven, 2020). The first element, institutions, provides the fundamental preconditions for economic action (Granovetter, 1992) and for resources to be used productively (Acemoglu et al., 2005). Institutions are not only a precondition for economic action to take place, they also affect the way entrepreneurship is pursued and the welfare consequences of entrepreneurship (Baumol, 1990). Informal institutions also have strong effects on the prevalence of entrepreneurship, one example being entrepreneurship culture, reflecting the degree to which entrepreneurship is valued in society (Fritsch and Wyrwich, 2014). Networks of entrepreneurs provide an information flow, enabling an effective distribution of knowledge, labour and capital (Malecki, 1997). Leadership provides direction for the entrepreneurial ecosystem. This leadership is critical in building and maintaining a healthy ecosystem (Feldman, 2014). This involves a set of 'visible' entrepreneurial leaders who are committed to the region (Feldman and Zoller, 2012). The high levels of commitment and public spirit of regional leaders might be a reflection of underlying norms dominant in a region (Olberding, 2002). A highly developed physical infrastructure (including both traditional transportation infrastructure and digital infrastructure) is a key element of the context to enable economic interaction and entrepreneurship in particular (Audretsch et al., 2015). Access to financing-preferably provided by investors with entrepreneurial knowledgeis crucial for investments in uncertain entrepreneurial projects with a long-term horizon (see e.g. Kerr and Nanda, 2009). Perhaps the most important condition for entrepreneurship is the presence of a diverse and skilled group of workers ('talent': see e.g. Acs and Armington, 2004;Lee et al., 2004;Qian et al., 2013). An important source of opportunities for entrepreneurship can be found in knowledge, from both public and private organizations (see e.g. Audretsch and Lehmann, 2005).
The supply of support services by a variety of intermediaries can substantially lower entry barriers for new entrepreneurial projects, and reduce the time to market of innovations (see e.g. Clayton et al., 2018;Howells, 2006;Zhang and Li, 2010). Finally, the presence of financial means in the population to purchase goods and services-preferably locally, but possibly also on a further distance-is essential for entrepreneurship to occur at all. The presence of demand thus is an important element of the entrepreneurial ecosystem. Income and purchasing power in a region is both a cause and an effect of entrepreneurship in a region (Berkowitz and DeJong, 2005), already hinting at the role of feedback effects in the evolution of entrepreneurial ecosystems.

An entrepreneurial ecosystem framework
The empirical literatures on the geography of entrepreneurship and economic growth reveal several factors to be of relevance in explaining the spatial heterogeneity in entrepreneurship. This suggests that there is a limited set of factors, or elements that affects the prevalence of entrepreneurship in a region. We integrate the insights from the empirical literatures on the geography of entrepreneurship and economic growth into one figure, reflecting an entrepreneurial ecosystem framework with ten elements (see Fig. 1). This framework with ten elements provides a compromise between other frameworks with five (Vedula and Kim, 2019), six (Isenberg and Onyemah, 2016) and 14 elements (Ács et al., 2014). We build on these frameworks and develop them further by separating inputs and outputs of the system, providing an academically grounded set of elements, and using empirical indicators more closely reflecting productive entrepreneurship.

