The debate about the link between innovation and competition has a long history. One view, dating back to Schumpeter (1934), regards large firms operating in a concentrated market as the main engines of technological progress. Monopolistic firms can more eagerly perform R&D than firms in competitive markets because of rents, low market uncertainty, and stable funding. Theories from various fields, such as industrial organization, international trade, and endogenous growth theory, have confirmed that markups and market barriers are associated with intense innovation (Dasgupta and Stiglitz, 1980; Delbono and Denicolo, 1991; Kamien and Schwartz, 1972; Loury, 1979; Spence, 1984; Vives, 2008). Although empirical support was weak initially, several empirical studies have provided evidence to support this view (Hashmi, 2013; Kraft, 1989; Mulkay, 2019). The opposite view, that competition stimulates innovation, was suggested by Arrow (1962) and also supported both theoretically and empirically (Aghion et al., 2001; Amiti and Khandelwal, 2013; Bento, 2020; Bloom et al., 2020; Lee and Wilde, 1980; Nickel, 1996). In particular, Aghion et al. (2001) argue that firms in a competitive market have greater incentives to innovate and receive the large rent from post-innovation market power than firms protected from competition.

A hybrid of these two views is the inverted U-shaped relationship hypothesis, which harmonizes both the Schumpeterian and Arrowian views. At low levels of initial competition, an increase in the competition level stimulates innovation. However, the marginal effect of competition diminishes as the level of competition increases, and the incentives for innovation reach a peak at an intermediate level of competition. If the initial competition is already intense, then a further increase in the competition level decreases innovation incentives because the margin of economic rent becomes prohibitively small. Aghion et al. (2005) empirically find such a relationship between product market competition and R&D investment based on UK industry data. Tingvall and Poldahl (2006), Askenazy et al. (2013) and Peneder and Woerter (2014) also found similar results, using data from Sweden, France, and Switzerland, respectively.

The literature has also argued that the effect of competition on innovation can depend on surrounding conditions and institutional factors. Hashmi (2013) argues that the distance to the technology frontier influences the shape of the competition–innovation link. Hashmi (2013) finds a mildly negative relationship between competition and citation-weighted patents among US manufacturing firms, which differs from an inverted U-shape for the UK industry found by Aghion et al. (2005), and relates the difference in these results to the advanced technology levels of the US industry.

Institutional conditions also play a role. In their study of EU market reforms, Aghion et al. (2015) provided evidence that competition stimulates innovation conditional on an adequate patent protection system. Firms under a weak patent protection system confront the risk of imitation by competitors, whereas a strong system removes this risk, which is the very rationale for patent protection, and the innovation-stimulating effect of competition can play a role. However, institutional conditions can have the opposite influence on the competition–innovation link. In a laggard economy in which innovation is more of imitation and generics of the existing technologies than a technological breakthrough, weak institutions can rather facilitate these types of innovation and form a positive competition–innovation link. Nuruzzaman et al. (2019), using a dataset covering the Middle East and North Africa, find that strong institutions weaken the positive competition–innovation link.

Further, the relationship between competition and innovation can change by the type of innovation: namely product innovation, which improves the quality­ and variety of products, and process innovation, which reduces costs and improves the efficiency of production and sales processes. Although economic theories tend not to distinguish these two types of innovation, firms’ incentives, costs, obstacles, and required technology levels for these two types of innovation can differ, and this can affect the shape of the competition–innovation link (Weiss, 2003). Although earlier empirical studies tended to use R&D investment and patent as the primary measures, several recent empirical studies separately examine product and process innovation and show that these two types of innovation react differently to competition (Bessonova and Gonchar, 2019; Hecker and Ganter, 2013; Tang, 2006).

