Firm size and growth barriers: a data-driven approach

This article uses a probabilistic model to test the likelihood that top managers perceive a certain factor to be a barrier to growth given firm and top manager characteristics. In line with previous studies, it focuses on whether top managers face significant growth barriers (e.g., Coad and Tamvada 2012; Lee 2014; Lee and Cowling 2015). In other words, the outcome variables, perceived growth barriers, are treated as binary, where top managers either perceive a given factor to be a significant growth barrier or not.⁷

Formally, a probit model is used to test the likelihood that the top manager of firm i at time t perceives factor j to be a significant growth barrier in the following model:

The dependent variables of this article comprise eight binary variables, which constitute all comparable growth barriers available in the SCE over the studied period. More specifically, the analysis concerns growth barriers related to competition (Competition), access to credit (Credit), lack of demand (Demand), access to equity financing (Equity financing), current plant capacity (Plant capacity), lack of profits (Profits), recruiting staff (Recruitment), and regulations (Regulations).⁸

The variable of interest in this article is firm size (Size). The reason for studying this particular variable, as opposed to a range of firm characteristics, is because firm size constitutes a key variable in both research and policy analysis on firm performance, whereby its academic and economic significance is argued to warrant a dedicated and in-depth analysis. Studies of perceived growth barriers have previously analyzed their relationship to firm size by use of ad hoc–defined size groups (e.g., Orser et al. 2000; Beck et al. 2005; Lee and Cowling 2014; Lee and Cowling 2015).

Although appealing in their simplicity and comparability, however, a major drawback to the use of ad hoc firm size groups is that they are unlikely to correspond to the heterogeneity of most economic problems. This incompatibility implies that by adopting these strategies, researchers are also likely to restrict their abilities to capture economic phenomena. Given these constraints, this article aims to instead capture the relationship between firm size and perceived growth barriers through a data-driven approach. This aim implies, in turn, a need for careful methodological consideration.

First, there are a number of established ways to define firm size, such as in terms of value added, sales, or the number of employees. In this article, size is defined as the total number of employees per firm. Employment is chosen over alternative definitions because it has proven to be a more consistent and stable measure across industries and time (Delmar 1997; Davidsson et al. 2006; Coad and Hölzl 2012).⁹ Next, having decided on a definition of firm size, the next question is how to analyze it. In principle, there are two ways to approach this issue: (a) by treating firm size as a continuous estimator or (b) as a discrete estimator. At first glance, it may seem that the obvious way to approach this problem is to opt for (a), i.e., to treat firm size as a continuous estimator and thereby use all available information to assess its relationship to perceived growth barriers. However, due to data limitations, this is not necessarily the case. In particular, due to the structure of the data, i.e., left-skewed with relatively few observations for firms with 50 employees or more, a continuous estimator will tend to be disproportionally imprecise for these firms.¹⁰ Meanwhile, given that this article aims to explore the general relationship between perceived growth barriers and firm size, a continuous estimator of firm size is likely to be unsuitable for this context; rather, it implies the need for a discrete measure.

In contrast to a continuous estimator, a discrete measure of firm size is appealing in that it allows for analysis of wide sets of firm sizes. Moreover, this approach also offers an intuitive way to evaluate non-linear relationships. However, a drawback of this approach is that there is little consensus on how to assign firm size groups. Furthermore, by wrongfully assigning size groups, researchers run risk of understating, overstating, or even obscuring the mechanisms studied.

To address this challenge, this article aims to identify firm size groups based on the statistical relationship between their size and perceived growth barriers. In this way, it aims to incorporate part of the advantages of a continuous estimator, i.e., flexibility and adaptability, while also incorporating part of the advantages of a discrete estimator, i.e., inclusiveness. To approach this task, a set of firm and top manager characteristics are included in a number of ordinary least squares (OLS) regression models along with a set of dummy variables that assume the value of “1” for each consecutive firm size interval between 0 and 249 employees.¹¹ Each firm size interval is included individually for each growth barrier in a number of regressions, as follows:where Ω denotes a set of firm and top management characteristics, in excess of firm size, and j denotes each category of perceived growth barriers. In addition, Z denotes each individual firm size group. For brevity, time and individual indices are suppressed.

