In the search for gains in economic growth and competitiveness, many countries have stimulated entrepreneurship through supportive public policies (Farinha et al. 2020; Salman, 2016). Policymakers, however, must define the type of enterprise, whose creation and development they intend to promote (Autio & Rannikko, 2016; González-Uribe & Reyes, 2021), and then prioritize the removal of barriers and strengthening of facilitators of entrepreneurship (Kaya & Persson, 2019).

Entrepreneurship is a dynamic process of resource mobilization for the exploration of opportunities, perceived in the operationalization of a new business, whose growth and performance potential is moderated by the behavior and competence of the entrepreneurs, and affected by contextual and institutional factors (Ács et al., 2014). From this perspective, therefore, policies must be formulated from a systemic view of entrepreneurship, which considers the interactions between individuals and the context (Ács et al., 2014).

The approach of entrepreneurial ecosystems makes it possible to identify such interactions and capture exchanges between the stock of entrepreneurial capital, knowledge and socioeconomic, political, institutional, industrial and technological contexts (Lafuente et al., 2016). Known as the National Entrepreneurship System (NSE), this approach enables policymakers to measure interactions between individuals and context, and to implement national entrepreneurship policies (Szerb et al., 2020).

To capture the complex and multifaceted interactions between entrepreneurs and context, and portray the NSE, Ács & Szerb (2009) formulated the Global Entrepreneurship Index (GEI), which became the first entrepreneurship composite index (ECI). The GEI differs from other indices, such as the Global Entrepreneurship Monitor (GEM) and Doing Business, because it is not limited to measuring just one aspect of entrepreneurship, such as the characteristics of entrepreneurs/businesses or contextual factors, but combines individual and contextual aspects, thereby providing both micro and macro perspectives.

Since 2011, researchers associated with the GEI have annually published studies on entrepreneurship at the country level, and the index has been used as an analytical framework to understand this phenomenon from a systemic perspective, in countries and/or regions (Ács & Correa, 2014; Atiase et al., 2018; Ha & Hoa, 2018, Szerb et al., 2014; Szerb & Trumbull, 2018).

Despite the use and wide dissemination of this ranking and, consequently, the indicators selected and organized to portray and monitor entrepreneurial ecosystems at the national level, there are still no studies that validate this methodology as a way of measuring entrepreneurship. Attempts to show the validity and reliability of this methodology were limited to correlation matrices between the indicators that make up the GEI (see Ács & Szerb, 2009). These tests attest to the correlation between the indicators, but do not emphasize their importance for the construction of the sub-indices, nor do they validate the methodology.

Given this gap, the question is: Are the Global Entrepreneurship Index (GEI) indicators valid and reliable, from a statistical point of view, to measure entrepreneurial activity at the country level? To answer this question and assess whether the GEI is, in fact, a valid methodology for measuring national entrepreneurship systems, in this study, a sophisticated statistical technique known as Structural Equation Modeling (SEM) was applied to the indicators of the GEI, through the SmartPLS software, as the SEM provides information that explains the relationships between multiple variables (Hair et al., 2017) and their factors/dimensions, thus performing the analysis of the measurement model. With this, it will be possible to identify if the GEI has plausibility, that is, if it can be validated as a methodology capable of measuring, in fact, what it proposes, that is, the entrepreneurial ecosystems.

In addition to this introduction, this article presents: an overview of entrepreneurship systems; the synthesis of the Global Entrepreneurship Index; the methodological procedures used; the results found, and the discussion derived from them; final considerations and suggestions for future studies.

In the NSE approach, the emphasis is on high-impact entrepreneurship – activity that contributes to the generation of jobs and the advancement of sectors in which technologies and market development are at less advanced stages (Ács et al., 2018a). In these cases, despite the uncertainty involved, entrepreneurs usually assume central roles in defining new technological trajectories, creating markets and establishing technological standards (Lattacher et al., 2021).

The GEI was developed to measure the quality of entrepreneurial systems at the country level, through measures of attitudes, skills and entrepreneurial aspirations, individually (micro level), as weights in adjusting the importance of contextual and institutional factors (macro level), in regulating the quality of the dynamics of entrepreneurship.

