1. Introduction

Innovation studies at the firm level have made significant strides in integrating the logics of technological change, competition, and industrial organization. Over the past several decades, a substantial body of empirical and theoretical research has contributed to this approach, resulting in a deeper understanding of the complexity of innovation. This understanding extends beyond individual firms to encompass sectoral and regional aggregated levels, providing a comprehensive perspective on innovation dynamics.

Empirical research on innovation has been strengthened through the widespread implementation of National Innovation Surveys since the early 1990s. These surveys have undergone continuous updates and improvements, incorporating insights from influential manuals such as the Frascati Manual (OECD, 1963), the Oslo Manual (OECD, 1992), and the Bogotá Manual (JARAMILLO; LUGONES; SALAZAR, 2001). These key contributions have facilitated the use of comparable evidence on industrial innovative activity, allowing for cross-temporal and cross-national analysis. The availability of such comprehensive data has greatly enhanced our understanding of innovation processes and outcomes across different industries and countries.

The literature recognizes that drivers that foster innovation, such as formal training, capital investments, and institutional collaborations, are critical for achieving innovative success (CASSIMAN; VEUGELERS, 2006). In spite of this, the evidence on the innovative performance (IP) of industrial firms remains varied, and the relationship between firm size and innovation is still a subject of extensive examination. Some studies support a positive relationship, emphasizing the advantages larger firms have in terms of resources and capabilities (GALBRAITH, 1952; MANSFIELD, 1963; SCHERER; ROSS, 1990; COHEN; LEVINTHAL, 1989). In contrast, others suggest a negative relationship, highlighting the agility and entrepreneurial spirit of smaller firms (ACS; AUDRETSCH, 1988; TEPLOV; ALBATS; PODMETINA, 2019; PARRILLI; BALAVAC; RADICIC, 2020).

This variability and heterogeneity regarding the relationship between innovative performance and firm size have been extensively highlighted in different works (BECHEIKH; LANDRY; AMARA, 2006; HALL; MAIRESSE, 2006; SANTOS et al., 2015). However, academic consensus largely favors the idea of a positive relationship between IP and firm size, particularly in light of the role played by research and development (R&D), technological capacities, and learning efforts (COHEN, 2010; DAMANPOUR, 2010; KNOTT; VIEREGGER, 2020).

Empirical results can vary due to differences in data, measurement choices, or analytical methods. This paper introduces a Meta-Regression Analysis (MRA) approach to explain such phenomena, focusing on the evaluation of key empirical findings considering the specific features of each study. MRA is a quantitative method that synthesizes accumulated empirical evidence, such as regression model results or statistical data from existing academic literature (STANLEY; DOUCOULIAGOS, 2012; UGUR et al., 2015). This method allows for the identification of patterns and the quantification of average effects while accounting for heterogeneity across studies.

In this study, we analyze 655 comparable econometric results found in 95 articles in the field of the economics of innovation, all published between 1993 and 2017. These studies, all built upon econometric evidence, provide various inquiries into the relationship between firm size and innovative performance.

The primary objective of this paper is to identify key factors contributing to the observed variability in empirical evidence regarding the relationship between innovative performance (IP) and firm size. Specifically, we aim to test two hypotheses: H1 posits that firm size is positively related to innovative performance due to economies of scale in R&D investment and greater resource availability. H2 suggests that the relationship between firm size and innovative performance is moderated by contextual and methodological factors, such as measurement choices, type of innovation, and geographic context, which contribute to the heterogeneity observed in empirical results. To test these hypotheses, we provide meta-regression estimations derived from existing research that analyzes how product and process innovations relate to firm size and other explanatory variables.

Our results confirm a positive and statistically significant relationship between firm size and innovative performance, in spite of the observed heterogeneity derived from the analyzed literature. We argue that this heterogeneity can be partially explained by firms' characteristics and empirical strategies developed by researchers, particularly in the way in which IP and size are measured (GRAZZI; PIETROBELLI, 2016; STANLEY; JARRELL, 2005; BACHMANN et al., 2021).

This study contributes to the literature by providing a comprehensive meta-analysis of the relationship between firm size and innovative performance. By incorporating a broader range of studies and effect sizes, and by introducing new moderator variables, this research offers fresh insights into the complex dynamics of firm size and innovation. Our analysis not only consolidates existing findings but also illuminates potential avenues for future research in exploring the determinants of divergent results in this area of study.

The rest of the paper is organized as follows. Section 2 provides the theoretical framework for innovation and presents our hypotheses. Methodology is detailed in Section 3, including the data collection process and the meta-regression analysis approach. Section 4 presents a description of the data and econometric results. Finally, Section 5 discusses the implications, and Section 6 concludes.

2. Theoretical framework

Technological change has long been recognized as a crucial driver of economic development (YOUNG, 1928; SCHUMPETER, 1934, 1942; NELSON; WINTER, 1982). In this context, technology is seen as a result of accumulated knowledge that enhances efficiency in firms' activities (ANTONELLI; SCELLATO, 2013; MONTOBBIO; KATAISHI, 2014). Innovation, defined as the introduction of new products or processes, is expected to have positive impacts on competitive performance and productivity (MORRIS, 2018). Empirical evidence supports a clear relationship between technological progress and economic performance at the firm level (BOWEN; ROSTAMI; STEEL, 2010; ROSENBUSCH; BRINCKMANN; BAUSCH, 2011; ROUSSEAU et al., 2016; SANTOS et al., 2015), sectoral level (KATZ; STUMPO, 2001; LALL, 2000; MALERBA; ORSENIGO, 1997; MALERBA, 2003), and national level (LUNDVALL, 1992; MALERBA, 2003; CASSIOLATO et al., 2013).

