Innovation strategies and firm performance

Abstract

Innovation is often seen as crucial for firm survival and as a way for firms to differentiate themselves from their rivals. However, innovation studies are vague about the actual importance of different innovation strategies. In this study, we distinguish between pure product, process, organizational, and marketing innovations and their combinations. We use a (balanced) panel data set with more than 15,000 firm-year observations for manufacturing firms to analyze the performance of firms with different innovation strategies. Additionally, we investigate from a societal perspective whether innovation facilitates less efficient firms to catch up, or whether firms already utilizing best practices are the main beneficiaries. Using Data Envelopment Analysis (DEA), we find the highest increase in firms’ performance among the firms with innovation strategies that combine product innovation with other innovation types. This finding applies to both the short and the longer term. We also conclude that catch-up is strongest among the firms adopting pure process innovation, whereas the other innovation strategies are primarily associated with frontiers shifts.

1 Introduction

Innovation is often considered one of the most important business and policy tools today. According to a recent study by McKinsey, 84% of executives say that their future success is dependent on innovation.¹ Likewise, politicians in many countries emphasize the need for innovation and allocate considerable resources to boost innovation in the private and public sectors.

It has been widely acknowledged that innovation significantly contributes to firm performance (see, e.g., Hashi and Stojcic (2013)). However, it is less clear which innovation types improve performance and whether innovation types need to be combined to enhance performance. The focus in most studies has been on the impact of innovation in general or product innovation in particular on average firm performance. However, some practitioners and industry experts argue that if firms focus primarily on product innovation, they miss out. For example, Damanpour and Evan (1984) and Damanpour (1991) conclude that organizational and marketing innovation are essential to the growth and effective operation of firms. This finding supports the idea that more innovation types should be considered when making strategic innovation decisions.

Our analysis shows that focusing – as has traditionally been done – on only one innovation type is usually insufficient. It is important to consider combinations. Conceptually, this is not surprising. Different types of innovation often go hand in hand. For example, a product innovation in a firm that produces bread could be a new bread mix that consumers bake themselves. To produce the mix, the production process might need to be updated (process innovation). Such an update may also imply a reorganization of the tasks between workers (organizational innovation). Finally, the performance of the new product on the market may depend on the way it is marketed, especially if it is a product that is significantly different from the other products that the firm makes (marketing innovation). Thus, one might expect an innovation strategy that combines several innovation types to be more beneficial.

In this paper, we use data envelopment analysis (DEA) which allows us to understand not only the general importance for firms, but also the importance for the most efficient firms. The use of DEA to identify best practices is common in the productivity and efficiency literature. The advantage of using DEA is that it does not require the specification of a functional form to be fitted. Further DEA does not suffer from multicollinearity problems (Cubbin and Tzanidakis 1998).

This study makes three important contributions. First, we consider innovation strategies, i.e., combinations of innovation types, rather than individual innovation types in isolation. Thus, we can analyze whether firms combining innovation types rather than practicing just one type have higher performance. In theory, with 4 innovation types, there are 16 potential innovation strategies, but we disaggregate the group of innovative firms in several ways to understand which strategies are more important.

Second, in addition to examining the average importance of innovation, we use nonparametric DEA to focus on best practices.² This allows us to investigate whether weak firms with innovation primarily catch up to stronger firms or whether strong firms with innovation primarily increase their lead. Such information has policy relevance and will facilitate the development of more targeted innovation-boosting activities that are likely to have a significant importance.

Third, in addition to the association between innovation and performance in a single period, we examine the association after 3 years, which allows us to better understand the changing performance of different groups of firms over time.

In the first part of the article, by using DEA we find similar results as in previous articles, e.g. Tavassoli and Karlsson (2016), Karlsson and Tavassoli (2016) and Aldieri et al. (2021). However, we can also conclude that only innovation strategies that encompass product innovation and at least one other type of innovation have a positive correlation with performance. Such combinations are associated with a 10% higher value added. Since we estimate an efficiency frontier, we can conclude that the most productive firms with innovation activities increase performance more that firms with weak productivity, which increases the performance inequality rather than reducing it.

The paper is organized as follows. Section 2 presents the research background and main hypotheses. In Section 3, the research methodology is presented. Section 4 introduces the underlying data, and Sections 5 and 6 present our empirical findings. Finally, Section 7 contains the discussion, conclusions, and final remarks.

2 Literature and hypotheses

The literature on the economic impacts of innovation activities has gone from studying the use of innovation inputs such as R&D expenditures (see, e.g., the seminal paper by Griliches (1979)) to examining the whole innovation process, including innovation output, through productivity equations (Crepon et al. (1998)). The argument is that high levels of R&D expenditures do not guarantee any given innovation level, and innovation in general may occur through channels other than R&D expenditures. Most recent articles have used innovation output (such as a dummy variable taking the value of 1 if the firm has introduced a new product) as an indicator for innovation activities. For an overview of the results, see, e.g., Hall (2011) and Hashi and Stojcic (2013). In this literature review, we focus on the literature examining combinations of innovation types.

In 2006, Chudnovsky et al. (2006), Griffith et al. (2006), and Parisi et al. (2006) were among the first to use binary indicators for different types of innovation. All three articles examine two innovation types: product and process. However, only Chudnovsky et al. (2006) allow for different effects depending on the occurrence of no innovation, one innovation type, or both innovation types. Studying manufacturing firms in Argentina, they find a positive effect of approximately 14% arising from combining product and process innovations but no effect arising from product innovation alone. This is an early demonstration of the importance of examining innovation strategies, i.e., combinations of innovation types, rather than innovation types in isolation.³

The role of organizational and marketing innovation has also been investigated. Junge et al. (2016) use Danish data to show that a combination of product and marketing innovation in skill-intensive firms results in significantly faster productivity growth, an approximately 13% increase over a 3-year period. However, there is no effect from adopting only product or marketing innovation.

Polder et al. (2010) and Ballot et al. (2015) examine the relation between firm performance and three innovation types – product, process, and organizational innovation. Polder et al. (2010) find that product and process innovations do not exert a positive effect without organizational innovation and conclude that the strongest productivity effects are derived from organizational innovation.

To the best of our knowledge, the only two studies based on sufficiently large data sets that examine how different combinations of four innovation types impact performance are Evangelista and Vezzani (2010) and Tavassoli and Karlsson (2016).⁴ Evangelista and Vezzani (2010) use cluster analysis and divide firms into four categories based on innovation mode (product, process, organizational or complex). They include these four innovation modes in a performance model and conclude that all four groups of firms on average perform better than noninnovative firms, with complex innovation having the highest impact. Unlike our strategy, the authors rely to a large extent on firm characteristics and not solely on actual innovation types to divide their sample firms into the four innovation mode categories. This approach makes it difficult to conclude anything about the impact, for example, of product innovation adoption compared to that of product innovation adoption in combination with other innovation types. This limitation is unfortunate since such information would clearly be relevant for those firms considering becoming innovators.

Similarly, Tavassoli and Karlsson (2016) consider four innovation types but divide firms into four categories defined by innovation strategies, which are based on the number of innovation types present. They distinguish between simple, low-, medium-, and high-complexity innovation strategies. They find that firms that practice all four innovation types on average have higher labor productivity than noninnovative firms. Somewhat surprisingly, they find that firms combining three of the four innovation types have significantly lower labor productivity than noninnovative firms. Additionally, when comparing firms that practice one innovation type, independent of which type it is, to firms that do not practice innovation at all, they find no significant effect in the presence of sufficient controls for unobserved heterogeneity.

In conclusion, both Evangelista and Vezzani (2010) and Tavassoli and Karlsson (2016) find that firms that combine all four innovation types gain more. This is in line with the findings of Walker (2004), who concludes that different innovations influence each other and need to be implemented in conjunction. This finding is important since firms often choose to implement different innovation types simultaneously (Karlsson and Tavassoli 2016). Our study extends this work by examining whether firms with some innovation strategies experience higher growth in performance than others. Furthermore, both of the studies reviewed above examine the static average effect, whereas we also analyze firm performance relative to that of the firms implementing best practices and how performance changes over time.

