Firm dynamics and regional resilience: an empirical evolutionary perspective

1. Introduction

The concept of regional resilience, which has become popular among scholars and politicians who are concerned with the development of regions, seeks to understand how regional economies are able to cope with disturbances like the recent economic crisis ( Martin, 2012 ). Empirical attempts to measure regional resilience usually look at changes in some regional indicator, say, unemployment rate, employment or income level, to assess the impact of an external shock on a regional economy’s growth path. Besides a vast amount of case studies of individual regions, few systematic cross-sectional studies exist (e.g., Chapple and Lester, 2010 , Fingleton et al. , 2012 ). In most of these studies, an equilibrium-oriented neoclassical notion is prevalent in which the immediate effect on the growth path of a region or the time to recovery is analyzed. However, the evolutionary perspective on regional resilience is strongly related to processes like adaptation and structural re-orientation. These processes work at the level of firms, which Frenken and Boschma (2007) call the true agents of change. For instance, new technological trajectories have to be explored by the region’s firms, leading to “turbulence underneath the big calm” ( Dosi et al. , 2012 ). Hence, firm dynamics are intrinsically related to regional resilience. In particular, extremely growing as well as extremely shrinking firms indicate a region’s potential to de-lock from its old paths and to re-invent itself. Hence, the questions arise of how the way firms grow differ across regions and which region-specific factors are related especially to the occurrence of extreme growth events and, consequently, might contribute to regional resilience from an evolutionary point of view.

To answer these questions, this article breaks down the stochastic analysis of firm growth rates to the domain of regions. Extreme growth events are more likely to occur than a normal distribution would suggest. Meanwhile, it counts as a stylized fact that growth rate distributions show fat tails and often an asymmetric shape. Therefore, the flexible Asymmetric Exponential Power (AEP) density is fitted to firm data for each German region during the years of economic downturn (2008–2010). Peculiarities of employment growth are explicitly taken into account to improve the quality of estimation. The estimated parameters measuring the tails’ fatness are then related to various region-specific factors that are discussed in the literature on regional resilience. This approach provides a framework to operationalize the evolutionary perspective of regional resilience.

Results show that firm growth rate distributions, albeit remaining asymmetric and fat tailed at the spatially disaggregated level, markedly differ across regions in their shape. Extreme growth events are found to be more likely to occur in regions which show stronger aggregate performance and have a higher number of employees with university degree. The latter confirms Glaeser et al. (2011) , who ascribe the workforce skill a key role in making regions resilient. Furthermore, the fatness of the tails depends on the regions’ industrial structure. In line with evolutionary economic geography, variety seems to be crucial for new technological trajectories to unfold and old ones to decline ( Castaldi et al. , 2015 , Boschma, 2014 ).

The remaining article is structured as follows. Section 2 bridges three different streams of literature. First, it shows how the theoretical concept of regional resilience can be enriched by considering the heterogeneous responses and dynamics at the level of firms. Second, it extends the literature of firm growth rate distributions to the domain of regions, allowing for new insights by systematically comparing moments other than the distributions’ mean as is the case in ordinary regression approaches. Third, it argues that additional measures have to be taken into account when fitting the AEP distribution function for employment growth, which is, strictly speaking, discrete in nature. Finally, the main propositions to be investigated are presented. Section 3 discusses both the firm-level and regional-level data, while section 4 introduces the AEP distribution function and the estimation procedure. After setting up a regression model to explain regional differences in the distributional parameters, section 5 discusses the results. Section 6 concludes.

2. Literature

2.1 Regional resilience—insights from growth processes at the level of firms

The theoretical concept of resilience is increasingly applied to the domain of regional economic development. Within this rather broad and multifaceted concept, Martin (2012) identifies four dimensions of regional resilience: resilience as resistance, recovery, structural re-orientation, and renewal or resumption of a growth path. The first two roughly correspond to the concepts of engineering resilience, which focuses on the resistance of a system to disturbances and the speed it takes to return to its pre-shock state, and ecological resilience, which analyses the magnitude of shocks that can be absorbed before the system changes form, function or position ( Hudson, 2010 ). The two latter dimensions provide an evolutionary perspective. Resilience as a dynamic process can mean the ability of a regional economy to reconfigure and adapt its structure to maintain an acceptable growth path or the ability to create novel variety in response to external shocks ( Martin, 2012 ). The creation of novelty, the “ultimate cause of endogenous change” ( Witt, 2008 ), is ascribed a prominent role. However, the ability of a region to permanently re-invent itself might be hampered by the regional socio-economic conditions ( Gilbert, 2012 ). In this context, disturbances, which are often reinforced by recessions, can have positive effects by releasing potential for structural adaptation: “A deep recession may sweep away outmoded and unproductive activities, the removal of which opens up opportunities for the development of new sectors and a new phase of growth” ( Martin, 2012 : 11).

