Agglomeration externalities of fast-growth firms

ABSTRACT Small groups of fast-growth firms contribute disproportionately to job creation, yet little is known about their broader impact on the economy. This paper provides the first evidence of the agglomeration externalities of fast-growth firms, examining their economic impact on non-fast-growth firms operating within the same region (NUTS-2) and industry (SIC2), and through backward and forward linkages. Using comprehensive firm-level data on UK firms between 1997 and 2013, the analysis shows robust evidence of positive spillovers of fast-growth firms on the labour productivity of non-fast-growth firms in the same industry and region. However, the externalities in relation to the employment growth of non-fast-growth firms are negative, suggesting labour poaching and local competition effects.


INTRODUCTION
Fast-growth firms have attracted increasing attention from policy-makers and academic researchers because of their disproportionate contribution to economic growth and job creation. Since the recent financial crisis, fast-growth firms have been considered a viable option to foster economic recovery and are central to the political debate on economic performance and industrial resilience (Anyadike- Danes et al., 2013;Bleda & Del Rio, 2013;Brown et al., 2017;Coad et al., 2012;Mason & Brown, 2013; Organisation for Economic Co-operation and Development (OECD), 2013; Storey & Greene, 2010). However, the existing literature has focused so far almost exclusively on the characteristics of fast-growth firms, seeking to identify the drivers and to predict the likelihood of fastgrowth episodes (Haltiwanger et al., 2013;Hölzl, 2014;Lawless, 2014).
Following a different approach, recent studies have investigated the emergence of the fast-growth phenomenon at the regional level, examining if and how location-specific characteristics, industrial agglomeration and specialization could promote fast-growth (Duschl et al., 2015;Stam, 2005). The idea that region-specific characteristics affect firms' productivity and growth is well established in economic geography and regional science, with both theoretical and empirical analysis focusing on local agglomeration externalities (Glaeser et al., 1992;Jacobs, 1969). However, empirical evidence about the ways in which agglomeration externalities occur and how they may affect firms' growth is still mixed (Abukabarr & Mitra, 2017;De Groot et al., 2009).
The study fills this gap by analysing the impact of fastgrowth firms on the economic performance of industrially related and proximately located non-fast-growth firms. We define fast-growth firms using both employmentand productivity-based definitions to capture different business population and alternative spillover channels. To the best of our knowledge, this is the first study to examine the spillover effects of fast-growth firms. By using firm-, region-and industry-level data for the UK over the period 1997-2013, we identify the main channels through which these firms indirectly affect the productivity and employment growth of other firms in the region, and investigate if these externalities spread horizontally or through forward and backward linkages.
The results show that, on the one hand, a higher proportion of fast-employment-growth firms has negative effects on the average employment growth of other firms in the same industry and region, consistent with competition-led crowding-out and labour-poaching effects. On the other hand, a higher proportion of fast-productivity-growth firms has positive spillover effects on the labour productivity of non-fast-growth firms, suggesting competition-led efficiency improvement and potential knowledge spillovers. By analysing the externalities among vertically integrated industries, we find that an increase in demand by fast-growth firms has positive market-creating spillover effects on other firms in upstream sectors. Also, a higher proportion of fast-growth suppliers results in increased productivity growth in downstream sectors, potentially because of learning and demonstration effects as a result of knowledge spillovers.
The analysis reveals the heterogeneous effects of fastgrowth externalities. First, these results are particularly strong for small and old non-fast-growth firms, especially in low-tech sectors. Second, stronger negative externalities on employment growth mainly affect peripheral areas, while the most agglomerated core regions experience positive spillover effects from increased proportions of fastgrowth firms, suggesting that the negative externalities on employment growth might be exacerbated by a limited supply in peripheral local labour markets. In contrast, the stronger positive externalities on labour productivity from fast-growth firms in highly agglomerated areas suggest the presence of knowledge spillovers and efficiency improvements because of increased competitive pressure and learning effects stimulated by fast-growth firms.
The paper is structured as follows. The next section reviews the main theoretical and empirical contributions in the existing literature. We then discuss the data and present the summary statistics, before explaining the methodological approach. Finally, we present and discuss the econometric results, and conclude by highlighting the policy implications and future directions for research.

