Growth and Performance: Business Model Innovation in Family Firms

: A business model, defined as the underlying logic of a company, is not permanent over time. Instead, companies need to introduce innovations in the business model to be competitive in the market. This is even more critical for family firms which are continuously looking for a way to obtain sustainable growth, together with satisfactory performance. The objective of this research is to analyze the impact that business model innovation activities have in the short/long-term growth and performance of family firms. This study was obtained from panel data made up of 112 valid responses from family firms involved in business model innovation. A composite model approach has been used for data analysis. The significant components of BMI that lead to greater growth and performance are identified, the distinction between long-term and short-term effects of BMI on those outcomes is made, and BMI is proven as an authoritative source of competitive advantage and growth in family firms. Those aspects are valuable insights for researchers and managers with regards to which innovation propositions help sustain growth and performance over time.


Introduction
A business model (BM), defined as the underlying logic of a company [1], is not permanent over time [2].Therefore, companies need to innovate to be competitive in the market [3] and develop new tools to face future challenges [4].Product innovation has received extensive attention in the academic literature and is considered fundamental for improving the firm's competitive offerings and capturing the attention of customers [5].However, research on business model innovation started to take off less recently, and even today there are many questions about its impact on different types of firms and sectors [6].As a result, research on business model innovation (BMI) has received significant attention in the last fifteen years [7], searching for accurate measure of the construct [8] or exploring the connections with other variables inside the firm [9].One of the main conclusions of previous research is that BMI is not specific for new companies and entrepreneurs [10] as almost any company needs to continually transform the business model to face opportunities and threats [11].Accordingly, the authors of Ref. [12] have recently suggested making BMI a distinctive concept in differing economic contexts and types of firms.
In the contemporary dynamic business landscape, the necessity for enterprises to modify their business models as a means of securing a novel competitive advantage has become paramount.Increased globalization has brought with it an increase in business competitiveness so that companies are no longer just competing with the companies they used to compete with, but a large number of companies are now potential companies to compete with in terms of delivering value to the customer.But this requirement presents substantial challenges for organizations entrenched in traditional, long-standing operational frameworks, notably family-owned enterprises [13].In the European Union, there Businesses 2024, 4 212 are more than 17 million family businesses that employ more than 100 million workers and represent over 60% of organizations [14].These family firms represent, in many countries, more than 70% of the private workforce and generate 60% of the GDP.A vast majority of family firms are also SMEs that are also the primary source of wealth and employment in their respective countries, which stands for more than 90% of a total number of companies and over 60% of employees [15].
Family firms, often seen as traditional or conservative, tend to stick to tried-andtrue business methods due to their reliance on existing resources, inherent inertia, and organizational rigidity; added to these are challenges unique to family businesses, such as generational transitions, emotional connections, and a focus on non-financial objectives [16].These companies frequently blend both business and family ambitions, often finding these goals overlapped.This is due to the nature of this type of firm and the family character that defines them.At the heart of these non-financial ambitions lies the desire to generate and safeguard socio-emotional wealth-the intangible benefits family business owners cherish from their enterprises [17].
This could indicate that the intention to preserve socio-emotional wealth and other family priorities is deduced from decision-making in family businesses even though these decisions are not optimal from a purely financial point of view [18,19].Furthermore, these entities are also inclined towards the pursuit of non-monetary objectives that distinctly mirror the controlling family's interests, visions, and predispositions.This key motivator is indicative of the family's concerted efforts to both cultivate and maintain its socio-emotional wealth, and it not only shapes their strategic choices but also sets them apart from other organizations [20].
The aforementioned elements combine to influence how family firms approach innovation, presenting both obstacles and opportunities for growth and change in the landscape of family-owned enterprises [21,22].For most of these firms, size limits business model innovation activities, and, in turn, productivity and competitiveness are lower than in larger firms [23].Despite these facts, research related to BMI in family firms or SMEs has been limited [24], and past research has been mainly focused on large corporations or start-up companies [25].Therefore, family firms demand further knowledge on the mechanism that might help them to create wealth and employment [26] and to obtain sustainable growth and performance [27].
Firm growth is related with strategic and organizational practices [28] or managers' attitude toward growth [29], among other variables.Several family businesses rank as some of the most innovative companies globally, and innovation is seen as an essential driver of firms' growth, especially of family firms' long-term growth [30].The authors in Ref. [24] identify three innovation patterns for family businesses (conserving, persisting, and legacy-building) and therefore provide an additional view: it is the focus on long-term orientation of these firms that serves as a catalyst for innovation.In the analysis of growth, to consider the family influence is mandatory since objectives and strategies are affected by family governance [31].Family firms adopt strategies less oriented to growth.Ref. [32] mention a set of elements constraining growth in family firms: maturity of industrial sectors dominated by family firms, shortage of financial resources, reluctance to change, a discrepancy of common objectives, value, and needs, among others.Another stream of research considers the smaller size as an intentioned decision.Ref. [33] find risk aversion the reason for a conservative growth in that family wealth is concentrated in the firm.
Recent studies have recommended BMI to take a long-term perspective as a way of obtaining sustainable growth together with financial profitability [34].Prior research also suggests that the effects of innovation on growth are not immediate [35]; long time lags exist, though [36].We suggest that BMIs affect short-term and long-term growth and performance [37].Based on the review of existing literature, we have found that there are two important GAPs that need to be addressed further.Specifically, it is necessary to analyze the implications of business model innovation for family businesses due to the peculiarities of this type of organization that differentiate them from others in the industry.The findings could be critical to improve the business competitiveness of this type of company when they decide to transform their business model into a more innovative one.In addition to the above, we have found that there is a clear GAP on the repercussions that business model innovation has in the short and long term.The transformation of the logic of the business model requires time to adapt to the organization, and therefore, through this study we intend to delve deeper into the performance implications of these business initiatives, but unfortunately these types of considerations have received little attention to date in the academic literature.As a result, the objective of this research is to analyze the impact that BMI proposition activities have on the short/long-term growth and performance of family firms.This study was obtained from a dataset of 112 family firms involved in BMI activities.Data were collected through a web survey managed by a Chair of the family firm association.By applying a composite model approach, this research explores the impact of different components of business model innovation on short/long-term growth and performance of family firms.The outcomes of this study could be beneficial to focus on the most relevant topics and obtain a competitive advantage in the market in this type of firm.The remaining sections are structured as follows.Next, the literature on family firms, growth, and BMI is reviewed.Based on prior research, a conceptual model is proposed, and hypotheses are posited.Following, methodological details for the empirical study are explained.Later, results are presented and discussed.Finally, conclusions implications and future research guidelines are summarized.