The theoretical foundation for understanding innovation at the firm level can be traced back to Schumpeter (1934, 1942), who emphasized the role of entrepreneurs and innovation as engines of economic growth. In his 1942 work, Schumpeter shifted the focus from individual entrepreneurs to R&D investments within corporations, highlighting how organized efforts in research and development drive technological advancements and economic progress. However, it is important to note that Schumpeter's influence primarily pertains to market structure and entrepreneurial roles in innovation, whereas the specific focus on firm size in innovation research was introduced by Galbraith (1952). This perspective underscores the importance of institutional structures and corporate strategies in fostering innovation. Galbraith (1952) further expanded this line of thought by highlighting the significance of firm size in innovation, arguing that larger firms possess advantages due to their ability to finance and manage large-scale R&D projects. According to this perspective, economies of scale in R&D and the capacity to absorb risks make large firms more innovative (MANSFIELD, 1963; SCHERER; ROSS, 1990).

This argument for a positive relationship between firm size and innovative performance is further elaborated through several theoretical considerations. Firstly, larger firms can spread the fixed costs of R&D over a greater output and have more diversified portfolios, allowing them to exploit economies of scale and scope in innovation activities (GALBRAITH, 1952; SCHERER; ROSS, 1990). Secondly, big firms possess greater financial resources, enabling them to invest more in R&D and innovation projects (COHEN; LEVINTHAL, 1989). Mediating factors such as organizational structure and decision-making processes also play a crucial role in determining how firm size impacts innovative performance. Larger firms may have more complex hierarchical structures, which can either facilitate or hinder innovation depending on the efficiency of their internal processes. Additionally, the technological life cycle of products can influence the innovation strategies of firms. In the early stages of a technology's development, smaller firms may lead with radical innovations, while larger firms might dominate in later stages with incremental improvements and scaling. The continuity or discontinuity of technical change also affects whether larger or smaller firms have the upper hand in driving innovation within different sectors.

Furthermore, larger firms have a higher probability of acquiring patents, absorbing smaller firms, and appropriating innovation rents, which enhances their innovative capabilities and market positioning (HALL; ZIEDONIS, 2001). The ability to attract and retain highly qualified human resources is another critical factor. Big firms often offer better compensation and possess stronger reputations, making them more attractive to top talent. The quality of human resources is strongly associated with the types of technologies and investments firms pursue, thereby reinforcing the link between firm size and innovation (CASSIOLATO; LASTRES, 2000; KATAISHI; BRIXNER, 2023). Moreover, large firms benefit from complementary assets, including sophisticated marketing channels, established customer bases, and extensive distribution networks, which facilitate the successful commercialization of new products and processes. The integration of complementary assets ensures that innovations are not only developed but also effectively brought to market, thereby maximizing their economic impact (TEECE, 1986). Additionally, sectoral and geographical factors further contextualize the relationship between firm size and innovative performance. In high-tech sectors, larger firms may have the resources to invest in cutting-edge technologies, whereas in traditional sectors, smaller firms might excel in niche innovations. Similarly, firms in developed countries may face different competitive and regulatory environments compared to those in developing countries, influencing their innovation capabilities and strategies. All of these factors contribute to larger firms having higher absorptive capacity, allowing them to recognize, assimilate, and apply external knowledge more effectively than smaller firms (COHEN; LEVINTHAL, 1989; ZAHRA; NIELSEN, 2002; AUDRETSCH; LEHMANN, 2005).

Building upon these theoretical foundations, empirical studies have found that firm size positively influences innovative performance, particularly when innovation is measured by inputs such as R&D expenditure or patents (CAMISÓN et al., 2002; DAMANPOUR, 2010; KNOTT; VIEREGGER, 2020; BACHMANN; KATAISHI, 2020). This position is supported by a robust body of research that consistently demonstrates the advantages larger firms possess in fostering innovation through resource allocation, strategic investments, and capacity for knowledge absorption.

Contrarily, other theoretical perspectives argue for a negative relationship between firm size and innovative performance. Larger firms may suffer from bureaucratic rigidity, slowing decision-making processes and reducing flexibility, which can hinder innovation (ROTHWELL; ZEGVELD, 1982; CRETINI; ROBERT, 2022). In contrast, small and medium-sized enterprises (SMEs) may be more agile and responsive to market changes, allowing them to innovate more rapidly in niche markets (FORÉS; CAMISÓN, 2016). SMEs may favor radical innovation, while larger firms prioritize incremental improvements, with both firm types demonstrating a preference for knowledge at different stages of maturity (ACS; AUDRETSCH, 1988).

Additionally, evidence suggests that the link between firm size and innovation is more nuanced and context-specific than previously believed (LAFORET, 2013). This complexity is illustrated by a minority of findings indicating that in specific scenarios, smaller enterprises demonstrate higher rates of innovation, especially when measured by outcomes like the introduction of new products (ROTHWELL; ZEGVELD, 1982; ACS; AUDRETSCH, 1988;). It's worth noting, however, that these observations often pertain to specialized sectors and emerging technologies, rather than widely adopted innovations (NOTEBOOM, 1994).

Following this path, some studies suggest that the relationship between firm size and innovative performance is non-linear or moderated by other factors. Technological regimes, market structure, and competition can influence the incentives for firms of different sizes to innovate (DOSI, 1982; MALERBA; ORSENIGO, 1997; DAMANPOUR, 2010), while participation in networks, clusters, and alliances can affect innovation outcomes irrespective of firm size (DEBRESSON, 1989; KATAISHI; MORERO, 2020).

Firm size measurement can be operationalized using various indicators, including, but not limited to, the number of employees, sales revenue, and total assets. Each measure captures different aspects of firm size, potentially influencing its relationship with innovation. For instance, the number of employees often reflects the scale of operations and workforce size, while sales revenue typically indicates market size and financial capacity. Similarly, innovative performance is measured using diverse approaches, such as input and output indicators. Common innovation inputs include R&D expenditure and the number of R&D personnel, representing the financial and human capital devoted to innovation activities. Innovation outputs frequently encompass patents granted, new product introductions, and innovation sales, reflecting the tangible outcomes of innovation efforts. For example, R&D expenditure is often positively associated with firm size as larger firms can allocate more resources to extensive research and development initiatives. In contrast, patents and product innovation may exhibit a negative association with firm size in certain contexts, as smaller firms might be more agile in developing and commercializing innovative products due to their flexibility and focus on niche markets. These measurement choices may lead to varying results, as input measures tend to show stronger relationships with firm size due to larger firms' greater resources, while output measures might capture the effectiveness of innovation processes, potentially favoring smaller firms in some contexts (NOTEBOOM, 1994; MALERBA, 2003; BACHMANN; KATAISHI, 2020). It's important to note that these examples represent common approaches, but the range of measurement methods in the literature is extensive and evolving (BECHEIKH et al., 2006; CRETINI; ROBERT, 2022).