Several studies have examined the relationship between innovation and competition in Russia and transition economies and provided mixed results. In the early years of transition, the effects of competition on firms’ reforms or innovative activities were found to be weak (Bhaumik and Estrin, 2007; Djankov and Murrell, 2002; Earle and Estrin, 2003). However, Carlin et al. (2004) showed that non-monopolistic firms were more likely to engage in innovation than mono­polists in transition countries, suggesting the innovation-stimulating effect of competition. Friesenbichler and Peneder (2016), focusing on almost all European and former Soviet Union transition countries with the ES data, supported an inverted U-shaped relationship between the number of competitors and the R&D expenditure. Likewise, Bessonova and Gonchar (2019) found an inverted U-shaped relationship between product innovation and competitive pressure, although a significant effect was not found for process innovation. Further, the shape of the relationship between competition and innovation is not uniform across all firms, and the techno­logy level and ownership structure are considered factors affecting the shape (Bessonova and Gonchar, 2017, 2019). Institutions can also be a factor affecting the shape of the competition–innovation link, considering their condition in Russia and their effects suggested in the literature (Aghion et al., 2015; Nuruzzaman et al., 2019). However, their effects on the competition–innovation link have not been examined in the case of Russian firms.

In the light of foregoing discussion, we propose the following three main hypotheses in the case of Russian firms.

H1. The relationship between competition and innovation can be an inverted U-shape. Such a relationship is widely observed in the literature, including studies­ on Russia, and could be considered a benchmark hypothesis. Nevertheless, we do not preclude the possibility of other shapes, particularly under the following two cases.

H2. Weak institutions can affect the shape of the competition–innovation link. Although the role of institutions in the competition–innovation link is not straightforward, firms can have additional incentives and disincentives for innovation under weak institutions. Specifically, we focus on the court fairness, informal payments (corruption), and the presence of informal firms as institutional conditions, which would be related to weak patent protection and distorted market incentives. We hypothesize that problems in these conditions can hinder the innovation-stimulating effect of competition since the risk of imitation would grow as the number of competitors increases. Consequently, among firms confronting these problems, the shape of the competition–innovation link can deviate from the one among firms not confronting these problems (or those confronting these problems to a lesser extent).

H3. The shape of the competition–innovation link can differ by the type of innovation. The incentives and obstacles for product and process innovation can differ, and this can differentiate the relationships of these types of innovation with competition. The shape of the relationship can further vary by the novelty of innovation.

This study employs the firm-level data obtained from the fifth round of the ES in Russia, jointly financed by the European Bank for Reconstruction and Develoment (EBRD) and World Bank and conducted in 2011/12 (World Bank, 2012). The implemented questionnaire covers a broad range of items on business environments, including innovation activities, the degree of competition, and institutional conditions. The sample firms were selected based on a stratified random sampling and include those operating in the manufacturing, construction, IT, and service sectors and employing at least five workers. Firms in the agricultural sector, employing less than five employees, or operating informally were not covered by the survey. In total, 4,220 firms from 37 regions (oblast) of Russia were surveyed,² and we use 3,774 of them in the main analysis after dropping firms with missing data for the variables to be explained.

In addition, we use the data of the next round survey, the ES 2019 (World Bank, 2019), conducted under basically the identical sampling and questionnaire frameworks, in supplementary estimations.³

The ES 2012 reports various types of innovation activities conducted within the three years prior to the survey. We mainly use the following three binary variables: innovation of all kinds, product innovation, and process innovation. Product innovation takes the value of one if a firm introduced a new or significantly improved product or service in the three years prior to the survey, including both the products new to the market and the imitations and generics of existing products. Process innovation takes the value of one if a firm introduced a new or significantly improved method for production, supply, organizational and management practices, and marketing in the three years prior to the survey. Innovation of all kinds covers both product and process innovation. In supplementary estimations, we divide product innovation by the novelty level and process innovation into three items, innovation in production and supply methods, that in organizational and management practices, and that in marketing methods. Further, we consider the binary variable for firms having invested in R&D.

