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## The role of innovation

The recent empirical literature on high-growth firms suggests that innovativeness might represent a distinguishing feature of this type of firms. High-growth firms tend to be more concentrated in high-tech sectors or in sectors closer to the techno-logical frontier, and they also tend to be more involved than other firms into R&D and patenting activity. There is no direct evidence, however, about the innovation patters of persistent high-growth firms. In this section we replicate our regression analysis including among the regressors the value of intangible assets (INTASS) as a firm-level proxy for innovativeness.

In Table 2.9 we show the results of the specification pooling data across man-ufacturing and services. Point estimates and patterns of statistical significance for the economic and financial variables are substantially identical to the main results presented in the previous Section. The picture is basically unchanged also concern-ing size and age, although adding intangibles aﬀect the estimated coeﬃcient of these two latter variables. Intangibles present themselves a negative and significant co-eﬃcient in the odds of being “other” vs HG firms, at least in some cases (pooled analysis, and in Italy and the UK), in accordance with the evidence that high-growth firms tend to be more innovative. However, intangibles do not have any statistically significant discriminatory power in distinguishing persistent high-growth performers from “simple” high growers.

We find consistent results also when distinguishing manufacturing and services, in Table 2.10 and Table 2.11. Once again, structural and demographic variables can discriminate between HG and other firms, but they have limited role in distinguish-ing persistent high-growth firms. The only noticeable diﬀerence with respect to the aggregate analysis is in services, where intangible assets are found to increase the probability to be in the HG group (in Italy and in the UK) or in the PHG category (in France), but at very low levels of statistical significance.

Overall, we confirm our key finding that firms who display a subsequent pat-tern of persistent high-growth performance are neither more productive, nor more profitable, nor characterized by peculiar financial conditions in the initial years.

### Growth and innovation: descriptive evidence

As a first assessment of the relationship between sales growth and innovation, we compare the growth rates across “innovators” and “non-innovators”, that is split-ting the sample between firms that do or do not undertake each specific innovative activity. Of course, non-innovators according to one variable may still be innovative firms, in the sense that they may be engaged in other types of innovative activ-ity. This issue becomes relevant when we build a set of “innovation strategies” (see Section 3.6).

Table 3.3 shows basic descriptives of sales growth across the diﬀerent subgroups. We see that “Innovators” tend to display larger mean and median growth rates than “non-innovators”, regardless the innovation variable. The median, in particular, is positive for “innovators” and negative for “non-innovators” for all the proxies.

We next look at the unconditional distribution of sales growth rates, again across “innovators” and “non-innovators”. Kernel densities (on log-scale) are reported in Figure 3.1. The estimates reveal diﬀerences between the two groups, with “non-innovators” generally more concentrated in the left part of the support. These asymmetries in the left tail are particularly pronounced for the two R&D indica-tors. The diﬀerences in the right tails are less clear-cut, with the two distributions substantially overlapping, irrespective of the innovation variable considered. This implies that “non-innovators” are nevertheless able to enjoy extreme positive growth events. The visual inspection is confirmed by a Fligner and Policello (1981) test of distributional equality (henceforth FP), allowing to assess which of the two distribu-tions stochastically dominates the other along each innovation variable considered. The null hypothesis of stochastic equality is always rejected (except for technological acquisition) and the positive FP statistics imply that “innovators” present a larger probability to experience superior growth performance than “non-innovators”.

Overall, the observed distributional asymmetries suggest that the larger average growth observed within innovators can be due to innovators being more able to avoid below-average growth rates, rather than to stably reach a positive and high-growth performance. All these findings, however, just provide an unconditional picture.

**Growth and innovation: main results**

In this Section we present our main analyses. The empirical strategy is to separately investigate the relationship between sales growth and each innovation activity, con-ditional on a set of controls. We first look at the eﬀect of innovation variables on average growth, through standard panel techniques, and then exploit fixed-eﬀects quantile regressions to estimate asymmetries in the innovation-growth relationship across growing and shrinking firms.

The baseline empirical model is a panel regression equation Gi,t = α IN N OVi,t−1 + β × Zi,t−1 + ui + ǫi,t , (3.3).

where IN N OV stands alternatively for one of the diﬀerent innovation variables, Z is a set of firm-level control variables, ui is a firm fixed-eﬀect, and ǫi,t a standard error term.

Both IN N OV and the controls enter with a 1-year lag, at least partially control-ling for potential simultaneity.2 The set of controls includes the lagged dependent variable (Gt−1), a proxy for size in terms of number of employees (in log, ln Empl), firm age computed by year of foundation (in log, ln Age) and three dummy variables, respectively taking value 1 if firm i is exporting (Export), or receiving public finan-cial support to innovation (P ubF und), or belonging to an industrial group (Group) in year t − 1, and zero otherwise.3 Table 3.4 reports the corresponding descriptive statistics. All the specifications also include a full set of industry (2-digit) and year dummies.