Recently Aldieri et al (2021) have studied the relationship between product, process, organizational, and marketing innovation activities combined with human and physical capital. They conclude that innovations may be considered capital-augmenting. They also conclude that combining innovation types often increase the positive effects on firm’s productivity. However, they study innovation types and not innovation strategies.

In another strand of the literature complementarities between different innovation types are examined. The most recent article, Zhang (2022) uses survey of SME Chinese firms, and studies 6 innovation types. The conclusion is that the only additive benefits arise from a combination including product innovation. Also, there is no gain from process innovation unless it is combined with organizational innovation.

Considering the literature, our first hypothesis is general and concerns the positive relationship between innovation and firm performance:

Hypothesis 1: Firms with innovation have higher performance than noninnovative firms.

In testing Hypothesis 1, the main goal is to determine whether firms with innovation perform better on average than firms without innovation. The next goal is to understand whether firms with certain innovation strategies perform better than others. If, for example, product innovations are typically developed together with organizational innovations, a comparison of the product and organizational innovation dummies may suggest that firms with product innovation and organizational innovation have higher performance than firms with only product innovation or organizational innovation. Empirically, it has been found that innovation types are interdependent (see Carboni and Russu (2018)). Therefore, an interesting question is whether firms with both pure and combined innovation strategies experience higher performance and, if so, whether one group or the other group experience the highest performance, which leads to the next hypothesis:

Hypothesis 2: Firms that combine types of innovation have higher performance than firms with only one type of innovation.

In addition to the validity of the above hypothesis, firms may be interested in knowing whether there are any combinations of innovation types that dominate others. Gunday et al. (2011) conclude that the higher the level of organizational, process or marketing innovation, the higher the level of product innovation. Additionally, in the literature, the success of new products is linked especially to an increase in sales since successful innovation contributes considerably to the satisfaction of existing customers and the gaining of new customers (e.g., Wang and Wei (2005)). Based on insights from firm visits and conversations with innovation consultants, we propose the following hypothesis:

Hypothesis 3: Firms that pursue innovation strategies that include product innovation have the highest performance.

Thus far, the discussion has been on the gains from adopting innovations for the average firm. However, it is also interesting to understand whether all innovative firms have higher performance or whether some types of firms have higher performance than others. From a policy perspective, it might be interesting to have more knowledge about whether the most productive firms with innovation increase the lead to other firms or whether less efficient firms catch up. Knowledge about how the most productive firms are affected is also interesting because the effects on these firms not only suggest how the very best can benefit right now but also indicate how less efficient firms might benefit in the years to come. We have not been able to find anything about this issue in the literature. Therefore, our last hypothesis is built on our belief.

Given that more efficient firms are better at translating input into output, we believe that they are also better at being innovative. Hence, we expect that the best performing companies that are already at the frontier compared to other companies within the country will become even more competitive from being innovative and will thus be able to more easily compete with the best performing companies from other countries. We therefore propose the following hypothesis:

Hypothesis 4: The most productive firms with innovation activities have so strong performance that they expand their lead to other firms, which implies that inequality in performance increases.

The next section explains the analytical approaches that we use to test the above hypotheses.

3 Analytical approach

As discussed in the previous section, we are interested in more knowledge about the impact of innovation on performance. First, we are interested in the average association between innovation and firm performance because it may give us an idea of the potential industry-wide benefits of such impacts. Second, we are interested in better understanding whether new practices are associated with performance converge or diverge, i.e., whether these practices primarily is associated with weak firms catching up or benefit only strong firms.

To conduct these evaluations, we use a nonparametric production model estimated from the observed firm data and a minimal set of general economic production properties. Below, we briefly explain the idea behind our model. For details, see Appendix 1.

We begin with a conceptual model, where innovation is considered a separate activity a that affects the transformation of inputs x in the form of labor and capital to output y in the form of value added. Of course, this transformation and the impact of innovation may also depend on other factors z, such as the industry, the skill intensity of the workers and how efficiently the firm has transformed labor and capital into value added in the past (see Fig. 1 below). We thus allow for the possibility that a given innovation type or strategy a has different impacts among different firm types z and among firms that are more or less labor or capital intensive, x.⁵

Fig. 1

Conceptual model

To analyze the model, we use DEA-based performance evaluations. DEA (data envelopment analysis) has previously been proven to be a useful tool for evaluating firm performance either before and after a change or by comparing the performance of a group of firms that change their business practices with a group of firms that do not (see, e.g., Abri and Mahmoudzadeh (2015), Giokas et al. (2015), and Chen and Ail (2004)). In this article, we use both methods.

Given that DEA might be unknown to some readers, Fig. 2 presents the underlying idea. The red dots represent firms that innovate, and the blue dots represent firms that do not innovate. The red (blue) line envelopes the frontier, i.e., the best-performing firms, of the innovative (noninnovative) group of firms. DEA-based performance evaluations examine the distance from the dots, i.e., firms, to the frontier, which is called their efficiency (the efficiency score). In this article, we use output efficiency, which refers to the efficiency score measuring how much a firm could expand its value added without changing its inputs if it were as productive as those firms on the frontier. These efficiencies are most commonly measured using the so-called Farrell (1957) measures, where larger values of the output (in)efficiency score indicate worse firm performance – or greater possibilities for improvement. To calculate the Farrell (1957) output efficiencies, we use linear programming. For information on practical implementation, see Bogetoft and Otto (2011) and Bogetoft and Otto (2011).

Fig. 2

Possible impacts of innovation a for firm type z

Removing outliers is particularly important in DEA because individual observations can have a considerable impact on the frontier. Therefore, for the data set we use in this study, we first removed all firms that have capital or value-added values in the top and bottom 1%. Next, we removed additional outliers by using the so-called super-efficiency method, designed specifically for frontier outlier identification; see Bogetoft and Otto (2011).⁶

More specifically, Fig. 2 illustrates a situation in which innovation, a, increases productivity for large firms and lowers it for smaller firms using best practices compared to a situation of no innovation, a_NO. Compared to noninnovative firms, the group of innovative firms has a frontier that is shifted outward for larger values of x. At the same time, we see that there is more variation in the red dots below the best-practice frontier than in the blue dots below the frontier. Hence, innovators are positively associated with an increase in the performance spread.

Using the Farrell measures, it is possible to measure not only average performance but also changes in performance across time and to decompose these changes into catch-up effects and frontier shifts, as just discussed in relation to Fig. 2.

To analyze the average impact of innovation, output efficiencies are averaged within and compared across innovation groups. To analyze the catch-up effect, the average output efficiencies are compared within the innovation groups before and after adopting an innovation strategy. If the average distance to the frontier increases over time, it indicates that over time, the weak firms are falling further behind the firms that use best practices. To analyze a frontier shift, we compare the frontiers from the different innovation strategy groups against a fixed reference frontier constructed from all the firms in our data set across years. If the frontier for an innovation group moves closer to the reference frontier, then the best firms have improved.

Our catch-up and frontier effect analysis is similar to so-called Malmquist analysis, which is particularly popular in the productivity analysis literature for studying changes over time (see, e.g., Bogetoft and Otto (2011)). One difference is that we use a fixed base, which avoids the so-called circularity problem of traditional Malmquist analysis. Another and more significant difference is that we use subsampling to enable comparisons between different innovation strategy groups. For more details, see the last part of Appendix 1.

4 Data

The data used in this study are taken from several sources made available by Statistics Denmark. Information on innovation activities is from a mandatory survey about innovation called the Community Innovation Survey (CIS). After removing outliers and firms with missing information, we have 3621 firms with both survey information for year t-2 to t and register data for t-3, t, t + 1, t + 2, and t + 3, leaving us with a data set from 2005–2015 with more than 15,000 firm-year observations.