Already Reggiani et al. (2002 : 215) distinguished between the robustness and changeability of a system: “resilience points out the ‘possibility to change’, while stability emphasises the ‘impossibility to change’.” Empirical studies (e.g., Davies, 2011 , Diodato and Weterings, 2012 , or Fingleton et al. , 2012 ), on the contrary, find it rather difficult to go beyond resistance and recovery: an evolutionary view can hardly be conceptualized by remaining at the level of regions and industries. Evolutionary processes work at the level of firms, the true agents of change ( Frenken and Boschma, 2007 ). These processes are hidden by spatial or industrial aggregation. For example, new technologies or business models emerge within firms, but are reflected only decades later in the static industrial classification scheme. Following the Schumpeterian notion of innovation, successful firms are often accompanied by a comparable or even higher share of firms that stagnate or are on their way to demise, but are averaged out in the spatial or industrial aggregation process. As Martin (2012) states, a key to understanding regional resilience is the analysis of reactions and adjustments of firms, which ultimately drive the development of regional economies. The (un)successful adaptation of firms translates into different economic performances, resulting in firm-level turbulence, which are often reinforced by external conditions and might even push the whole regional economic system beyond thresholds of bifurcation points to new stability domains. Essentially, such turbulence is required to de-lock from path dependencies ( Simmie and Martin, 2010 ). In the context of the recent crisis, Archibugi et al. (2013) uncovered that this crisis led to a concentration of innovative activities within a small group of fast-growing new firms which were already highly innovative before the crisis. They argue that during phases of economic uncertainty about technological trajectories, demand conditions and new market opportunities, the exploration of new products and markets become even more important. Firms engaging in this risky strategy will be more exposed to either success or failure. In other words, turbulence, manifested by extreme positive and extreme negative growth events at the level of firms, is the driver of evolutionary development processes and the related adjustment to recessions. As Setterfield (2010 : 8) put it, “extreme experiences that propel a system sufficiently far from its current state are thought to result in structural change.” Focusing on the frequency distribution of firm growth rates, fat tails can be conceptualized as an indicator of highly dynamic, vibrant, and re-inventing regional economies.

Arriving at the level of firms, one has to ask which role the firms’ location plays in shaping their dynamics. Barbosa and Eiriz (2011) distinguish between two ways of how the spatial dimension matters, namely by general environmental factors, which are external to firms, unevenly distributed across space and imperfectly mobile, and by the role of proximity. The latter has recently become popular in studies analyzing the effects of industrial agglomerations, although its roots can be traced back to Marshall’s (1890) trinity of external economies. Mainly focusing on spatially bounded knowledge spillovers, empirical studies have analyzed the impact of agglomerations on the growth of firms. These studies also indicate that the regional dimension is especially relevant for highly shrinking and expanding firms (e.g., Fornahl and Otto, 2008 , Duschl et al. , 2014 ). Briefly stated, the way firms grow is often shaped by factors external to them, but internal to regions.

As noted above, the dynamics at the level of firms are crucial to understand processes and outcomes at the level of regions. However, the responses of firms to economic crises, which might be mediated or constrained by regional factors ( Hoogstra and vanDijk, 2004 ), are far from straightforward: “Some firms prosper in recessions while others fare very badly” ( Geroski and Gergg, 1996 : 551). What these authors call selectivity is a ubiquitous and persistent heterogeneity of firms and their responses, letting Dosi et al. (2012) make a plea for considering entire distributions instead of averages for assessing the relationship between the micro and the macro. This is confirmed by Higson et al. (2004) and Holly et al. (2013), who find that firm growth rate distributions change systematically over business cycles and even contribute to shaping macroeconomic fluctuations. An example may illustrate what firm dynamics reveal about the resilience of a regional system. Two regional economies A and B, both with an unchanging number of total employees, might show quite different dynamics at the level of firms. In A, not any single firm is growing, whereas B is confronted with turbulence due to many shrinking and expanding firms. Even though the short-term effect on regional growth is equal, the long-term outcomes of both regions probably will differ: B seems to be more able to reconfigure its structure and to adapt to changing environments, hence ultimately exploiting new technological opportunities. I argue that the evolutionary dimension of regional resilience is hidden in the dynamics of firms and thus can be uncovered by analyzing their distribution of growth rates. Hereby, the average growth rate has little to tell because it obscures turbulence, as the example has demonstrated. Besides, most firms are able to withstand external forces and even remain unaffected at all by macroeconomic recessions. Only after exceeding a certain threshold are some firms badly hit, while others might benefit strongly from such path-breaking crisis. Put differently, the secret lies in the tails of the distribution.

To conclude, this article argues that turbulence at the level of firms allows for a first assessment of a region’s long-term ability to adapt its structure and to re-invent itself, key aspects of evolutionary regional resilience, especially so but not exclusively during times of economic crises.

