Para garantizar la obligación de responder por los defectos y vicios ocultos de los

2.2.1 Gibrat’s law and scaling relationship

GIBRAT’s law of Proportionate Effect is a widely used starting point in the firm growth

literature. Although economically meaningless, it provides a useful benchmark model to test the basic independence assumption of growth processes of economic entities (BOTTAZZI et al. 2011). For the weak version to apply it requires that growth rates are independent from the initial entities’ size. Additionally, it is based on the assumption that successive growth rates are uncorrelated in time. Empirical findings on GIBRAT’s law in

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aspects like firms’ age, size or the specific growth rates quantile under consideration

(SUTTON 1997, or more recently COAD 2009 and LOTTI et al. 2009 provide an overview on

the literature). Hence, we begin by assuming for regional economies:

Hypothesis 1a (Gibrat’s law for the mean growth rate): Regional employment

growth rates are independent from the regions’ number of employees and the regions’ past growth experience.

Beyond its’ relevance in and of itself, hypothesis 1a also allows us to decide whether or not growth rates from different regions (in terms of number of employees) as well as years can be considered as random draws from the same population and, thus, can be pooled together for a subsequent analysis of the growth rates. For the strong version of GIBRAT’s

law to hold, two additional requirements must be met. First, the variance of the growth rates must be independent of the entities’ size and secondly, growth rates must converge to a normal distribution. The former dates back to HYMER and PASHIGIAN (1962), who first discovered that the variance of the firms’ growth rates is inversely related to their size, and by this violating GIBRAT’s law for variance (GABAIX 2009). STANLEY et al. (1996) formalize

this scaling relationship as a power law:

𝜎(𝑆) = 𝑐𝑆𝛽

𝑙𝑜𝑔 𝜎(𝑆) = 𝑐 + 𝛽𝑆

(5)

with S being the entities’ size, σ(S) the standard deviation of their growth rates conditional on S, c a constant and β the scaling exponent. Empirical studies for firms in different industries (e.g. AMARAL et al. 1997) and for national economies (e.g. LEE et al. 1998)

estimate that β mostly ranges between -0.15 and -0.20. This robust power-law scaling regularity is declared to be a universal feature of the growth of complex economic organizations involving large numbers of interacting subunits (STANLEY et al. 1996, AMARAL

et al. 2001). Two explanations for the observed scaling behaviour can be put forward. The first is supported by CANNING et al. (1998) and others, who consider the scaling exponent

β as an indicator for the strength of micro-economic interactions between the subunits of

a system, here the firms of a region.5 _{If β is 0, a perfect correlation between the subunits}

exists, since there is no dependence of the dispersion of growth rates on the number of employees. If β is -0.5, any correlation between the subunits is absent, meaning that the volatility of a system falls with the square root of its size. Finally, if β lies between the two limiting cases, the variance of the growth rates decays as a power law, but not as fast as the square root, here indicating the presence of some considerable positive interactions between the firms within a region. BOTTAZZI and SECCHI (2006b) argue that the observed

scaling relationship can be explained as a diversification effect, since larger economic entities tend to operate in a higher number of sub-markets of an industry due to scope economies of diversification. Up-scaling this argumentation from the level of firms to

5 _{Scaling law models rely on the assumption of an identical size of the subunits, which strictly speaking does}

not hold in the reality of regional economies. This restricts to some degree the explanatory power of the scaling exponent as an indicator of the strength of the interactions between the firms within a region.

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regions, the dispersion of overall growth may be reduced over-proportionally for regions with a higher number of employees. Both explanations lead us to:

Hypothesis 1b (scaling relationship): The higher the number of regional

employees, the smaller the variance of the conditional distribution of the respective growth rates.

Finally, growth is assumed in GIBRAT’s framework to follow a random walk process leading

to log-normal growth rates distributions. In this paper, the main emphasis is on the characteristics of these distributions in case of regional industry-specific employment growth. Theoretical expectations will be deduced in the next section.

2.2.2 Firm-like behaviour of regional economies

A significant departure from normality suggests that some other mechanisms than the central limit theorem are at work (CANNING et al. 1998: 340). Confronted with the

empirically observed firm growth rate distributions, BOTTAZZI & SECCHI (2006a) developed

a stochastic model of firm growth. In contrast to Gibrat, they assume that economic opportunities, which sum up to a firm’s growth rate in a given time period, are limited in their amount available to the firm and are not independent: a kind of increasing returns mechanism induces a cumulative and self-reinforcing process in the assignment of economic opportunities.6 _{Successful firms which have realized more of those opportunities}

in the past exhibit a higher probability of taking up new ones. Due to the limitedness of economic opportunities, competing firms directly affect each other – if one firm’s market share grows the market shares of its competitors shrink. Tent-shaped distributions with fat tails can emerge due to the increased probability that a large fraction of growth opportunities is assigned to a few firms only, whereas most other firms do not receive any at all.