The main variables of interest in this paper are from the innovation information in the CIS survey. Four different innovation types are included, namely, product innovation, process innovation, organizational innovation and marketing innovation, as defined by the Organisation for Economic Co-operation and Development (OECD) (2005). The innovation can either be new only to the firm or new to the world. The four innovation types are measured as binary variables. For more information on the data and the variables, see Appendix 2.

As discussed in Section 2, there are likely some benefits from combining innovation types; therefore, we need to work with what we term innovation strategies.

We initially divided firms into 16 = 2⁴ groups according to innovation strategy, which depends on the presence or absence of each of the four innovation types. The largest group in our sample is composed of noninnovators (35%). The second largest group is at the other extreme, with all four innovation types present at the same time (14%). All other groups have between 1 and 7% of the firm-year observations. To simplify the analysis, we considered different possibilities for aggregating the strategies. Based on conceptual similarities and the number of observations present in each group, we combined the original 16 strategies into 7 innovation strategy groups. Table 5, column 4, in the results section presents an analysis of all 16 strategies and confirms that our grouping is an appropriate way to aggregate the strategies:

NO: no innovation.⁷

Product (PROD): only product innovation (new physical products).

Process (PRCS): only process innovation (new production processes).

Organizational (ORG): only organizational innovation (new organizational methods).

Marketing (MAR): only marketing innovation (new marketing methods).

Product combined (PROD + ): product innovation and at least one of the other innovation types.

Other combined (OTHER + ): observations with no product innovation but with two or more of the other innovation types.

In the following, the data on the firms in the seven innovation strategy groups are described. Table 1 shows the distribution of firms across the seven innovation strategy groups as well as across industries and size groups. Interestingly, 48% of all firms and 74% of all innovative firms use a combined strategy, confirming the importance of examining innovation strategies rather than innovation types. The industry groups are aggregations of the Statistical Classification of Economic Activities in the European Community (NACE) codes according to technological intensity, ranging from high-technology (M1) to low-technology (M4).

Table 1 Distribution of firms across industries and firm sizes by innovation strategy groups

We see that the high technology-intensive sectors, M1 and M2, have larger shares of firms with the product combined strategies than the less technology-intensive sectors, M3 and M4. We also see that in the less technology-intensive sectors M3 and M4, almost half of all firms engage in no innovation activities. The size groups are defined by the number of employees and range from firms with fewer than 50 employees to firms with 250–500 employees. A large share of the firms have fewer than 50 employees, among which 48% are not innovative and 35% use a combined innovation strategy. Only 10% of firms with 250–500 employees are not innovative, and 72% use a combined innovation strategy. These differences will be controlled for in the empirical analysis.

Table 2 shows the average number of employees, capital, value added (for period t) and share of educated employees (for period t-3) in the different innovation strategy groups. Firms that do not innovate tend to be smaller in terms of the number of employees, the amount of value added and the capital level and have a smaller share of employees with at least 16 years of formal schooling.

Table 2 Average number of employees, amount of capital, value added and share of highly educated workers by innovation strategy groups

5 Empirical results

To analyze the importance of innovation, we calculated the efficiency scores for each firm against a pooled variable-returns-to-scale DEA frontier based on all firms in year t. For details on the estimation procedure, see Appendix 1.

Table 3 shows the efficiency scores from the DEA, first for all observations in the first row and then dividing firms into those adopting and not adopting innovation in periods t-2 to t in rows 2 and 3, respectively. There are sizable differences in efficiency scores across firms, with a mean efficiency score of 3.09 and a standard deviation of 1.14. Hence, the mean firm could expand its value added by a factor of 3.09 before reaching the pooled frontier. Twenty-eight firms constitute the reference frontier and hence have an efficiency score of 1. Five percent of the companies could improve their value added by a factor of 5.32 or more if they were as efficient as the most efficient firms in terms of transforming their inputs into output, whereas 5% of the more efficient firms could improve their value added by a factor of only 1.46 or less.

Table 3 Efficiency scores from a pooled DEA

In general, firms that engage in innovation have lower mean efficiency scores, i.e., are closer to the pooled best-practice frontier, than noninnovative firms. This is the case for both firms with innovation close to the frontier and firms with innovation farther away, as the efficiency scores are lower for firms that engage in innovation not only at the mean but also at different percentiles.

To obtain a more hands-on understanding of the importance of innovation, we can compare the mean efficiency score among innovative firms and the mean score in the NO group. We see that the NO group value of 3.29 is 10% higher than the mean value of 2.98 for innovative firms ($\frac{3.29}{2.98}=1.10$). We can intuitively think of this 10% as the potential average percentage increase in value added for a given level of capital and labor usage when a firm adopts at least one innovation type 1.5 years after the innovation is introduced relative to engaging in no innovation activities.⁸ The size of the impact is similar to that in earlier findings (see Section 2).

5.1 Tobit regression

The efficiency scores from the DEA, reported in Table 3, are based on the simplifying assumption that all firms using a given innovation strategy are comparable. We correct for the mix of labor and capital used, but we do not account for other factors that may impact the transformation of the production factors into value added. This means that when examining mean efficiencies, the results might penalize “good” performers that operate in an unfavorable external environment or have unfavorable firm characteristics and reward “poor” performers that operate in a favorable external environment or have favorable firm characteristics.

To remedy this problem, our approach is to perform a so-called second-stage analysis, where a Tobit model is applied to the efficiency scores from the pooled DEA model to separate the effects of innovation from the effects of business cycles (time), the technological intensity of the industry, and the extent to which firm workers are highly educated.⁹ We can also include lagged efficiencies to control for unobserved characteristics that allow some firms to be better at transforming inputs into output. The Tobit approach assumes that the distributions of the efficiency scores are truncated normal.¹⁰ Tables 4 and 5 show the results of seven different Tobit regressions. First, Hypotheses 1–3 are tested in Table 4. In Table 5, the innovation decisions are disaggregated to better clarify whether some of the active innovation strategies are better than others.¹¹

Table 4 Tobit regressions

Table 5 Tobit regressions

Instead of the Tobit regression, propensity score matching could be considered as an alternative method to investigate the importance of innovation from other factors. However, propensity score matching is typically employed when the control group (firms with no innovation activities) outweighs the treatment groups substantially. This is not the case in our study. Therefore, we suggest that Tobit regressions offer a superior choice in our context.

In the first column of Table 4, the abovementioned control variables are included together with a variable that takes on the value 1 if the firm succeeded in adopting at least one of the four innovation types and 0 otherwise. This variable is labeled “Active strategy” and has a significantly negative coefficient, indicating that firms with an active innovation strategy are closer to the frontier, i.e., better at transforming inputs into output, than noninnovative firms. This finding supports Hypothesis 1, which states that firms with innovation have higher performance than noninnovative firms. Furthermore, the coefficients on the other firm characteristics in column 1 indicate that firms with a higher share of educated workers are more efficient in their use of labor and capital. The coefficient on the lagged efficiency scores from year t-3 is positive and significant, indicating that the firms that are more efficient in year t-3 are also more efficient in year t. In addition, column 1 shows, somewhat surprisingly, that medium-to-low technology-intensive firms have the lowest efficiency scores on average. However, this effect is significant only at the 10% level.¹²

In column 2, instead of including the “active strategy” dummy, we include a dummy for whether the firm had 1 new innovation (labeled a pure strategy) and another dummy for whether the firm successfully introduced innovations within more than one of the four innovation types (labeled a combined strategy). These variables allow us to test Hypothesis 2: Firms that combine types of innovation have higher performance than firms with only one type of innovation. First, only the coefficient of the combined innovation strategy is significant; for firms with a pure innovation strategy, we see no association between innovation and firm performance (this finding is similar to that of Tavassoli and Karlsson (2016)). Interestingly, Hypothesis 1 is no longer supported after disaggregating the group of innovative firms. Second, we test whether Hypothesis 2 is supported by testing whether the coefficient for the firms with combined innovation strategies is significantly lower than the coefficient for the firms with pure innovation strategies at the bottom of Table 4, column 2. The result confirms that the coefficient for the combined strategies is significantly lower. The test has an F score of 7.82 and a P value of 0.00, supporting Hypothesis 2.