Based on the theoretical perspectives discussed, we formulate two main hypotheses. The first hypothesis posits that firm size is positively related to innovative performance due to recurrently stressed explanatory factors, such as economies of scale in R&D investment, greater resource availability, enhanced ability to acquire patents, absorb smaller firms, appropriate innovation rents, and the capacity to attract and retain highly qualified human resources. The second hypothesis suggests that the relationship between firm size and innovative performance is moderated by contextual and methodological factors, including industry characteristics, technological regimes, market competition, measurement choices, and econometric specifications, thereby contributing to the heterogeneity observed in empirical studies. These hypotheses guide our meta-regression analysis, aiming to uncover the underlying factors that contribute to the variability in empirical findings regarding the firm size–innovation nexus.

3. Data and methods

MRA technique enables systematic summaries based on quantitative (econometric) empirical evidence (NELSON; KENNEDY, 2009). This method relies on statistical information provided by scientific sources (papers, books, working papers) looking for answers to three main questions: What is the average (or “genuine”) effect size? Can we identify sources of heterogeneity beyond sample error in the evidence? Thus, the population is composed of papers that study IP-size relations making use of (one or several) econometric models from 1993 until 2017. To promote replicability, all analyses were conducted using the open-source programming language R (version 4.1). The code used for these analyses is publicly available, allowing researchers to reproduce our findings¹. To achieve a representative sample, this research implemented a wide search followed by a data filter, excluding papers that didn’t implement econometric exercises relating IP with firm size (qualitative studies, inverse effect-size studies). Besides structural information (such as number of observations), the data also contains information regarding the IP-size estimator, standard errors, and other papers features, such as region, date, and other model specifications (DIMOS; PUGH, 2016; ROUSSEAU et al., 2016). The analysis period from 1993 to 2017 was chosen to capture over two decades of empirical research on firm size and innovative performance, reflecting significant developments in innovation theory and econometric methodologies.

3.1 Meta-Regression Analysis

Meta-Regression Analysis (MRA) is a specialized technique that enables the scrutiny of statistically significant effect sizes, which are metrics that quantify the association between two variables and their distribution within a population (NELSON; KENNEDY, 2009). One of the key features of MRA is the use of Partial Correlation Coefficients (PCC). These are considered homogeneous effect sizes derived from primary regression coefficients. Importantly, PCCs lack a measurement unit, but they are valuable for indicating both the magnitude and direction of statistical associations (DIMOS; PUGH, 2016; STANLEY; DOUCOULIAGOS, 2012). The PCC and its standard error are mathematically defined as follows:

Where t is the statistical value of the significance test and df are the estimate’s degrees of freedom (ALOE; THOMPSON, 2013; DIMOS; PUGH, 2016). PCCs are typically assumed to be unbiased and normally distributed, with mean β₀ and variance v_i (VIECHTBAUER, 2010). As so, estimation of the average effect size is given by:

Here, PCC is the effect size on each paper i, β₀ is the average effect size and e_i∼N(0; v_i) is the error term. This approach aggregates each result considered in the analysis, where every effect size refers to a single population parameter and is called homogeneous effect model². If equation [3] is heteroscedastic, an error correction through Weighted Least Squares (WLS) is required. In this paper we use the inverse of PCC variance (w_i=1/v_i) as a weighing strategy, which gives higher relevance to regression estimates that show more precision (RICE; HIGGINS; LUMLEY, 2018).

Heterogeneity of effect sizes is measured by a Q test, which is essentially a chi-squared test with the null H₀: PCC₁=…=PCC_n (VIECHTBAUER, 2007). The rejection of the null hypothesis provides evidence of heterogeneity (that goes beyond sampling error). Homogeneous effect sizes rarely apply in social sciences, because effect sizes can usually differ from a single average result. In this case, the unobservable u_i is added to the model (HIGGINS; THOMPSON; SPIEGELHALTER, 2009; RHODES, 2012) to take that effect into account. Consequently, we get PCC_i∼0(β₀; τ²+v_i) with τ² representing the variance between papers or its heterogeneity level. This leads to the heterogeneous effects model³:

Where u_i∼N(0; τ²) and e_i∼N(0; v_i) are the additive error terms that assume Cov(e_i; u_i) = 0. Since total variance is defined as τ²+v_i, average effect estimation weighting stands as w_i=1/(τ²+v_i).

Equations [3] and [4] are the simplest, univariate models in MRA. However, moderator variables (also called Z matrix) may be added to explain heterogeneity in the same fashion as conventional regression analysis does (STANLEY; DOUCOULIAGOS, 2012). Taking that into account, Multivariate MRA model is defined as:

Usually, papers can report more than one effect size and may include different models and results. In this case, PCCs cannot be assumed as independent, because they can be correlated within each paper. Hence, data acquires a hierarchical or multilevel structure, with observed effects grouped into clusters representing each paper -and their multiple estimators- (NELSON; KENNEDY, 2009; STANLEY; DOUCOULIAGOS, 2012; VIECHTBAUER, 2007). Regression models that better reflect this structure allow the coefficients to vary randomly among clusters. Considering such effect, intra-study correlation leads to the following expression:

Where i is the i-th effect in j-th cluster. Random intercept for each paper is given by β₀+u_j. Intra-paper effects are tested through the LM test under the null hypothesis that effect sizes are independent of each other (BALTAGI; LI, 1990).