The main measure of the degree of competition is the number of competitors. The ES 2012 asked firms to report the number of competitors in the market of their main products, which could be local, national, or international. The number was continuously reported up to 100 but reported as “too many to count” for firms faced with more than 100 competitors.

To supplement our discussion, we also use the PCM as a measure of competition. The PCM is defined by

PCM_i = (p_i – c_i)/p_i, (1)

where p_i is the market price set by firm i and c_i is its marginal cost, although we instead calculate the PCM from the sales and variable costs following the practice in the literature (Aghion et al., 2005).⁴ The PCM takes the value of one at the maximum, and higher values indicate a monopolistic market. The PCM close to zero indicates that the market is close to perfect competition. However, since the information needed to calculate the PCM was asked only to manufacturing firms, and approximately a half of them reported the information, we use the PCM only in supplementary analyses.

These two measures of competition have strength and weakness. The number of competitors is the most straightforward measure and would reflect the actual competition conditions that firms encounter in their main markets although, due to its self-reported nature, its value can be disturbed by recalling and cognitive errors. The PCM can reflect further characteristics of competition. For example, two firms in the same market may be faced to different competition conditions if their market powers are different (e.g. one of them is a leader and the other is a follower). The PCM reflects such a difference better than the number of competitors since that difference would be reflected in their prices (sales), although the weakness in our case is the missing information as described above. These two measures also have strength compared to other measures. For example, the Herfindahl–Hirschman Index (HHI) is another measure of competition defined by the sum of the squared market shares over all firms in a market, and a market is conventionally defined by industry or geographic area (or their configuration) in a statistical analysis. However, since a market is more segmented than an industry or its sub-category and the area coverage of a market can vary by firm and product, the HHI may fail to reflect the actual competition conditions faced by firms (Peneder and Woerter, 2014; Tang, 2006). Our measures have strength in this respect since the reported number of competitors and prices (sales) would reflect the conditions of the markets where firms actually compete. Among previous­ studies focusing on Russia, Bessonova and Gonchar (2019) used a unique measure, the level of competitive pressure obtained from the question: “How does competition […] impact the performance of your enterprise?” (Bessonova and Gonchar, 2019, p. 19). Our measure could be considered more neutral since it does not refer to the impact on the firm performance.

Fig. 1 demonstrates the distribution of the number of competitors. The distribution is dense around five and ten competitors. Certain firms were in monopolistic or oligopolistic competition. Firms reporting more than 100 competitors represent approximately 36% of the samples.

Fig. 1.

Distribution of the number of competitors.

Note: Observations are restricted to 3,774 firms used in the estimations to be presented. Source: Compiled by the authors based on World Bank, (2012) data.

Fig. 2 demonstrates the percentages of firms engaging in innovation of all kinds, product innovation, and process innovation, grouped by the number of competitors. Among all firms, competition appears to have inverted U-shaped relationships with innovation of all kinds and process innovation. The percentage of firms engaging in product innovation is constant up to 25 competitors but then tends to decrease with the number of competitors, suggesting a possibility of a threshold effect. Fig. 2 also separately demonstrates the percentages in manufacturing and IT sectors and those in construction and service sectors.⁵ While the intensity of innovation is generally higher in manufacturing and IT sectors, the relationship between innovation and competition also appears to differ. Among manufacturing and IT sectors, innovation, by any measure, reaches a peak at 11–25 competitors. The percentage of product innovation drops starkly with 26 competitors or more. In construction and service sectors, the relationship is relatively flat but appears to be a weakly inverted U-shape by any measure of innovation.

Fig. 2.

Proportions of firms engaging in innovation.

Note: Observations = 3,774 for innovation of all kinds, 3,762 for product innovation, and 3,772 for process innovation (the same observations as those used in the estimations to be presented). Source: Compiled by the authors based on World Bank, (2012) data.