2.2 The distribution of firm growth rates—a regional perspective

The previous section argues that the entire distribution provides a more complete picture than single moments like the arithmetic mean. Although knowing the distributional form of a specific phenomenon is a valuable insight by itself, further information is revealed by comparing it to a reference distribution. As such, three options are conceivable.

First, empirically estimated distributions can be used to verify expectations derived from theoretical models. Gibrat’s (1931) “law of proportionate effect,” meanwhile a common starting point in the literature of industrial organizations, requires in its strong version normal distributed growth rates ( Amaral et al. , 1997 ). But instead of a bell-shaped normal curve, a tent-like shaped exponential one, also known as the Laplace distribution, is observed on the basis of firm-level data from several countries (e.g., Stanley et al. , 1996 for United States) and at the disaggregated level of industries ( Bottazzi et al. , 2001 for the pharmaceutical industry). To account for this stylized fact, stochastic models of firm growth have been developed (e.g., Bottazzi and Secchi, 2006 ). Furthermore, empirical evidence was also reported for the income growth rates of countries, that is, at a much higher level of economic aggregation (e.g., Lee et al. , 1998 ). Only recently, a research gap at the intermediate level of industries ( Castaldi and Sapio, 2008 ) and regions ( Duschl and Brenner, 2013 ) was filled, indicating that these models can be generalized to hold for the growth of all complex economic organizations irrespective of the level of aggregation. Besides, empirical evidence is emerging that these distributions show tails significantly fatter than the Laplacian ones and often an asymmetric shape, motivating Bottazzi and Secchi (2011) to introduce the even more flexible five-parameter AEP.

Second, distributions can be conditioned on further variables. Ordinary regression models represent a specific case of this general prediction problem by focusing on one specific point of the conditional distribution, like the mean or any other quantile ( Varian, 2014 ). By comparing the shape of the conditional and unconditional distribution, a more complete picture of the impact of the conditioning variables on the distribution can be drawn. For instance, this exercise is found in Bottazzi et al. (2014) and Maasoumi et al. (2007 : 499). The latter authors note already that in the residual growth rates “control is only achieved on the mean of the growth rates, and the variables may continue to impact on other distributional characteristics.” A first approach to capture the complex shifts in the entire growth rate distributional mass is introduced by Duschl and Peng (2015) , who simultaneously condition all five parameters of the AEP density.

Third, distributions of the same type of observational unit can be compared by taking empirical snapshots in various contexts. Growth rate distributions of firms belonging to different industries (e.g., Bottazzi and Secchi, 2003 ) are used to confirm that predictions from stochastic models survive at different levels of industrial disaggregation. Introducing the time dimension, Dosi et al. (2012) point out the heterogeneous impact of the Euro adoption on the performance of Italian manufacturing firms. At the regional level, Barbosa and Eiriz (2011) investigate the way firms grow by visually comparing the evolution of the firm size densities of 19 Portuguese regions. The article at hand aims to uncover the region-specific factors leading to differences in the distributional characteristics of the regions’ firm growth rates by relating them to the estimated parameters. It focuses particularly on explaining the tails of the distribution, which are a measure of internal turbulence and, as such, an indicator of resilience from an evolutionary perspective.

Each of the three strategies has its own advantages in highlighting specific aspects of a complex phenomenon. The latter approach of systematically comparing estimates of distributional parameters is particularly insightful in situations in which a high number of comparable samples, say, the regions of a country, are available. By letting the data speak, it is also a response to difficulties of theoretical models and simulation studies, which are confronted by the existence of a hypothetically unlimited number of economic mechanisms that may be able to explain the emergence of fat-tailed distributions ( Alfarano and Milakovic, 2008 ).

2.3 Estimation of the AEP density—specificities of employment growth

Up to here, nothing has been said about the various measures of firm growth, like sales, turnover, productivity, or employment, all governed by distinct mechanisms ( Coad, 2009 ). Whereas the first three primarily concern business managers, employment growth is of utmost relevance for regional policy makers, even more so during times of economic crisis ( Martin, 2012 ). All measures share the common property that the underlying change events are not, strictly speaking, continuous. An inherent discreteness becomes particularly apparent for employees, which are by nature indivisible. Coad (2012 : 17) takes this reasoning seriously by putting the reactions of firms to growth stimuli at the heart of his stochastic model: “The lumpy nature of resources within a firm implies that firm expansion is characterized by non-constant marginal costs that depend on the degree of utilization of the firm’s resources.” Consequently, fat-tailed distributions of growth rates emerge as firms tend towards a critical state of full utilization of resources: if resources are already more or less fully employed, then growth will only be possible with addition of extra resources, while the “interdependent nature of discrete resources may lead to triggering off of a series of additions to a firm’s resources.” The resulting growth process might show non-linearities as firms add indivisible resources to arrive at efficient levels of production.