Employment in a region is the sum of firms’ employees located within this region. Hence, regions compete for limited economic growth opportunities at the level of firms. If regions, which have received such firm-level growth opportunities, are exposed to higher probabilities to receive even further opportunities, the stochastic model of firm growth would apply mutatis mutandi to regional economies and the distribution of their growth rates should consequently depart from normality. However, CASTALDI and DOSI (2009: 489)

argue that inter-regional competition differs in many aspects from inter-firm competition. On the one hand, it is reasonable to consider territorial competition as a competition for mobile production factors and firm locations, which may cause dynamic and turbulent processes (CHESHIRE/MALECKI 2004: 260) and are in line with the basic idea of this model.

On the other hand, limited growth opportunities may be bypassed by collective efforts in the regional policy arena, for example by trying to achieve higher growth rates in the overall regional system through cooperation and coordination or by diversifying the regional production portfolio into new areas of activity. Due to the latter issue, it is important to focus on the regional growth dynamics of single industries because industry-specific markets are

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the very locus of competition for economic opportunities. Moreover, the drivers of positive and negative feedback loops in the context of opportunity accumulation are also industry- specific (CASTALDI/DOSI 2009, CASTALDI/ SAPIO 2008). Referring to the language and

concepts of the New Economic Geography (e.g. KRUGMAN 1991), localization economies,

which are by definition industry-specific, might induce increasing returns and imply an inter-regional dependency of the growth rates. Already MARSHALL (1890) observes that

firms might benefit from the localisation of new or existing firms in the same region and industry due to the trinity of mechanisms of labour pooling, economies of scales in intermediate inputs and knowledge spillovers. The exit of a firm from the region or market might decrease the chance of survival for other co-located firms of that industry analogously. Finally and in accordance with endogenous growth theories (e.g. ROMER

1990), the diffusion of growth opportunities stemming from innovation throughout the economy has both a geographical and technological dimension (see

DÖRING/SCHNELLENBACH 2006 for an overview on the issue of knowledge spillovers): the

resulting feedback loops are bounded to some degree to work within regions and the capacity to absorb knowledge spillovers depends amongst others on the regions’ industrial structure, making the disaggregated level of industries an adequate observational unit for the analysis of regional growth processes.

Briefly stated, we argue that regions compete over a finite set of industry-specific growth opportunities and that the regions’ firms interact and learn at the industrial level, leading to self-reinforcing dynamics in opportunity catching. This reasoning leads us to:

Hypothesis 2a: Self-reinforcing mechanisms still prevail at the regional level.

Consequently, fat tails as signs of a higher probability of extreme positive and negative growth events emerge as a key feature of regional industry-specific employment growth.

However, it could be argued that the influence of the mechanisms responsible for fat tails may fade if longer than one year time lags are considered. Growth events become more independent over time and a progressive normalization of the growth rates’ distribution should take place as the central limit theorem comes into force (BOTTAZZI/SECCHI 2006a). Hence, we should expect:

Hypothesis 2b: The longer the time lag for which growth rates are calculated, the

closer their distribution is to the normal one.

2.2.3 Relationship between type of industry and stochastic characteristics of regional growth

Two arguments make a finer break-down of the regional economy into single industries necessary. First, stochastic properties at a higher level of aggregation may be a sheer outcome of the aggregation process (BOTTAZZI/SECCHI 2003: 218, BROCK 1999: 431). As

argued above, true economic mechanisms of regional economic growth operate at the level of specific industries. Hence, it has to be tested whether the findings survive at different levels of aggregation. Second, the stochastic properties may also differ across heterogeneous industries. A systematic comparison of different types of industries could

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provide new insights for the explanation of the characteristics and mechanisms of regional growth dynamics.

Three lines of distinction seem to be relevant. First, industries differ in their knowledge intensity in production (SMITH 2002). Using data on German labour market regions,

SCHLUMP and BRENNER (2010) prove that the effects of universities and public research

and development on regional employment growth differ significantly across industries. FORNAHL and BRENNER (2009) point out that especially industries which rely on a scientific knowledge base, show a higher geographical concentration of innovation activities. As innovations are strongly connected to growth and their diffusion is bounded in space, it is expected that these industries are more prone to experience extreme regional growth events. Secondly, patterns of innovation per se vary across industries. PAVITT (1984)

demonstrates the differences in underlying production technologies, competition processes and learning modes. The extent of opportunities for innovations and thus growth obviously depends on the particular technological regime of an industry (DOSI 1988).

Finally, we are the first in literature to explicitly include service industries in the study of the stochastic characteristics of growth. Thus, it is natural to contrast the growth dynamics of service and manufacturing industries. This results in the following hypothesis:

Hypothesis 3: The stochastic characteristics of regional employment growth

depend on the type of industry under consideration.