Finally, in column 3, Hypothesis 3: Firms that pursue innovation strategies that include product innovation have the highest performance. Again, new variables are constructed as follows: one dummy variable taking the value of one if a firm has one new innovation (labeled as a pure strategy), another dummy variable taking the value of one if a firm has more than one new innovation and includes product innovation (labeled as PROD + ), and still another dummy variable taking the value of one if a firm has more than one new innovation and does not include product innovation (labeled as OTHER + ).

Of the three active innovation groups, only PROD+ has a significant coefficient; only companies with new product innovations and at least one other innovation type are associated with higher returns relative to companies without any new innovations. To test Hypothesis 3, we test whether the coefficient on PROD+ is significantly lower than the coefficient on the pure strategies and OTHER + . The test results are at the bottom of Table 4, column 3. Both tests show that the coefficient on PROD+ is significantly lower, supporting Hypothesis 3.

In conclusion, the results in Table 4 support Hypotheses 2 and 3 even after controlling for other firm characteristics. It should be emphasized that the results presented in Table 4 are consistent with the conclusion that innovation strategies improve the efficiency of firms. It should, however, be noted that an alternative interpretation is that there may be some unobserved shock that both gives incentives to introduce innovation strategies and to improve performance. Since we do not use data with random assignment of innovation across firms, the innovation strategy coefficients may be biased. While we cannot rule out the interpretation that omitted variables are important, we do a few things to reduce this possibility. Specifically, we try to handle simultaneity, reverse causality, and sample selection by using control variables in the year before innovation takes place, calculating the efficiency score after innovation takes place, and conducting the second stage analysis using the Tobit model to the efficiency scores of the DEA model as presented in the table. These modifications make it less likely that omitted variable bias is an important issue. Still, for this reason we do not make causal conclusions throughout the paper. Finally, it should be mentioned that to the best of our knowledge other papers similar to ours face the same challenge as we do with respect to causality.

We now turn to the question of whether there is any particular active innovation strategy that is better than the others, and we present different disaggregation’s of innovation activities in Table 5. For comparability with earlier studies, column 1 of Table 5 first shows the results of a Tobit regression that includes innovation types. We conclude that firms with each of the innovation types, except marketing, have significant higher value added for a given level of labor and capital input and this result is not explained by covariation with technological intensity, business cycles or past performance. Firms could on average expand their value added by a factor of 3.366 as measured by the constant term before reaching the pooled frontier. The introduction of at least product innovation reduces the potential for improvement from 3.366 to 3.249 ( = 3.366-0.117). This shows that a firm engaged at least in product innovation has a value added level that is a factor of 1.036 ( = 3.366/3.249) of firm without innovation, i.e., has 3.6% higher value added.

As discussed in Section 2 and shown in Table 4, there are likely some benefits from combining innovation types. The simple approach of grouping firms according to the presence or absence of a given innovation type may therefore be somewhat misleading. We, therefore, next in column 2 include dummies for each of the 6 active innovation strategy groups.

Dividing the pure strategies into four types, the results indicate that on average, none of the groups of companies with pure strategies do better than the noninnovative group of firms, which is similar to our findings in Table 4, column 2. As in Table 4, column 3, the combined innovation strategy PROD+ has a considerable and significant coefficient, while OTHER+ has no significant coefficient when controlling for other firm characteristics. The group of firms in PROD+ has an average efficiency of 3.349-0.288 = 3.061. The average value added level for firms practicing PROD+ innovations is therefore 10% ( ≈ (3.349/3.061)-1) higher than the value added level of firms without any innovation activities. This result highlights how important it is to examine innovation strategies rather than innovation types. A suggestion for firms to improve performance, if we just looked at innovation types would be to implement production innovation; however, the analysis of innovation strategies reveals that other types of innovation might also be required.

In a final set of Tobit regressions, we identify the coefficients on the different types of PROD+ and OTHER+ strategies. First, we tried to split up the PROD+ and OTHER+ observations according to the number of innovation types involved. This is similar to what Tavassoli and Karlsson (2016) do in their study. The resulting coefficients (corrected for employee education, industry, time and lagged efficiency scores) are shown in column 3 of Table 5. We see that the coefficients decrease with the number of innovation types that we combine with product innovations, i.e. efficiencies improve. This suggests that firms with product innovation have higher performance for each additional innovation type that they add. For the two subgroups of OTHER + , neither coefficients are significant.

Finally, in column 4 of Table 5, we split the PROD+ and OTHER+ strategies according to the exact combinations of the four innovation types involved and again examined the efficiency scores. All combined strategies that include product innovation (except for the combination of product and marketing innovation) have a significant effect, whereas none of the combined strategies that do not include product innovation have a significant coefficient. This indicates that firms with combined innovation strategies that include product innovation have higher performance, except for the innovation strategy combining product and marketing innovation. Of course, in general, the more innovative strategies we allow for, the smaller the groups become, and therefore, the standard deviations of the estimates become larger. We therefore do not want to draw any final conclusions as to which combinations are most performance-enhancing. Nevertheless, the results emphasize our general finding that combining innovation types is attractive, and the table indicates that these results are not explained by just a few of the PROD+ strategies. Firms with a combined innovation strategy including product innovation have higher performance than other firms. The combination with other innovation types turns out to be of less importance as long as the firms have adopted product innovation and have adopted more than one innovation type.

In summary, the lack of higher firm performance from having only one innovation type is interesting (Table 4, column 2). Even more interesting, the lack of higher firm performance applies to all four innovation types (Table 5, column 2). It seems that a winning strategy is not to engage in any particular innovation type. Combining product innovation with other innovation types, on the other hand, is linked to considerably higher firm performance (Table 4, column 3 and Table 5, column 2). This indicates that product innovation is a very important type of innovation for manufacturing firms, but firms that combine product innovation with other innovation types have higher performance. However, the types of innovation combined with product innovation is less important as long as firms have product innovation and have adopted more than one innovation type (Table 5, column 4). Finally, the results suggest that firms achieve even higher performance with each additional type of innovation (Table 5, column 3). Of course, we cannot conclude that a single innovation type is not useful, only that the effects achieved by our given measurement approach are not large enough to be significant and that the combination of innovation types is valuable.

After disaggregating the innovation activities, as shown in Table 5, Hypotheses 1 and 2 are no longer supported, as none of the firms that adopt pure strategies nor any of the firms that adopt combined strategies without product innovation have on average more efficient relative to the group of firms with no new innovations. However, Hypothesis 3 is still supported even after disaggregating the innovation activities and removing the covariation with technological intensity, employee education, business cycles and past performance. Hence, the findings in support of Hypotheses 1 and 2 in Table 4 were driven by firms with PROD+ strategies.

Our findings can be compared to a recent article by Aldieri et al (2021), who examine the same four innovation types. As in our conclusions, they find that both process and product innovation have positive effects on firms’ productivity, which is also in line with findings in Corsino et al (2011) and Hall et al (2009). They also highlight the importance of joint implementation of the two innovation types. In Table 5 we show that the association is significant only when product and process innovations are combined with other innovation types, while pure innovation strategies do not have a significant positive link to firm performance – Aldieri et al (2021) are not able to comment on that due to the structure of their study. They also conclude that organizational activities are beneficial when combined with process innovation. Our study shows that this only holds if the two types are combined with product innovation. In our finding there are no significant efficiency gains when only combining organizational and process innovation – unfortunately Aldieri et al (2021) did not analyze this particular innovation strategy. However, Guisado-Gonzalez et al. (2017) did, and they found conditional complementarity between process and organizational innovation, but only when product innovation is present. As suggested by Hollen et al (2013), this is probably due to the fact that the introduction of organizational innovation reduces the tension within the firm that is going to implement process innovation. Finally, both Evangelista and Vezzani (2010) and Tavassoli and Karlsson (2016) find that firms that combine all four innovation types gain the most. But they were not able to draw conclusions about the individual innovation strategies.