Understanding entrepreneurial economies as complex systems
To understand the long-term development of (regional) economies and the role of entrepreneurship, the approaches of entrepreneurship and economic growth and geography of entrepreneurship need to be combined. Entrepreneurship plays a double role: it is the output variable in the geography of entrepreneurship approach, and it is the input variable in the entrepreneurship and economic growth approach. To complicate matters even more, entrepreneurship and economic growth also affect the inputs of the geography of entrepreneurship approach, for example with serial entrepreneurs becoming venture capitalists and creating networks; and with economic growth leading to growth in demand, investments in knowledge, and congestion effects in the physical environment. One solution to these conceptual complications is to build on complex systems approaches (Arthur, 2013;Hidalgo and Hausmann, 2009;Ostrom, 2010;Simon, 1962) to develop and use a complex systems perspective on the evolution of entrepreneurial economies (Roundy et al., 2018;Stam and Van de Ven, 2020). A complex systems perspective is able to integrate the geography of entrepreneurship (environmental conditions of entrepreneurship) and the entrepreneurship and economic growth literature (the conditions and effects of productive entrepreneurship). We build on the integrative model of entrepreneurial ecosystems by Stam and Van de Ven (2020), which includes institutional arrangement and resource endowment elements (see Fig. 1). They focus on three key mechanisms: interdependence and coevolution of elements, upward causation of the ecosystem on entrepreneurship, and downward causation of entrepreneurial outputs on the quality of the ecosystem (Stam and Van de Ven, 2020).
Entrepreneurial eco(logical) systems do not exist as such, in contrast to economies that do exist, and can be more or less complex, systemic, and entrepreneurial. Systemic in the sense of elements interacting with each other, and complex in the sense of creating distinct properties that arise from these interactions (including nonlinearity, emergence, adaptation, and feedback loops). In this paper we focus on emergence, and conceptualise economies as complex systems from which transformative innovations can emerge. Transformative innovations are the product of interacting agents, enabled by interdependent components of the system in which they act (Arthur, 2013).
Complex systems have distinct properties that arise from interdependencies, such as nonlinearity, emergence, tipping-points, spontaneous order, adaptation, and feedback loops. A complex systems perspective on the evolution of entrepreneurial economies can provide new answers and new questions to the literature on entrepreneurship and economic development. We take a complexity perspective to better understand the dynamics of economic systems and the interdependencies between the elements of a system. Our complexity approach provides the tools for tracing nonlinear dynamics. Small changes in the conditions of an ecosystem can have big effects: just like the introduction of a wolf can change a whole natural ecosystem, the introduction of a new law or a new actor can change a whole economic system. Also, when a threshold (tipping point) is reached in producing scale-ups in a particular territory, this might trigger a virtuous cycle of successful exits that provide a fertile breeding ground for next generations of scale-ups, as these successfully exited entrepreneurs may become venture capitalists, role models, and network builders in their home-region (Mason and Harrison, 2006). Such analyses provide novel insights into the recursive causal connections between entrepreneurship and elements in the economic system such as venture capital (Lerner, 2012) and culture (Minniti, 2005).

Measuring entrepreneurial ecosystems
The ecosystem framework discussed above identifies ten key elements of an entrepreneurial ecosystem. In this section we operationalize these elements into measurable variables at the appropriate geographical level. First, we discuss the boundaries of an ecosystem to determine the relevant level of analysis. Then we shortly illustrate the main data sources and describe the operational measure of each ecosystem element (for an overview see Table 1).

Level of analysis
The outputs and outcomes of entrepreneurial ecosystems are the result of a complex set of actors and factors that occur in a temporal and varying regional setting. As Feldman and Lowe (2015, p. 1785) rightly state there is often a disconnect "between the theoretical definition of a region as integrated contiguous space and the political and census geography for which data are readily available." In addition, since ecosystems are continuously evolving and are not limited to a specific sector, it is hard to precisely determine their boundaries (Stam and Van de Ven, 2020). The primary demarcation criterium should be the spatial reach of the causal mechanisms involved. This does not lead to one straightforward unit or spatial level of analysis. First, given the multiplicity of causal mechanisms involved in nurturing entrepreneurship, there will be different spatial reaches: for talent it may be the daily urban system (within a 50 mile radius), while for credits it may be the local bank, and for venture capital a two hour drive radius (which may overlap with the regional level in large countries, but may be beyond the national level for small countries). Second, there is a spatial nestedness of contexts: formal institutions at the municipal, regional, national and supranational level may be important context conditions. These first two considerations make it difficult to delineate the spatial boundary of entrepreneurial ecosystems, from a causal mechanism point of view. From a practitioners', the stakeholders of entrepreneurial ecosystems, point of view the relevant boundaries will again be different depending on their role in the ecosystem. For civil servants it will be a particular jurisdiction, while for entrepreneurs it may be a multiplicity of layered (regional, national) or connected ecosystems (different city-regions). To determine the spatial level of analysis (although almost always imperfect) we therefore search for a common spatial denominator in combination with data availability (to allow for comparisons). It should nevertheless also be kept in mind that even though we choose a spatial unit to represent the entrepreneurial ecosystem, entrepreneurial ecosystems are not closed containers, but open systems.
In the European context, the most relevant spatial level of analysis is likely to be between the municipal and national level, since the spatial reaches of the different elements are most likely to overlap with regional boundaries (e.g. the 50 mile radius for talent). The regional level in Europe is best defined through the NUTS 2 classification, which identifies 281 geographical regions over the 28 member states. Hence, we use the NUTS 2 level as the level of analysis. The boundaries of these areas are based on existing administrative boundaries and population thresholds. The population of a NUTS 2 unit is roughly between 800,000 and 3 million people (European Commission, 2018). By defining entrepreneurial ecosystems at the NUTS 2 level we use the same region size as the recent study by Stam and Van de Ven (2020). Our study looks at a larger set of observations than Stam and Van de Ven (2020) since we include all countries in the European Union instead of only one. This also results in a substantial larger variety in our data. Studying regions instead of countries allows us to look at entrepreneurial at a more detailed and appropriate scale. A disadvantage of looking at regions instead of countries is that data on a regional level is scarcer than national data. However, the European Union performs several large data collection exercises on regional level to inform regional policy, this results in the availability of a fairly large amount of regional data. Furthermore, we use a number of novel methodologies to create new metrics at the NUTS 2 level. Finally, we use several national measures to account for the aforementioned spatial nestedness of for example institutions. This combination of data on different geographical levels is discussed in detail for each element below and summarized in Table A1 in the appendix.

