What does (not) characterize persistent corporate high-growth?

The sector of principal activity in the AMADEUS dataset is time invariant, measured in the last available year. Manufacturing includes section C, while services include sections G, H, I, J, K, L, M, N, R, S.

The normalization implicitly removes common trends, such as inflation and business cycles effects in sectoral demand. This is in line with many previous studies on firm growth. Also notice that both employment and sales growth rates distributions display the usual fat-tails shape already found in previous studies. In case of employment growth, maximum likelihood estimates of the shape parameter b of a power exponential distribution (see Bottazzi and Secchi 2006) range indeed from 0.45 for French firms to 0.87 for UK firms. The distributions of sales growth rates have b very close to 1 in all countries, thus close to a Laplace distribution. The estimates are stable over the years of the sample period.

One year is obviously lost in computing the log differences.

The number of PHG firms increases, but it never exceeds the 5 % of the total population, depending on sector or country.

Sales and employment are indeed the most frequently chosen size proxies in the literature. They are relatively easily accessible, they can be compared within and between industries (for instance, physical output does not benefit of the same property) and they are not too much related to the capital intensity of the industry (as opposed to total assets).

A large literature indeed examines the role of financial constraints on firm investment and growth, since the seminal contribution in Fazzari et al. (1988). See Almeida et al. (2004) and Farre-Mensa and Ljungqvist (2013) for discussion of empirical measurement of financial constraints, and Bottazzi et al. (2014) for a study of the effect of access to credit on growth dynamics.

We do not discuss here the determinants of differential innovativeness and efficiency. A large literature does (reviewed in Syverson 2011), while we take efficiency and innovation as summary measures of firm competitiveness stemming from heterogeneities in within-firm processes. Similarly, one could also refer to managerial literature on resource-based or capability-based view of the firm to search for other determinants of growth, high growth and persistent high growth. These theories offer complementary explanations, but we do not have data to measure any of these more detailed firm characteristics.

The estimates are performed pooling firms within the same 2-digit sector, taking number of employees and fixed tangible assets as measures of labor and capital inputs, respectively, and value added as the proxy for output, while we use the cost of material inputs as the instrument to control for endogeneity of labor inputs. As an alternative measure of efficiency, we have also considered a standard labor productivity index computed as the ratio between value added and number of employees. Results are in line with those presented along this work.

In this sense, the variable has some issues related to mixing different activities and also concerning difficulties in going from book to real value of such assets. In this choice of innovation proxy, we are constrained from the data, however. AMADEUS is known to lack detailed information about R&D. R&D expenses are present, in principle, but missing for the vast majority of firms. Intangible assets have instead a good coverage and represent a suitable alternative proxy, repeatedly adopted (despite limitations) in innovation studies (see, e.g., Hall 1999). In a robustness check, we also used the number of new patent applications filed (at whatsoever patent office worldwide) by the sampled firms in the years 2000–2005. Only a minority did applied for patent, however, considerably reducing the number of firms available for estimation, and indeed, we could only replicate the estimates pooling data across countries and sectors. Our main conclusions are not affected. The results are available upon request.

Results do not change if we use employment.

Recall indeed that the two sets of PHG and HG firms are non-nested. See Sect. 5 for a discussion of alternative estimation methods.

Since the variables are in z-scores, the marginal effects at the sample mean of the covariates are proportional to the corresponding coefficients. Standard errors are obtained out of 100 bootstrap runs, which were enough to obtain convergence. As a further check, we have also computed the usual sandwich-White type of robust standard errors, obtaining the same patterns of statistical significance. The same holds for all the analysis presented in the rest of the paper.

We also estimated our baseline multinomial probit augmented with dummies distinguishing the firms according to the innovative characteristics of their sector of activity. For manufacturing, we experimented with dummies for low-tech vs. high-tech industries (EUROSTAT classification) and distinguishing by the four classical Pavitt (1984) taxonomy classes. For services, we used dummies for KIS versus non-KIS sectors (EUROSTAT taxonomy). The results about the main structural and demographic characteristics remained unchanged. Moreover, sectoral dummies turned out as statistically significant only in few cases, thus providing a weak contribution to predict persistence of high-growth status. In a further robustness check, we also included value added over sales as an indirect proxy for the degree of vertical integration. The results confirm our main conclusion about the lacking explanatory power of non-demographic firm characteristics. Finally, since AMADEUS has limited coverage of micro-firms, and this issue is particularly problematic in all countries for single-employee firms, we have re-estimated our main model excluding firms with only one employee. Also in this case, our main conclusion is confirmed. All these additional analyses are available upon request.

An issue of reverse causality may still be present if one thinks that initial firm characteristics in years the 2004–2005 are not predetermined with respect to growth status in the following years. Although our empirical design does not allow to test this assumption, it seems reasonable that this concern is only valid for the very first years of the 2006–2011 period, and the relatively long period we use to define the growth status should cure for most of this issue.

And the literature already does, as mentioned above.

To our knowledge, methods controlling for rare-events are not available for multiple discrete choice models, mimicking our preferred multinomial setting. Moreover, a different binary model where we group “other firms” together with HG firms into a control category of “Non-PHG firms” would artificially increase the probability that PHG firms differ, while our main interest lies into genuine differences between HG and PHG firms.

In unreported estimates, we repeated the two-step conditional probit and the rare-event logit analysis also separately by manufacturing and services. Results were in accordance with the main conclusions drawn from multinomial probit estimates presented in the previous Section.