The ES 2012 further asked about the institutional conditions with which the firms were faced. We focus on three factors: namely, the court fairness, the frequency of informal payments to government officials, and the presence of informal competitors. For the court fairness, the survey asked firms if they strongly disagreed, tended to disagree, tended to agree, or strongly agreed with the statement: “[t]he court system is fair, impartial and uncorrupted.” We regard firms that tended to disagree or strongly disagreed as ones perceiving that the court system was unfair. The frequency of informal payments refers to the commonness of such payments in the business of each firm, not the payments by the firm itself.⁶ The survey asked firms if the following statement is always, usually, frequently, sometimes, seldom or never true: “[i]t is common for firms in my line of business to have to pay some irregular ‘additional payments or gifts’ to get things done with regard to customs, taxes, licenses, regulations, services etc.” We regard firms choosing “always” to “sometimes” as ones perceiving informal payments common. The presence of informal competitors was directly asked in the survey with the following question: “[d]oes this establishment compete against unregistered or informal firms?”

These measures reflect the degree of the rule of law and formal protection, although the proportions of firms confronting these problems demonstrate a variation: 66.3%, 40.3%, and 31.2% of firms, respectively, reported that the court was unfair, that informal payments were common, and that they competed against informal firms. Since these measures are subjective, the strength and weakness analogous to the competition measures apply. That is, although these measures may be disturbed by recalling and cognitive errors, they can reflect the actual conditions with which each firm is faced better than objective measures, such as regional or subregional indices of institutional conditions.

We econometrically examine the relationship between competition and innovation. Since the three dependent variables we consider are binary, we employ the Probit model that estimates the probability of innovation. Specifically, we estimate the following equation as our benchmark model, based on the litera­ture of Russia and other transition countries (Bessonova and Gonchar, 2019; Friesenbichler and Peneder, 2016):

Pr(innovation_i = 1) = Φ{f (competitors_i) + X_i δ + θ_j + τ_r}, (2)

where i, j and r — index for firms, industries, and regions, respectively; innovation_i is one of our binary measures of innovation; competitors_i is the number of competitors; X_i is the vector of control variables; θ_j and τ_r are the industry and region fixed effects (or the federal district fixed effects); Φ is the cumulative distribution function of the standard normal distribution; δ is the vector of para­meters to be estimated. We estimate the equation by the maximum likelihood.

We consider several specifications for f (competitors_i). To flexibly reflect a potentially non-linear relationship, such as an inverted U-shape and a threshold­ effect, we mainly use a categorical specification, in which we divide firms into six groups: those competed with 0–2 competitors, 3–5 competitors, 6–10 competitors, 11–25 competitors, 26–100 competitors, and more than 100 competitors. The dummy variables for these groups are used, with 0–2 competitors being the reference category. Although the behaviors of monopolist firms and those competing with one or two firms can be different, the proportion of mono­polist firms is not sufficiently large to be classified as an independent group. Alternatively, we use the following linear and quadratic specification to check the robustness:

f (competitors_i) = I (competitors_i ≤ 100) × [β₁ competitors_i +

+ β₂ competitors_i²] + β₃ I (competitors_i > 100), (3)

where I (∙) is an indicator function taking the value of one if the argument condition is satisfied; β₂ competitors_i² is dropped if a linear form is assumed. As the number of competitors is continuously reported only up to 100 in our data, the effect of having more than 100 competitors is measured by the dummy variable­ for such firms.

To supplement discussion and further check robustness, we first separately examine firms in manufacturing and IT sectors and those in construction and service sectors. Second, several alternative measures of innovation will also be used (we describe the details before demonstrating the results). Third, we estimate the probability of innovation after pooling the data of the ES 2019 to the main dataset. Fourth, we use the PCM instead of the number of competitors.

Then, we examine if and how institutional conditions affect the relationship between competition and innovation with the following model:

Pr(innovation_i = 1) = Φ{f (competitors_i) × institution_i +

+ γ institution_i + X_i δ + θ_j + τ_r}, (4)

where the categorical specification is assumed for f (competitors_i); institution_i represents one of the three dummy variables for firms confronting problems with the institutional conditions. This model allows the relationship to be heterogeneous between firms perceiving and not perceiving these problems.