The GEI conceptual model assumes that entrepreneurs allocate resources to exploit perceived opportunities. However, the resource mobilization process is influenced by contextual/institutional factors (Lafuente et al., 2020). Examples of this are the quality and dynamics of interactions between science, technology and innovation institutions (STI) and entrepreneurs, which regulate the potential for innovation. In this way, low interaction directly impacts the ability to innovate in new ventures. Therefore, macro-level factors are institutional and contextual moderators of entrepreneurs' attitudes, skills and aspirations.

The GEI is composed of 14 indicators aggregated into three sub-indices: (1) attitudes (ATT) – associated with indicators that measure the entrepreneurial behavior of the adult population (from 18 to 64 years old) in a country; (2) skills (ABT) – provide a picture of the characteristics of entrepreneurs with high impact potential, measured by metrics associated with motivation to undertake, the technological intensity of the business, the level of education of the entrepreneurs, and the uniqueness of a product and /or service offered, compared to competitors; and (3) entrepreneurial aspirations (ASP) – which deal with high-impact entrepreneurial activity, which spreads new technologies, and generates wealth and jobs (Table 1). This impact is measured by the entrepreneurial ambitions of: internationalization, growth (of jobs), technological innovation, and the availability of venture capital to finance the expansion of new businesses.

Each of the 14 indicators is the result of the combination of an individual variable and an institutional variable, both of which capture the context of each of the participating countries. The individual variables – obtained from the annual adult population survey (APS), carried out by the GEM (Bosma et al., 2020) – describe the entrepreneurial behavior of the population and the characteristics of early-stage entrepreneurship. The institutional variables, in turn, made available by international organizations (World Economic Forum, Heritage Foundation, World Bank, Unesco, among others), identify the context of entrepreneurs (market dynamics, existence of services and policies to support entrepreneurship, quality of teaching and research institutions, among others).

By combining variables representing the micro and macro levels, the GEI goes beyond the existing entrepreneurship indices, which are limited to measuring only one of the levels, such as the Doing of Business and the National Expert Survey, which assess only the constraints of entrepreneurship; and the GEM and Kauffman surveys, which look only at entry rates and entrepreneurial attitudes.

Table 1 Table 1 Global Entrepreneurship Index Structure Table 1 Global Entrepreneurship Index Structure

Table 1
Global Entrepreneurship Index Structure
	Pillars	Individual variable	Institutional variable
Entrepreneurial Attitudes (ATT)	(Pillar_1): Opportunity perception	Opportunity recognition	Freedom and property
	measures perceived opportunity, economic freedom and intellectual property rights.
	(Pillar_2): Startup skills	Skill perception	Education
	Measures startup skills and the quality of the education system.
	(Pillar_3): Risk acceptance	Risk perception	Country risk
	Combines the inhibiting effect of fear of failure with an assessment of country risk.
	(Pillar_4): Networking	Know entrepreneurs	Agglomeration
	Measures the size of the network of entrepreneurs and their ability to access and mobilize resources.
	(Pillar_5): Cultural support	Career status	Corruption
	Combina a percepção da população sobre os empreendedores e os níveis de corrupção
Entrepreneurial Skills (ABT)	(Pillar_6): Opportunity startup	Opportunity motivation	Governance
	Measures the proportion of entrepreneurs per opportunity, and the effect of taxation and government services.
	(Pillar_7): Technology absorption	Technology level	Technology absorption
	Measures the proportion of technology-based entrepreneurs in relation to the level of technology absorption of firms.
	(Pillar_8): Human capital	Educational level	Labor market
	Measures the proportion of entrepreneurs with higher education, the expenditures of firms on training, and the characteristics of the labor market.
	(Pillar_9): Competition	Competitors	Competitiveness
	Measures the level of uniqueness of products, the characteristics of competition and the effects of antitrust regulation.
Entrepreneurial Aspirations (ASP)	(Pillar_10): Product innovation	New product	Technology transfer
	Proportion of entrepreneurs offering new products to some of their customers, combined with the technology transfer capacity of firms in a country.
	(Pillar_11): Process innovation	New technology	Science
	Proportion of entrepreneurs using new production technologies, expenditure on R&D, and quality of science and technology institutions.
	(Pillar_12): High growth	Gazelle	Finance and strategy
	Measures the proportion of entrepreneurs with high growth expectations, availability of venture capital and sophistication of business strategies.
	(Pillar_13): Internationalization	Export	Economic complexity
	Measures the proportion of internationalized entrepreneurs and the level of economic complexity of a country.
	(Pillar_14): Risk capital	Informal investment	Depth of capital market
	Combines the level of informal funding and the depth of the capital market.
Note : In parentheses are the codes used in the in SEM. Source: Elaborated by authors from Ács et al. (2018a).