The incentive to exploit unused resources provides an intentional perspective on growth, in contrast to G ibrat ’s law and island models (e.g., Ijiri and Simon, 1997 , Bottazzi and Secchi, 2006 ), in which growth opportunities are passively absorbed and accumulated ( Coad, 2009 ). Taking both perspectives into account, a conceptual two-step firm growth model is proposed, which disentangles the outcome of a change in the number of employees from the actual growth processes. Put simply, in a first step each of the N firms is confronted with the options to grow or not grow based on its internal resource composition and the external business opportunities. Both options can be modeled as a binomial process with probability p , in which p*N firms change the number of employees and (1-p)*N firms remain at the previous level. In a second step, all of those firms which experience such a kind of growth impulse due to the mismatch between opportunities and their level of resources try to respond by integrating new resources or by releasing existing ones. This ultimately leads to h expanding and k shrinking firms. The remaining p*N−(h + k) firms are those which would grow but are not able to, thus delaying their growth momentum.

Leaving aside the question of whether or not both steps represent analytically distinguishable phenomena, they are appropriate from a stochastic point of view. Assuming a continuous probability distribution function, the realization of a specific empirical value occurs in the limit with zero probability. This clearly contrasts with the observed occurrences of zero-growth events in typical databases—in Bureau van Dijk they account for up to 50% of all events, and Coad and Hölzl (2009) even report that 65% of small establishments listed in the Austrian Social Security files do not display any changes in employment from one year to the next. This abundance of zero-growth events calls for an explanation. First, following the proposed model, firms simply may prefer to remain at the previous level of employees. This can be an economically rational choice in absence of any changes in business opportunities, but it can also be the preferred choice in cases when opportunities have changed. To name just a few examples, firms might be reluctant to expand because the inclusion of new employees is costly, as it implies re-organization of internal tasks and management functions, the labor market might only insufficiently meet the demand for (qualified) workers, or the fear of losing control might frighten some managers ( Coad, 2009 ). In a similar vein, firms can be reluctant to shrink despite reduced business opportunities. Firms invest in building up redundancies in difficult times instead of immediately dissolving existing working contracts, or managers might not be fully aware of the necessity of down-sizing. Second, there are those firms which would grow but are not able to due to the discrete nature of employees, which inhibits these firms from marginally increasing or decreasing their size by, say, a quarter of employees. Instead, these firms tend to respond by re-organizing tasks internally. Although it is still an issue for actually growing firms, it becomes statistically less and less relevant as the number of employees to change increases. Around zero, however, the discreteness is fully noticeable with respect to the firms’ ability to grow. Third, firm databases sometimes lack a regular updating of their entries, resulting in many zero-growth events as simple extrapolations. To sum up, zero-growth events arise due to the choice of avoiding growth, the inability to grow and data problems. The latter make it impossible to recover p , hence restricting the analysis to the actual growing firms. However, an entire exclusion of zero-growth rates would bias the estimation of a continuous probability distribution function because those firms are not able to grow because the discrete nature of employees would be dismissed. Therefore, this article deals with a new method for estimating the AEP to account for possible biases resulting from the discrete nature of employees.

2.4 Main propositions

Placing dynamics of firms’ employees at the heart of regional resilience, two general propositions can be stated.

The first proposition arises from the empirical observations which show that how firms grow depends on factors and conditions specific to the region they are located in (see section 2.1). Although the stylized facts on the general shape of firm growth rate distributions are expected to be manifest already with regions as the reference system, important differences across regions might be observed, especially for the fatness of tails and the degree of asymmetry. On the one hand, aggregate shocks, which tend to be differently pronounced across regions, affect the entire distributional shape in a complex way. For instance, Holly et al. (2013) find that especially the left-hand side of the distribution is responsive to economic shocks. On the other hand, the mechanisms leading to the fat tails, like the increasing returns in the model of Bottazzi and Secchi (2006) , can vary in their extent across regions. This is strongly related to the idea of localization economies (e.g., Krugman, 1991 ), which might foster this self-reinforcing accumulation of growth opportunities of the region’s firms, and thus contribute to the emergence of fat tails. However, it is one thing to study regional differences in the distributional parameters, but quite another to ask about the economic meaning of these differences:

This proposition needs to be further elaborated. The underlying firm dynamics of a regional economy reveal whether it is resilient, from an evolutionary view. As Capasso et al. (2013 : 612) state it: “A major economic implication of heavy tails is that fast-growing and shrinking firms account for a non-negligible share of an industry population and significantly affect the industry dynamics.” Positive fat tails indicate the ability of a regional system to adapt its structure: extreme positive growth events result from the exploration of new technologies or business models, which creates new opportunities to spur growth. The other side of the coin is that evolution driven by the creation of new variety implies that existing modes of activities become outdated. But only in competitive regional environments will firms unable or unwilling to adapt perform worse, thus increasing the likelihood of extreme negative growth events. In short, a regional economy with fat tails on both sides of the firm growth rate distribution is assumed to have a higher adaptive capacity. This is defined as resilient from an evolutionary perspective.