To account for confounding factors, we employ the following factors as X_i. First, we use the dummy variable for exporting firms and that for firms not exporting but mainly serving the national market (firms not exporting and mainly serving a local market are the reference category). Firms in a large market can be exposed to frontier technologies, which can facilitate their innovation activities. However, this can also confound the competition–innovation link since firms in a large market are likely to confront a large number of competitors, and we directly control for such a confounding effect. Second, we use the dummy variable for foreign-owned firms (the capital of a firm is owned at least partially by foreigners) and that for state-owned firms (the capital is owned at least partially by the Russian national or regional government), with private firms owned exclusively by Russian nationals being the reference category. Foreign ownership can provide technology spillover from international market, whereas the ownership structure can affect incentives and financial flexibility for innovation, particularly in case of Russia (Bessonova and Gonchar, 2017). Third, we use the dummy variable for firms that have training programs. It captures human capital levels of employees and firms’ intentions to invest in human capital, which are expected to be positively correlated with innovation. Fourth, we use the age and size of a firm, the latter of which is represented by the log of the number of employees. These variables reflect the resources, experiences, knowledge, creativity, and the market power that can affect innovation incentives. The list of these variables, as well as the measures of competition, innovation, and institutional conditions, are provided in the Appendix A, with descriptions and summary statistics.⁷

Although we use several control variables and the industry and region fixed effects, our primary focus is to provide a refined association between innovation and competition and our methodology does not fully eliminate endogeneity bias. Two sources of endogeneity could be noted. First, firm-level unobservable factors and omitted variables can be simultaneously correlated to competition and innovation. Second, the reverse causality can also be a concern. For ­example, successful innovation by a firm can increase its market power and cause exit of competitors, leading to a negative association between competition and innovation.

Previous studies have widely used instrumental variables to deal with possible endogeneity. For instance, Aghion et al. (2005), in their panel data study of UK firms, exploited the external shocks of market reform programs and their differentiated timing across industries. Friesenbichler and Peneder (2016), in their cross-country study, used the appropriability in each sector and country. Bessonova and Gonchar (2019) used the regional unemployment and the industry-level entry barrier as instruments. However, an instrumental variable approach can also have cautions, particularly for a cross-sectional study focusing on a single country like ours. Industry- and region-level instruments do not allow the respective fixed effects, making it unable to control for the general differences in the intensities of competition and innovation across industries and regions. Further, in practice, it is generally difficult to apply an instrumental variable to a non-linear model, particularly the one with a categorical specification. Bessonova and Gonchar (2019) employed instrumental variable regressions only for a linear specification and dropped fixed effects in these estimations.

Thus, rather than to employ an instrumental variable in exchange for reduced control of confounding factors, we choose to keep industry and region fixed effects that control for the unobservable factors of the respective groups. This would at least mitigate an endogeneity bias and spurious correlation, even if not fully eliminating them.

We first estimate Equation (2) and employ the categorical specification for the number of competitors. The three measures (innovation of all kinds, product innovation, and process innovation) are used as dependent variables. Table 1 shows the coefficients. The first three columns correspond to the model in which the region dummies are used. On the innovation of all kinds and process innovation, competition has a positive and significant coefficient if the number of competitors is 3–5, 6–10, and 11–25, with the coefficient volume reaching the peak and the significance level being 1% at 11–25 competitors. However, the coefficient volume decreases and becomes insignificant for 26–100 competitors and more than 100 competitors. This implies an inverted U-shaped relationship, with the probabilities of these two measures of innovation reaching the highest around 11–25 competitors. On product innovation, competition does not have a significant coefficient up to 100 competitors. Only firms competing against more than 100 competitors have a lower probability of product innovation with the significance level of 1%. The results are almost the same in the rightmost three columns, where the federal district dummies are used instead of the region dummies, although most coefficients shift slightly downward.⁸

Throughout these estimations, most of the coefficients of other control variables are intuitive and consistent. Exporting firms and firms serving national markets have significantly higher probabilities of innovation than firms operating in local markets (p-value of 1%). Foreign ownership has a positive coefficient, albeit significant only for process innovation (p-value of 5%). Training programs are positively associated with innovation (p-value of 1%). Firm age is not significantly associated with innovation, but the firm size has a positive and significant association (p-value of 1%).