Next, once each growth barrier has been regressed against all firm sizes, the model fit of each size group is evaluated in terms of adjusted R². All regression models are thereafter ranked based on their adjusted R² value, where the firm size group that yields the highest predictive power is included in the model. Thereafter, the process is repeated to identify the second interval for each barrier following the same principle, where the first firm size group is now included in each regression. This process is repeated for all growth barriers until all firm sizes have been categorized from 0 to 249 employees.

The adjusted R² measure is, however, sensitive to variance. For the context of this article, this sensitivity poses a problem. As previously discussed, the data contain relatively few observations for firms with 50 employees or more, which means that estimates for this group exhibit relatively high variance. Therefore, if firm size intervals were to be assigned based on adjusted R² alone, the resulting groups would tend to focus on firms in this category while obscuring relationships among smaller firms. Therefore, to yield more inclusive estimates, the predictive value of each firm size group is weighted by its estimated Kernel density (Epanechnikov).¹² Analysis shows that this approach does not affect the identification of groups among firms with 50 employees or more but rather allows the algorithm to also identify such groups among smaller ones.

Moreover, to reduce the number of possible categories, the Kernel estimator is also used to identify Kernel bandwidths. This property is utilized to restrict the model in that it cannot fit two complete firm size groups within the same Kernel bandwidth. By use of this restriction, the risk of introducing small, affluent groups is reduced. This approach yields an initial total of 50 firm size groups per growth barrier.

Finally, to increase econometric efficiency and to make the results more readable, the above process is repeated for the initial 50 groups in an effort to increase group sizes (the number of observations per group), where Kernel density weights are now assigned to each group rather than to each individual firm size. By this, the possibility of merging groups is explored, where the influence of individual firm sizes is lower than in previous steps. Following this procedure, the total number of firm size groups is reduced from 50 to approximately 5 to 10 groups per growth barrier. The above discussion is summarized in Fig. 1 below.¹³

The above approach is chosen over competing strategies, such as restricted cubic regression splines, as the latter (ideally) require knowledge of inflection points on beforehand. Moreover, their estimates are determined mainly by the number of inflection points included in the analysis rather than their absolute position (e.g., Harell 2015). Due to this, regression splines are likely unsuitable for the purposes of the current analysis.

Lastly, although the current application concerns perceived firm growth barriers, the method developed in this section is general and can be applied to a variety of empirical settings. Prominently, the presented method provides a versatile tool for solving a common methodological issue in research on entrepreneurship and small business, i.e., how to assign discrete firm size groups. This capability is likely to be of particular use for exploratory settings where there is little or no prior theory nor evidence to guide researchers in their empirical design. Through this, the presented strategy does also contribute to an emerging interest in using data-driven methods to study firm growth (Miyakawa et al. 2017; Coad and Srhoj 2019).

Having identified the model’s dependent variables and having developed a method for assigning firm size groups, the task remains to identify its control variables.

To evaluate the performance of each respective size measure, the measures are compared in terms of McFadden’s pseudo R² (McFadden 1973). For additional robustness, pseudo R² is also calculated using Tjur’s D (Tjur 2009). These strategies are chosen over alternative approaches, such as Akaike’s Information Criterion (AIC) or the Bayesian Information Criterion (BIC), as these latter methods are based on parsimonious principles, i.e., they seek model simplicity, which is not necessarily an aim of the current article.¹⁶

Table 1 presents descriptive statistics and definitions for the included variables. As shown in Table 1, the typical (median) top manager is a male who was born in Sweden. Moreover, the typical firm is an independent firm that was established 12 years ago and has four employees.