Note : In parentheses are the codes used in the in SEM. Source: Elaborated by authors from Ács et al. (2018a).

Like the GEI, the Index of Dynamic Entrepreneurship (IDE) also measures the micro and macro levels of entrepreneurship but does not provide diagnoses about the entrepreneurial attitudes of the population and the quality of entrepreneurship, that is, whether they are innovative, technology-based and/or or export-oriented.

The GEI results in a composite indicator, developed according to the international recommendations of the OECD, discussed in detail in its manual “Handbook on Constructing Composite Indicators: Methodology and User Guide” (OECD, 2008).

A prominent element in the GEI is the so-called “penality for bottleneck”, which is not found in any other aggregate indicator. It is the procedure based on the assumption that the performance of a system is dependent on its bottleneck, that is, the overall performance is determined by its weakest link. Thus, countries with greater imbalances among the ten pillars have, as a result, a smaller GEI.

The convergent validity of the latent variables was verified by redundancy analysis of each construct, with the original formative construction marked as “original”, and the single-item construction as “global”. All path coefficients were higher than the recommended limit of 0.70, which indicates that the LVs exhibit convergent validity (Figure 2).

Figure 2 Figure 2 Convergent validity Figure 2 Convergent validity Note: Elaborated by authors (2021).

The assessment of the collinearity of the indicators was performed using the variance inflation factor (VIF), and resulted in values lower than 5.0 - indicative of the absence of redundancy, which does not require the correction of collinearity problems, the removal or merging of indicators (Table 2).

Table 2 Table 2 Variance inflation factor (VIF), external weights and loads Table 2 Variance inflation factor (VIF), external weights and loads

Table 2
Variance inflation factor (VIF), external weights and loads
Pillar	VIF	External weights (External loads)	t Statistic	p value	BCa Confidence Interval
					[2,5%; 97,5%]
1	3,911	-0,084 (0,817)	0,867(ns)	0,397(ns)	[-0,283; 0,104]
2	1,483	0,198 (0,663)	2,89***	0,005**	[0,065; 0,344]
3	2,610	0,528 (0,923)	5,614***	0,000***	[0,334; 0,700]
4	1,822	0,052 (0,683)	0,658(ns)	0,508(ns)	[-0,098; 0,209]
5	3,511	0,465 (0,890)	5,392***	0,000***	[0,229; 0,649]
6	3,981	0,488 (0,958)	6,658***	0,000***	[0,343; 0,625]
7	2,776	0,370 (0,911)	5,725***	0,000***	[0,237; 0,499]
8	1,955	0,128 (0,752)	2,323**	0,021**	[0,034; 0,251]
9	2,624	0,120 (0,829)	1,906*	0,055*	[-0,007; 0,239]
10	1,731	0,037 (0,654)	0,572(ns)	0,559(ns)	[-0,090; 0,156]
11	2,416	0,347 (0,883)	5,194***	0,000***	[0,220; 0,481]
12	2,532	0,135 (0,800)	1,704*	0,087*	[-0,027; 0,280]
13	2,415	0,319 (0,880)	3,366***	0,001***	[0,134; 0,508]
14	2,959	0,317 (0,887)	2,673***	0,008**	[0,089; 0,557]
Notes : ns = not significant; * = significant at 10% (t ≥ 1.65; p < 0.1); ** = significant at 5% (t ≥ 1.96; < 0.05); *** = significant at 1% (t ≥ 2.57; p < 0.001).
Elaborated by authors (2021).