Literature Review
Business model innovation focuses on how a company transforms resources and communicates value to customers [7].In this study, researchers follow [12] and define BMI as "designed, novel and nontrivial changes to the key elements of a firm's BM or architecture linking these elements."These changes, which may be new to the firm and/or new to the industry [38], are introduced into a firm's principal business activities [2] to enable new opportunities in the market [8].
Interest in innovation within family firms has surged over the past ten years, as noted by [39].Recent scholarship on family firms has expanded, applying economic theories like agency-and resource-based theories to distinguish family from non-family firms and to explore diversity within family businesses, considering subjects like family governance, family management, strategic response, intergenerational succession or innovation.
Although agency theory has been utilized to explain the heterogeneity in strategic behavioral responses of family firms [40], there is still a limited understanding of how intergenerational succession and the governance relationships between family owners and family managers impact firm behaviors, particularly in areas such as innovation.Precisely, innovation is crucial for the performance outcomes and long-term competitiveness of family firms [41], and accomplishing a successful intergenerational replacement assures the fulfilment of the objective of the long-term orientation, thereby preserving the family wealth both in economic and social terms [42].This is a key element, especially considering the fact that the majority of family firms (owned and managed by a single family) face the risk of becoming unsustainable within the first two generations of their founding [43].
The governance of the family firm is an important issue, since the success of this type of firm depends, to a great extent, on the family, its processes, its structures, and how the organization copes with disruptions [44].Family governance aims to make clear the demands and rewards of family participation in the firm, to share information to create trust and reduce manipulation by members of the family, to communicate opportunities for involvement in the family firm, and to cultivate a sense of belonging to the firm among the extended family [45].
Assuming the above, as stated by Chrisman et al. [46], yet a tailored economic theory for family businesses remains elusive, and general economic models fall short as they overlook unique elements of family firms, notably their pursuit of socio-emotional wealth.In fact, there is no dominant consensus on the classification of family firms, and although multiple categories have been established in order to classify and understand the behavior of family businesses, these same categories fail to explain aspects related to strategy and performance in family firms [47].
Despite the importance of BMI and family firms for the economy, there are hardly any studies that combine these two-BMI and family businesses [48].Family firms perform differently [49], and research typically considers family businesses as traditional and risk-averse [26], valuing more stability and a conservative approach instead of innovativeness [50].Recent research has delved into the component of socio-emotional wealth as a determining factor for family businesses, harming collaboration with external agents to protect their business even in cases where the economic reward was clearly greater [51].Most prior research on innovation within family firms has focused on other types of innovations [31], namely product, process, organizational and managerial innovations, neglecting the analysis of BMI.
Family involvement differentiates family firms from another type of firm [52].This idiosyncrasy has been labeled as familiness, referring to the set of resources and capabilities that originated from the interaction of family and firm [53].Due to their peculiarities, family firms are long-term-oriented, less likely to grow and present in traditional industries where competence is intense.Pittino and Visintin [54] studied innovation strategies in family firms in Italy.Using Miles and Snow's strategic typologies, they found that high scores of BMI are present in family firms categorized as Prospectors and Analyzers.Chrisman et al. [55], in turn, conceptually studied the ability and willingness to innovate technology in family firms in comparison to non-family firms.A review on technological innovation research in family businesses by De Massis et al. [56] includes one article on BMI in family firms in their analysis, but the review does not mention BMI elsewhere throughout the study.However, as previously stated, there has been a significant lack of research regarding BMI in family firms, and accordingly, it is difficult to propose valuable recommendations for this type of firm.
