Method

33

Formal institutions

Corruption, Measure;

Government, Rule of Law

Corruption (Jauregui et al., 2021); Rule of law index (Levie &

Autio, 2011) Culture culture, Uncertainty

avoidance; culture, Entrepreneurial culture

Uncertainty avoidance (Autio et al., 2013); Self-employment rate, 1989 (Fritsch & Wyrwich, 2014)

Physical infrastructure

Infrastructure, ICT;

urban, Settlement structure

Internet penetration rate (Kolokas et al., 2020);

Metropolitan city dummy (Iacobucci & Perugini, 2021)

Demand Demography, Population growth; GDP per capita

Population growth (Armington & Acs, 2002); GDP per capita (Avnimelech et al., 2014)

*categories based on own coding procedure (see chapter 2.3.2)

34

full-text screened to determine their relevance and examine their reported quantitative results. The eligibility criteria used to select empirical studies were that the study contained at least one measurement of EA (dependent variable of this meta-analysis) and one variable that could be attributed to the EE framework of Stam (2015). In the literature, there are different ways to measure the EA output metric of an entrepreneurial process (Ahmad &

Hoffmann, 2012; Henrekson & Sanandaji, 2014). Therefore, we included studies that reported at least one of the following EA measures previously discussed in the literature: self-employment rates, new firm formation, churn rates, number of start-ups, and total-early stage entrepreneurial activity (TEA). The EE framework was defined rather broadly to include many diverse studies.

After we screened all 9,435 papers based on these criteria, 443 studies remained. A forward and backward citation search on those empirical studies resulted in a second screening of 11,019 additional papers, resulting in a total of 20,454 screened studies. During the screening process, we filtered out studies with missing data and contacted the authors. Out of 56 contacted authors, 9 provided data. In total, 545 studies fulfilled all the criteria and were included in the final dataset (see the Appendix for a list of the included studies). Some of these contained data for two or more time periods or individual data from multiple countries, and these were then added as individual studies (75). Additionally, studies with multiple dependent variables (e.g., new firm formation and TEA) were included separately for each independent variable (292). As a result, a total K of 912 studies were used for the analysis.

This K covered a total N of 2,584,110 space-time observations.

This meta-analysis used the Pearson product-moment correlation, which is a measure of the direct relationships between two variables commonly used in the field of systematic literature reviews, as an effect size indicator (Aguinis et al., 2011). In this meta-analysis, one of these variables is a measure of EA (our dependent variable) and another is a variable attributable to the Stams EE framework (our independent variable) Any missing correlation coefficients from the studies were calculated based on Hedges’ g (Borenstein et al., 2009). The final set of correlation coefficients was used for effect size estimation and meta-regression modeling.

After coding the independent variables into the EE framework, for each study, we used the average pooling of the correlation coefficients of the independent variables belonging to the same framework element (K). This helped us avoid sampling errors and oversized study

35

weights. Last, study characteristics (e.g., publication type, research method, peer-review status, journal impact factor, time span, responses, imputation, and ecosystem variable included in the model) were extracted and used in the meta-regression. To complement the analysis, secondary data at the country level were added to the dataset (Human Development Index, Gross Domestic Product, federalism country (1=yes), cultural tightness, cultural looseness, and several cultural indices from the GLOBE project) (House, 2011). The moderator matching required that the data of each empirical study belong to one country. Studies that cover multiple countries were set to “not available” for the moderators. A list of the countries covered by the empirical papers that could be identified is provided in Appendix B. These vast sets of moderators help explain the heterogeneity across the studies (Borenstein et al., 2009).

2.3.2 Grouping of variables

A challenging aspect of this meta-analysis was the assignment of the numerous extracted variables and their corresponding different measurements to the constructs that were used in the meta-analysis (Lipsey & Wilson, 2001). To accomplish this task, we used a systematic step-by-step grouping similar to that of Martin et al. (2013).

Grouping the antecedents of EA (our independent variables) based on the elements of EEs can be challenging when multiple elements can match, as the framework does not provide clear definitions for the elements or identify the measurements that could belong to them. The grouping process strictly adhered to the following procedure. First, all the variable names and variable sources were unified. Second, a coding procedure was applied to group similar variables based on their sources and their objects of measurement (resulting in 152 categories). Third, these categories were assigned to the elements of the Stam framework. To accomplish this, a theory-based rationale was written down for each group based on the definitions and explanations of Stam (2015, 2018), Stam & van de Ven (2021), and Leendertse et al. (2021). For example, measures of human capital were grouped into the talent element based on the argument that a skilled group of workers is a key element of an EE and that this factor thus belongs to the talent element (Leendertse et al., 2021; Stam, 2015). Examples of this matching process and example literature references are presented in table 2.1. A necessary condition for the assignment was that it coincided with Stam's reasoning regarding each element. Each of these procedures were performed by the authors separately.