Notes : ns = not significant; * = significant at 10% (t ≥ 1.65; p < 0.1); ** = significant at 5% (t ≥ 1.96; < 0.05); *** = significant at 1% (t ≥ 2.57; p < 0.001). Elaborated by authors (2021).

Regarding the results of the evaluation of the indicators and the relative importance (external weights), in terms of significance and relevance, only three of them showed low significance regarding the t statistic. They are: Pillar_1 (-0.084); Pillar_4 (0.052); and Pillar_10 (0.037). As for the absolute importance, represented by the values of external loads, all indicators showed values greater than 0.50, thus proving to be significantly relevant for the FMM (Table 2).

To achieve the results related to the consistency of the measurement model, based on data from two GEI editions (2017 and 2018), the permutation method was used, by calculating the MICOM test (measurement invariance of composite models), which evaluated the invariance of the FMM (Bido & Da Silva, 2019) in the years analyzed (Table 3 e Table 4). All permutation p-values are non-significant (p>0.05), which confirms the inexistence of differences between the two observed periods (Table 3 e Table 4).

Table 3 Table 3 Permutation p-values for the constructs of the years 2017 e 2018 Table 3 Permutation p-values for the constructs of the years 2017 e 2018

Table 3
Permutation p-values for the constructs of the years 2017 e 2018
Constructs	ATT	ABT	ASP
Original correlation	0,995	0,992	0,979
Correlation permutation average	0,971	0,983	0,976
5.0%	0,932	0,957	0,932
Permutation p-values	0,942	0,701	0,475
Original average difference	0,011	-0,035	-0,050
Permutation Mean Difference	-0,006	-0,003	-0,001
Confidence interval	[-0,249; 0,228]	[-0,246; 0,232]	[-0,234; 0,237]
Permutation p-values	0,922	0,678	0,766
Original variation	0,009	-0,127	-0,042
Permutation average variance	0,002	-0,001	0,003
Confidence interval	[-0,338; 0,357]	[-0,376; 0,354]	[-0,305; 0,303]
Permutation p-values	0,947	0,500	0,788
Note: Elaborated by authors (2021).

Note: Elaborated by authors (2021).

Table 4 Table 4 Permutation p-values for the correlation relationship between the pillars and the constructs of the years 2017 e 2018 Table 4 Permutation p-values for the correlation relationship between the pillars and the constructs of the years 2017 e 2018

Table 4
Permutation p-values for the correlation relationship between the pillars and the constructs of the years 2017 e 2018
Pillar	Original values		(2017-2018)		Confidence interval	Permutation p-values
	2017	2018	Original difference	Permutaion difference
1	-0,066	-0,085	0,018	-0,002	[-0,281; 0,262]	0,907
2	0,147	0,198	-0,051	-0,003	[-0,202; 0,206]	0,618
3	0,562	0,528	0,033	0,002	[-0,278; 0,259]	0,821
4	0,072	0,052	0,020	0,002	[-0,217; 0,259]	0,862
5	0,420	0,465	-0,046	0,000	[-0,255; 0,269]	0,728
6	0,579	0,488	0,091	0,000	[-0,213; 0,204]	0,407
7	0,314	0,370	-0,056	-0,001	[-0,163; 0,169]	0,535
8	0,110	0,128	-0,018	0,001	[-0,192; 0,181]	0,838
9	0,113	0,120	-0,007	-0,002	[-0,201; 0,196]	0,942
10	0,174	0,037	0,138	-0,001	[-0,183; 0,183]	0,181
11	0,289	0,347	-0,057	-0,006	[-0,231; 0,234]	0,546
12	0,057	0,135	-0,079	0,000	[-0,239; 0,260]	0,501
13	0,274	0,319	-0,045	0,002	[-0,239; 0,260]	0,732
14	0,361	0,317	0,043	0,004	[-0,329; 0,360]	0,808
Note: Elaborated by authors (2021).

Note: Elaborated by authors (2021).

The results of the FMM evaluation show that all LVs have convergent validity; however, with regard to the significance and relevance of the indicators, Pilar_1, Pilar_4 and Pilar_10 have non-significant external weights. Even so, they have significant external loads (>0.5), which suggests the permanence of the indicators in the FMM, as long as there is empirical support for this.

