1. Introduction

Higher education institutions are the centers for creating professionals who, due to their characteristics, can impact a country's productive structure. In this context, the training of entrepreneurs becomes one of the most important aims of these educational centers. Entrepreneurship is related to a country's capacity to create and consolidate local companies, as well as to create jobs and income and influence economic activity, thus becoming a bastion for regional development and international competitiveness (^{Awad and Salaimeh, 2023}; ^{McKinsey and Company, 2011}; ^{NACIE, 2013}).

In the last two decades, particularly after the 2008-2009 international economic crisis, policies to promote higher education institutions as centers for entrepreneurship have increased using different strategies. These include updating educational programs, professionalizing teachers, strengthening infrastructure, and carrying out different activities to encourage the development of students' entrepreneurial spirit.

It is important to recognize that entrepreneurial models in universities are linked to the infrastructure for the generation and landing of new ideas and are an important link to the local, national and international environment, which allows students, institutions, governments and companies involved to remain in a globalized and competitive context.

Currently, these institutions are undergoing a transformation with respect to the role they play in the economy and, in addition to performing an educational and research function, they are required to focus on participating in solving the problems of society, government, business and significant national challenges. The latter has been called the third mission that gives them the title of "entrepreneurial universities" (^{Shvedova and Maevskaya, 2019}; ^{Etzkowitz, 2016}; ^{Clark, 1998}). To fulfill this mission, universities implement various strategies such as participating in technology transfer offices (TTOs), the creation of incubators, spin-offs, startups, industrial-scientific-technological-research parks, specialized laboratories, research centers, industrial clusters-districts, new companies, sale of specialized services such as patents, intellectual property, the creation of collaboration and financing networks, and so on. This phenomenon is also known as the Knowledge Production System, which facilitates in a more friendly and efficient way the application and exploitation of knowledge and technology (^{Leydesdorff and Meyer, 2006, p. 1441}; ^{Neri, 2019}; ^{Secundo and Giovanni, 2018, p. 3}; ^{Etzkowitz, 2000}).

In this context, the participation of higher education institutions in the economy becomes strategic, especially because of their ability to influence development and address the problems of society. This study seeks to contribute to the knowledge of the extent to which public universities in Mexico have the capacity to act as entrepreneurial universities by referring to the international characteristics that have been identified. It focuses on those that offer educational programs in Administration, Entrepreneurial Development and Business, as areas of knowledge, which, by their very nature, place greater emphasis on promoting the development of competencies so that students can create enterprises or consolidate businesses. This will allow us to identify both strengths and weaknesses and thus move forward in the design of a better and more relevant higher education model.

This research is organized into four sections - the first deals with the different theoretical approaches that analyze universities as agents that promote entrepreneurship. The second presents the methodological model that enables the measurement of entrepreneurial characteristics in a university. The third section presents the evaluation results in public universities and, finally, the conclusions section shows the strengths and weaknesses of public universities in Mexico as sources of entrepreneurship.

2. Context

The university is an institution that offers professional training services that provide knowledge, skills, and abilities to students to enter the labor market, either as employees or by setting up companies that, in turn, create new jobs and income and contribute to economic growth (^{Aparicio et al., 2016}). For this function to be fulfilled, universities seek to train human capital willing to take risks and participate in creating companies, placing greater emphasis on those involved in educational programs related to business administration.

The development model proposed for the countries, which began in the 1980s, focused on reducing the number of states and addressing the needs of society through the free market. This gave way to an education in which the aim is for students to have the necessary skills to tackle their professional life by implementing ventures to provide goods and services required by the population, cities and governments. As a result, new models, such as entrepreneurial ecosystems, were promoted (^{Malecki, 2018}; ^{Durazo et al., 2021}).

^{Guerrero and Urbano (2017)} note that, in the context of dynamic structural changes, such as those occurring in the political, social, and economic fields, universities become key players in promoting the development of regions by being the leading promoters of innovation and entrepreneurship. Nevertheless, they recognize the need for universities to redefine their management structure and carry out networking initiatives, update their educational programs, define support mechanisms, consolidate an entrepreneurial and innovative culture to facilitate the generation-transfer of knowledge and be aware of the social, economic and technological impact in the context (^{Fini et al., 2017}).