The model displayed in [6] is analogous to those frequently used in unbalanced panel data structures analysis, where each paper is considered as an individual with several observations, in addition to an unobservable component u_i (STANLEY; DOUCOULIAGOS, 2017). If u_i and the explanatory variables are correlated, random effects coefficients will be biased and inconsistent. In this case, the unobservables are extracted from the error term through usual fixed effects panel estimation. Another option is to add an identification dummy for each cluster or paper (this approach is called least squares dummy variable - LSDV) in order to capture the unobservable effect. To decide whether fixed or random effects estimators are accurate, a traditional Hausman test (WOOLDRIDGE, 2002) can be applied to MRA results.

3.2 Sample and moderator variables

The target population consists of quantitative academic articles that investigate the sources of Innovative Performance (IP) at the firm level. Keywords and inclusion criteria were developed based on contributions from Becheikh, Landry and Amara (2006) and Cohen (2010). Consequently, the main sample includes 95 articles that meet the following criteria: i) are published between 1993 and 2017; ii) are written in English; iii) analyze the firm level; iv) are oriented towards the manufacturing sector; v) have econometric models that take into account IP; vi) consider IP as a dependent variable; vii) are related to technological innovation topics; viii) have a continuous operationalization of firm size; ix) are extracted from journals ranked in Citescore.

The empirical articles considered in the sample come from several sources: American Economic Association database (ECONLIT), JSTOR, SCOPUS, SSRN, SciELO, Bielefeld Academic Search Engine (BASE), and the specialized journal Technovation. Finally, Google Scholar was consulted to attend for geographical representativeness.

Figure 1 depicts the PRISMA flow diagram illustrating the identification phase of the study. From approximately 1,600 pieces of evidence, selection process ended up with 95 articles reporting a total of 655 econometric estimations⁴. The sample covers diverse countries, regions, sectors and econometric strategies. These features constitute the moderator variables utilized to carry out the multivariate MRA. Typically, moderators refer to geographical origin of data, (type and number of) variables included in the analysis and econometric specifications (STANLEY; DOUCOULIAGOS, 2012). Table 1 displays the variables explaining heterogeneity in current MRA. Moderator variables were selected based on their theoretical relevance to the firm size–innovation relationship, as they capture key contextual and methodological factors that could influence empirical findings. Table 1 displays the variables explaining heterogeneity in current MRA. The analysis period from 1993 to 2017 was selected to encompass over two decades of empirical research, capturing significant developments in innovation theory and econometric methodologies.

FIGURE 1
PRISMA flow diagram.
Source: authors.

Table 1

Moderator variables

Source: authors.

4. MRA results

With respect to the MRA results, Figures 2 and 3 provide an initial overview of the data analysis. The PCC histogram in Figure 2 reveals both positive and negative effects, with positive effects being notably more prevalent, constituting approximately 77% of the sample. Figure 3 displays a funnel plot that shows a quasi-symmetrical distribution. Similarly, positive effects dominate and become more precise as they increase, clustering toward the positive side of the axis. In contrast, negative effects are less precise in general, and display greater variability, which can be theoretically explained by the differing mechanisms through which firm size impacts innovation, as larger firms benefit from economies of scale while smaller firms may exhibit greater agility (GALBRAITH, 1952; ROTHWELL; ZEGVELD, 1982).

FIGURE 2
PCC histogram.
Source: authors.

FIGURE 3
PCC funnel plot.
Source: authors.

The MRA conducted in this study utilizes five different econometric models. In our univariate meta-regression analysis (MRA), several key observations are made. First, there is a positive average effect on firm size and Innovative Performance (IP), aligning with previous meta-analyses such as those by Camisón et al. (2002) and Damanpour (2010). This supports the theoretical perspective that larger firms can leverage their resources to drive innovation (Galbraith, 1952; Mansfield, 1963). Second, the Partial Correlation Coefficient (PCC) is notably centered around a value of 0.13. Lastly, there is evidence of heterogeneity that goes beyond sample error, as demonstrated by the p-value of the Q test being less than 0.01 in every case. This heterogeneity underscores the importance of contextual and methodological factors in shaping the relationship between firm size and innovation, as posited in our theoretical framework.

Table 2 presents the estimations for both homogeneous (models 1 and 3) and heterogeneous size effects, using both random (model 4) and fixed cluster effects (model 5). The LM test indicates cluster effects within papers, which are correlated with variance as per the Hausman test. Therefore, our conclusions are primarily based on model 5 (FE-LSDV). While the FE-LSDV model accounts for 72% of the observed variability, its R² value is not sufficiently high for a direct comparison with random effects models. As Verbeek (2004) notes, fixed effects models or LSDV typically have higher R² values due to the inclusion of dummy variables. This highlights the complexity of modeling the firm size–innovation relationship, where accounting for unobserved heterogeneity is crucial for accurate effect estimation.

TABLE 2

Univariate MRA

*** 0** 0.01 * 0.05 Source: authors.

Table 3 shows the multivariate MRA results for LSDV and WLS models. In these models, the intercept is not the average effect but represents the value of PCC when all explanatory variables are set to zero. Consistent with our theoretical framework, the sources of heterogeneity include methodological dimensions (such as data structure, variable operationalization, and industry controls) and firm characteristics (like country development status, technological trajectory, and type of innovation). This aligns with previous findings (CAMISÓN et al., 2002; DAMANPOUR, 2010), suggesting that these factors play a significant role in moderating the firm size–innovation relationship.

TABLE 3

Multivariate MRA

*** 0** 0.01 * 0.05 Source: authors.

When it comes to the characteristics of firms or the data used in the studies, the geographic origin of the firms in the samples introduces a level of variation. Specifically, studies that use data from developed countries tend to show a more pronounced effect of firm size on Innovative Performance (IP) compared to studies that use data from other countries. This can be explained by the fact that developed countries have stronger statistical systems, which provide not only more accurate evidence but also allow for the inclusion of more variables in the models. Additionally, the availability of panel data is determinant. Consistently, cross-sectional evidence (typically found in studies from developing countries) shows a weaker link between firm size and IP. The use of panel data structures allows for the tracking of cumulative effects over time, capturing the development of a firm's capabilities along an evolutionary path (DIMOS; PUGH, 2016; NELSON; WINTER, 1982). This issue is an important source of heterogeneity in several MRA studies and applications (FELD; HECKEMEYER, 2011; Havránková, 2015). The observed variation underscores the importance of considering both methodological and contextual moderators in understanding the firm size–innovation relationship. This aligns with our theoretical framework, which posits that factors such as data structure and geographical context significantly influence empirical findings.