Pillar_1 is composed of the variables “opportunity recognition” and “business and property”. The first (individual) measures the population's perception of opportunities to undertake; and the second (institutional), provided by the Economic Freedom Index (EFI), captures the effects of the regulatory environment on entrepreneurship and private property rights.

When looking at the EFI database, it can be noted that developed countries are characterized by the quality of the regulatory environment; the GEM database, in terms of the individual variable, shows that underdeveloped and developing countries have greater opportunities to undertake (from the point of view of the adult population), compared to developed countries.

This is, therefore, a limitation of the GEM, given that the research considers any type of entrepreneurship, not necessarily productive, innovative and/or knowledge intensive. Thus, there is no differentiation between perceived opportunities in high-tech sectors and low-productivity opportunities (such as selling homemade cakes, for example, due to the scarcity of quality jobs and the need to earn income to survive). This methodological option, therefore, provides distorted results of what could be understood as productive or high-impact entrepreneurship.

Although there is theoretical support for maintaining Pillar_1, since opportunities are the core of entrepreneurship (Wood & Mckinley, 2017), some authors (Neill et al., 2017; Welter & Alvarez, 2015) argue that it is necessary to distinguish them between discovery and creation. On the other hand, measuring only the opportunities perceived in technology sectors would generate new results, being able to identify the ability of an economic system to favor entrepreneurs (Radosevic & Yoruk, 2013).

Although the focus on the perception of entrepreneurial opportunities in technological sectors penalized less developed countries, a change in this indicator would minimize the distortions of results, when comparing countries at different stages of development. For example, the United States has 0.73 points in the variable “recognition of opportunities”, while Chad, the last place out of 137 countries, has a performance of 0.94, surpassing the United States, the first place in the GEI ranking. In this context, this variable may indicate that Chad's economic system generates more opportunities (perceived by the population of that country) to undertake than the US system. These results distortions would be minimized if the indicator captured other aspects of opportunity perception, especially those related to technology.

Pillar_4, consisting of the individual variables “known entrepreneurs” and institutional “agglomeration”, assesses the ease of meeting an entrepreneur, the ability to connect individuals, the degree of urbanization and the quality of the countries' infrastructure. Several researchers (Audretsch & Belitski, 2017; Belitski & Desai, 2016; Bosma & Sternberg, 2014; Stam & Van de Ven, 2021) claim, in this sense, that urban environments, with quality infrastructure, drive innovative and high-quality entrepreneurship growth, due to agglomeration economies (Krugman, 1991). Thus, knowledge flows are denser in cities, where different skills and resources are concentrated, and they become more accessible. In addition, these environments facilitate market access (Lattacher et al., 2021).

Likewise, entrepreneurs known by the majority of the population become models and successful references for potential entrepreneurs, acting as leaders, in strengthening the NSE (Stam & Van de Ven, 2021; Sternberg et al., 2019).

There is, therefore, theoretical support for maintaining Pillar_4, despite the low significance of the indicator, which is associated with the methodological limitations of the GEM, for which any individual involved in the creation of a new business is considered an entrepreneur, whether he is dedicated to an activity with the potential to become a unicorn, be it a subsistence activity.

This becomes clearer when comparing the United States and Mauritania (number 136 in the ranking of 137 countries), regarding the variable “known entrepreneurs”. The first country has a score of 0.57; and the second, 1.0 point, indicating that there are more entrepreneurs in Mauritania than in the United States.

Although less developed countries have larger “stocks” of entrepreneurs than more developed ones (Ács et al., 2014), quantity does not represent quality, as they are primarily need-oriented entrepreneurs (Autio & Fu, 2014; Lederman et al., 2014), with low visibility and/or less known than innovative entrepreneurs. As a result, they find it more difficult to access the same resources and knowledge flows held by an innovative new (Kantis et al., 2018; Ordeñana et al., 2019).

With regard to Pillar_10, the low external weight can be attributed to the characteristics of the GEI database, which measures entrepreneurship in 137 countries, most of which are characterized by economic systems based on factors of production or efficiency, which are known dependence on the global economy and the importation of technology. Only a small number of countries diffuse the technology, through knowledge-intensive activities and business sophistication and demand (WEF, 2017). Thus, when using a relatively large database on entrepreneurial innovation, in which most countries have few innovative initial entrepreneurs, it is expected to obtain low significance.