Business models are heavily dependent on the joint strategic orientations of the industry and also on the circumstances in which the firm was created and developed [2].These factors are capital in family businesses due to a higher presence in mature industries with more intense competition [31].BM is a source of competitive advantage and driver of performance [57].BMI embraces the analysis of changes in the business model to improve competitiveness and outcomes with hardly any empirical works [12].As stated by Clauss [7], business model innovation needs support from top management as it cannot be considered as minor modifications in single BM elements.In their work, Kraus, Pohjola, and Koponen [50] put forward the influence of managerial innovations on corporate success in family firms.Frequently, when BMI occurs, the change in BM elements due to path dependency [58] and interactions among individual BM components [3] will have a positive impact on performance.Based on these arguments, we propose the following hypothesis: H1.Business model innovation will have a positive impact on short-term performance.
BMI has been shown as a valid mechanism to impact firm's growth [59].Empirical research proving the impact of BMI on growth is, however, scarce and limited [60].A limited number of studies around BMI and growth have considered BM design (efficiency or novelty) [61] or BMI replication [62] on firm's growth.Moreover, prior research is limited to non-family firms, forgetting the importance of family businesses in most economies [63].Conceptually, innovation is seen as an essential driver of firms' growth [30].Innovative family firms can grow markets and generate profits [15].In family firms, managers are looking for innovations with a social impact on their local community, growth, and wealth [32].A vast majority of family firms are older than SMEs' average age [27].Prior research suggests that older firms may suffer from several drawbacks that hinder their ability to innovate and to translate R&D investment into higher growth [64] rates due to organizational inertia [36].Hamelin [33] confirms a negative relationship between family ownership and small business growth.Nonetheless, the findings of Brenner and Schimke [65] revealed that innovation is acknowledged as one of the critical drivers of firm growth.Accordingly, we propose: H2.Business model innovation will have a positive impact on short-term growth.
Short-term growth is a critical indicator of entrepreneurship success, especially for SMEs [66].Short-term growth is essential for established firms [67] to survive in the market.Most new firms follow the same pattern; an entrepreneur with scarce resources creates a firm where family support is essential [31].Additionally, family firms try to keep low levels of debt to avoid harming their reputation and losing all their economic wealth [33].Reluctance to incorporate external capital and managerial capabilities constrain growth capacity [63].Successful companies had been able to adapt their business model to changes in the environment and competition [62].Based on these arguments, we propose the following hypothesis: H3.Short-term growth will have a positive impact on short-term performance.
Despite the fact that product innovations and BMI are not the same [10], a similar approach could be adopted for studying the effects of BMI on performance and growth [64].BMI takes time to leverage [2], and making a distinction between short-term and long-term effects on performance and growth may make sense [37].Beyond the actual influence of scarce financial resources, family firms deliberately limit their growth or produce peculiar growth behavior (conservative growth behavior) [33].The underlying reasons consist of family wealth at risk, long-term orientation, and founder's motivations [31].The former refers to the concern for employees' well-being, a loss of small business atmosphere, the fact that for some owners just being in business is success enough [68], as well as lifestyle choices [24].Some owners cite deliberate "lifestyle" choices [68], expecting little or no growth.Consequently, lifestyle-oriented SMEs can be conceptualized as businesses set up [60] to undertake an activity that provides adequate income to the owner.Accordingly, we propose: H4.Short-term performance will have a positive impact on Long-term growth.
A firm's growth is considered a key indicator of entrepreneurial success [66,69], but knowledge about the relationship between firm characteristics and enduring firm growth is rare [65].In product innovation literature, there have been exciting studies distinguishing short-term and long-term performance in different contexts: product development process [70], communication strategy [71], or competitive positioning [37].Indeed, Molina-Castillo and Munuera-Alemán [72] have demonstrated that the importance managers give to various performance indicators in the short term differs from the importance they give to long-term performance indicators.Therefore, the short-term and long-term performance measures provide a useful contextual factor in the analysis of performance [37].BMI is considered a source of firms' competitive advantage [73] and proven as a significant driver of higher firm performance [74].Accordingly, in today's dynamic environments, BMI is essential to survive [75] and sustain a competitive advantage [76] in the market in the long run.Moreover, long-term orientation and the desire to pass the firm to the next generation lead them to offer high-quality services/products [24] and to create long-lasting ties with stakeholders (employees, customers, suppliers, and local communities).Based on these arguments, we propose the following hypothesis: H5.Long-term growth will have a positive impact on long-term performance.
The proposed model is depicted in Figure 1: H5.Long-term growth will have a positive impact on long-term performance.
The proposed model is depicted in Figure 1:

Sample
The dataset was collected from an online panel that is frequently used for this type of study.The sample used in this study comprises 112 SME Spanish family firms.It was decided to choose Spanish firms for three reasons.First, in the Spanish economy, family companies are dominant.Casillas et al. [77] indicate that family firms, which represent 90% of private firms, account for 85% of the private workforce.In the second place, the Spanish economy is relevant to the OECD.In 2021, Spanish gross domestic product per capita was 23rd among the 38 OECD countries OECD [78,79].Finally, the researcher's proximity to Spanish companies enables them to gain a deeper understanding of the research objectives.
Data were collected through an online survey managed by a Chair of a family firm as a part of the Observatory of Family Firm, a project aiming to measure outcomes and expectations twice a year.The panel of participants is made up of 200 firms.In addition to permanent questions each semester, a specific topic is analyzed.Information for this research comes from the study of strategy and business model.The survey included all the items to measure the variables and an ethics and confidentiality statement for data treatment.Complementary data were extracted from the OSIRIS database (Van Dyck Bureau of Electronic Publishing).Therefore, sample representativeness is guaranteed.The sample consists of companies working in different industries: service providers (33%), trade (24%), manufacturing (30%), and construction (13%).Regarding the firm's size, 40% of surveyed family firms are micro-sized, while 60% are SMEs.The average firm's age is 34 years.Prior to data collection, the questionnaire was reviewed by several academics and business people who validated the understanding of the different questions asked.