The number of positive and negative extreme growth events that a region encounters might not necessarily be balanced. If the asymmetric distribution is skewed towards the left, then the negative events outweigh the positive ones. In this case a regional economy is considered to be more vulnerable , as its firms are more sensitive to the negative effects of a shock, without having an equally large fraction of firms that prosper.

3. Data

3.1 Firm-level data

This article analyses firm dynamics and compares their distributional properties across different regions. Firm-level data are retrieved from the BvD Amadeus database in early 2012. It provides the most comprehensive data entries for the time period from 2007 to 2010, which roughly concurs with the years of macroeconomic downturn. However, it is not free of data problems. For instance, zero growth rates make up 44.5% of all entries. Although excluded from further consideration, they still could bias the results insofar as growth rates in the subsequent year must be artificially higher. Several heuristics are applied to identify zero growth events stemming from data inconsistencies based on extrapolation, and the subsequent non-zero growth rates are eliminated. ¹

The Amadeus database discloses the address of the firms’ headquarters location. As operational and strategic decisions are often made within this organizational unit, their regional environment will be most decisive in affecting their growth prospects ( Beaudry and Swann, 2009 ). This rationale breaks down for larger firms, which tend to be less focused on their headquarters, but disperse their activities in many establishments across the country and beyond. Therefore, the analysis is restricted to firms with no more than an annual average of 1000 employees. Also, very small firms with less than five employees, whose growth processes are known to be rather erratic and which have limited abilities to generate jobs, are excluded ( Coad, 2009 ). Furthermore, industries are affected differently by macroeconomic recessions. Following Porter (2003) , traded cluster industries can be distinguished from local cluster, resource-based cluster and non-cluster industries. This article focuses exclusively on firms from traded cluster industries, e.g., firms from traded industries that tend to co-locate. For Europe, these industries are defined within the EU Cluster Observatory Project. The motivation for focusing on this subset of firms is twofold. On the one hand, traded-cluster industries are more exposed to the global economy just as they depend on their regional environment, and on the other hand, they are expected to be more influential in shaping long-term technological trends within their home region. Although they account for less than half of the employment, they “register much higher wages, far higher rates of innovation and influence local wages” ( Porter, 2003 : 549).

In total, 37,403 growth events, different from zero, are analyzed. These growth events stem from 20,962 firms, which are spatially distributed across German labor market regions.

3.2 Regional-level data

Labor-market regions as defined by Eckey et al. (2006) serve as the regional reference space for firm locations. Combining insights from empirical studies of firm growth and regional resilience, several region-specific variables that might be related to the underlying micro-dynamics are identified. These variables can be classified into four broader categories: the region’s (i) general socio-economic conditions, (ii) innovation conditions, (iii) workforce qualification, and (iv) industrial structure.

Being an obstacle to the ability to adapt, unfavorable general socio-economic conditions are expected to reduce regional resilience. These are approximated by the population density ( PopDensity ), the unemployment rate ( UnemplRate ) and the aggregate regional growth performance ( RegGrowth ). PopDensity , being rather independent from the surrounding industrial structure, reflects urbanization economies ( Buerger et al. , 2012 ). The UnemplRate indicates the vitality of the regional labor markets. In the special case of Germany, it also accounts for structural differences along the east-west and north-south divide. Data for both variables is obtained from the German Federal Statistical Office (destatis). Finally, RegGrowth , the (logarithmic) change of regional employment in the study period from 2007 to 2010, measures the aggregate growth performance of a region’s economy during the time of macroeconomic recession. Better performing regions are expected to be more able to reconcile turbulent processes at the level of firms. Like all subsequent variables based on employees, data are retrieved from the German Institute of Employment Research.

The innovation conditions might directly measure a region’s “ability to replace declining or uncompetitive activities with new, dynamic and competitive ones” ( Fingleton et al. , 2012 ). Innovativeness is measured by the university third-party research funding ( ResFunding ). Here data are obtained from destatis. Alternative measures, like universities’ budget, patents or employees in R&D-related occupations, were tested beforehand but showed an inferior fit compared to ResFunding . Due to multicollinearity issues, they are omitted from further analysis.

Among researchers (e.g., Chapple and Lester, 2010 , Martin, 2012 ) it is widely acknowledged that the region’s workforce skills are a key factor for regional resilience: “human capital and urban reinvention” are strongly connected, making skills “particularly valuable in places that are hit with adverse shocks” ( Glaeser et al. , 2011 : 4). The regional qualification level is measured by the number of employees with university degree ( EmplUniv ).