5. Implications

Evidence indicates that among innovative firms, the effect size related to firm size is weaker. While firm size is crucial for distinguishing between innovators and non-innovators, this distinction becomes less pronounced when comparing firms that have already engaged in innovation and meet a minimum threshold of capabilities. In this context, a firm's prior trajectory serves as a moderating factor. A company's innovation history significantly shapes how its size impacts innovative performance, emphasizing the critical role of accumulated capabilities and established routines. The persistence observed in innovative processes, which enhances technological capabilities and consequently improves innovative performance, underscores this point (HALL; MAIRESSE, 2006). These findings highlight the significance of multiple virtuous cycles linking innovation to better performance, and then back to further innovation (BOWEN et al., 2010; KNOTT; VIEREGGER, 2020). As organizations incorporate innovative practices into their operations, the impact of firm size on innovation performance generally diminishes (UGUR et al., 2015). This phenomenon underscores how internal processes and continuous innovation practices can outweigh the impact of firm size in sustaining innovative performance.

Although the distinction between product and process innovation in studies helps explain observed differences, its significance is moderate. For both process and product innovation, larger firms typically show higher innovative performance. However, research suggests that product innovation may have stronger effects in Small and Medium-sized Enterprises (SMEs), even though they innovate less often. This shows that while larger firms have more resources for innovation, SMEs can achieve important innovations through flexibility and focus on specific markets. Effect sizes increase when product and process innovation are analyzed separately. This finding partly supports discussions in the conceptual review about the interconnected relationships between product development, firm size, and overall firm performance. It also shows the importance of looking at different types of innovation separately when studying how firm size relates to innovation, as each type may interact differently with company characteristics.

Another key feature that affects results is how IP is measured in each study. Effect sizes show higher values when innovation is measured through inputs (investment, R&D budget, and patents) in contrast to considering it as an output (product innovation or sales derived from innovation). Despite arguments regarding big firms’ financial advantages to innovate (CAMISÓN et al., 2002; COHEN, 2010), when innovation is considered as an output, weaker effects are obtained, suggesting that capabilities are critical to innovative performance (NELSON; WINTER, 1982; COHEN; LEVINTHAL, 1989). This result complements previous findings, showing that once innovative processes are ongoing, size is not as relevant to achieving economic profit, but its relevance is critical to capabilities construction and accumulation (DAMANPOUR, 2010).

Technological differences across industries are also key moderators in this relationship. The meta-regression analysis reveals that the inclusion of sectoral controls leads to stronger correlations between firm size and IP. These results hold for studies including only one or multiple sectors. Methodological influences, such as firm size measurements and control variables in each study, are considered both as main effects and interaction effects within our models. These two groups of variables are able to partially explain the correlation between PCC and its variance, indicating that both contextual and methodological factors contribute to the observed heterogeneity in the firm size–innovation relationship.

With respect to the firm size effect, results show a positive coefficient that links IP and size, especially when the former is measured with financial indicators. In other words, results support that financial capabilities are related to process innovation in big firms (DAMANPOUR, 2010; GRAZZI; PIETROBELLI, 2016). This type of measurement accurately captures firms’ economic constraints and, therefore, the financial advantages of large enterprises. Interaction between sales and variance is not statistically significant, which implies that this metric does not lead to more precision in the effects analyzed.

Lastly, when firm size is included as a control variable, it does not constitute a source of heterogeneity. Nevertheless, negative coefficients on the interaction between control variables and their variance imply that stronger size effects are more precise within estimations that include size as a control. A possible explanation for this may lie in the characteristics of this group of models, which are related to panel data and larger samples.

Two key findings emerge from the multivariate Meta-Regression Analysis (MRA). First, it confirms the existence of a positive size effect on average, strongly supporting H1. This reinforces the long-standing notion that larger firms generally demonstrate higher innovative performance. Secondly, the analysis reveals that heterogeneity in this relationship is significantly explained by both contextual features and methodological influences, robustly supporting H2. This underscores the complexity of the firm size-innovation relationship, highlighting that it's not a simple, uniform correlation but one that varies depending on industry context, measurement methods, and other factors. These results not only validate our hypotheses but also provide a nuanced understanding of how firm size interacts with innovation across different settings. They emphasize the need for a multifaceted approach when examining this relationship, considering both the overarching trend and the specific contexts that can modify it. This comprehensive view offers valuable insights for both researchers designing future studies and practitioners seeking to understand and leverage the relationship between firm size and innovative performance in various business environments.

Altogether, econometric estimations seem to indicate that the average effect is based upon a direct relationship between size and innovative efforts. Bigger firms possess larger resources to invest, providing them with more opportunities to successfully achieve innovations. Nevertheless, there is a gap between technological improvements and their introduction into the market, which defines a successful innovation. For smaller firms, capabilities are achieved partly through transitioning along an innovative path that allows them to embody innovative routines, thereby enhancing their innovation drivers. This highlights the importance of internal capabilities and innovation processes in sustaining innovative performance beyond mere size advantages.

6. Conclusions

The presented meta-analysis, encompassing 95 empirical studies from 1993 to 2017, offers a comprehensive examination of the relationship between firm size and innovative performance. Our findings corroborate the prevailing academic consensus, confirming a positive average effect size that underscores the robustness of the link between organizational scale and innovation capacity. However, this relationship is not monolithic and varies depending on different contextual factors and methodological approaches, highlighting the need for a deeper theoretical understanding of the underlying mechanisms.