Studies on entrepreneurship are no longer theoretical but instead models that focus on analyzing its determining factors. These are especially useful because they permit the creation of relationships and explanations that facilitate the design of institutional business policies. Some studies include mathematical models, which provide a better understanding of the relationship between entrepreneurship and the factors that encourage it. Two main approaches to entrepreneurship have been identified: one that studies it from the perspective of young people and the other that approaches it from the viewpoint of the universities themselves. These approaches include those that make theoretical contributions and those that use mathematical factors and models.

Some studies measure entrepreneurship based on the perception of students. A particular case is represented by studies on the theory of planned behavior or entrepreneurial intention, identifying the factors that characterize an entrepreneur. In this type of study, it is common practice to use structural equation modeling (SEM), which permits the definition of constructs based on variables that measure specific skills, qualities or perceptions on a particular topic. Thus, entrepreneurship, as seen from the students' point of view, was able to be narrowed down to dimensions such as: attitude towards entrepreneurship, normative beliefs, subjective norms, perception of personal self-efficacy, perceived behavioral control, perceived risks and entrepreneurial intentions (^{Ajzen, 1985}; ^{King and Dennis, 2006}). The cases conducted using this approach include the following:

An increasing number of studies on entrepreneurship are trying to explain it using statistical models, which allow an analysis not only of each of its factors but also of the relationships generated between them. This analytical evolution has been possible thanks to models such as SEM, which have extended its application to different problems in other areas of knowledge.

Furthermore, studies on entrepreneurship exist that use theoretical-quantitative methods focused on higher education institutions and, while they are in the minority, they have been carried out using various study techniques. These studies include the following:

Studies show that entrepreneurship has been analyzed more from the perspective of students than universities, with the same frequency with respect to the use of mathematical models to explain its determining factors.

Finally, the proposal of the OECD and the European Commission (^{OECD, 2012}) is a qualitative self-evaluation instrument for European universities. This was designed taking into consideration experts' opinions and available scientific literature. It is applied online and permits obtaining information on the "ideal" situation of universities with respect to the criteria considered to be the most important for a higher education institution to be considered "entrepreneurial". This methodology reflects a theoretical model considering seven major dimensions reflecting entrepreneurial competencies.

Although the issue of higher education institutions generates considerable controversy in Mexico, both for the attempt to fit them into a single development model and for the inequalities that exist among them (type of educational system, enrollment, educational program, funding amounts, quality, coverage, dropout rate, relevance, infrastructure, faculty, geographic location, etc.), their study is relevant because the future of higher education and its salvation as an agent of development need to be rethought.

Theories on entrepreneurial universities, whether officialist or progressive currents, propose more active participation and linkage to address society's problems and train professionals capable of influencing it. However, the dominance of teaching and incipient research activities in public universities limits these objectives (^{Mendoza, 2022}; ^{Acosta, 2014}; ^{UNESCO, 2021}).

Given the lack of entrepreneurship models in the country, this study uses a methodology developed by the ^{OECD (2012)} to be applied in public universities and to identify areas of opportunity for improvement.

The relevance of the model proposed by the OECD is that it takes into account the international context and rescues the role of universities in addressing social and economic problems. Although its design and approach are not identified with Mexican public universities, it is an appropriate methodology to understand the challenges of moving towards more functional institutions identified with development.

The purpose of this research is not only limited to taking the OECD theoretical model as a reference but also to evaluate it with robust statistical tools using reliability indices in an SEM and to perform an integral analysis to obtain a version tailored to the characteristics of public universities in Mexico. In this way, the results are timely, relevant and valuable to support the design of long-term strategies with reliable information.

3. Methodology

The purpose of this research is to identify the "entrepreneurial" characteristics of public universities in Mexico that offer educational programs related to business management in order to measure their ability to adapt to the new roles demanded by society. To achieve this, the following specific objectives were proposed: to use the methodology developed by the OECD and the European Commission (^{OECD, 2012}) to measure the characteristics of an entrepreneurial university; to validate the adaptation of the study model to the local case through an SEM, and; to identify the entrepreneurial strengths and weaknesses of public universities in Mexico.