The recent macroeconomic recession has also revealed that the region’s industrial structure matters: different industries were affected differently ( Groot et al. , 2011 , Davies, 2011 ). Two variables control for the share of observations which are associated with the Manufacturing and Construction industries. The region’s share of manufacturing is also a proxy for export orientation, and hence measures the exposure to global markets ( Chapple and Lester, 2010 ). Besides, it is often observed that localization economies are more relevant among manufacturing industries ( Beaudry and Swann, 2009 ), which might lead to fatter tails according to the model of Bottazzi and Secchi (2006) . During the last recession, especially the construction industry was targeted with fiscal stimuli and hence might show different growth dynamics.

However, it is not only the concentration of certain industries that is expected to matter, but also how the economic activities are technologically related to each other (see Boschma, 2014 for an extensive discussion of the role of industrial variety and regional resilience). A high degree of relatedness means the existence of many inter-industry technological linkages and interdependencies ( Boschma and Iammarino, 2009 ). If the region’s industries are too similar, i.e., the regional economy is diversified only to a small degree without showing much variety, few recombinatory options are available, but these are essential to develop new growth paths ( Boschma, 2014 ). In regions in which strong industrial clusters have been established, the ability to transition to new technological forms might be constrained by a higher inertia and myopia of its actors and institutions ( Gilbert, 2012 ). In contrast, variety may enhance the region’s adaptability by increasing the potential to make new recombinations ( Boschma, 2014 ). Drawing on recent empirical evidence based on patent data ( Castaldi et al. , 2015 ), it is argued here that especially unrelated variety, reflecting the presence of very different activities, increases the number of potential sources for technological breakthroughs, which often translate into the tails of the firm growth rate distributions. Thus, unrelated variety is expected to enhance the region’s long-term ability to renew its growth path. This is different from the often discussed portfolio effect of unrelated variety ( Frenken et al. , 2007 ), which is more a matter of immediate vulnerability than a matter of adaptability. The three variables representing variety, RelVar , UnrelVar , and Similarity , are based on entropy measures and are adopted from the literature (e.g., Frenken et al. , 2007 , Boschma and Iammarino, 2009 ).

All region-specific variables are calculated for the base year of 2007. The highly asymmetric distributed variables of EmplUniv and ResFunding are first normalized by division through their mean value and then made symmetric by the transformation $x˜=(x−1)/(x+1).$ Descriptive statistics and correlations are reported in the Appendix.

4. Methodology

4.1 AEP density

4.2 Contemporaneous left and right tail estimation

Endogenizing N is not without any consequences. Obviously, it reduces the estimation bias stemming from the discrete nature of changes in the number of employees. It does so by raising the competition of the countervailing forces of the scale and shape parameters, which both simultaneously try to account for (extreme) positive and negative events. Leaving out the central part, this flexibility regarding asymmetry increases, hence implying that higher peaks might be reached and distributional mass shifted from the variance to the tails. Based on empirical data from one arbitrarily chosen region, Figure 1 displays the main aspects and implications of this refined estimation procedure: in (a) the empirical firm growth rate distribution is plotted. The points represent the midpoints of the frequency bins, using a log-scale on the y-axis. It is instantly visible that zero-growth events are dramatically over-represented. In (b) all zero-growth events are removed. The parameters of the AEP distribution (light-blue line) fitted to the zero-cleaned data are biased because some zero-growth events result from firms that would have grown if employees were not discrete in nature. To reduce this bias, in (c) the same distribution (dark-blue line) is estimated by leaving out the central part around zero, which is colored in black, and by making the number of observations lying within this part endogenous. This endogenization increases the number of actually growing firms h and k by around 4%.

4.3 Regression model

In the next step, the distributional parameters, which are estimated for each region m , are related to regional factors in a regression model estimated by OLS. Turbulence arises through both positive and negative extreme growth events. Instead of explaining the fatness of the tails for both sides of the distribution separately, the two-dimensional space of the shape parameters is rotated such that the sum of $br$ and $bl$ is finally explained. This sum represents overall turbulence that is expected to accompany processes like adaptation and structural re-orientation. Recall that smaller shape parameters mean fatter tails. Hence, the smaller the value of the sum of $br$ and $bl$ , the more likely extreme events are to occur in a regional economic system. The other dimension in the rotated space, $br$ minus $bl$ , measures the asymmetry of the distribution and indicates a kind of vulnerability: this value is positive for $br>bl$ , implying that extreme negative growth events are more likely to occur than positive ones.

Two models are estimated, one for resilience$(br+bl)$ and one for vulnerability$(br−bl).$ Each model contains two control variables: the number of firms in the sample and the respective opposite dimension in the rotated space. The former accounts for the issue that fat tails might be sensitive to extreme events in the case of just a handful of observations. The latter should capture distortions from the possible relationship between the resilience and vulnerability measures, say, if more vulnerable regions are at the same time more resilient, as it is often argued regarding the recovery dimension of resilience (e.g., Martin and Sunley, 2014 ). The resulting models read:

4.4 Limitations

However, this empirical perspective on regional resilience, based on firm growth rate distributions, is not without any limitations. Especially three points deserve further discussion.