Our results reveal that the strength of the size-innovation relationship is moderated by a range of variables, including the geographic context of firms (developed versus developing countries), industry sectors, and the specific types of innovation under scrutiny (product versus process). Notably, the operationalization of both firm size and innovative performance emerges as a critical factor in explaining the observed heterogeneity in effect sizes. Input-based measures of innovation, such as R&D expenditure and patent applications, demonstrate stronger correlations with firm size compared to output-based metrics like new product introductions or innovation-derived sales. This distinction underlines the direct link between organizational scale and the capacity to invest in innovation, while simultaneously highlights the complex nature of translating these investments into market-ready innovations, as supported by resource-based and absorptive capacity theories.

The analysis further reveals a non-linear aspect to the size-innovation relationship. Among firms already engaged in innovative activities, the effect of size diminishes, suggesting that the accumulation of innovation capabilities and the integration of innovative routines into standard operations play a more significant role than mere organizational scale. This finding emphasizes the importance of path dependency and learning processes in shaping a firm's innovative trajectory, aligning with theories that stress the role of dynamic capabilities in sustaining innovation over time.

Methodological considerations, including data structure (panel versus cross-sectional) and the inclusion of sectoral controls, significantly influence the observed relationships. These findings underscore the critical importance of research design in studies examining the firm size-innovation nexus and call for careful consideration of methodological choices in future investigations. Theoretical models that account for these methodological variations are essential to fully capture the dynamic nature of the size-innovation relationship.

While larger firms generally demonstrate higher innovative performance, our analysis also highlights the significant innovation potential of Small and Medium-sized Enterprises (SMEs), particularly in product innovation and niche market contexts. This nuanced understanding challenges simplistic notions of size advantage and points to the complex interplay between organizational scale, market positioning, and innovation strategies. It suggests that SMEs may leverage their agility and specialized focus to achieve significant innovations despite limited resources, thus contributing to a more balanced theoretical perspective on firm size and innovation.

The study's findings have important implications for both theory and practice. They suggest that while firm size remains a significant factor in innovative performance, its impact is moderated by a complex interplay of internal capabilities, external context, and methodological considerations. From a theoretical standpoint, this underscores the necessity of integrating multiple theoretical lenses, such as the resource-based view and institutional theory, to understand the multifaceted nature of innovation dynamics. For policymakers and practitioners, this implies that fostering innovation requires a multifaceted approach that goes beyond simple size-based considerations. Policies aimed at enhancing innovation should consider firm-specific capabilities, industry characteristics, and the broader economic context to effectively support both large and small firms.

Several limitations of this study warrant mention and provide directions for future research. First, the analysis period (1993-2017) may not capture the most recent developments in innovation dynamics, particularly in rapidly evolving fields such as digital transformation and open innovation. Future studies should explore more recent data to address this limitation. Second, the predominance of quantitative studies in our sample may overlook valuable insights from qualitative research. Integrating mixed-method approaches in future meta-analyses could provide a more holistic understanding of the size-innovation relationship. Additionally, incorporating theoretical frameworks into meta-regression models could enhance the explanatory power of the analysis and bridge the gap between empirical findings and theoretical propositions.

Additionally, the relative scarcity of data from developing countries in our sample limits the generalizability of our findings across diverse economic contexts. Future research should prioritize the inclusion of studies from a broader range of geographical and economic settings to enhance our understanding of how the size-innovation relationship manifests across different developmental contexts. This would contribute to a more inclusive and globally relevant theoretical framework that accounts for diverse economic environments.

This meta-analysis provides a comprehensive overview of the relationship between firm size and innovative performance. While confirming the general positive association, it highlights the complex, context-dependent nature of this relationship. The study emphasizes the need for future research to adopt more sophisticated, multidimensional approaches to capturing both firm size and innovative performance. Moreover, it calls for greater attention to the mediating factors and organizational processes that link size to innovation outcomes, thereby advancing theoretical understanding beyond empirical regularities. As the landscape of innovation theory and practice continues to evolve, ongoing research in this field remains crucial for advancing our understanding of the drivers of innovation in organizations of all sizes.

ANNEX 1

References

ACS, Z. J.; AUDRETSCH, D. B. Innovation and firm size in manufacturing. Technovation, Oxford, v. 7, n. 3, p. 197-210, 1988.

ALOE, A. M.; THOMPSON, C. G. The synthesis of partial effect sizes. Journal of the Society for Social Work and Research, Washington, v. 4, n. 4, p. 390-405, 2013.

ANTONELLI, C.; SCELLATO, G. Complexity and technological change: knowledge interactions and firm level total factor productivity. Journal of Evolutionary Economics, Heidelberg, v. 23, p. 77-96, 2013.

AUDRETSCH, D. B.; LEHMANN, E. E. Does the knowledge spillover theory of entrepreneurship hold for regions? Research Policy, Amsterdam, v. 34, n. 8, p. 1191-1202, 2005.

BACHMANN, F.; KATAISHI, R. El análisis de meta regresión (AMR) aplicado a la relación entre desempeño innovador y tamaño de la firma: Un abordaje epistemológico sobre nuevas metodologías en economía. Madrid: Asociación Civil Red Pymes Mercosur, 2020.

BACHMANN, F.; KATAISHI, R. MRA innovation size Bachmann Kataishi 2024 RBI public script Source Code. 2024. Available from: <https://github.com/rkataishi/codeanddata/blob/main/MRAinnovationsizeBachmannKataishi2024RBIpublicscript.R>. Access in: 11 Oct 2023.

BACHMANN, F.; LISERAS, N.; GRAÑA, F. M. Desempeño innovador y tamaño de la firma: heterogeneidad y sesgo de publicación abordados desde un análisis de meta-regresión. Innovar, Bogotá, v. 31, n. 81, p. 75-99, 2021.

BALTAGI, B. H.; LI, Q. A Lagrange multiplier test for the error components model with incomplete panels. Econometric Reviews, New York, v. 9, n. 1, p. 103-107, 1990.

BECHEIKH, N.; LANDRY, R.; AMARA, N. Lessons from innovation empirical studies in the manufacturing sector: A systematic review of the literature from 1993–2003. Technovation, Oxford, v. 26, n. 5–6, p. 644-664, 2006.