Pillar_10, then, due to the institutional variable “technology transfer”, which measures the quality of a country’s science and technology system (Ács et al., 2018b), has theoretical support, which guarantees the their stay in the FMM. According to some researchers (Belitski & Desai, 2016; De Bernardi & Azucar, 2020; Malerba & McKelvey, 2020; Radosevic & Yoruk, 2013), the quality of the innovation environment drives the creation of new innovative companies. On the other hand, the individual variable “new product”, which measures whether entrepreneurs introduce new products to some of their customers, combined with the institutional variable that assesses the “quality of the S&T system”, represent an advance in relation to the indexes of entrepreneurship that provide a diagnosis of the quality of the innovation environment, but do not inform whether innovation actually occurs.

To assess the NSE, for example, the IDE uses metrics, such as the S&T platform and the business structure, to assess the quality of the S&T system and the technological maturity of established companies (Kantis et al., 2018). However, it is not possible to correlate these metrics with the proportion of innovative entrepreneurs, as the FDI only includes an entrepreneurship indicator, which measures the growth orientation of new businesses, not whether they are innovative.

Assessing the proportion of early entrepreneurs who innovate is relevant to support decision makers in formulating policies that minimize market failures associated with knowledge externalities, inducing investments and facilitating the dissemination of knowledge (Ács et al., 2016).

In this research, it was asked whether the GEI indicators are relevant and significant to measure the performance of the NSE. To obtain the answers, the SEM and the evaluation procedures related to the FMM were used – configuration through which the indicators form/cause the construct (phenomenon). The results showed that all constructs have convergent validity and the indicators are not redundant.

When evaluating based on external weights, Pillar_1, Pillar_4 e Pillar_10 showed low significance. On the other hand, in terms of relevance, given the value obtained in the examination of external loads, the indicators proved to be significant.

As it is a relevant metric to assess the quality of entrepreneurship, this article suggests the permanence of Pillar_10. However, it is necessary to replace the individual variables of Pillar_1 and Pillar_4, in which entrepreneurship encompasses any attempt to create a new business, including from autonomous activities to the expansion of an existing business (GEM, 2017). Because of this, they provide distorted results, based only on quantity, not measuring the quality and impacts of entrepreneurship.

From the perspective of these variables, therefore, as a suggestion to the developers of indicators or policymakers, this article recommends the elaboration of more specific questions, in order to avoid, as a parameter to measure the visibility of entrepreneurs, the use of negligible forms of entrepreneurship. for economic growth or that do not constitute references for new business models (Feld, 2012; Ordeñana et al., 2019).

By validating the GEI and suggesting the replacement of some components, this research methodologically contributes to studies proposing regional and/or local applications of the aforementioned index. To avoid distorted results, however, it is recommended to limit the scope of evaluation to effectively productive forms of entrepreneurship.

In addition, this study contributes to the entrepreneurship literature, as it is the first to assess the validity of the GEI, using the SEM method. So far, research has correlated the index with indicators – a procedure that does not allow identifying whether it is valid as a methodology or as a model for measuring NSE.

For future research, we suggest the validation of other entrepreneurship indices, such as FDI; and the evaluation of the GEI over time, using techniques such as data envelopment analysis (DEA) and the Malmquist index (Bogetoft, 2012), to measure the efficiency of the countries' EE.

The authors are grateful for the contributions of the evaluators.

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

The authors declare that there is no conflict of interest.

Authors’ statement of individual contributions
Roles	Contributions
	Dionisio EA	Silva D	Carvalho RQ	Inacio Jr. E
Conceptualization	∎			∎
Methodology	∎	∎		∎
Software	∎	∎		∎
Validation	∎	∎		∎
Formal analysis	∎	∎		∎
Investigation	∎			∎
Resources	N.A.
Data Curation	∎			∎
Writing - Original Draf	∎	∎	∎	∎
Writing - Review & Editing	∎		∎	∎
Visualization				∎
Supervision			∎	∎
Project administration				∎
Funding acquisition	∎