In the social sciences, SEMs represent a valuable tool to confirm theoretical models related to problems of society or its individuals so that their application is viable in different fields of knowledge. Modeling consists of identifying related variables that can explain a problem, so it is important to validate the consistency of this relationship.

In this respect, SEM allows the estimation of these latent variables that cannot be measured directly. Therefore, it is carried out using observable variables, at the same time estimating the relationship between them, thus verifying the relevance of the theoretical approach (such as the OECD methodology) with respect to an observed one (in this case, in Mexico). A multivariate statistical analysis is performed, which consists of contrasting their variance and covariance matrices, estimating both the correlation and the association between these variables and the estimation errors. In addition, it allows the graphical representation of the relationship between variables, which gives increased reliability, dependability and capacity to analyze the results (^{Arbuckle, 2020}; ^{Manzano, 2018}; ^{Schermelleh and Moosbrugger, 2003}; ^{Chin, 2013, p. 295}; ^{Ortiz and Fernandez, 2018}).

The guiding questions of the research are: what are the most important factors that characterize an entrepreneurial university? Is it possible to verify the consistency of the entrepreneurial university model through an SEM? Is it possible to identify areas of opportunity to consolidate an entrepreneurial model in public universities in Mexico? In this study, 327 professors of educational programs related to administration and business participated, of which 21 were coordinators of educational programs, 98 full-time professors and 208 hourly professors, belonging to 24 higher education institutions in 14 Mexican states. To select participants, 86 coordinators of educational programs in different public universities in the country were invited to answer the survey and share it with their professors. The information was collected through digital media between October 2021 and March 2022.

It is important to mention that the methodology defined at the international level by the OECD was validated for the results obtained in the case of Mexico through the SEM. This made it possible to adapt the theoretical model and adjust the variables considered for the case of public higher education institutions in Mexico.

The degree of institutional and cultural management of entrepreneurship in universities was evaluated based on seven dimensions, considering a total of 41 variables (5, 7, 6, 6, 7, 6, 5 and 5 for each in the OECD model). These record the perception of entrepreneurship on a scale from 1 to 10, where 10 reflects a greater consolidation of the entrepreneurial profile. In this respect, the research is based on a quantitative empirical study. The structural equation analysis was carried out with the help of the AMOS module of the SPSS (Statistical Package for the Social Sciences) software.

Various studies exist that define an entrepreneurial university (^{OECD, 2022}; ^{Boruck and Mafra, 2020}; ^{Bacigalupo, 2019}; ^{Guerrero et al., 2015}; ^{Armbruster, 2008}; ^{Etzkowitz, 2003}). However, taking into account the factors of analysis in this research, an entrepreneurial university is defined as one that recognizes itself as part of the development of its environment, measures its impact and has a physical, financial and administrative infrastructure that facilitates the interaction of its administrative staff, faculty and students with national and foreign stakeholders (business, government, social and productive organizations), to carry out joint activities that allow it to meet their needs through training, research, innovation, technology transfer, the use of knowledge and the best available methodologies, which contributes to entrepreneurship, employability and change management.

The conceptual model of this study is based on the analysis of the relationships between the following seven latent variables, which are considered characteristics of a university that successfully promotes entrepreneurship (^{OECD, 2012}):

As shown in Figure 1, the SEM of the study that represents the observed variables (rectangles) and the latent variables (ellipses) that characterize an entrepreneurial university makes it possible to show the variables that measure each dimension and how each dimension relates to the others.

Source: compiled by the author based on ^{OECD (2012)}.

Figure 1 Conceptual model for assessing the entrepreneurial profile of universities 

An advantage of SEM models over multivariate procedures is that they adopt a confirmatory approach (hypothesis testing), where structural (or regression) equations represent causal observation processes on multiple variables. This allows them to be statistically tested simultaneously and their consistency to be verified with a goodness-of-fit test where it is possible to evaluate estimation errors, thus requiring a confirmatory rather than an exploratory analysis.