Data sources
To measure entrepreneurial ecosystem elements we combine three datasets from studies executed by the European Commission and complement this with data from other sources as well as new data we collected using innovative data analytics. The three main datasets are all available for NUTS 2 units in the European Union. The Regional Competitiveness Index (RCI) is a large study performed every three years (Annoni and Dijkstra, 2019). It uses multiple data sets to construct indicators for areas such as infrastructure, human capital and innovation, and subsequently computes an index that is said to reflect the competitiveness of a region. A related dataset that is more explicitly focused on entrepreneurship is the Regional Ecosystem Scoreboard (RES) (Léon et al., 2016). In addition to combining several statistical sources, this study also performs its own survey among cluster organizations and regional development agencies. The data used in the RES is mainly from the 2010-2015 period and we obtained this through web scraping. Finally, we also take data from the Regional Innovation Scoreboard (RIS) which is a smaller dataset solely focused on the innovation performance of regions (Hollanders et al., 2019). This is the regional version of the European Innovation Scoreboard (EIS) and measures for instance R&D expenditure, innovation by SMEs and human capital. These main data sources are combined with several statistics from Eurostat. For some indicators data is only available at the NUTS 1 level in certain countries. In those cases we follow the approach of the original datasets and impute the NUTS 1 for the NUTS 2 regions (Annoni and Dijkstra, 2019;Hollanders et al., 2019;Léon et al., 2016). Table 1 provides an overview of the data source for each measure while a more detailed version, including all original data sources, can be found in Table A1 in the appendix. All relative to EU average.

Element construction
Seven of the ten elements are constructed through multiple indicators. For these elements we calculate the element score by first standardizing the individual measures (mean as 0 and standard deviation of 1). This ensures that the different measures each have a proportionate influence on the composite indicator. We then take the average of the standardized measures. In section 3.14 we go into more detail on how the different elements are used to calculate an index for the entrepreneurial ecosystem.
To measure four of our variables, leadership, the number of incubators, and both output measures we use the location of individual organizations to determine our regional variables. We here explain the methodology of geocoding and region allocation which we use in all four occasions.
First, we use the nominatim package in R to geocode the given locations using OpenStreetMap (OpenStreetMap, 2019;Rudis, 2019). This is an online map which allows users to pass a list of locations into the software and obtain their coordinates. For the few regions without a match in this procedure we manually search and add its coordinates. With this procedure we obtained the coordinates for all organization. Subsequently, we used Eurostat shapefiles to determine in which NUTS 2 region these coordinates are located. The shapefiles contain an exact overview of the NUTS 2 boundaries (Eurostat, 2019). We then use the rgdal package in R to assign the coordinates to the corresponding NUTS 2 region (Bivand et al., 2019;Eurostat, 2019). Through this we are able to assign all except for about 0.1% of the organizations to a region. We filled in the remaining geocodes through the browser tool of Open Street Map. After this we were able to assign all organizations for each of the four variables to a region. For each of the four variables we then count the number of organizations/firms in each NUTS 2 region and divide this by the population of the region to obtain our final measure.

Formal institutions
Well-functioning institutions are essential for any entrepreneurship to take place at all (Granovetter, 1992). Even when fundamental conditions of the institutional framework, e.g. property rights, are in place, the quality of these institutions will affect entrepreneurship (Baumol, 1996;Boudreaux and Nikolaev, 2019;Webb et al., 2019). To operationalize this element, we use a generic and an entrepreneurship specific indicator. These indicators cover two different aspects of the institutional environment, namely the quality of government and the regulatory framework for businesses. To operationalize the general quality of government we use the Quality of Government study (QOG), which is the largest sub national governance study that has been performed (Charron et al., 2019a).
The quality of government indicator consists of three components: corruption, accountability and impartiality. These are each measured by a large citizen survey in each European region and complemented by the World Governance Indicators on a national level. The survey questions measure both experiences and perceptions of citizens and ask for example about the quality of public education in their region or corruption in the police force in their area (Charron et al., 2019b). 1 It is important to note that all questions specifically refer to the region of the respondent.
One potential threat is that some of the NUTS areas do not precisely coincide with local administrative units and in some countries local administrative units may not be very powerful.
However, NUTS 2 regions are devised to overlap with administrative regions as much as possible and even in more centralized countries previous studies found substantial regional variation. This measure thus accounts for the nestedness of the regional variation in quality of governance within national institutions.
To measure the entrepreneurship specific regulatory framework we use the composite indicator 'Regulatory framework for starting a business' from the RES (Léon et al., 2016). This consists of the following four measures: number of days to start a business, difficulties encountered when starting a business, the barriers to entrepreneurship, and the ease of doing business index (for a more detailed overview of all the indicators see Table A1 in the appendix). Using a combination of general and entrepreneurship specific institutions is a significant improvement over the operationalization of formal institutions as implemented by Stam and Van de Ven (2020).