Measures
Measures used were taken from previous studies (Appendix A).Due to the characteristics of the scales used, we have used a brand-new software (ADANCO) 2.4 for composite modeling that brings the possibility to analyze the short-term and long-term impact of BMI by using a composite approach in the measures.
The scale to measure BMI was based on Osterwalder et al. [80] and Taran, Boer, and Lindgren [38].Specifically, BMI was defined as changes the company has performed in the last five years in Osterwalder's components of BM by identifying one construct including resource assignment, channels, customers' relationships, key resources, and partners in the organization.Regarding growth, measurement scale refers to the number of

Sample
The dataset was collected from an online panel that is frequently used for this type of study.The sample used in this study comprises 112 SME Spanish family firms.It was decided to choose Spanish firms for three reasons.First, in the Spanish economy, family companies are dominant.Casillas et al. [77] indicate that family firms, which represent 90% of private firms, account for 85% of the private workforce.In the second place, the Spanish economy is relevant to the OECD.In 2021, Spanish gross domestic product per capita was 23rd among the 38 OECD countries OECD [78,79].Finally, the researcher's proximity to Spanish companies enables them to gain a deeper understanding of the research objectives.
Data were collected through an online survey managed by a Chair of a family firm as a part of the Observatory of Family Firm, a project aiming to measure outcomes and expectations twice a year.The panel of participants is made up of 200 firms.In addition to permanent questions each semester, a specific topic is analyzed.Information for this research comes from the study of strategy and business model.The survey included all the items to measure the variables and an ethics and confidentiality statement for data treatment.Complementary data were extracted from the OSIRIS database (Van Dyck Bureau of Electronic Publishing).Therefore, sample representativeness is guaranteed.The sample consists of companies working in different industries: service providers (33%), trade (24%), manufacturing (30%), and construction (13%).Regarding the firm's size, 40% of surveyed family firms are micro-sized, while 60% are SMEs.The average firm's age is 34 years.Prior to data collection, the questionnaire was reviewed by several academics and business people who validated the understanding of the different questions asked.

Measures
Measures used were taken from previous studies (Appendix A).Due to the characteristics of the scales used, we have used a brand-new software (ADANCO) 2.4 for composite modeling that brings the possibility to analyze the short-term and long-term impact of BMI by using a composite approach in the measures.
The scale to measure BMI was based on Osterwalder et al. [80] and Taran, Boer, and Lindgren [38].Specifically, BMI was defined as changes the company has performed in the last five years in Osterwalder's components of BM by identifying one construct including resource assignment, channels, customers' relationships, key resources, and partners in the organization.Regarding growth, measurement scale refers to the number of changes in clients and markets [65].Performance was assessed by means of sales turnover and return on investment based on the recommendations of several authors [72,81].The distinction between short term and long term is consistent with the time frame recommended by [37,82] and therefore evaluated the last five years and the next five years as short term and long term.Finally, environmental turbulence [83] was introduced as a control variable and accounted for the environmental turbulence at a national, regional, and sector level of each firm.
The research team used the composite approach, as suggested by van Riel et al. [84].Recently, authors have increased their attention in the so-called composite measures where a composite construct is assumed to be composed by its indicators [85].Thus, the composite construct is made up of the indicators.The model fit was very satisfactory, with SRMR below the recommendations of the literature as well as the Dijkstra-Henseler's ρA.Convergent validity was confirmed.As can be observed in Table 1, all items were significant and with t-values above the recommended cut-off points.Discriminant validity among multi-item measures was assessed using the comparison of square root of Ave with correlations [86] as well as confidence intervals [87].Both methods are still recommended in most studies.However, we also included more advanced techniques, such as the HTMT method that confirmed that discriminant validity did not threaten our analysis [88].We have checked for the reliability and validity of our measures, confirming the quality of the scales used (Tables 1 and 2).

Results
After performing data analyses to test the reliability and validity of the scales used to measure main constructs, structural models with Adanco software 20.0 were tested, and they showed interesting results with regards to the impact of BMI on growth and performance (Figure 2).