BOWEN, F. E.; ROSTAMI, M.; STEEL, P. Timing is everything: A meta-analysis of the relationships between organizational performance and innovation. Journal of Business Research, New York v. 63, n. 11, p. 1179-1185, 2010.

CAMISÓN, C. et al. Meta-análisis de la relación entre tamaño de empresa e innovación. Castellón: Instituto Valenciano de Investigaciones Económicas, 2002.

CASSIMAN, B.; VEUGELERS, R. In search of complementarity in innovation strategy: Internal R&D and external knowledge acquisition. Management Science, Hanover, v. 52, n. 1, p. 68-82, 2006.

CASSIOLATO, J. E. et al. FDI and national systems of innovation: lessons from the experience of BRICS. In: CASSIOLATO, J. et al. (Org.). Transnational corporations and local innovation. India: Routledge, 2013. p. 67. http://doi.org/10.4324/9780367818562

CASSIOLATO, J. E.; LASTRES, H. M. M. Local systems of innovation in Mercosur countries. Industry and Innovation, London, v. 7, n. 1, p. 33-53, 2000.

COHEN, W. M. Fifty years of empirical studies of innovative activity and performance. In: HALL, B.H; ROSENBERG, N. (Ed.).Handbook of the Economics of Innovation. Berkeley: Elsevier, 2010. p. 129-213. http://doi.org/10.1016/S0169-7218(10)01004-X.

COHEN, W. M.; LEVINTHAL, D. A. Innovation and learning: the two faces of R & D. Economic Journal, London, v. 99, n. 397, p. 569-596, 1989. http://doi.org/10.2307/2233763.

CRETINI, I. O.; ROBERT, V. Firm size, foreign capital and modes of innovation: an analysis of manufacturing firms in Argentina. Revista Brasileira de Inovação, São Paulo, v. 21, p. e022006, 2022.

DAMANPOUR, F. An integration of research findings of effects of firm size and market competition on product and process innovations. British Journal of Management, Oxford, v. 21, n. 4, p. 996-1010, 2010.

DEBRESSON, C. Breeding innovation clusters: a source of dynamic development. World Development, Oxford, v. 17, n. 1, p. 1-16, 1989.

DIMOS, C.; PUGH, G. The effectiveness of R&D subsidies: a meta-regression analysis of the evaluation literature. Research Policy, Amsterdam, v. 45, n. 4, p. 797-815, 2016.

DOSI, G. Technological paradigms and technological trajectories: a suggested interpretation of the determinants and directions of technical change. Research Policy, Amsterdam, v. 11, n. 3, p. 147-162, 1982. http://doi.org/10.1016/0048-7333(82)90016-6.

FELD, L. P.; HECKEMEYER, J. H. FDI and taxation: a meta-study. Journal of Economic Surveys, Oxford, v. 25, n. 2, p. 233-272, 2011.

FORÉS, B.; CAMISÓN, C. Does incremental and radical innovation performance depend on different types of knowledge accumulation capabilities and organizational size? Journal of Business Research, New York, v. 69, n. 2, p. 831-848, 2016.

GALBRAITH, J. K. American Capitalism: the concept of countervailing power. New York: Houghton Mifflin, 1952.

Grazzi, M.; Pietrobelli, C. Firm innovation and productivity in Latin America and the Caribbean: the engine of economic development. Washington, DC: Springer, 2016.

HALL, B. H.; MAIRESSE, J. Empirical studies of innovation in the knowledge-driven economy. Economics of Innovation and New Technology, Abingdon, v. 15, n. 4–5, p. 289-299, 2006.

HALL, B. H.; ZIEDONIS, R. H. The patent paradox revisited: an empirical study of patenting in the US semiconductor industry, 1979-1995. Rand Journal of Economics, Santa Monica, v. 32, p. 101-128, 2001.

Havránková, Z. Six essays on meta-regression analysis. 2015. Dissertation (Doctoral) - Charles University in Prague, Prague, 2015.

HIGGINS, J. P. T.; THOMPSON, S. G.; SPIEGELHALTER, D. J. A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society. Series A, (Statistics in Society), London, v. 172, n. 1, p. 137-159, 2009.

JARAMILLO, H.; LUGONES, G.; SALAZAR, M. Normalización de Indicadores de Innovación Tecnológica en América Latina y el Caribe: Manual de Bogotá. Bogotá: Colciencias, 2001.

KATAISHI, R.; BRIXNER, C. Entre lo exógeno y lo exótico: las periferias, los supuestos económicos sobre Ciencia, Tecnología e Innovación y sus implicancias para el desarrollo tecno-productivo. Ensayos de Economía, Bogotá, v. 33, n. 62, p. 77-99, 2023.

KATAISHI, R.; MORERO, H. Taxonomies, technological opportunities, and global value chains in developing countries: a literature review and a conceptual approach proposal. Investigación y Desarrollo, Buenos Aires, v. 28, n. 2, p. 168-220, 2020.

KATZ, J.; STUMPO, G. Regímenes competitivos sectoriales, productividad y competitividad internacional. Revista de la CEPAL, Santiago, v. 75, p. 137-158, 2001.

KNOTT, A. M.; VIEREGGER, C. Reconciling the firm size and innovation puzzle. Organization Science, Maryland, v. 31, n. 2, p. 477-488, 2020.

LAFORET, S. Organizational innovation outcomes in SMEs: effects of age, size, and sector. Journal of World Business, Amsterdã, v. 48, n. 4, p. 490-502, 2013.

LALL, S. The Technological structure and performance of developing country manufactured exports, 1985‐98. Oxford Development Studies, Oxford, v. 28, n. 3, p. 337-369, 2000.

LUNDVALL, B. A. National systems of innovation: towards a theory of innovation and interactive learning. London: Pinter, 1992. vol. 242.

MALERBA, F. Sectoral systems and innovation and technology policy. Revista Brasileira de Inovação, Campinas, v. 2, n. 2, p. 329-375, 2003.