Entrepreneurship culture
The next element of entrepreneurial ecosystems, culture, represents an informal institution.
Specifically, how much entrepreneurship is valued and stimulated in a society (Fritsch and Wyrwich, 2014

Networks
When actors in a region are well connected in networks this allows information, labour and knowledge to flow to firms which can use it most effectively (Malecki, 1997). Networks are essential for entrants as it helps new firms to build social capital, which firms can leverage to get access to resources, information and knowledge (Eveleens et al., 2017;van Rijnsoever, 2020). The connections between firms can be measured through their cooperation projects. Our focus on entrepreneurship entails that we specifically want to measure cooperation on innovative projects.
Therefore, we measure networks as the number of Small and Medium Enterprises (SMEs) with innovation cooperation activities as percentage of all SMEs in a specific region. The focus on innovation projects means this measure captures the kind of productive collaboration that is likely to contribute to entrepreneurial output. In addition, the size of SMEs (enterprises with between 10 and 250 employees) matches with our focus on entrepreneurial growth since it does not include micro firms (less than 10 employees) which are less relevant for our output measure. Larger firms are also excluded from this measure, mainly because almost all large firms participate in some cooperation activities so this does not provide relevant information. Stam and Van de Ven (2020) use a similar measure in their study. We use the data from the RIS, complemented with the European Innovation Scoreboard for countries with only one NUTS 2 region. The RIS and EIS base their data on the Community Innovation Survey (Arundel and Smith, 2013).

Physical infrastructure
Infrastructure is essential for economic interaction between actors and thus essential for entrepreneurship (Audretsch et al., 2015). In this highly digital world not only physical infrastructure enables this interaction but also digital infrastructure. Digital infrastructure provides the opportunity to meet other actors, even if they are not in close physical proximity. Therefore, it is important to include this when creating an empirical measure of infrastructure. For our indicator we follow the approach of the RCI which uses the accessibility by road, accessibility by railway and number of passenger flights to measure the physical (transportation) infrastructure of a region (for details see Table A1). To this we add a measure for the digital infrastructure of a region, which is the percentage of households with access to internet and also available in the RCI (Annoni and Dijkstra, 2019).

Finance
An important condition for starting a new firm and growing an existing firm is access to capital (see e.g. Kerr and Nanda, 2009;Samila and Sorenson, 2010). We measure the availability of capital with two indicators from the Regional Ecosystem Scoreboard (RES): the availability of venture capital and the availability of bank loans for capital investments (Léon et al., 2016). The data is taken from the RES survey which measures the perceived availability of capital on a 5-point scale.
Venture capital is defined as equity not noted on the stock market including replacements and buyouts. It would arguably be better to have the actual amount of venture capital in a region.
However, although this data is available on a national level from the EIS, there is not sufficient regional data on the actual availability of venture capital. 3

Leadership
Leadership in an entrepreneurial ecosystem is necessary to provide the actors in the ecosystem a certain direction or vision to work towards and can make the ecosystem function more effectively (Normann, 2013). Leadership can be provided by individual leaders but also by collaborative efforts that try to guide the system in a certain direction. Since leadership is such an intangible concept it is quite hard to measure and remains understudied (Sotarauta et al., 2017). In our study we operationalize leadership as the number of project coordinators of Horizon2020 innovation projects in a region. We thus follow the approach of Stam and Van de Ven (2020)  inhabitants.