Disagreements were resolved by discussion until full consensus was reached (B. C. Martin et

36

al., 2013). In some cases, variables were excluded due to limited relevance (e.g., CO2 emissions) or missing variable descriptions.

This meta-analysis aimed to investigate effect sizes on different spatial levels and on different types of EA. The different measures of EA and their grouping originated from Leendertse et al. (2021), and they were designed to capture the effect of productive EA, which is a subset of total EA. Productive EA contributes to the output of the economy (Baumol, 1990) and is commonly measured in terms of knowledge-intensive, innovative new firms or high-growth firms. These productive EA measures are associated with increases in regional development through employment and production growth (Acs, 2011; Fritsch & Schroeter, 2011).

Therefore, a binary dummy variable was created to capture this relationship moderator and how EE elements differ between productive EA and total EA. The created variable equaled one if the EA-type measures in a given empirical study could be attributed to productive entrepreneurship and zero otherwise. Thus, if the empirical study used variables such as the number of gazelles (Zhang & Roelfsema, 2020) or number of knowledge-intensive start-ups (Fritsch & Schilder, 2008), the binary indicator was equal to one. Please note that every variable that measures productive EA is a measure of productive EA only, while measures of general EA (e.g., business entries per 1,000 inhabitants) could include productive EA as well.

We further included factor variables to account for the empirical EA measure itself. The spatial levels were factor-coded according to the observational level of the included study. The other extracted study-related characteristics and most of the moderating factors were binary coded.

The country effect moderators were continuous variables and matched to the study characteristics. When matching was not possible, the corresponding cells were set to “not available”. The main criterion used for matching was that the moderators were required to fit the observational time and space of the corresponding study.

2.3.3 Analytical approach

The large, heterogeneous body of empirical studies required the use of random-effects-based meta-analytical models. According to Borenstein et al. (2009), a random-effects model was preferable since it accounts for heterogeneity within and between studies. We tested for heterogeneity between studies using Cochrane’s Q test for heterogeneity, the H test statistic, and I² (Cooper et al. 2019). Based on the results of these tests, the random-effects model was used for data analysis and interpretation. The weights of the random-effects meta-analysis

37

were constructed using the common inverse variance weighting method (Borenstein et al., 2009). To estimate the summary effect sizes, we relied on Fisher z-transformation to accommodate skewed distributions of the correlation coefficient. To ensure that our results were relatively conservative, we relied on the Sidik-Jonkman estimator with a Knapp-Hartung (-Sidik-Jonkman) adjustment. As pointed out by Jackson et al. (2017), this method performs well and, if the meta-analysis is complemented by a sensitivity analysis and robustness checks, it leads to conservative results.

Threats to inference, such as selection bias, publication bias, and the method-related biases mentioned by Cooper et al. (2019), were addressed by the research strategy in the following way. The pooling, reliability correction and transformation of the effect sites within the empirical studies reduced the biases affecting the primary studies and the way in which they influenced the results of the meta-analysis. We addressed biases due to missing information by using only empirical studies for which all the necessary information for an effect size estimation was available.

Considerations regarding the meta-analysis itself were accounted for with a wide range of robustness models and estimation techniques. This meta-analysis used a meta-analysis regression analysis (MARA) in combination with a three-layer model to validate the empirical findings. This procedure is in line with Cheung (2019) and Borenstein et al. (2009) because it addresses both the problem of publication biases and unit-of-analysis errors. Within a meta-analysis, it is important to evaluate the behavior of the effect size estimate jointly with the presence of country-level specifics and study-specific characteristics. According to Cooper et al. (2019), addressing publication bias with the MARA framework is important within meta-analysis because it reduces the potential bias arising through major, influential studies that might be published due to the professional networks of the authors. The search strategy used in this meta-analysis to find empirical studies was not restricted to particular keywords, search terms or publication types. Moreover, because of the full-text screening process employed, many different types of empirical work were included in the meta-analysis. Last, due to the large number of collected studies and entries per study, it was reasonable to assume that the individual effect sizes were not independent. Therefore, a nested three-layer model was used (Cheung, 2019).

38

The three-layer MARA models were used for robustness checks and not for interpretation because the choice of reference categories influences the outcome. To compensate for this drawback, the robustness of the results was additionally evaluated; first, this was done with different subsets and aggregation levels, and second, variations in the weightings of how the final effect sizes were computed were employed. The use of the median and the arithmetic mean as unweighted measures and the fixed-effects model, which uses a different between-study variation, helped validate the estimated effect sizes with respect to applying different weights in the effect-size aggregation process. To further investigate how sensitive the results were to different weights, we used the total number of observations reported in the studies in a complementary random-effects model. To check for the coding of the antecedents of EA, we employed another random-effects model with only variables that could be directly attributed to Stams’ (2015) framework. These variables were same empirical variables used by Stam (2015, 2018), Stam & van de Ven (2021), and Leendertse et al. (2021). Following Harrer et al. (2021) all the estimations and calculations were performed using the statistical software R.