Results
After performing data analyses to test the reliability and validity of the scales used to measure main constructs, structural models with Adanco software 20.0 were tested, and they showed interesting results with regards to the impact of BMI on growth and performance (Figure 2).This research focuses on BMI as a way to align innovation, resources, capabilities, objectives, and firm strategy.Additionally, growth is considered as a means to improve performance [69].Prior research had difficulties in identifying a significant impact of innovation efforts on firm growth.For instance, Brenner and Schimke [65] reviewed the literature concerning the impact of innovation on growth, finding that innovation is acknowledged as one of the critical drivers of firm performance and growth.Recent research such as Hacklin et al. [89] provides evidence on the financial outcomes of BMI in terms of firm growth.On the contrary, Hamelin [33] confirms a negative relationship between family ownership and small business growth.Our structural model proves that BMI has a significant favorable influence on firm growth, both in the short term and in the long term, thus contributing to academic research and managerial practice.Table 3 summarizes the support for the posited hypotheses.
The results obtained show that the temporal consideration of the impact of business model innovation is very important to analyze the consequences on the performance and growth of the company.As can be seen, all of the relationships presented offered significant coefficients in accordance with the hypotheses proposed.In the same way, the R 2 values of the explained variables are very acceptable and explain an important part of performance.
Specifically, the results show that significant components that change to increase growth and performance are those linked to firms' relationships with customers and partners together with the corresponding resources assignment.Whereas, there are no changes in value proposition nor customer segments.These results are consistent with a more extended strategy of SMEs and family firms focused on specialization and closeness with customers.This BMI produces growth in the number of customers and markets, i.e., expand their base of customers with no changes in value offering and activities.That finding supports the idea that high-growth firms are proactive in selecting partners that grow This research focuses on BMI as a way to align innovation, resources, capabilities, objectives, and firm strategy.Additionally, growth is considered as a means to improve performance [69].Prior research had difficulties in identifying a significant impact of innovation efforts on firm growth.For instance, Brenner and Schimke [65] reviewed the literature concerning the impact of innovation on growth, finding that innovation is acknowledged as one of the critical drivers of firm performance and growth.Recent research such as Hacklin et al. [89] provides evidence on the financial outcomes of BMI in terms of firm growth.On the contrary, Hamelin [33] confirms a negative relationship between family ownership and small business growth.Our structural model proves that BMI has a significant favorable influence on firm growth, both in the short term and in the long term, thus contributing to academic research and managerial practice.Table 3 summarizes the support for the posited hypotheses.

Hypothesis Result
H1: Business model innovation will have a positive impact on short-term performance.Supported H2: Business model innovation will have a positive impact on short-term growth.Supported H3: Short-term growth will have a positive impact on short-term performance.Supported H4: Short-term performance will have a positive impact on long-term growth.Supported H5: Long-term growth will have a positive impact on long-term performance.Supported The results obtained show that the temporal consideration of the impact of business model innovation is very important to analyze the consequences on the performance and growth of the company.As can be seen, all of the relationships presented offered significant coefficients in accordance with the hypotheses proposed.In the same way, the R 2 values of the explained variables are very acceptable and explain an important part of performance.
Specifically, the results show that significant components that change to increase growth and performance are those linked to firms' relationships with customers and partners together with the corresponding resources assignment.Whereas, there are no changes in value proposition nor customer segments.These results are consistent with a more extended strategy of SMEs and family firms focused on specialization and closeness with customers.This BMI produces growth in the number of customers and markets, i.e., expand their base of customers with no changes in value offering and activities.That finding supports the idea that high-growth firms are proactive in selecting partners that grow with them [90].Also, Hacklin, Björkdahl, and Wallin [89] and Brink [27] recently reported how successful firms like Apple or high-growth SMEs, respectively, implemented BMI through partnering with other companies and achieved remarkable firm growth.
A primary contribution of the present research is the distinction between short-term and long-term effects of BMI, growth, and performance.Our findings support the idea that family firms' long-term view embraces both the past and the future [24].Specifically, we find that changes in current BM (BMI) have and will have an impact on growth and performance both in the short term and in the long term.
In sum, the results suggest that BMI is an authoritative source of competitive advantage [73] and growth in family firms.Our findings support the idea that SMEs' complementary proximities of geographical, organizational, temporal, technical, cognitive, vision, and primarily virtual proximities are essential for innovation and growth providing predominantly robustness of the SMEs [27].