Talent
Human capital (or talent) encompasses the skills, knowledge and experience possessed by individuals (Stam and Van de Ven, 2020). Human capital is a critical input for entrepreneurship and has been shown to be linked to new firm formation (see e.g. Acs and Armington, 2004). It is clearly quite a broad concept which asks for several empirical measures to properly cover the different facets. We break human capital down into two different components, general human capital and entrepreneurship-specific human capital (Becker, 1964;Rauch and Rijsdijk, 2013).
General human capital is not directly related to a certain job (Rauch and Rijsdijk, 2013). To compute the human capital indicator we use data from the RES which offers an extensive measure 3 To test the robustness of our measure we performed a correlation between the actual venture capital data for the UK and DE with the RES data which results in a correlation of 0.40. of education and skills (Léon et al., 2016). The general indicator includes the percentage of population having completed tertiary education, the percentage share of companies providing vocational training and the percentage of population aged 25-64 that participates in education or training (lifelong learning).
Entrepreneurship specific human capital is directly related to start-up activities (Brüderl et al., 1992;Rauch & Rijsdijk, 2013). We include five measures, measuring entrepreneurship and business education, innovative skills training given at companies, creative skills, technical skills, and e-skills. The inclusion of digital skills is highly relevant since digital literacy is almost essential for working in any type of enterprise in the current digital society. In addition, a lot of innovation nowadays involves some digital aspect. The talent measure we use is a significant improvement over earlier papers which almost solely focused on formal education.

Knowledge
The creation of new knowledge by either private or public organizations provides new business opportunities (Kim et al., 2012;Qian et al., 2013). It is therefore an important source of entrepreneurship. We measure this element with intra-mural R&D expenditure as a share of the total Gross Regional Product (GRP). This measure includes R&D spending in both public and private sectors. The data for this variable is available in both the Regional Competitiveness Index (Annoni and Dijkstra, 2019) and Regional Innovation Scoreboard (Hollanders et al., 2019). We chose to use the data from the RCI as this is available at the NUTS 2 level for a larger number of regions.

Demand
The purchasing power and potential demand for goods and services is important for entrepreneurs, since it will only be interesting to market new products if the population has the financial means to buy them. Several studies have shown that market growth increases firm entry (Eckhardt and Shane, 2003). Even though most firms nowadays serve larger markets than just those in their own region, it will be important for start-ups to have a potential regional market which they can easily access (Cortright, 2002;Reynolds et al., 1994;Schutjens and Stam, 2003). We measure the demand using data from the RCI which combines three measures to create an indicator for market size (Annoni and Dijkstra, 2019). The measures are disposable income per capita, potential market size expressed in GRP and potential market size expressed in population.

Intermediate services
Intermediate services or producer services can help producers to start a new enterprise and market an innovation. The supply of support can substantially lower entry barriers of new entrepreneurial projects and speed up the introduction of innovations (Howells, 2006;Zhang and Li, 2010).

Entrepreneurial Ecosystem Index
The ten elements of the entrepreneurial ecosystem which we have operationalized in the previous sections are then used to calculate an index. This is done using the same method as applied in Stam and Van de Ven (2020). We have first standardized the composite indicators which we have calculated. This ensures that all elements get similar weights in the creation of the index. So the calculation of the index is based on the assumption that all ten elements are of equal importance in the ecosystem. Future research could investigate whether the index can be improved by giving certain elements more weight than others. Subsequently, we take the inverse natural log of the indicators and then normalize them by setting the European average of each element to 1 and by letting all other regional values deviate from this. If an element in a region performs less than average this results in a value between 0 and 1, above average performing regions have a value above 1. This allows us to compute an index value based on the ten elements and compare the quality of different entrepreneurial ecosystems. We calculate the index values in three ways. First, in an additive way where (E1 + E2 +…En). Regions with an average value on each element will thus score an index value of 10. Second, to better account for the complex system nature of the entrepreneurial ecosystem we also calculate the index in a multiplicative manner (E1*E2*…En).
The disadvantage of the multiplicative index is that values above 1 have a stronger effect on the index than below average values (which are between 0 and 1). We therefore take the natural logarithm to let the values oscillate symmetrically around 0, this logarithmic way (log(E1) + log(E2) +….log(En)) is our third index value.