Thus far, we have documented that product innovation inside most combinations is associated with higher value added in the short run. We have studied the average impact on firms, and we have corrected business cycles (time), technological intensity, the education level of workers and the earlier performance of the firm.¹³ In Section 6, we investigate in more detail the importance of innovation over time.

5.1.1 Complementarities in efficiency between innovation types

Recent articles have tested whether the additional effect that companies achieve by combining innovation types leads to complementarity between innovation strategies or whether it is more of an additive effect. We can do this on the regression in Table 5 column 4. To test complementarities between innovation strategies, we use the conditional supermodularity procedure of Ballot et al. (2015). Following Guisado-Gozalez et al. (2017), Serrano-Bedia et al. (2018) and Zhang (2022), we conducted the test in two steps. First, we conduct a Wald test to test the relationship between two types of innovation. If the relationship is not statistically significant, no further testing is required, and we can conclude that there is no complementarity or substitution between the two types of innovations. Second, if the relationship is statistically significant, we wanted to conduct a test for inequality to determine whether the two types of innovations are complements or substitutes. Unfortunately, all Wald tests were insignificant, and we therefore conclude that firms with simultaneous execution of multiple types of innovations have additive effects on firm performance. It is important to understand that this does not mean that companies with innovation strategies that include multiple types of innovation do not have higher value added than firms without these strategies. Rather, it simply means that firms that, for example, introduce both product and marketing innovations have higher value added of a magnitude that is equal to the sum of the extra value added in firms with product innovation only and the extra value added in firms with marketing innovation only.

The finding is somewhat consistent with previous findings. For example, when testing the complementarity/substitutability of performance between product, quality, and organizational innovation, Zhang (2022) found only additive effects. Guisado-Gozalez et al. (2017) examine the complementarities between exploration, exploitation and organizational innovation and conclude that in most cases there were no complementarities. The exception was between exploration and organizational innovation when exploitation is present and between exploitation and organizational innovation when exploration is present. Ballot et al. (2015) examines product, process and organizational innovations, examining conditional complementarities in performance in the United Kingdom and France. They conclude that in both countries there was only one case of conditional complementarities, namely in product and process innovations, when organizational innovation was not present. Furthermore, they conclude that process and organizational innovations are substitutes when product innovations are present. In summary, previous studies have also had difficulty finding complementarities between innovation types. In our case, the lack of complementarity between innovation types could well be a data issue related to the relatively small sample for four innovation types.

6 The dynamic importance of innovation on performance variation

In this section, we analyze how innovation is associated with both the level of (subsection 6.1) and the changes in (subsection 6.2) firm performance over time.

6.1 Performance level over time

In this subsection, we examine the performance levels of the seven different innovation groups in the years after the innovation strategy is decided. We use the same Tobit regression as in Tables 4 and 5, changing only the efficiency score (the dependent variable) from period t to periods t + 1, t + 2 and t + 3. The results are shown in Table 6.

Table 6 Tobit regressions over time

The first column is identical to column 2 in Table 5. Columns 2, 3, and 4 show the coefficients on the different innovation strategy groups for periods t + 1, t + 2 and t + 3, respectively. Over time, none of the pure strategies result in performance that is significantly different from that of the no group except for organizational innovation in period t + 3. It is not surprising that this effect is not present in the short run but only after some time, as organizational changes take time to implement, and their importance takes time to emerge.

Examining the combined strategies, PROD+ has a significantly negative coefficient in all years, with its value increasing from t to t + 3, which is true even though we control for the lagged efficiency score and share of educated workers, ensuring that it is not just the more efficient firms that use this innovation strategy. We can therefore conclude that the most promising innovation strategy is a combined strategy that includes product innovation both in the short run and in the longer run.

6.2 Performance changes

In this subsection, we examine performance changes (instead of levels) among firms in the seven different innovation strategy groups in the years after their innovation strategy is decided. This is done to better understand whether all companies potentially gain from innovativeness or whether only weak companies seem to catch up or strong companies seem to become even stronger.

To examine this, we first calculate the efficiency scores using DEA and a bootstrapping technique to take into account different sizes of innovation strategy groups (for details, see Appendix 1). Second, we calculate the following ratio:

$${Efficiency\; ratio}=\frac{{{Efficiency}}_{t}}{{{Efficiency}}_{t+3}}$$

The ratio shows how firm performance changes over time.

To study whether weak firms catch up, we perform a DEA for each of the seven innovation strategy groups, measuring the output efficiencies relative to the frontier within the group. Since we compare only against the frontier of firms using similar innovations, we do not measure whether one innovation type is more productive than another. Instead, the efficiency scores measure how much firms deviate on average from the frontier of firms with similar innovations. If the mean efficiency ratio is larger than 1, then it indicates that the performance spread decreases from period t to period t + 3; i.e., there is convergence in performance from period t to period t + 3.

The results are shown in Table 7 labeled “Catch-up effect” (columns 1–3). Three ratios are above 1: Companies not having any innovations, those only conducting process innovation and those combining several innovation types, not including product innovation. In these innovation strategy groups, the performance spread decreases from period t to t + 3. We can therefore conclude that for these groups, weak firms have been catching up to their strong counterparts.

Table 7 Catch-up effect and frontier shift estimates

On average, the weak companies in the NO group catch up to efficient firms by 40%, which is surprisingly high; we therefore perform some extra analyses to see if this group differs from the other groups. The NO group does, in general, consist of younger companies, and we therefore believe that this high number is due to young companies becoming more efficient and taking over a larger share of their respective markets. These firms have new products and, therefore, do not need innovation in the same way as do already established firms. Within the group of companies carrying out pure process innovation and combining innovation not including product innovation, weak companies catch up to their stronger counterparts by 9 and 3%, respectively.

For the groups of pure product, pure organizational, pure marketing and product combined with other innovation strategies, the ratios are all below 1. In these groups, the performance spread increases from period t to t + 3. Weak firms are not able to catch up to their stronger counterparts; e.g., on average, the weak companies in the product combined group have moved 20% further away from the frontier.

When comparing the groups of firms with active innovation strategies to those without an active innovation strategy, column 2 shows that all ratios are smaller for the different active innovation groups than for the NO group. Hence, high performing firms with innovation increase the lead to weak firms with innovation, which increases the inequality in performance among these firms relative to that among noninnovators.

To test whether the different innovation combinations is associated with significant reductions in the performance spread, we conduct several tests: exact permutation t test, a t test with unequal variance, a bootstrap t test and finally a Wilcox rank sum test. We tested the hypothesis that among innovators, innovation is associated with a catch-up effect that is smaller (spread that is larger) than that in the NO group. Given that all tests reach the same conclusions and have similar p-values, we include only 1 column with test results, column 3. We see, for example, that in the case of process innovation, there is significant performance divergence compared to the NO group. The less efficient firms engaging in process innovation catch up less than weak companies in the NO group.

In conclusion, innovation is associated with increased equality in performance within some groups and to increased inequality for other groups, but for all groups, we can conclude that innovation is associated with increased inequality in performance relative to that in the NO group.

Next, we investigate how different types of innovation affect best practices. Here, we compare the frontiers that result from the different types of innovation against the same fixed reference frontier constructed from all the firms in our data set across years (for details, see Appendix 1). Hence, the efficiency score measures how close the frontier for the group is to the reference frontier. The efficiency ratio measures the change in best-practice performance over time. An efficiency ratio above 1 indicates that the frontier of the group is moving closer to the reference frontier.

The results are given in Table 7, labeled “Frontier shift” (columns 4–6). For all 6 active innovation strategy groups, the value of the efficiency ratio is above 1, meaning that the frontier of the group is moving closer to the reference frontier. The product combined strategy group has the largest efficiency ratio. In this group, strong firms become, on average, 46% better at transforming capital and labor into value added. The pure process strategy has the lowest efficiency ratio above 1. In this group, strong firms move only 4% closer to the reference frontier.