It is important to recognize that one of the critical aspects in the use of SEM is to maintain the assumption of normality of the data, which is difficult to fulfill when a study is proposed with a large population (more than 250) since it increases the differences between the variance-covariance matrix of the sample and the proposed model. This problem is reflected in the non-compliance of the goodness-of-fit indices, especially the absolute ones such as Chi-square, X2 adjusted for degrees of freedom, RMSEA and RMR. To avoid this problem, it is recommended to consider additional goodness-of-fit indices such as incremental CFI, GFI, IFI, TLI, NFI or parsimony indices pGFI, pNFI, pCFI (^{Manzano, 2018}; ^{SS, 2022}; ^{Boomsma and Hoogland, 2001}; ^{Ruiz et al., 2010}). However, in this research, it was not necessary because, as a result of the adjustment of the model through confirmatory analysis and the reduction of variables, it was possible to verify the quality and significance of the relationships of the model of entrepreneurial universities, the case of public institutions in Mexico.

4. Results

The results obtained from the research are presented in three subsections: a) verification of the consistency of the dimensions of the undertaking, b) application of the SEM, andc)validation of the relationships between variables.

Validation of relationships between variables

The results show that entrepreneurial leadership, management, and entrepreneurial routes are the most consolidated dimensions. However, those dimensions related to International University and Organizational capacity of entrepreneurship show less consolidation (see Figure 2).

Source: compiled by the author using data from the entrepreneurial survey (scale from 1 to 10)

Figure 2 Perception of entrepreneurship in public universities in Mexico, by dimensión 

Meanwhile, the observed variables that allow the evaluation of entrepreneurship in Mexican public universities, according to their degree of consolidation, are shown in Table 2, where those related to the promotion of entrepreneurship are significant. However, the lack of international links, the attraction of entrepreneurial personnel and the recognition of stakeholders are less weighted.

Table 2 Variables for measuring the entrepreneurial management capacity of public universities, according to the consolidation 

Dimension	The university (is / has / promotes):	Mean	D. Est.
LyG	A driver of entrepreneurial spirit	8.82	1.64
LyG	Highly committed to entrepreneurial strategy	8.67	1.62
RE	Raises awareness of the importance of entrepreneurship	8.55	1.95
RUE	Promotes Exchange with industry, society and government	8.52	1.90
LyG	Has an entrepreneurial model	8.50	1.75
RE	Encourages people to become entrepreneurs	8.44	2.02
RUE	Demonstrates involvement in partnerships and interested parties	8.43	1.89
DEE	Staff adopts an entrepreneurial approach	8.39	1.96
DEE	Supports the development of entrepreneurial mindsets and skills	8.33	1.89
RE	Provides opportunities to experience entrepreneurship	8.33	2.10
DEE	Validates entrepreneurial learning outcomes	8.20	2.11
IUE	Evaluates participation in entrepreneurial teaching and learning	8.19	2.17
IUE	Evaluates the impact of entrepreneurial teaching and learning	8.17	2.10
RUE	Participates in activities with businesses and the external environment	8.14	2.09
IUE	Evaluates the impact of its entrepreneurial strategy	8.02	2.22
CO	Encourages entrepreneurial relationships	7.98	2.15
CO	Invests in staff development	7.86	2.38
CO	Recognizes interested parties	7.85	2.37
UII	Participates in international networks	7.84	2.38
UII	Demonstrates internationalization in its approach to teaching	7.82	2.39
UII	Seeks ot and attracts international and entrepreneurial staff	7.75	2.52

Notes: D.Est. = Standard deviation. The mean is estimated for an interval between 1 and 10. Dimensions: LyG = Leadership and Governance; CO = Organizational Capacity, People and Incentives; DEE = Entrepreneurial Development in Teaching and Learning; RE = Entrepreneurial Pathways; RUE = University-Enterprise Relationship for Knowledge Exchange; UII = Entrepreneurial University as an Internationalized Institution; IUE = Entrepreneurial University Impact.

Source: compiled by the author using SPSS v. 25 software.