Output
The output of the entrepreneurial ecosystem is productive entrepreneurship (see Fig. 1). This kind of entrepreneurship contributes to net output of the economy and consequently leads to aggregate value creation, which is the outcome of the system (Baumol, 1990). Previous research has shown that productive entrepreneurship indeed has a strong effect on economic growth and job creation (Criscuolo et al., 2014;Haltiwanger et al., 2013;Wong et al., 2005). Productive entrepreneurship is a subset of total entrepreneurship and thus requires another measure than, for example, the total number of new firms.
In this study we take the number of new enterprises, founded less than 5 years ago, that are registered in Crunchbase as our measure for entrepreneurial output (Crunchbase, 2019;Dalle et al., 2017). Crunchbase predominantly captures venture capital oriented/innovative entrepreneurial firms and largely ignores companies without a growth ambition and is thus a good source for data on productive entrepreneurship (Dalle et al., 2017). We choose this specific timeframe to ensure that we select firms who experience their growth phase during the same time period (2015-2019) as most of our indicators are measured (see Table A1). The data on Crunchbase mostly comes from two channels, a community of contributors and a large investor network. In addition, the data is validated with other data sources using AI and machine-learning algorithms. A limitation of the Crunchbase dataset is that it is uncertain if the coverage of start-ups is equal among the different countries. However, we found no evidence that this was the case. We further acknowledge that not all start-up entrepreneurs are innovative (cf. Autio et al., 2014), and are also aware that our measure of entrepreneurial output does not capture all innovative activity in the economy, nevertheless Crunchbase is currently the most comprehensive dataset available to measure high growth entrepreneurship as an entrepreneurial output (Dalle et al., 2017). While Crunchbase is increasingly used by scholars for different purposes (Dalle et al., 2017) we are, to the best of our knowledge the first to employ this dataset to measure the output of entrepreneurial ecosystems.
We also explored using the ORBIS data of Bureau Van Dijk as an alternative (Bureau van Dijk, 2020; Dalle et al., 2017). However, we elected not to do this because we found relatively low serial correlation between the different years in the database and found disproportionally large differences between countries which were hard to render and thus influenced our ability to perform cross country regional comparisons.
In addition to the Crunchbase output measure we use a measure for extreme entrepreneurial output in the form of unicorns, which are entrepreneurial ventures valued above $1 billion. We used the 2018 CB Insights unicorn dataset and identified a total of 24 unicorns in Europe (CBInsights, 2018). We then used the geocoding procedure to allocate these unicorns to a total of 17 NUTS 2 regions. As such, unicorns are a very rare and selective form of high growth entrepreneurship that is only present in a small number of regions.

Outliers
Since the European Union covers a large and diverse set of regions, the data show a lot of variety.
In and DK01 (Hovenstaden) for leadership. Second, we set the maximum score for any single element to 5 in order to prevent a disproportionate influence of strong performing ecosystem elements on the overall index. We perform a number of robustness checks on the construction of our index which we discuss in section 4.5.

Descriptive statistics
The descriptive statistics of the empirical measures for the ten ecosystem elements, entrepreneurial outputs, and the index scores are shown in Table 2. In total our data covers 274 NUTS 2 regions divided over the 28 EU member states. We standardize all variables relative to the EU average to account for the different scales of measures. The mean is calculated based on the corrected maximum values and can therefore be below one. We also see a large variation around the mean for several variables, from regions with less than 2 percent of the EU average to regions who have over 160 times the average value. These findings are nevertheless in line with our expectations since we study regions across different countries and levels of development. Looking at the three index values that we calculated using the methods of Stam and Van de Ven (2020), we find that the difference between the smallest and largest value for the multiplicate index is a factor 10 14 . This difference is disproportionately large in comparison with the actual variation in the data as a result of the multiplicative way of calculating the index. Hence, we deem the external validity of the multiplicative index to be insufficient and instead use the additive index in our further analyses with the logarithmic index as a robustness check.

Entrepreneurial Ecosystem Index
To provide a closer insight in the strongest and weakest regions in Europe according to the Entrepreneurial Ecosystem Index, we display the scores for the ten highest (Fig. 2) and lowest ranking (Fig. 3)        Correlation matrix (correlation coefficient is indicated by colour and the significance level by size, only correlations that are significant at 5% level are shown)

Interdependence between entrepreneurial ecosystem elements
The interdependencies between the ten elements are shown in the form of a network plot in Fig. 5.
Physical infrastructure, formal institutions and also demand take the most central position in the interdependence web. This central role is supported by the finding that when looking at interdependencies with a correlation above 0.5 where physical infrastructure and formal institutions each have five interdependencies (Fig. 6a), and again confirmed by the interdependency web with correlations above 0.6 (Fig. 6b). This provides an indication for a potential role of these elements as fundamental conditions of the entrepreneurial ecosystem.  As a second alternative approach to classify regional economies we perform a cluster analysis on the ten ecosystem elements. We use the k-means clustering method which minimizes the total intra-cluster variation (sum of squared errors) using Euclidean distance measures for an a priori fixed number of clusters (Tan et al., 2018). The K-means clustering technique is the most popular clustering technique and was originally proposed by MacQueen (1967). The number of clusters is a parameter that has to be set by the user. After considering the total intra-cluster variation, the average silhouette of clusters, the gap statistic, and the interpretability of the outcomes we selected the approach with three clusters. The results show a small first cluster which consists of high performing regions including Berlin, London, and Brussels. The second cluster forms a middle group and includes Manchester, Cologne and North Brabant (including Eindhoven). Finally, the third cluster contains the low-performers and forms the largest group, including Athens, Budapest and Sicily. The average index values for these three clusters are, as shown in Table 5, in line with our expectations. A particularly interesting finding is that the regions in the first cluster have clearly higher outputs than the middle and laggard group, both in terms of Crunchbase and unicorn output. Table 5.
Summary statistics of index and output by cluster