The only group with a ratio below 1 is the NO group, meaning that the frontier of the group is moving further away from the reference frontier.

When comparing the groups with an active innovative strategy to that without an active innovation strategy, we see in column 5 that all the ratios are larger for the different active innovation groups than for the NO group. Pure process innovation is the only group with a ratio close to 1. Compared to the noninnovative firm’s frontier, that of firms involved in product innovation combined with other innovation strategies moves an additional 67 percentage points further out over time.

To investigate whether the observed differences are significant, we use the same tests as above. We test the hypothesis that there is no difference between the frontier improvements relative to those in the NO group against the alternative hypothesis of an additional positive innovation-based improvement in best practices. We see from column 6 that the effects are significant in all cases. The pure organizational and product combined groups, for example, are associated with a significant improvement in best practices of 37 and 46%, respectively, from year t to t + 3. During the same timeframe, the noninnovative firms deteriorated by 21% in terms of improvement.

In summary, innovation is associated with increased frontier performance for all active innovation strategy groups.

Looking at the numbers from Table 7, we see that the innovation strategy impacts the groups quite differently. For example, for the pure process innovation group, weak companies catch up, whereas strong companies barely improve. Hence, in this group, innovation gains mainly those weak companies. The effect is not strong enough for the average company to have a significant association in the Tobit regression. If, instead, examining those companies with a combined strategy without product innovation, weak firms again are shown to catch up, and here, strong companies improve. Hence, in this group, innovation is associated with improving performance for both weak and strong companies relative to other companies.

For the rest of the active innovation groups, weak companies do not catch up. However, for pure product innovation, for example, weak companies stay around as inefficient as they were in period t, but strong companies catch up to more efficient companies from other groups. Hence, in this group, innovation is mainly associated with improving performance for strong companies compared to other companies.

Finally, the most extreme case occurs for the product combined strategy group. Here, weak companies deteriorate by 20% relative to the frontier of the strategy group, i.e., the coefficient equals 0.80, whereas strong companies move the frontier 46% closer to the reference frontier, i.e., the coefficient equals 1.46. Hence, in this group, innovation is associated with improving performance for strong companies, which is not the case for weak companies. This is not to say that performance in weak companies is not associated with improved performance; they simply cannot mimic the improvement speed of strong companies. We know from the Tobit analysis that on average, there is a positive association between innovation and firm performance.

Based on these findings, we generally confirm Hypothesis 4: The most productive firms with innovation activities have so strong performance that they expand their lead to other firms, which implies that inequality in performance increases. The only exception is the pure process innovation group. Pure organizational innovation and the product combined strategy provide an extreme illustration of Hypothesis 4.¹⁴

In contrast to Tables 4 and 5, the results in Table 7 are based on the simplifying assumption that all companies applying a particular innovation strategy are comparable. We correct for the mix of labor and capital employed and use bootstrapping to take into account that the innovation strategy groups are of different sizes, but we do not consider other factors that can influence the conversion of production factors into value added. To address this issue, we reran the result for Table 7 using propensity score matching to include only comparable companies. The variables used are company size and company share of the workforce with a higher education, as these two variables explain a large part of the differences in value added between companies. We use nearest-neighbor matching without replacement to shrink the no group so that it is the same size as the treatment group it is being compared to. The results are not included, but not surprisingly, the mean difference between the no group and the different treatment groups narrows. For 10 of the 12 cases – 6 for the catch-up effect and 6 for the frontier shift – the conclusions are however the same. Innovation is associated with increased performance inequality between innovative firms compared to non-innovative firms even after ensuring that the firms compared are similar.

7 Summary and conclusions

In this paper, we analyzed how different types of innovation in firms are related to firm performance. To understand the role of these innovation types, we distinguished among product, process, organizational, and marketing innovations as well as different combinations of these. Additionally, we studied the relationships between innovation strategies and firm performance in both static and dynamic settings based on a balanced panel of more than 15,000 firm-year observations. Finally, we investigated whether within the different innovation strategy groups less efficient firms catch up or whether the higher performance is more at the firms that are already using best practices.

Economic performance was measured at the firm level using Farrell output efficiencies in a model in which labor and capital are the inputs, value added is the output, and the underlying relationship between the inputs and outputs is estimated using nonparametric DEA models. Using bootstrapping, we ensured that sample size biases were corrected, and to test the significance of the results, we used several tests as well as more traditional Tobit regressions.

In our sample of Danish manufacturing firms, 35% engage in no innovation, while 17% engage in innovation within one innovation type. Interestingly, 48% of all firms and 74% of all innovative firms use a strategy of combining innovation types, confirming the importance of examining innovation strategies rather than innovation types. Using DEA, we demonstrated that in general, the different types of innovation have significant and sizable association with performance for different types of firms.

When moving from the study of innovation types (done in earlier studies) to the study of innovation strategy groups, we can no longer confirm that firms with innovation perform better than firms without innovation (Hypothesis 1) for strategies that include only one innovation type. Even more interesting, the lack of improved firm performance (relative to noninnovative firms) applies to all four innovation types when studied individually.

After dividing the combined strategies into those that include product innovation and those that do not, we cannot even confirm that firms that combine innovation types perform better than firms that practice only one type of innovation (Hypothesis 2). Only firms with combined strategies that include product innovation tend to be more efficient on average than those firms with strategies that include only one type of innovation (confirming Hypothesis 3). Firms that combine product innovation with one or more other innovation types have value added that is on average 10% larger after approximately 1.5 years after the introduction of the innovations compared to the average of the group of firms without innovation.

The dynamic analyses indicate that firms that combine innovation strategies that include product innovation have higher performance not only in the short run but also in the longer run. This is so even after ensuring that this result is not driven by better performing firms adopting these innovation strategies.

What is interesting is the lack of higher performance among companies that adopt only one type of innovation. In order to achieve significantly higher performance on average, companies apparently have to combine product innovations with other types of innovations. It is less important what types of innovations a firm has, but rather the more types of innovations there are, the higher the average performance is likely to be.

Finally, within active innovation strategy groups, the most productive firms tend to increase their lead, and weak firms do not catch-up leading to increasing inequality in performance (Hypothesis 4). However, innovation strategies impact the groups of firms quite differently. For example, in the group of firms with a pure process or combined strategy without product innovation less efficient firms catch up, whereas for a product combined strategy, weak companies deteriorate, and efficient companies become even stronger. Therefore, companies can choose an innovation strategy that aligns with their goals and objectives.

From the policy perspective, our findings suggest that innovation plays a central role in the growth of firms. Nations and industrial organizations are therefore well justified in creating innovation-friendly environments. There are, of course, many more specific tools available, e.g., R&D tax rebates to incentivize innovation further and the dissemination of information about the possible importance that different innovation strategies have on performance.¹⁵ With regard to resources intended to improve firm performance, this study suggests that they be limited to manufacturing firms engaged in product innovation and at least one other type of innovation.

Many of the insights above can help fine tune the innovation focus of firms depending on their industry, capital, labor, performance, and primary aims, e.g., catching up to or further improving best practices. According to our study, 66% of the companies can potentially improve their performance by altering their approach to innovation. From the management perspective, our findings suggest that it is not enough to be innovative. Companies need to adopt product innovation and combine it with other innovation types. Furthermore, if the firm knows that it is among the less efficient firms, it is worth putting extra emphasis on process innovation.

Of course, our findings raise many additional issues to investigate. Let us point to just one conceptual issue and one methodological proposal. Conceptually, it would be relevant to better understand and possibly split the group of noninnovative firms. Some of these are likely doing relatively well despite their lack of innovation, e.g., due to a lack of competitive pressure, while others would benefit from innovation but face various roadblocks that would be interesting to better understand.

Methodologically, it would be interesting to find better counterfactuals than the group of noninnovative firms. Using propensity score matching as in Bogetoft and Kromann (2018), we might potentially identify firms with more similar characteristics and thereby remove (or at least reduce) the observable differences among the firms that self-select into the different innovation types. In view of the extensive comparisons introduced above using both individual and pooled frontiers, however, we leave these matched comparisons to future research.