MALERBA, F.; ORSENIGO, L. Technological regimes and sectoral patterns of innovative activities. Industrial and Corporate Change, Oxford, v. 6, n. 1, p. 83-118, 1997.

MANSFIELD, E. Size of firm, market structure, and innovation. Journal of Political Economy, Chicago, v. 71, n. 6, p. 556-576, 1963.

MONTOBBIO, F.; KATAISHI, R. The international dissemination of technological knowledge. In: ANTONELLI C.; LINK A.N. (Eds.). Routledge handbook of the economics of knowledge. London: Taylor & Francis, 2014. p. 165-189

MORRIS, D. M. Innovation and productivity among heterogeneous firms. Research Policy, Amsterdã, v. 47, n. 10, p. 1918-1932, 2018.

NELSON, J. P.; KENNEDY, P. E. The use (and abuse) of meta-analysis in environmental and natural resource economics: An assessment. Environmental and Resource Economics, Amsterdã, v. 42, n. 3, p. 345-377, 2009.

NELSON, R. R.; WINTER, S. G. An evolutionary theory of economic change. Cambridge: Harvard University Press, 1982.

NOTEBOOM, B. Innovation and diffusion in small firms: theory and evidence. Small Business Economics, Dordrecht, v. 6, p. 327-347, 1994.

OECD. Frascati Manual: the measurement of scientific and technical activities. Paris: OECD, 1963.

OECD. Oslo Manual: proposed guidelines for collecting and interpreting technological innovation data. Paris: OECD, 1992.

PARRILLI, M. D.; BALAVAC, M.; RADICIC, D. Business innovation modes and their impact on innovation outputs: Regional variations and the nature of innovation across EU regions. Research Policy, Amsterdã, v. 49, n. 8, p. 104047, 2020.

RHODES, W. Meta-analysis: an introduction using regression models. Evaluation Review, Los Angeles, v. 36, n. 1, p. 24-71, 2012.

RICE, K.; HIGGINS, J. P. T.; LUMLEY, T. A re-evaluation of fixed effect(s) meta-analysis. Journal of the Royal Statistical Society. Series A, (Statistics in Society), London, v. 181, n. 1, p. 205-227, 2018.

ROSENBUSCH, N.; BRINCKMANN, J.; BAUSCH, A. Is innovation always beneficial? A meta-analysis of the relationship between innovation and performance in SMEs. Journal of Business Venturing, v. 26, n. 4, p. 441-457, 2011.

ROTHWELL, R.; ZEGVELD, W. Innovation and the small and medium sized firm: University of Illinois at Urbana-Champaign’s Academy for Entrepreneurial Leadership Historical Research Reference in Entrepreneurship. Lincoln, United Kingdom: Frances Pinter Publishers, 1982.

ROUSSEAU, M. B. et al. Innovation, firm performance, and appropriation: A meta-analysis. International Journal of Innovation Management, Singapore, v. 20, n. 03, p. 1650033, 2016.

SANTOS, J. H. D. A. et al. Searching for a path: A bibliometric study on innovation and technological capabilities. International Journal of Innovation, London, v. 3, n. 2, p. 54-66, 2015.

SCHERER, F. M.; ROSS, D. Industrial market structure and economic performance (3rd ed.). Boston: Houghton Mifflin, 1990.

SCHUMPETER, J. A. Capitalism, socialism and democracy. New York: Harper & Brothers, 1942.

SCHUMPETER, J. A. The theory of economic development. Cambridge: Harvard University Press, 1934.

STANLEY, T. D.; DOUCOULIAGOS, H. Meta-regression analysis in economics and business. New York: Routledge, 2012.

STANLEY, T. D.; DOUCOULIAGOS, H. Neither fixed nor random: weighted least squares meta-regression. Research Synthesis Methods, Hoboken, v. 8, n. 1, p. 19-42, 2017.

STANLEY, T. D.; JARRELL, S. B. Meta‐regression analysis: a quantitative method of literature surveys. Journal of Economic Surveys, Oxford, v. 19, n. 3, p. 299-308, 2005. http://doi.org/10.1111/j.0950-0804.2005.00249.x.

TEECE, D. J. Profiting from technological innovation: Implications for integration, collaboration, licensing and public policy. Research Policy, Amsterdam, v. 15, n. 6, p. 285-305, 1986.

TEPLOV, R.; ALBATS, E.; PODMETINA, D. What does open innovation mean? Business versus academic perceptions. International Journal of Innovation Management, Singapore, v. 23, n. 01, p. 1950002, 2019.

UGUR, M. et al. R&D and productivity in OECD firms and industries: a hierarchical meta-regression analysis. Research Policy, Amsterdam, v. 45, n. 10, p. 2069-2086, 2015.

VERBEEK, H. M. W. Verification of WF-nets. 2004. Thesis (Phd ) - Industrial Engineering and Innovation Sciences. Technische Universiteit Eindhoven, Eindhoven, 2004.

VIECHTBAUER, W. Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, San Francisco, v. 36, n. 3, p. 1-48, 2010. http://doi.org/10.18637/jss.v036.i03.

VIECHTBAUER, W. Hypothesis tests for population heterogeneity in meta-analysis. British Journal of Mathematical & Statistical Psychology, Oxford, v. 60, n. 1, p. 29-60, 2007.

WOOLDRIDGE, J. M. Econometric analysis of cross section and panel data. Cambridge: MIT Press, 2002.

YOUNG, A. Increasing returns and economic progress. Economic Journal, London v. 38, n. 152, p. 527-542, 1928.

ZAHRA, S. A.; NIELSEN, A. P. Sources of capabilities, integration and technology commercialization. Strategic Management Journal, Haboken, v. 23, n. 5, p. 377-398, 2002. http://doi.org/10.1002/smj.229.

ANNEX 1

Table 1A Studies included in MRA

Note: last column summarises the main results in each article. Significantly positive and negative effects are labelled as “positive” and “negative” respectively, while non-significant are “null”; extremely heterogeneous evidence is classified as “various”. Source: authors.

Notes

Conflict of interest declaration