Next, it is noted that the two most common growth barriers concern recruitment and regulations, where approximately 27 and 24% of top managers face these growth barriers, respectively. The fact that these two barriers are the most common is perhaps to be expected. Swedish firms have previously been noted to face high regulatory burden compared with other OECD firms, where the primary source of these liabilities has been linked to legislation on labor and recruitment practices (Swedish Agency for Economic and Regional Growth 2018a, b; OECD 2018a, b). The third most commonly cited growth barrier is that of competition, which constitutes a substantial growth barrier for approximately 21% of all top managers.

In contrast to the above, additional findings shown in Table 1 suggest that a relatively low share of the surveyed firms face barriers relating to credit, consumer demand, equity financing, plant capacity, and profits—between approximately 8 and 13%. The fact that relatively few managers face financing constraints is notable given that this factor constitutes the most commonly cited growth barrier throughout the literature (e.g., Beck et al. 2005; Wang 2016; Mol-Gómez-Vázquez et al. 2019). This finding can likely be partially explained from the supply of small business financing. Sweden and the EU recently introduced a number of small business credit programs, which can be expected to have significantly alleviated the overall financing constraints of the sector (European Commission 2013).¹⁷ These policy initiatives have also been coupled with innovations in banking, where financial institutions have been noted to use mixed loan structures consisting of both soft and hard lending technologies to successfully overcome small firm information asymmetries (e.g., Hernández-Cánovas and Martínez-Solano 2010; Beck et al. 2011; Cucculelli et al. 2019).

Figure 2 presents results on all analyzed perceived growth barriers and their relationship to firm size using the developed identification strategy. For illustrative purposes, the results have been divided into three graphs; Fig. 2 a, b, and c, respectively. As shown in the Fig. 2 b and c, five out of eight growth barriers are only marginally related to firm size. These barriers are those that concern access to credit, demand, plant capacity, profits, and regulations.¹⁸ For the sake of brevity, these results will be discussed first, after which the remaining growth barriers, i.e., competition, equity financing, and recruitment, as depicted in Fig. 2a, will be studied in greater depth based on their particularly strong relationships to firm size.

The results of Fig. 2b suggest that there are only marginal differences in credit constraints across firm size, where differences in the likelihood of facing this growth barrier range between 0 and 3% across groups. Therefore, the results shown in Fig. 2b seem to largely corroborate the previous statements that Swedish small businesses have access to a relatively abundant supply of credit financing.

Furthermore, the results of Fig. 2b suggest that firms with 85–91 employees are approximately 14% more likely to face growth barriers relating to a lack of consumer demand than are firms with fewer than 61 employees. This finding is in accordance with previous studies, although the majority of prior findings lack statistical significance (Robson and Obeng 2008; Coad and Tamvada 2012; Lee and Cowling 2014, 2015). While it is interesting in its own merit, however, this finding is perhaps most noteworthy when compared with equivalent ad hoc estimates, where the OECD (2005) and World Bank (2001) definitions of firm size completely obscure the observed differences.

The results shown in Fig. 2b suggest that firm size is weakly related to perceived growth barriers regarding plant capacity, where the largest difference across firm sizes constitutes approximately 6%. The fact that plant capacity constraints are weakly related to firm size is perhaps to be expected given that these concepts are more likely to be linked to geographical conditions, e.g., firm and population density, than to the size of individual firms (e.g., Krugman 1991; Ciccone and Hall 1996; Lee and Cowling 2015).

Next, the results of Fig. 2c suggest a weak relationship between firm size and perceived growth barriers regarding profit, where the largest difference across firm sizes constitutes approximately 5%. The fact that profit constraints do not differ across firm size is notable, given the otherwise strong support in favor of a pervasiveness in liquidity and profitability issues among small firms (e.g., Oliveira and Fortunato 2006; Donati 2016). A plausible explanation for this lack of heterogeneity may be that many firms are not growth-oriented, and hence, the average profit requirement of firms may be very low (e.g., Storey 1994; Hansen and Hamilton 2011; Gherhes et al. 2016). Lastly, the findings suggest that there are no significant differences in regulatory constraints across firm size. This finding is consistent with prior findings (Beck et al. 2005; Lee and Cowling 2014; Lee 2014; Lee and Cowling 2015). Therefore, the results shown in Fig. 2 do not seem to support the anecdotal observation that small firms are disproportionately encumbered by regulatory pressure (e.g., Kitching 2006; Kitching 2015). A plausible explanation for this finding may be that the term “regulation” encompasses a wide array of growth barriers and, thus, the expression itself may contain considerable heterogeneity.