Appendices

Appendix 1: Analytical approach

(Figures 3, 4)

Fig. 3

Performance measurement, F = B/A

Fig. 4

Catch-up effect and frontier shift

In this study, we use a nonparametric production model estimated from observed firm data and a minimal set of general properties of economic production.

1.1 Conceptual model

We use performance evaluations based on data envelope analysis (DEA). The DEA approach was originally proposed by Charnes et al. (1978). This seminal contribution was subsequently refined and applied in a rapidly increasing number of papers. In his 1992 bibliography, Seiford (1994) lists no fewer than 472 relevant published articles and Ph.D. theses. In his 2002 bibliography, Tavaras (2002) includes more than 3000 contributions. DEA now involves a well-established set of methods and is also described in several textbooks, including Bogetoft (2012), Bogetoft and Otto (2011), Coelli et al. (1998), and Cooper et al. (2007).

Formally, let us consider a general case in which each of n decision-making units (DMUs), i ∈ I = { 1, 2…, n}, transforms p inputs, $x=\left({x}_{1},{x}_{2},\ldots ,{x}_{p}\right)$, into q outputs $y=({y}_{1},{y}_{2},\ldots ,{y}_{q})$. In our specific application the DMUs are firm-year observations that transform labor and capital into value added for a specific year. Hence, p = 2 and q = 1, implying that for any firm i we have two inputs, ${{x}^{i}=(x}_{1}^{i},\,{x}_{2}^{i})$, and one output, denoted by ${{y}^{i}=y}_{1}^{i}$.

Additionally, let T* be the production possibility set:

$${T}^{* }=\{\left(x,y\right)\in {R}_{0}^{p+q}\,|{x}\,{\rm{can}}\,{\rm{produce}}\,y\}$$

The non-parametric DEA approach estimates T* from the observed production $\left({x}^{i},{y}^{i}\right),{i}\in I$, and evaluates the efficiency of the DMUs relative to that of the estimated technology. The estimation T of T* is constructed according to the so-called minimal extrapolation principle: The estimated technology is the smallest subset of ${R}_{0}^{p+q}$ that contains the actual observations, $\left({x}^{i},{y}^{i}\right),{i}\in I$ and satisfies certain production economic regularities. In our case, the regularities are convexity and free-disposability of inputs and outputs.¹⁶

As demonstrated in many papers and textbooks (e.g., Bogetoft and Otto (2011)), the minimal extrapolation empirical estimate T of T* is

$$T=\left\{\left(x,y\right)\in {R}_{0}^{p+q}{\rm{|}}\exists \lambda \in {R}_{0}^{n}\!\!:\,x\,\ge \,\mathop{\sum }\limits_{i\in I}{\lambda }^{i}{x}^{i},y\le \mathop{\sum }\limits_{i\in I}{\lambda }^{i}\,{y}^{i},\mathop{\sum }\limits_{i\in I}{\lambda }^{i}=1\right\}$$

That is, a production plan (x, y) is feasible if there exist a convex combination of actual observations that uses weakly less of all inputs to produce weakly less of all outputs. When there is only one output as in our application, we can also think of the approach in terms of an estimated production function:

$$P(x)=\max \left\{y{\rm{|}}\left(x,y\right)\in T\right\}$$

That is, P denotes the highest possible output (value added) which can be achieved with input x (given amounts of capital and labor). The production function is piecewise linear, increasing and concave; alternatively, it can be defined as the smallest increasing and concave production function for which no observations are above the function.

To measure the performance of a specific company, we generally use a measure known in the productivity analysis literature as the Farrell (1957) output efficiency measure. In the case of one-dimensional output, this measure is simply the ratio of the best-practice output to the actual output for a given input vector:

$${\rm{Output\; efficiency}}=\frac{{\rm{Maximal\; output}}}{{\rm{Actual\; output}}}$$

Formally, if a firm i uses xⁱ to produce yⁱ, then the Farrell output efficiency is

$${F}^{i}({x}^{i},{y}^{i})=\frac{P({x}^{i})}{{y}^{i}}$$

The numerator denotes what the output would have been if the firm was efficient while having xⁱ as input. The denominator shows the firm’s actual output while having xⁱ as input. Thus, larger values of the output (in)efficiency score Fⁱ indicate worse firm performance or large opportunities for improvement. If firm i is efficient, then Fⁱ = 1 which theoretically is the lowest possible value of Fⁱ. The output efficiency can be easily illustrated in the case with one input and output, as in Fig. 3. Here, a specific firm has used C to produce A. The firm is clearly not efficient, since for the same input level, the firm could have produced the level of output B. Thus, the efficiency of the firm is given by Fⁱ = B/A. A value of 1.3, for example, suggests that the company can increase its output by 30% simply by operating more efficiently and by taking advantage of the opportunities according to best practices.

It is worth mentioning that while firms with an output efficiency score greater than 1 certainly suffer from inefficiency, those with a score of 1 are deemed efficient simply because no other firms in the sample are more efficient. Obviously, this situation does not rule out the possibility of improved performance. We simply have not seen examples of this, i.e., we rely on best practices as opposed to some underlying true but unknown technology.

In a DEA model, the calculated efficiency score is a performance score relative to a chosen sample of firms. Thus, the same firm may be fully efficient when being measured relative to one sample and inefficient relative to another sample. In the first part of the article, we use a pooled production model, where each firm is measured relative to all firms in the sample. In the second part of the article separate production models are used, in which a firm is measured relative to the smaller group of companies that use the same innovation type. The use of both pooled and separate frontiers comes with several advantages; it provides an approach for comparing the best practices of different groups. Additionally, the mean efficiency of a group of firms relative to their separate frontier becomes a measure of the performance spread. Large average distances to an innovation-specific frontier suggest that this innovation type is associated with large variation in performance.

1.2 Measurement over time: Catch-up effect and Frontier shift measures

In our dataset firms are observed several years. In the analysis, observations from the same firm in different years are simply treated as different observations. In the second part of the analysis, we would like to see how a certain innovation strategy affects the firm’s performance in the future. The starting year is denoted by period t, while the following three years are denoted by periods t+1, t+2, and t+3 respectively. The starting year defines each firm’s innovation strategy. In this analysis we still use the Farrell measures, but we will measure changes in performance, rather than using the efficiency score from a single year and decompose these changes into catch-up effects and frontier shifts which are described in the following. Compared to the first analysis where the average effect was considered we here focus on whether the weak companies are able to catch-up or it is more the already efficient firms that mainly gain from innovation.

Consider the situation in Fig. 4. Here, a particular firm is observed at two different points in time, t and u. In our interpretations, we assume that t < u. The actual inputs and output of the company in the two periods are indicated by the two red dots. In addition, we have the period specific production frontiers, P(·| t) and P(·| u), as well as a common reference frontier, P(·| R). In our analyses, the latter is the frontier of all firms from all periods, independent of the innovation strategies used.

Now, to investigate the changes from time t to time u, we consider the extent to which the firm catches up to those firms that have implemented best practices. We can measure the firm’s performance relative to that of firms using best practices in the same period using $F\left(t\right)=\frac{P({x}_{t}| t)}{{y}_{t}}$ and $F\left(u\right)=\frac{P({x}_{u}| u)}{{y}_{u}}$. If the former is larger than the latter, then the firm is catching up to the firms using best practices. The extent to which the firm catches up (or falls behind) can therefore be measured as the ratio of output efficiencies:

$${CU}\left(t,u\right)=\frac{F(t)}{F(u)}=\frac{\frac{{y}_{u}}{{y}_{t}}}{\frac{P\left({x}_{u}|u\right)}{P\left({x}_{t}|t\right)}}$$

Here, values of CU(t, u) above 1 mean that the firm catches up and that performance variation is reduced; this finding also means that the growth in actual output exceeds what is expected from the change in frontier. Note that the calculation of catch-up corresponds to comparing the red and the blue points in two periods.