First, firms that enter and exit are omitted from the analysis because they are qualitatively different from growth processes of existing and surviving firms. Growth rates become infinite when the size changes towards zero. However, entry and exit events, which are known to show different regional dynamics and determinants ( Combes et al. , 2004 ), are an important aspect regarding all dimensions of structural change and regional resilience ( Neffke et al. , 2014 , Boschma, 2014 ), but cannot be tackled within the framework of growth rate distributions. Yet the author believes that a huge bulk of the processes of adaptation and re-orientation occurs within existing firms, and these are thus revealed by their growth performance. This is confirmed by studies like Bergek et al. (2013) , arguing that the ability of new entrants to destroy and disrupt established industries is often overestimated, while the ability of incumbents to absorb and integrate new technologies with their existing capabilities is often underestimated. Besides, Metcalfe and Foster (2010) argue that the effects of exit and entry on aggregate dynamics, by inducing structural change, operate at time periods much larger than analyzed in this article.

Second, instead of being a longitudinal approach, a cross-sectional snapshot of growth rates is analyzed. Here, the data stems from the years of macroeconomic recession. However, a systematic comparison to pre- and post-crisis growth processes might be particularly interesting at the level of firms, as the temporal auto-correlation patterns of firm growth rates tend to be especially pronounced at the tails ( Coad, 2007 ).

This relates to the third point, as short-term approaches do not allow for a direct analysis of the evolutionary dimension of regional resilience ( Davies, 2011 ). From an evolutionary perspective, regional resilience is not bound to describe the immediate reaction to shocks, but it is understood as an on-going process of adaptation and structural re-orientation. However, Simmie and Martin (2010 : 34) argue that resilience “depends both on longer term, region-wide processes and on shorter term microscale processes and on how these interact.” The latter can have permanent effects on the potential long-term output ( Cross et al. , 2012 ). By focusing on yearly growth rates, at least a first assessment of the potential for long-term adaptability and structural re-orientation can be provided.

5. Results

5.1 Inter-regional heterogeneity in the firm growth rate distributions

Summary statistics of the estimated AEP parameters are reported in Table 1 . On average, the tails are to a considerable degree fatter than the normal and even Laplace distribution, accompanied by an asymmetric shape towards the left: extreme negative growth events are much more likely to occur than their corresponding positive ones. These findings confirm the recent literature on firm growth rate distributions within national economies (see section 2.2). However, the high variances of the two shape parameters $bl$ and $br$ point to a significant inter-regional heterogeneity.

Furthermore, this table compares the estimates resulting from the extended estimation technique, which leaves out the central part around zero, with the ones resulting from the conventional approach of optimizing the log-likelihood of $fAEP$ . For the latter, all zero growth events are excluded. The new technique makes the distributional mass shift from the center to the tails: on average, both $bl$ and $br$ become smaller as compared to the conventional technique without zero data. Simultaneously, the variance decreases. Despite one additional degree of freedom, asymmetry is reduced by the new technique. The absolute difference between $bl$ and $br$ slightly decreases, on average, from 0.493 to 0.415 and between $al$ and $ar$ from 0.042 to 0.029.

5.2 Regional factors accounting for the fat tails

The spatial distribution of the values for $bl$ and $br$ as well as their sum $(bl+br)$ and their difference $(br−bl)$ are mapped in Figure 2 . The high regional heterogeneity of firm growth rate distributions already suggests that they might reveal more about the underlying dynamics of regional economies. In section 2.1 it is argued that turbulence at the level of firms allows for a first assessment of a region’s long-term ability to adapt its structure and to re-invent itself, key aspects of evolutionary regional resilience. This leads to the question of which region-specific factors are related to a higher potential for regional resilience. Results from the regression models are summarized in Table 2 .

The two base models solely control for the number of observations and the perpendicular dimension. The models 1–4 include further regional variables. For each independent variable, two models are devised because the variables of related and unrelated variety happen to be empirically correlated. Therefore, the variable of similarity, into which both variety measures can be decomposed, is included in models 2 and 4. Regression diagnostics do not reveal any problems. ³

By relating the tail measure $(bl+br)$ to various regional variables, the explained variance (R ² ) of models 1 and 2 increases compared to the base model from 27% to almost 40%. Regarding the general socio-economic conditions, neither PopDensity nor UnemplRate turns out to correlate with the tails’ fatness, meaning that no evidence is found that the stochastic properties of firm growth rate distributions differ along the urban-rural as well as east-west or north-south divides. However, RegGrowth is highly relevant. The better the aggregate regional growth performance, the lower are the shape parameters and hence, the fatter the tails. This result shows that firm-level turbulence is predominantly a phenomenon of better performing regions. Yet it remains an open question whether more resilient regions manage to grow faster or whether aggregate regional growth, by providing new opportunities for the firms, but also by requiring them to change and to adapt, is the cause for regional resilience.