Entrepreneurial Ecosystem Index and entrepreneurial output
After discussing the creation and reliability of the Entrepreneurial Ecosystem Index we now use regression analysis to study if regions with better ecosystems indeed have higher entrepreneurial outputs. The results of the regressions with the indices as independent variable and the Crunchbase output as dependent variable are shown in Table 6 and graphically displayed in Fig. 7. 5 The results of the regression analyses with the unicorn output as dependent variable are consistent with the findings reported in Table 6. However, we chose not to report these results because of the limited number of regions with unicorn observations (17 out of 274). In all regressions the index has a the regression with the additive index at 0.198. The graph in Fig. 7 shows that the relation between the index and entrepreneurial output does not appear to be linear, since an increase in performance on the index goes together with a disproportionate increase in high growth entrepreneurial ventures.
To capture this nonlinearity in the relation between the quality of an entrepreneurial ecosystem and its entrepreneurial outputs, we added quadratic effects to the model. This resulted in a significant improvement of the model as the non-linear effect is also significant (p<0.001) and increases the R 2 to 0.319. Since we compare regions in different countries, it is important to check whether the index does not just capture between country differences but also has explanatory power within countries. We therefore run a multilevel analysis with country-specific intercepts and our Entrepreneurial Ecosystem Index. The results of the multilevel analysis are presented in Table 7. The index variables still show a significant and positive relation with the entrepreneurial output (p<0.001).

Fig. 7. Entrepreneurial Ecosystem Index and entrepreneurial outputs
Adding country specific intercepts improves the model as evidenced by an increased R 2 as well as the likelihood ratio tests. The random effects in the bottom of the table show the regional variation that even when we compare regions within countries the regions with a higher index value have a significantly higher entrepreneurial output. The high regional variation in entrepreneurial output and index values supports our choice to focus on the regional level when studying entrepreneurial ecosystem performance. Table 7.

Crunchbase output
(1) We find that many of the top performing regions are regions in which a capital region is located (Fig. 3). To test whether the explanatory power of our index holds after controlling for the influence of capital cities on the output variable we run the regressions with a capital city indicator added, which is a dummy variable indicating whether a region contains a capital city (no = 0, yes = 1). The results are displayed in Table A2 and confirm that capital regions perform significantly better than non-capital regions (p<0.001). Nevertheless, the linear and quadratic effect of the Entrepreneurial Ecosystem Index remain significant (p<0.001) and only show a small decrease in coefficients.

Robustness to outliers
In addition, we performed three robustness checks on the sensitivity of our index to outliers. The results of which are presented in Table A4-6. First, we do not conduct the modifications outlined in section 3.16. This robustness test actually results in an R2 of 0.99. However, the results are now strongly influenced by the outlier regions that we discussed in the methodology. Therefore, we performed a second robustness test which removes those regions with a value higher (or lower) than one standard deviation of the second highest values. This concerned Inner London-West (as a result of a high number of incubators and Crunchbase start-ups per population), Braunschweig (as a result of the high R&D intensity) in Germany, and Hovenstaden in Denmark. Since we prefer not to discard observations of which the data is reliably measured, we also performed the regression with all observation after transforming the data. For the variables with a huge range of variation (standard deviations above 10) we transformed the data using the Tukey transformation (Tukey, 1957). The result of this transformation is a distribution of data which is close to a normal distribution, thus reducing the standard deviations from the variables with outliers. All three robustness tests show findings qualitatively similar to those presented in the main analysis, indicating the robustness of our index to outliers.