Discussion
Due to the high interest of policymakers in identifying and supporting innovative SMEs that generate employment and promote economic growth, our research contributes to the knowledge of the strategies followed by family SMEs growing and improving their performance.Moreno and Casillas [60] found that growth is heavily dependent on slack (unallocated) resources within the firm.Following the recommendation by Arora and Dharwadkar [91], changing key resources in the business model contributes to performance directly and through growth.Resources need to show high discretion, providing both available and potential slack.In most economic literature, growth attitude is taken for granted, but in the small business context, founders' attitudes and objectives need to be considered [29].A large number of SMEs are not ready to grow but perceive themselves as successful [68].
Economic growth relying excessively upon non-family SMEs might be risky [92].Therefore, studying the unique, innovative behavior of family firms contributes to understanding the links between BMI, growth, and performance.Also, we distinguish direct and indirect effects on both short-term and also long-term variables.
The academic and practical contributions of the study deal with (1) the identification of the significant components of BMI that lead to greater growth and performance, (2) the distinction between long-term and short-term effects of BMI on those outcomes, and (3) the proof that BMI is an authoritative source of competitive advantage and growth in family firms.Those aspects are valuable insights for researchers and managers.
Our research focuses only on two of the sub-dimensions of business models as stated by Clauss [7], value proposition and value creation, which consider new channels for distribution/communication, relationships with customers, vital resources, and critical partners.However, contributions in the literature have suggested that other main dimensions of a business model, such as value capture, could influence the firm's growth and performance.As many companies combine business model innovations with other types of innovations, further studies are needed to understand the antecedents and effects of combining several innovations (BMI, product innovation, process innovations, etc.).Exploring differences between product and service companies is beyond our scope, but it might be interesting to consider variations in our analysis among countries or types of firms (depending on the firm's size and age).

Limitations and Future Research
We acknowledge that our study suffers from some limitations.Due to the nature of this research, it was not possible to consider all variables around BMI, and therefore, it will also be advisable to explore other consequences of BMI on competitive advantage [73], survival [75], or sustainability [76].Although we focus on family firms' BMI, growth, and performance in the short term and the long term using a set of performance measures, further research should compare the specific behavior towards innovation in family versus non-family firms in order to provide the needed insights to confirm and confront the results with other performance measures such as ROE and ROS [9].Analogously, following the line of exploring the repercussions that innovation in the business model has on business results at different moments in time, it would be interesting to carry out longitudinal studies that would allow for measuring the variables in different years.This type of work has an added difficulty due to the need for the companies themselves to answer the questions posed on more than one occasion, but it would undoubtedly help to shed light on the repercussions that business model innovation has on the performance and growth of family businesses.We are aware that data collection in a single country is also a limitation.However, it is also an opportunity to isolate those external factors that could alter the results most directly related to BMI activities.However, to overcome this limitation, it would be interesting to replicate this study in other countries.From a business perspective, there is a need to adapt to internal and external changes to remain competitive [12].Companies are aware of the increased competitive rivalry brought about by the increasing globalization of markets.Therefore, innovating the business model is considered a crucial variable to maintain market position.Family governance has been found to influence different business decisions [24] and should be further analyzed to see what impact it has on family businesses [61].Family firms exhibit some peculiarities in their strategic orientations in that they try to exploit their unique resources [63].Previous arguments drive us to claim for the need to tailor the tools of business modeling to fit the idiosyncrasy of family firms [26].But the research shows that there is still a long way to go before business model innovation is generally accepted by such companies.In addition, to help family firms to survive and keep their firms over time, existing tools need to be reviewed, and possibly some new tools might be developed.In the last years, a growing number of BMI studies [25] have emerged to help firms to reshape their business projects and be more competitive in the market.For example, previous reports alert that SMEs suffer from lower productivity due to a lack of innovation resources [93], and therefore, new tools to innovate in business models will help firms to remain competitive in the market.
Levels of significance.

Table 3 .
Synthesis of hypotheses support.