In Table 2, we assume a linear and quadratic form of competition up to 100 competitors (hereafter, the coefficients of control variables are omitted, and we demonstrate only the model with the region dummies unless specified otherwise). For innovation of all kinds and process innovation, the number of competitors has a significant coefficient only under a quadratic specification, supporting for an inverted U-shaped relationship (p-value of 10% for innovation of all kinds and 5% for process innovation). The number of competitors does not affect the probabi­lity of product innovation unless it exceeds 100 competitors, which is in line with the previous result in Table 1.

In Table 3, we separately estimate the innovation probabilities for the firms in the manufacturing and IT sectors and those in the construction and service sectors. The negative relationship between competition and product innovation becomes clearer for the manufacturing and IT firms, and competition begins to lower the probability of product innovation at 26–100 competitors with the significance level of 5%. In contrast, product innovation in construction and service firms is almost independent of competition. The relationship between process innovation and competition appears similar and inverted U-shaped in both groups of firms.

In Table 4, we use the pooled data of the ES 2012 and 2019. The estimation method is slightly modified here by adding the dummy variable for year 2019 and using federal district fixed effects instead of region fixed effects (the region-level location is not available in the ES 2019 data; for the definition of a region and federal district, see footnote 2). The coefficients of competition variables shifted upward compared to the benchmark estimates in Table 2. This can imply that the shape of the competition–innovation link changed slightly between the two years, whereas it can also reflect the bias from the inability to control for the regional characteristics. Nevertheless, the changes in the results are minor, and the overall relationship from the benchmark model is maintained.

Backed to the ES 2012 samples, in Table 5, we use alternative measures of innovation. First, we examine the novelty of product innovation with the following two binary variables: one taking the value of one only if products and services newly introduced by a firm were also new in its market, and the other taking the value of one if newly introduced products or services were neither licensed from other firms nor imitations of products already supplied by other firms (columns 1 and 2). In column 3, we estimate the probability that a firm spent in R&D. The coefficients are similar to those on product innovation in the previous tables. That is, having more than 100 competitors significantly reduces the probabilities of these measures (p-value of either 5% or 1%), but competition below that level does not have large effects (albeit the 10% significant coefficient of having 26–100 competitors in (1)). Thus, a negative relationship between competition and product innovation is robustly observed regardless of the novelty level. Then, we examine the details of process innovation, separately estimating the probability of innovation in production and supply methods, that in organizational and management practices, and that in marketing (columns 4–6). The competition–innovation link has an inverted U-shape in any type of process innovation, although the level of significance varies. Innovation in marketing is the most dependent on competition, and firms facing up to 100 competitors have significantly higher probability of innovation than firms facing 0–2 competitors (p-value of either 5% or 1%). Innovation in production and supply methods has the flattest relationship with competition, and even the peak coefficient (11–25 competitors) is of 10% significance.

Then, we use the PCM as the measure of competition instead of the number of competitors. Since the PCM is measurable only for manufacturing firms, we focus­ on them. Table 6 shows the estimated coefficients. We first employed a linear­ specification. The PCM has a 5%-significant coefficient on the innovation of all kinds. Note that, unlike the number of competitors, higher values of the PCM indicate less competitive market conditions. Thus, the positive coefficient implies that innovation and competition have a negative relationship. In the three rightmost columns, we employed a quadratic specification. However, the squared term does not have a significant coefficient on any measure of innovation. Therefore, with the PCM, an inverted U-shaped relationship is not observed. On the one hand, this suggests the possibility that the relationship between innovation and competition is sensitive with the measure of competition, although we need to pay attention to the decreased sample sizes owing to the missing information. On the other hand, both the results with the PCM and the number of competitors share the view that high levels of competition discourage innovation.