Discussion and conclusions
This paper discussed and applied new methodologies and metrics to quantify and qualify entrepreneurial economies, applying this to European regions. The objective of this paper was to quantify and qualify regional economies with an entrepreneurial ecosystem approach.
Quantification involves measuring its ten key elements with a wide range of data sources.
Qualification involved developing a network methodology that provides insight into the extent to which the elements are interdependent, the construction of an Entrepreneurial Ecosystem Index to capture the overall quality of entrepreneurial economies, and relating this to entrepreneurial outputs.
We have answered three main research questions. First, how can we compose a harmonized data set with which the quality of key elements of entrepreneurial economies can be measured? We built on prior entrepreneurial ecosystem research that developed a universal set of constructs for each element of entrepreneurial economies, and composed a harmonized data set to measure these constructs in the context of 274 regions in the 28 countries of the European Union. We sourced a wide variety of data and constructed a rich dataset. However, not all elements could be measured in a fully satisfactory way. Often, more adequate data is available, but not at the same regional level or for all regions. An example is the data we used for the finance element: we prefer to have a composite indicator that includes objective data on the supply of different types of finance, including bank loans for SMEs, debt and equity crowdfunding, and regular equity funding. This is not yet available for all European regions. Another example is the data we used for the networks element. Even though the data provided on the engagement of SMEs in innovative collaborations is very informative, additional network data on collaborative networks and influencer networks, for example based on twitter data, could enrich the diagnosis of entrepreneurial ecosystems. This kind of network data would also allow for more refined measures of network diversity and density.
For some elements there is no straightforward data available and new variables had to be constructed. This is the case for leadership, for which others (Stam and Van de Ven 2020) have constructed country specific indicators, and we have created a pan-European indicator. However, even though this indicator provides information of the prevalence of (public-private) leadership behaviour in regions, improvements can be made to measure leadership that is relevant for the quality of entrepreneurial economies, for example with the prevalence of public-private leadership in regional partnerships (see Olberding, 2002). Overall, there is a significant trade-off between getting richer context-specific data (often only available in a relatively small number of regions) and getting widely available, harmonized data, which enables comparisons between regions.
Second, to what extent and how are the elements of entrepreneurial economies interdependent?
We performed correlation analyses, principal component analyses, and developed a network methodology to visualize the interdependencies between elements. These analyses revealed that entrepreneurial economies are systems with elements that are highly interdependent, and are not a collection of isolated factors and actors. Our analyses also showed that in particular formal institutions and physical infrastructure provide foundational conditions for entrepreneurial economic systems.
Third, how can we determine the quality of entrepreneurial economies? We answered this question by composing an entrepreneurial ecosystem index and analysing its relation to entrepreneurial outputs. We used multiple data sources and metrics to determine entrepreneurial outputs at the regional level. We also used novel methods including web scraping and geocoding to determine the entrepreneurial outputs in the form of the number of high-growth firms in a region. We have shown that it is possible to measure the quality of entrepreneurial economies, in a way that has external validity: showing a ranking of European regions and range of variation that is credible.
Our analyses reveal the wide-ranging quality of entrepreneurial ecosystems in Europe, showing a large group of substantially lagging regions, while a smaller group of leading regions is clearly ahead of the European average. We also tested the internal validity using the fact that high quality entrepreneurial economic systems are more likely to produce emergent properties, which we measured with indicators of productive entrepreneurship. The prevalence of innovative new firms is strongly positively and statistically significantly related to quality of entrepreneurial ecosystems, as captured with differently constructed entrepreneurial ecosystem indices. This upward causation confirms earlier findings of Stam and Van de Ven (2020) and Vedula and Kim (2019). This internal validity should be tested more carefully, in particular with other (more direct) tests of causality, with longer time lags between changes in the quality of entrepreneurial ecosystems and the resulting entrepreneurial outputs, and with some quasi-natural experiments in which a set of similar regions is confronted with substantially different changes in one or a few elements. Other methods, including qualitative comparative analysis, could also play an important role in improving our understanding of the workings of ecosystem.
Did we fulfil the policy promise of the entrepreneurial ecosystem approach? We developed entrepreneurial ecosystem metrics to better measure entrepreneurial economies. These metrics enable adequate diagnosis of (regional) entrepreneurial economies and also enables monitoring economic change after policy interventions and other dynamics have changed the system. This paper thus takes heed of the old carpenter's adage "measure twice, cut once", reducing policy failures with better measurement tools.
There are nevertheless many opportunities for improvement of these metrics. Two directions deserve substantial attention in follow-up research. First, we need to move from a comparative static analysis to a dynamic analysis, and for this we need longitudinal datasets. This would make it possible to better trace processes within entrepreneurial ecosystems (Spigel and Harrison, 2018), and allow us to measure the distinct properties of complex systems that arise from interdependencies, such as nonlinearity, emergence, tipping-points, spontaneous order, adaptation, and feedback loops. Second, even though the European Union provides a wide variety of regions to develop and test our entrepreneurial ecosystem metrics, these metrics need to be developed and tested in other contexts as well, in large sets of regions in the US, Asia, Africa, and Latin America.
Statistical regions are not always overlapping with either the relevant jurisdictions or the spatial reach of the causal mechanisms involved (for example as related to culture and the provision of finance). Developing tailor made spatial units and taking into account the nestedness of elements (cities, in regions, in countries) and neighbourhood effects is also a task for future research.
Scientific progress and societal impact are often achieved with better tools. In this paper we developed entrepreneurial ecosystem metrics, with which entrepreneurial economies can be quantified and qualified. These metrics enables researchers and practitioners to gain insight in, and a better understanding of, these economies. Using measurement tools to capture and comprehend the current state of the economy is a necessary condition for effective policy.  Table A2.