The regions’ innovation conditions, approximated by ResFunding , reduce significantly the occurrence of turbulence at the level of firms. Thus, regions with a strong (basic research oriented) science base are not necessarily those regions where firms are able to economically take off. In contrast, EmplUniv , the qualification level of the region’s workforce, is strongly correlated with the fatness of the tails: the more employees with a university degree, the higher the likelihood of extreme growth events. This clearly confirms the literature, which attributes the region’s workforce skills an important role in its resilience and transformative capacity in general (e.g., Chapple and Lester, 2010 , Glaeser et al. , 2011 ).

Finally, the industrial structure matters. Regions with a higher share of firms belonging to Manufacturing are more exposed to extreme events. This result is reasonable, as the manufacturing industry was more strongly affected by the macroeconomic recession (e.g., Groot et al. , 2011 , Davies, 2011 ). Besides, it supports the expectation that increasing returns as a source of fat tails are more relevant among manufacturing industries. Regions with a higher share of the Construction industry do not show different stochastic properties in their firm dynamics. Besides the type of activity, the way these activities are distributed across a region’s industrial portfolio also matters. Unrelated variety turns out to have a significant negative effect, meaning that a less coherent and less interrelated technological base makes extreme growth events more likely. Related variety carries a positive sign, but remains insignificant. Inclusion additionally of the similarity measure confirms the direction of the effects, but reduces the significance of unrelated variety. Thus, unrelated variety in the region’s industrial structure seems to increase the likelihood that new technological trajectories unfold and old ones decline ( Castaldi et al. , 2015 ). Put differently, specialized regions, where activities of the same or similar type concentrate, either constrain the necessary competition leading to such turbulent processes, probably due to a higher inertia of its actors and institutions, or simply provide fewer potential sources for path-breaking technological solutions, which “can be taken from one industry and used to create innovations that solve problems in other fields” ( Gilbert, 2012 : 738).

Besides the explanation of the tails’ fatness, which is conceptualized as an indicator for regional resilience from an evolutionary perspective, the asymmetry of the distribution, measured by $(br−bl)$ and representing a kind of vulnerability, can also be analysed. However, the inclusion of further regional variables in models 3 and 4 does not increase the explanatory power, which remains at around 20% compared to the base model. With PopDensity only one variable shows a significant influence: the higher the population density, the more likely extreme negative growth events are to occur relative to positive ones. This result can be regarded as a consequence of the recession, as urban regions turned out to be affected more adversely ( Holm and Ostergaard, 2015 ).

6. Conclusions

This article studies turbulence in the firm dynamics of regional economies. Turbulence is an indicator for processes like structural adaptation and technological re-orientation. Regional economies that provide a competitive environment, which facilitates substitution of outmoded activities with new innovations and technologies, are assumed to be resilient in the long run from an evolutionary perspective. Such turbulence, otherwise hidden by aggregation, is revealed in the employment dynamics of firms. Here, the secret lies in the tails of the distribution of firm growth rates, i.e., in the extreme events, which tend to have a higher transformative impact on the regional economy. Therefore, this article is a first attempt at assessing the meaning of fat tails for the systems to which they correspond, and the factors which make them particularly pronounced. Above all, this analysis shows that firm-level turbulence is more likely in regions with a higher aggregate growth performance. Although the direction of causality is still unknown, this finding underlines the positive nuance of fat tails throughout the article. In this vein, a diversified industrial structure that provides unrelated variety as well as the presence of a qualified workforce seems especially to make regional economies more resilient. In contrast, a strong science base surprisingly attenuates the tails.

However, it is yet an open issue which types of institutions can better accommodate turbulence and translate it into fruitful changes and new long-term growth paths ( Boschma, 2014 ). It should also be noted that this kind of resilience—with an indisputable neoliberal notion—might have negative consequences for some workers, who face difficulties in becoming reemployed by reason of their individual skills within the implied environment of more flexible working conditions ( Martin, 2012 ). Moreover, it is yet to be debated how much change is desirable from a societal point of view ( Reggiani et al. , 2002 ). It is beyond the reach of this article to answer these questions, for which the short-term and long-term benefits and social consequences have also to be taken fully into account. The interested reader is referred to Consoli et al. (2016) , who analyses changes in the skill content of occupations.

Acknowledgements

The author would like to thank Giulio Bottazzi, Thomas Brenner, Alex Coad, the anonymous reviewers as well as the two guest editors, Lionel Nesta and Mauro Napoletano, for their valuable comments and suggestions. Any remaining inadequacies are the sole responsibility of the author.

References

Appendix