In order to focus on the changes in best practices over time we can measure the distance from these best practices to the reference technology with $G\left(t\right)=\frac{P({x}_{t}| R)}{P({x}_{t}| t)}$ and $G\left(u\right)=\frac{P({x}_{u}| R)}{P({x}_{u}| u)}$. Graphically, this corresponds to comparing the blue points to the black points. Again, if G(t) is larger than G(u), the frontier has improved. A measure of the improvement in best practices, frontier shift FS, is therefore

$${FS}\left(t,u\right)=\frac{G(t)}{G(u)}=\frac{\frac{P\left({x}_{u}|u\right)}{P\left({x}_{t}|t\right)}}{\frac{P({x}_{u}|R)}{P({x}_{t}|R)}}$$

Values of FS(t, u) above 1 mean that the best-practice frontier is getting closer to the reference frontier over time or, equivalently, that the output growth along the specific frontiers exceeds the output growth along the reference frontier.

Large values of the CU(t, u) and FS(t, u) are therefore attractive; it is attractive to catch up over time, and it is even more attractive to catch up to an improving frontier.

One important detail here is that it would be inappropriate to compare F and G ratios across different groups with different sizes because it is easier to be (relatively) efficient in a smaller group. In our analysis, different innovation strategy groups have very different sizes. To make efficiency scores comparable across different innovation groups, we use a bootstrapping technique to estimate efficiency scores for each observation. The approach will not be described in detail here. We simply note that each observation still gets an efficiency score, but that the efficiency score is obtained as an average of 1,000 draws with replacement.¹⁷ This approach allows us to compare F and G across all innovation strategy groups even though they have different sizes.

Notably, the CU measure is similar to the catch-up measure used in a so-called Malmquist analysis, which is particularly popular in the productivity analysis literature for studying changes over time (see, e.g., Bogetoft and Otto (2011)). The FS measure is also related to the idea of frontier shifts (technological progress) used in a Malmquist analysis. One difference between our method and Malmquist decomposition is that we use a fixed base, here referred to as the reference frontier. This allows us to look at changes over different periods of time and avoid the so-called circularity problem of traditional Malmquist analysis. Another and more significant difference between this approach and traditional Malmquist analysis is that we use subsampling to enable comparisons between different innovation groups, despite some innovation groups being larger than others.

Appendix 2: Data, survey questions and other details about the variables

(Figure 5)

Fig. 5

Timeline

2.1 Data

The data used in this study are taken from several sources made available by Statistics Denmark.

Information on innovation activities is from a mandatory survey about innovation, known as the Community Innovation Survey (CIS). This survey is sent yearly to a new sample of firms. Statistics Denmark selects the firms to generate a representative sample of Danish firms within the manufacturing and service sectors. In this study, we use survey data from the 5-year period 2008–2012 for manufacturing firms with more than 10 employees and fewer than 500 employees.¹⁸ A major strength of the CIS is that it collects data on a large sample of manufacturing firms. Even more importantly, since 2007, it has been mandatory for the selected firms to complete the CIS survey. The questions in the CIS relate to firm innovation activities over the previous three years. In Fig. 5 below, we label these as years t-2, t-1 and t.

We have enriched the survey data set by merging it with register data on individual firms. We use register data from 2005–2015 with more than 15,000 observations. The information extracted from this data concerns value added, fixed assets, the number of employees, industry, and workers’ educational levels. The survey about innovation activities contains answers from 1444 firms from 2008–2012. Combining these two data sets gives us 3621 firm-year observations for survey information for years t to t-2 and available register data for years t-3, t, t + 1, t + 2, and t + 3.

To account for the time that it might take for an innovation activity to affect firm performance, we introduce a time lag between the innovation and performance impact in the analysis. This lag structure also limits the problem of reverse causality between innovation and performance. There is no generally accepted length of time needed for innovation to affect performance. Studies have found that the average time it takes for innovation to impact firm performance varies across industries and may range from one to several years.¹⁹ In the main analysis, we therefore measure performance (via labor, capital and value added data) in year t (see Fig. 5). This approach allows for an average of 1.5 years for innovation to impact firm performance. In the dynamic study, we also consider the years t+1, t+2 and t+3.

In some of the analyses, worker education as well as industry and lagged efficiency scores are included. In other parts of the analysis, changes are used to control for fixed unobserved heterogeneity. Worker education is measured at the end of the year before the innovation activity has taken place (at the end of year t-3 in Fig. 5). This is done because the skill level of the workforce might impact whether a firm becomes involved in innovation, whether it succeeds in innovating, and the extent to which it gains from innovation. Lagged efficiency scores are included to account for unobserved firm characteristics that impact a firm’s skill in transforming input into output. The information is from a DEA model based on year t-3 data. Industry and year dummies are included to account for business cycle variations and industry differences.

2.2 Survey questions from Statistics Denmark

Product innovation:

INPDGD

New or significantly improved good into the market

Process innovation:

INPSPD	New or significantly improved method of production into the market
INPSLG	New or significantly improved logistics, delivery or distribution system into the market
INPSSU	New or significantly improved supporting activities into the market

Organizational innovation:

ORGBUP	New business practices for organizing work or procedures
ORGWKP	New methods of workplace organization
ORGEXR	New methods of organizing external relations

Marketing innovation:

MKTDGP	Significant changes to the esthetic design or packaging of a product
MKTPDP	New media or techniques for product promotion
MKTPDL	New methods for product placement or sales channels
MKTPRI	New methods of pricing goods or services

We construct four dummy variables taking the value 1 if at least one of the questions within the specific innovation type is answered with a yes. Otherwise, the value is 0, implying that the firm’s answer is no to all questions for the specific innovation type.

2.3 Other variable definitions

In our analyses we additionally use the following variables from Statistics Denmark:

Value added (gf_vtv): The difference between the value of production and consumption in whole kroner.

Value added is calculated as follows: Turnover + Work performed at own expense and entered under assets (AUER) + Other operating income (ADR) + Increase/decrease in inventory consumption - Purchase of goods for resale (consumption of goods, merchandise) (KVV) - Purchase of raw materials, consumables, finished goods and packaging (KRHE) - Purchase of energy (KENE) - Purchase of paid work and subcontracting (KLOE) - Expenditure on rent (UDHL) - Expenditure on the acquisition of small equipment/equipment with short life (UASI) - Expenditure on temporary employment agencies (UDVB) - Expenditure on long-term lease and operating leases (ULOL) + Ordinary losses on debtors (established losses and change in provision for losses (Item 11)) (OTDE) - Other external costs (excluding items of a secondary nature) * (Item 12) (EKUD) - Secondary expenses (SEUD).

Number of employees (gf_aarsv): Number of employees in full-time equivalent (FTE).

This variable should be regarded as an expression of the total workload performed by the company’s employees, regardless of whether they work full- or part-time or whether they have been employed all year or only part of the year.

Capital (gf_aat): Total fixed assets, measured in kroner. The part of assets that is intended for the permanent ownership or use of the company, e.g., buildings, machinery, furniture, patents, licenses and long-term investments of a financial nature such as shares and bonds.

Value added and capital are later manually deflated using the deflators from EUKLEMS.

In addition, we have used the following control variables used in Tobit regressions:

Worker education: The share of workers with 16 or more years of education (a bachelor’s degree or higher). The share is calculated from information on the education level of each of the workers in the company, and the share is merged at the firm level. The education information for each worker is information obtained by Statistics Denmark from each worker’s social security number.

Industry dummies: The manufacturing industry is divided into four groups using Statistical Classification of Economic Activities in the European Community (NACE) codes following the Eurostat indicators on High-tech industry, Annex 3 – High-tech aggregation by NACE Rev. 2: M1: High technology (21, 26); M2: Medium to high technology (20, 27–30); M3: Medium to low technology (19, 22–25); and M4: Low technology (10–18, 31–32).

Lagged efficiencies: Calculated from the DEA model at time t-3.

Year dummies: The year that the survey question was answered for the firm-year observation, which is year t in our descriptions.