Three growth barriers are found to have relatively strong relationships with firm size, namely, those concerning competition, access to equity financing, and recruitment, as presented in Fig. 2a. For the remainder of this section, these barriers and their relationship to firm size are examined.

Figure 3 presents results for perceived growth barriers regarding competition using the applied strategies for measuring firm size, i.e., the developed identification strategy, a continuous estimator, and the OECD (2005) and World Bank (2001) definitions of firm size.

Applying the developed identification strategy reveals that the likelihood of encountering growth barriers from competition increases incrementally with firm size. The first of these increments is found for firms with 5–9 employees, who are approximately 5% more likely to face this barrier compared with those with 0–4 employees. Next, this likelihood is found to further increase for firms with 10–14 employees, where these firms are significantly more likely to face this barrier compared with those with 0–4 and 5–9 employees, approximately 9 and 3%, respectively.

Next, by analyzing larger firm sizes, it is found that the likelihood of perceiving competition as a growth barrier is significantly higher among firms with 41–55 employees than among those with 0–4, 5–9, and 10–14 employees. These firms are found to be approximately 12, 7, and 4% more likely to face this barrier compared with the aforementioned firms. Lastly, firms with 76–144 employees are found to be more likely than the abovementioned groups to face growth barriers from competition. These firms are approximately 26, 20, 17, and 9% more likely to face this growth barrier compared with those with 0–4, 5–9, 10–14, and 41–55 employees.

Furthermore, by applying a continuous estimator of firm size, a positive relationship is identified, where a 1% increase in employment is found to be associated with a 3% increase in the likelihood to face growth barriers from competition. Conversely, by applying the OECD (2005) definition of firm size, it is found that firms with 10–49 and 50–249 employees are 9, versus 21% more likely to face this barrier, compared with those with 0–9 employees. Lastly, by applying the World Bank (2001) definition of firm size, it is found that firms with 5–50 employees and 51–249 employees are approximately 9, versus 23% more likely to face barriers from competition, compared with those with 0–4 employees.

A striking feature of Fig. 3 is the similarity in magnitudes among the three discontinuous measures of firm size, i.e., the developed identification strategy, the OECD (2005), and the World Bank (2001) definitions. At first sight, this similarity may seem to speak in favor of using ad hoc firm size measures as they are both relatively simplistic and produce point estimates comparable with the developed identification strategy. However, although the estimates themselves are similar, a critical distinction among the three strategies concerns the level of detail in which their respective predictions are made. In this respect, the identification strategy proposed here is argued to widely outperform the two other discontinuous strategies as it allows researchers to make detailed predictions on the specific size thresholds where firms incur growth barriers (i.e., 5–14 versus 41–55 and 76–144 employees) rather than to simply estimate their prevalence across generic groups, as occurs in the latter cases (i.e., 5–50 and 10–49 employees versus 51–249 and 50–249 employees). Furthermore, this increased precision in the discussion of firm size is arguably central for furthering our understanding of firm growth barriers and their antecedents.

The overall results of Fig. 3 are consistent with discussions in the strategic management literature, which suggest that larger firms are more likely than smaller ones to diversify their activities and to expand into new markets (Grossmann 2007; Benito-Osorio et al. 2015). Meanwhile, expansion into new markets is, in turn, thought to be associated with increased competition and substantial entry costs (e.g., Hölzl 2012). In contrast, the results are in opposition to those of Wang (2016), who found a negative relationship between competition barriers and firm size. However, these estimates were only obtained for SMEs as a group relative to larger firms, for which they are likely to contain a considerable degree of unobserved heterogeneity. Moreover, this difference is likely further exacerbated by differences in institutional context, as Wang (2016) studied firms in developing economies.