Now we consider if and how institutional conditions affect the relationship between innovation and competition, based on equation (4). We graphically show the results. That is, for each case of institutional conditions and at each level of competition, we estimated the probability of innovation, fixing the control variables at the means. Thus, the difference in the innovation probabilities between given two points indicates the marginal effect of the different levels of competition. We do not report the probit coefficients here since, in an non-linear probability model, a direct comparison of the coefficients of interaction terms can mislead interpretation (Ai and Norton, 2003).

Fig. 3 presents the results (the solid lines represent the probabilities and the shaded areas represent the 95% confidence intervals). In (a), we estimate the probabilities of innovation of all kinds, separately for firms perceiving that the court system is fair and for those perceiving that the court system is unfair. An inverted U-shape is more clearly observed among firms perceiving that the court system is fair, with the peak probability at 11–25 competitors (0.598) being significantly different at a 5% level from the probabilities at 0–2 competitors (0.384) and more than 100 competitors (0.382). The relationship is mostly flat among firms perceiving that the court system is unfair. Similar results are obtained if (c) the presence of informal firms is considered, and the relationship has an inverted U-shape among firms not confronting competition against informal firms, with the peak probability at 11–25 competitors (0.580) being significantly different at least at a 10% level from the probabilities at 0–5 competitors (0.457) and more than 100 competitors (0.383). A technical note is that, when we use the presence of informal firms, we grouped firms competing with 0–2 firms and 3–5 firms into one, since few of these firms compete with informal firms. The relationship is relatively flat if we divide the firms by whether they confront the problems of informal payments to government officials (b), although the peak probability of innovation at 11–25 competitors (0.522 among not confronting this problem and 0.614 among those confronting it) is higher than the probability at more than 100 competitors (0.367 and 0.453, respectively) at least at the 5% significance level.

Fig. 3.

Estimated probabilities of innovation at different levels of competition and institutional conditions.

Note: The solid lines represent the estimated probabilities, and the shaded areas represent their 95% confidence intervals. The levels of control variables are fixed at the means. Source: Authors’ calculations.

In (d) to (f), we consider product innovation. Among firms not perceiving or confronting problems with institutional conditions, the relationship appears to have a weakly inverted U-shape. Although the peak probability (0.321 in (d), 0.249 in (e), and 0.296 in (f)) is not significantly different from the probability­ at 0–2 competitors (or 0–5 for the presence of informal firms; 0.221 in (d), 0.196 in (e), and 0.250 in (f)), it is significantly different from the probability at more than 100 competitors in any case (p-value of 5%) (0.173 in (d), 0.140 in (e), and 0.176 in (f)). In contrast, among firms perceiving or faced with these problems, the relationship appears monotonically decreasing. Although the confidence intervals at 0–2 competitors are often wide, the probability at more than 100 competitors (0.186 in (d), 0.223 in (e), and 0.203 in (f)) is lower than the probabi­lity at 3–5 competitors (0.277 in (d) and 0.33 in (e)) or 0–5 competitors in (f) (0.341) with the p-value of around 5%. In (g) to (i), we consider process innovation. Unlike the previous two innovation measures, the relationship appears to have an inverted U-shape regardless of institutional conditions. Except for firms confronting competition with informal firms, the peak probability of innovation, which is 0.465–0.525 and located either at 6–10 or 11–25 competitors, is different from the probabilities at 0–2 (or 0–5) competitors (0.303–0.383) and those at more than 100 competitors (0.314–0.405) with a 5% or 10% significance level.