Figure 3 shows the relationship (covariances or correlations) between the variables and dimensions that characterize the entrepreneurial profile of public universities, as well as the relationship between each of the dimensions. The role of the Entrepreneurial development dimension and its relationship with the rest of the dimensions (correlation) stands out. On the other hand, the International university dimension shows a lower impact with respect to the rest of the dimensions.

Chi-square = 459.4, df = 168, P-value = 0.01, RMSEA = 0.073, CFI = 0.968.

Notes: bidirectional arrows show correlations, unidirectional arrows show saturation and non-standardized error data.

Source: compiled by the author using SPSS Amos v.25 software and based on ^{OECD (2012)}.

Figure 3 Model of entrepreneurial public universities in Mexico: dimensions and variables 

With the model obtained, the relationship between the observed and latent variables (dimensions of entrepreneurship) can be analyzed in Tables 3 and 4. This is where the values of covariances, correlations and regression estimates are found, reflecting the weight of the relationship and the p-values, which are less than 0.05, confirming the relationships as significant.

Table 3 Relationships of the structural model: latent variables (dimensions of entrepreneurship) 

Relationships	Covariance	S.E.	V. C.	p	Correlation
F1 <--> F2	1.167	0.078	14.974	***	0.844
F1 <--> F4	2.134	0.207	10.333	***	0.851
F1 <--> F6	0.958	0.079	12.151	***	0.693
F1 <--> F7	1.155	0.077	15.016	***	0.836
F1 <--> F5	1.156	0.078	14.885	***	0.837
F1 <--> F3	1.256	0.077	16.399	***	0.909
F2 <--> F3	0.938	0.013	74.366	***	0.938
F3 <--> F4	1.737	0.084	20.656	***	0.957
F3 <--> F6	0.785	0.025	31.776	***	0.785
F3 <--> F7	0.875	0.016	53.743	***	0.875
F3 <--> F5	0.911	0.014	63.424	***	0.911
F2 <--> F4	1.569	0.089	17.596	***	0.864
F4 <--> F6	1.421	0.091	15.539	***	0.782
F2 <--> F6	0.831	0.021	39.286	***	0.831
F6 <--> F7	0.854	0.017	49.953	***	0.854
F5 <--> F6	0.823	0.021	38.593	***	0.823
F5 <--> F7	0.905	0.013	68.048	***	0.905
F2 <--> F5	0.886	0.017	51.514	***	0.886
F4 <--> F5	1.715	0.085	20.256	***	0.945
F2 <--> F7	0.858	0.018	46.712	***	0.858
F4 <--> F7	1.575	0.088	17.96	***	0.867

Notes: SE: Standard Error of the regression weight; V.C.: Critical ratio value of the regression; *** = 0.000. F1 = Entrepreneurial Leadership and Management, F2 = Entrepreneurial Organizational Capacity, F3 = Entrepreneurial Spirit Development, F4 = Entrepreneurial Pathways, F5 = University-Enterprise Relationship, F6 = International University, F7 = Entrepreneurial University Impact.

Source: compiled by the autor using SPSS Amos v.25 software.

Table 4 Relationships of the structural model: observed and latent variables 

Relationship	β	S.E.	V. C.	p	β Std
LyG05 <-- F1	1				0.843
LyG03 <-- F1	1.093	0.056	19.561	***	0.863
LyG02 <-- F1	1.026	0.051	20.027	***	0.875
CO03 <-- F2	1.892	0.094	20.06	***	0.882
CO05 <-- F2	2.112	0.104	20.378	***	0.890
CO07 <-- F2	2.095	0.104	20.165	***	0.885
DEE04 <-- F3	1.927	0.09	21.461	***	0.914
DEE02 <-- F3	1.718	0.086	20.086	***	0.879
DEE01 <-- F3	1.708	0.081	21.023	***	0.903
RE01 <-- F4	1				0.935
RE02 <-- F4	1.037	0.032	32.23	***	0.933
RE03 <-- F4	1.027	0.037	27.664	***	0.891
RUE04 <-- F5	1.831	0.091	20.064	***	0.879
RUE02 <-- F5	1.713	0.081	21.267	***	0.910
RUE01 <-- F5	1.746	0.081	21.642	***	0.919
UII03 <-- F6	2.387	0.104	22.871	***	0.947
UII04 <-- F6	2.273	0.098	23.087	***	0.952
UII05 <-- F6	2.191	0.1	21.873	***	0.924
IUE03 <-- F7	2.015	0.085	23.581	***	0.961
IUE02 <-- F7	2.084	0.088	23.654	***	0.963
IUE01 <-- F7	2.088	0.092	22.68	***	0.941