Figure 4 presents results on perceived growth barriers related to a lack of access to equity financing.

By applying the developed identification strategy, it is found that firms with 0–2, 3–14, and 15–19 employees are approximately 3–4% more likely to face equity financing constraints compared with those with 41–60, 61–70, 71–91, 92–145, and 146–249 employees. In addition, it is found that firms with 20–40 employees are approximately 7% more likely to face this growth barrier compared with those with 146–249 employees.

Next, by applying a continuous estimator of firm size, a negative relationship is identified, where a 1% increase in employment is, on average, associated with an approximately 0.3% decrease in the likelihood to face growth barriers related to equity financing. Furthermore, by applying the OECD (2005) definition of firm size, it is found that firms with 50–249 employees are approximately 4% less likely to face this barrier compared with firms with 0–9 and 10–49 employees. Lastly, by applying the World Bank (2001) definition of firm size, firms with 5–50 and 51–249 employees are found to be more 1% more likely, versus 4% less likely, to face this growth barrier compared with those with 0–4 employees.

A prominent finding of Fig. 4 is the strong resemblance among point estimates using the three discontinuous strategies for measuring firm size. This consistency is, in turn, similar to the findings shown in Fig. 3. However, although the applied strategies produce similar point estimates, it is again noted that there are considerable differences in their respective abilities to capture firm size heterogeneity. In this regard, the developed identification strategy is argued to outperform its other discrete counterparts as it is able to account for the same mechanisms as the latter while also being able to produce detailed predictions on the size thresholds at which firms incur, versus overcome growth barriers. Specifically, findings using the proposed identification strategy suggest that perceived equity financing constraints are the most pervasive among firms in the range of 0–19 employees. This finding stands to be compared with the findings of ad hoc groups, which instead attribute this prevalence to a considerably wider and generic set of firm sizes, i.e., 0–50 or 0–49 employees. Based on this difference, the proposed identification strategy is argued to be more suitable for studying perceived equity financing constraints as it allows researchers to make substantially more detailed predictions on their nature and heterogeneity.

The results of Fig. 4 are in accordance with theory on financial accessibility, which predicts that small firms are more likely than larger ones to face financing issues due to adverse selection on the financial market (e.g., Berger and Udell 1998; Cenni et al. 2015). These findings are also consistent with related empirical findings, although the latter have identified the corresponding relationships for considerably wider spans of firm sizes (e.g., Beck et al. 2005; Wang 2016; Lee and Luca 2019). The results shown in Fig. 4 are consistent with Beck et al. (2005), who found that firms with 5–50 and 51–500 employees were approximately 29—versus 23—percent more likely to face financing constraints compared with those with more than 500 employees.

In contrast to the above, however, the results shown in Fig. 4 suggest that there is substantial heterogeneity within the group of 5–50 employees. This heterogeneity raises questions as to what extent the findings of Beck et al. (2005) are driven by financing constraints across the full 5–50 employee size range versus the extent to which they are a result of empirical limitations. Given the prevalent use of ad hoc measures in research and policy analysis of financial constraints, this latter distinction is likely to hold considerable practical implications.

Figure 5 presents the results for perceived growth barriers related to recruitment. Applying the developed identification strategy reveals that the likelihood to face recruitment issues increases sharply among firms with 3–14 and 15–19 employees relative to those with 0–2 employees, while remaining relatively constant across those with between 20 and 40 employees. Firms with 3–14, 15–19, and 20–40 employees are found to be approximately 16–17% more likely to face recruitment issues compared with those with 0–2 employees. In addition, this likelihood is found to increase for firms with 41–249 employees, where the latter are found to be approximately 13% more likely to face growth barriers related to recruitment, compared with those with 0–19 employees.

Here, it is worth noting that the findings shown in Fig. 5 largely mirror those of Fig. 4 regarding access to equity financing, although with reverse signs. It is possible that these results reflect the same relationship, i.e., changes in firm constraints over their lifecycle, where financing is more likely to be a binding constraint for smaller firms than for larger ones. In turn, once firms exceed a certain size, factors such as competence are more likely to be a prominent constraint.