#### Fixed-Eﬀects quantile regressions

The distributional analysis provided in Section 3.4 recalls one of the major stylized fact of industrial dynamics, stating that firm growth rates are characterized by a fat-tail distribution. This implies that standard regression analysis, capturing the eﬀect on the expected value of the dependent, can only deliver a partial picture. Quantile regressions have become popular in recent years in the literature on firm growth and innovation (see review in Section 3.2), exactly because one can uncover the asymmetries characterizing the innovation-growth relationship along the spectrum of the growth rates distribution. Existing studies, however, beyond focusing only on R&D and patents, apply basic quantile regression methods, which are easy to implement, but come at the cost of not controlling for unobserved firm-specific factors.

In this Section we exploit the Fixed-Eﬀects quantile regression estimator devel-oped in Canay (2011), explicitly allowing for firm-specific unobserved heterogeneity. Essentially, the method consists of a transformation of the response variable that allows to “wash out” the firm fixed eﬀect. First rewrite our baseline Equation (3.3) as Yi,t = Xi,t′β + ui + ǫi,t , with E(ǫi,t|Xi, ui) = 0 (3.4).

**Testing complementarity of innovation activ-ities**

In this Section we explore if sales growth originates from combinations of diﬀerent innovation activities, rather than from each single one. Indeed, firms in reality often pursue diﬀerent innovation strategies, undertaking diﬀerent innovation activities at the same time. The outcome of innovation in terms of sales growth can be diﬀerent depending on the complexity of the strategy pursued, in terms of the number and the type of activities performed at the same time. Each diﬀerent combination may entail specific costs and challenging coordination issues, while also increasing the ability to create and capture growth opportunities.

The key question is whether diﬀerent innovation activities are complements in their eﬀect on growth. We explore this issue through the concept of super-modularity. In general terms, consider a function f (X), where X is a vector of binary arguments, X={X1, X2, . . . , Xn}, with Xj = {0, 1} depending whether a certain action j is undertaken or not. Action Xj and Xi are complements if f is supermodular in Xj and Xi, that is f (Xj ∨ Xi) + f (Xj ∧ Xi) ≥ f (Xjc) + f (Xic) , (3.6).

The idea is simply that the eﬀect of choosing Xj on the objective function f is larger if also Xi is chosen at the same time, as compared to other possible combina-tions where Xj appears but Xi is not chosen. This approach to complementarity is adopted by a number of studies exploring complementarity of diﬀerent innovation inputs, or of obstacles to innovation, in generating innovation outputs (see, e.g., Mohnen and Roller, 2005; Cassiman and Veugelers, 2006; Catozzella and Vivarelli, 2014). We apply the same framework to explore super-modularity of the growth function with respect to innovation activities.

We proceed as follows. Firstly, we group our original seven innovation activities into four categories, capturing the diﬀerent types of innovation output (product vs. process) and the diﬀerent innovation inputs (R&D vs. other inputs), also distin-guishing between internal vs. external sources. Accordingly, we define the following dummy variables:

• Internal innovation (INT) = 1 if the firm performs intra-mural R&D, 0 other-wise.

• External innovation (EXT) = 1 if the firm performs extra-mural R&D or acquires embodied or disembodied knowledge, 0 otherwise.

• Product innovation (NEWP) = 1 if the firms introduces new products.

• Process innovation (PROC) = 1 if the firms introduces new or significantly improved processes.

**Table of contents :**

**1 Introduction **

**2 Economic and financial determinants of persistent high-growth per- formance **

2.1 Introduction

2.2 Background literature and motivation

2.3 Data and identification of persistent high-growth firms

2.3.1 Firm characteristics

2.4 Distributional analysis

2.5 Regression analysis

2.6 The role of innovation

2.7 Size and age

2.8 Alternative regression models

2.9 Conclusion

2.10 Appendix

**3 Innovation strategies and firm growth **

3.1 Introduction

3.2 Background framework

3.3 Data

3.3.1 Data and sample

3.3.2 Main variables

3.4 Growth and innovation: descriptive evidence

3.5 Growth and innovation: main results

3.5.1 Panel estimates

3.5.2 Fixed-Effects quantile regressions

3.6 Testing complementarity of innovation activities

3.7 Conclusions

3.8 Appendix

**4 Does persistence of innovation spur persistence of growth? **

4.1 Introduction

4.2 Background literature and research objectives

4.2.1 On the persistence of innovation

4.2.2 On the persistence of growth

4.2.3 Connecting persistence of innovation to persistence of growth .

4.3 Data and empirical setting

4.3.1 Source and variables

4.3.2 Measuring persistence of growth and innovation

4.3.3 Empirical methodology

4.4 Results

4.4.1 Descriptive evidence

4.4.2 Main evidence

4.4.3 Robustness checks

4.5 Conclusions

**5 French summary **