Notes: β= regression estimates; SE= Standard Error of the regression weight; V.C.= Critical ratio value of the regression; *** = 0.000; β Std: standardized regression estimates. F1 = Entrepreneurial Leadership and Management, F2 = Entrepreneurial Organizational Capacity, F3 = Entrepreneurial Development, F4 = Entrepreneurial Pathways, F5 = University-Enterprise Relationship, F6 = International University, F7 = Entrepreneurial University Impact.

Source: compiled by the author using SPSS Amos v.25 software.

Table 3 shows that the weakest relationships between latent variables are in the International University dimension with respect to the Entrepreneurial Leadership and Management dimension (F1-F6: 0.693), Entrepreneurial Pathways (F4-F6: 0.782) and Entrepreneurial Development (F3-F6: 0.785).

Table 4 shows a strong relationship and contribution of the observed variables with the constructs that enable the measurement of the dimensions of entrepreneurship in a public university in Mexico, with the p-values confirming this valid relationship. The coefficients that measure the relationship between the observed variables and the impact dimension of the entrepreneurial university (IUE) stand out.

5. Conclusions

This research enabled us to learn about the entrepreneurial profile of public universities in Mexico, according to the characteristics identified as "ideal" at the international level, as defined in the methodology of the OECD and the European Community. In this respect, it is worth noting that universities show strong leadership and management of entrepreneurship, where there is a declared commitment of the institution to the implementation of an entrepreneurial strategy, where the development of entrepreneurship is recognized as an agent of change (leadership and management) and as a creator of awareness of the importance of developing entrepreneurial skills among staff and students, encouraging their practice. However, the study shows that, although the public university is an entrepreneurial force, it does not have enough solid internal mechanisms to promote and launch it, such as infrastructure, incentives, training and networking.

The study also showed that entrepreneurship is a topic that tends to be increasingly crucial for the economies and institutions of Higher Education as entities that influence the training of professionals and the resolution of society's problems, but which require reforms in the model of Higher Education in Mexico to fulfill this function.

Using an SEM made it possible to validate the usefulness of the theoretical instrument for measuring the dimensions of entrepreneurship and its methodological consistency and to identify the need to adjust the number of variables used in the original model to obtain a suitable version for the local case.

Furthermore, the identified strengths were that public universities in Mexico promote links with companies, society and interested parties, which involves the participation of their professors and students (university-industry relationship dimension). However, the study also shows that efforts are needed to consolidate a consistent structure to encourage and stimulate the development of entrepreneurial mindsets and skills, which will allow the involvement of all the institution's personnel in the generation of entrepreneurial ideas and, at the same time, favor the evaluation of the results of entrepreneurship (entrepreneurial spirit development dimension).

The results reveal that public universities need to work on the mechanisms for monitoring and evaluating their entrepreneurship and the relevance of educational programs related to entrepreneurship and their relationship with the context (impact of the entrepreneurial university dimension). Finally, it is shown that public universities need to redefine or prioritize actions to implement new mechanisms to promote entrepreneurship involving professors, businesses, interested parties and students. They also need to invest in infrastructure to encourage entrepreneurship and in the development of its members (organizational capacity dimension), as well as define a financing model to launch the identified entrepreneurial initiatives (internal and external) and international networking that favor entrepreneurship through experts, institutions, both in teaching and their educational programs, as well as in research (international university dimension).

Undoubtedly, entrepreneurship is a topic with great development expectations for countries such as Mexico, with more emphasis on public higher education institutions. Therefore, progress in these studies is deemed necessary not only in social sciences and business programs but also in areas related to industrial engineering and information technologies, as well as postgraduate studies and areas of research, innovation, and technology transfer, which will allow progress to be made on an integral model of entrepreneurial universities.