Next, by applying a continuous estimator of firm size, a positive relationship is identified, where a 1% increase in firm employment is, on average, associated with a 6% increase in the likelihood of facing recruitment issues. Conversely, by applying the OECD (2005) definition, firms with 10–49 employees and 50–249 employees are found to be approximately 10, versus 26% more likely to face this growth barrier than those with 0–9 employees. Finally, by applying the World Bank (2001) definition, it is found that firms with 5–50 and 51–249 employees are approximately 14 and 28% more likely to face growth barriers related to recruitment compared with those with 0–4 employees.

Similar to the preceding analyses, the results shown in Fig. 5 suggest a high degree of similarity in point estimates between the three discontinuous strategies for measuring firm size. Furthermore, it is again noted that there are considerable differences in the strategies’ abilities to capture size thresholds at which firms incur, versus overcome, growth barriers. In the case of Fig. 5, findings using the proposed identification strategy suggest that firms with at least 41 employees are more likely than those with 0–19 employees to face recruitment issues. Additionally, ad hoc groups are found to attribute the same outcomes to substantially wider size groups, i.e., to firms with 5–50 and 10–49 employees versus 51–249 and 50–249 employees. Following these results, the proposed identification strategy is again argued to outperform its ad hoc equivalents as it is able to capture the studied mechanisms in considerably greater detail than the latter.

The results of Fig. 5 are consistent with the findings of Lee and Cowling (2015), who identified a positive relationship between firm size and the likelihood of facing recruitment issues. They found that firms with 0–49 employees were significantly less likely to face this growth barrier compared with those with 50 employees or more. Given the results of Fig. 5, it is possible that their results reflect the same relationships as observed here, although the use of ad hoc size groups may have restricted their ability to identify heterogeneity within the 0–49 employee firm size interval.

To formally evaluate the performance of the applied strategies for measuring firm size, each approach is also evaluated in terms of its model fit. Table 2 presents findings on the performance of each strategy, measured as their corresponding models’ predictive power (McFadden’s pseudo R²).

As shown, the proposed identification strategy yields the highest performance in terms of pseudo R² for a majority of barriers. In two cases, for competition and recruitment, it is found that a continuous estimator of firm size yields a higher explanatory power. A likely reason for this finding is that these variables involve relatively linear relationships with firm size, which a continuous estimator of firm size is able to capture without the discrete shifts employed by other strategies. However, given the limitations of a continuous estimator, i.e., a generally low precision in estimates for larger firms, this strategy may prove difficult to implement in practice.

A central finding shown in Table 2 concerns the fact that the developed identification strategy consistently outperforms the other two discrete strategies in measuring firm size. Therefore, these results appear to corroborate the statements made above in this article, i.e., that the proposed identification strategy can capture the relationship between perceived growth barriers and firm size in considerably greater detail than its ad hoc equivalents.

As a robustness analysis, the predictive power of each model is also presented in terms of Tjur’s D, which is given in parentheses. The results seem to be robust across methods for calculating pseudo R². The results change in only one case, namely, for recruitment, where the developed identification strategy is found to perform worse than the other measures in explaining this outcome.

Finally, a relevant concern is whether the results of Table 2 are driven by the inclusion of additional regressors. The proposed identification strategy employs a marginally higher number of control variables than the other measures, which may increase its explanatory power due to spurious correlation. However, this relationship is likely to have only a marginal influence on the results for two reasons. First, by including a number of determinants of firm growth, such as the firm’s age, industry, location, and ownership, the analysis drastically reduces the number of exogenous factors that are likely to influence this relationship. Next, the developed identification strategy is noted to favor relatively simplistic models over more intricate ones. In contrast, if the influence of spurious correlation were considerable, it would instead tend to select group numbers close to its theoretical maximum. Hence, based on this, it is argued that the results of Table 2 are explained by an increased precision in identifying firm size heterogeneity rather than by spurious correlation.