LITERATURE REVIEW
The study is mainly related to two broad literatures. First is the fast-growth firms literature that has expanded exponentially in the last two decades. This strand of the literature has extensively highlighted how fast-growth firms, although forming a small fraction of the business population, generate a disproportionately high rate of new jobs (Brown et al., 2017;Henrekson & Johansson, 2010; National Endowment for Science, Technology and the Arts (NESTA), 2009). Moreover, the exceptional growth of fast-growth firms is not linked to cyclical economic fluctuations, as their contribution to job creation has been observed in times of both economic upturn and recession . Since the recent financial crisis, fast-growth firms have been considered as a viable option by many governments to help foster economic recovery, and have become central in the political and academic debate about economic resilience and growth (Acs et al., 2008;Anyadike-Danes & Hart, 2018;Bleda & Del Rio, 2013;Coad et al., 2014a;Mason & Brown, 2013;OECD, 2013;Storey & Greene, 2010).
Recent studies have started investigating the spatial development of fast-growth firms, although little is known about how fast-growth firms might be related to regional development (Brown & Mawson, 2016;Li, 2016). Several studies suggest that regional characteristics play an important role in affecting the development of fast-growth firms, fostered by location-specific characteristics, industrial agglomeration and specialization (Duschl et al., 2015;Stam, 2005). The main regional factors usually discussed in this literature include industrial agglomeration, human capital, transportation costs, institutional factors and the entrepreneurial ecosystem (Arauzo-Carod et al., 2010). While these factors have been investigated to explain the incidence of fast-growth, much less attention has been paid to the external impact of such firms' activities and their interactions with the local economy. Given the relevant policy focus on fast growth, and the considerable resources allocated by governments to stimulate such growth, it becomes increasingly important to understand the wider economic impact of the fast-growth phenomenon in the economy.
In this regard, by linking the fast-growth literature to the main economic geography theories on agglomeration externalities, it would be possible to analyse the spillovers arising from the co-location in agglomerated regions and industries of fast-growth and other firms (Abukabarr & Mitra, 2017;Glaeser et al., 1992). In particular, following the Marshall-Arrow-Romer (MAR) theories on localization economies, the agglomeration of fast-growth firms in a given region and industry could generate both positive and negative externalities for other spatially proximate and industrially related non-fast-growth firms. Marshallian externalities linked to localization economies mainly operate through three different channels: sharing specialized suppliers, labour pooling and matching, and knowledge externalities (Glaeser et al., 1992;Marshall, 1920). First, by sharing intermediate inputs from specialized suppliers, fast-growth and non-fast-growth firms could reduce the costs of obtaining inputs or of shipping goods to customers (Fujita, Krugman, & Venables, 1999). In addition, fastgrowth firms could also generate spillover effects for other firms in vertically integrated industries. In particular, these could be for non-fast-growth suppliers and consumers, who could internalize the externalities related to increased demand, and introduce new improved inputs, innovation and efficiency gains induced by fast-growth firms in other related sectors (Humphrey & Schmitz, 2002;Jabbour & Mucchielli, 2007). However, while firms may be able to tap into better supply chains when co-locating with fast-growth firms, they may also have to bear increased costs of production because of the negative externalities related to higher agglomeration. These negative spillovers are usually linked to high rental and transportation costs, and crowding-out effects related to the tougher competition by fast-growth firms in both the upand downstream markets (Broersma & Van Dijk, 2007;Combes & Gobillon, 2015).
Second, by locating close to each other, fast-growth and other firms within the same industry could enjoy the benefits of 'thick' labour markets, having access to a large pool of suitably skilled workers (Combes & Duranton, 2006;Glaeser & Resseger, 2010). Clustering reduces the costs of managing labour needs, especially in an environment with high turnover, reducing the uncertainty about the future demand for labour and about the possible future skills required (De Groot et al., 2009). In addition, the clustering of firms within the same industry could facilitate the transfer of workers from unsuccessful firms to successful ones, facilitating the match between firms and workers, and result in the reinforcement of dense agglomeration (Duranton & Puga, 2004;Helsley & Strange, 1990). In this regard, the agglomeration of fast-growth firms could facilitate, on the one hand, the match between skilled workers and firms' requirements, or the flow of labour and skills from fast-growth to other firms within the same industry. However, on the other hand, a rapid increase in the agglomeration of fast-growth firms could also create negative spillover effects related to labour poaching, where tougher competition in the local labour market could draw the limited numbers of skilled workers available towards the most successful firms in the cluster, that is, the fast-growth firms (Coad et al., 2014b;Combes & Duranton, 2006;Morris et al., 2019).
Finally, an increase in the agglomeration of fast-growth firms could also generate relevant knowledge externalities for other firms within the same region and industry, where fast-growth and other firms could share ideas and knowledge, mainly through informal interactions and the movement of workers (Storper & Venables, 2004). Firms can learn from other firms, through localized knowledge spillovers, which are mainly relevant in the case of tacit rather than codified knowledge, and intensifying the benefits of the interaction within the local labour market and with actors along the supply chain (Polanyi, 1967). The existing literature suggests that firms operating in regions and sectors characterized by greater levels of agglomeration experience higher rates of growth, thanks to the indirect effect of tacit or explicit externalities originated from better performing companies (Audretsch & Dohse, 2007;Raspe & Van Oort, 2007). Thus, it is reasonable to hypothesize that fast-growth firms might indirectly affect the performance of spatially proximate and industrially related non-fast-growth firms because of their dynamism, innovation, productivity growth and employment creation. In addition, horizontal externalities could arise through imitation, cooperation, competition and the movement of workers between fast-and non-fast-growth firms. Thus, spatially agglomerated fast-growth firms operating within the same industry could, on the one hand, trigger positive externalities, through demonstration effects and competition-led efficiency improvements, but, on the other hand, they could also lead to competition-led crowding out effects as a result of the tougher competition for common resources and inputs of production, such as skills and intermediate inputs (Glaeser et al., 1992;Porter, 1990).
The processes through which agglomeration externalities from fast-growth firms may occur are indeed complex, and could be mediated by a mix of different economic forces, such as the level of agglomeration and concentration in the local industry, the availability of skills and the intensity of the vertical integration. Thus, fast-growth externalities may result in differentiated effects for other co-located firms within the same industry. As such, the overall effects of fast-growth agglomeration externalities may be context dependent, based on the resources and knowledge available across regions and industries (Neffke et al., 2011).

Data sources
The empirical analysis draws on a mix of data sources at the firm, industry and region level. First, we use firm-level data from the Office for National Statistics (ONS) Business Structure Database (BSD) covering all businesses in manufacturing industries in the UK between 1997 and 2013 (ONS, 2017). The BSD provides information on firms' age, ownership, turnover, employment, industrial classification and postcode. Second, we include several variables at the region and industry levels, calculated by aggregation from the BSD database at the NUTS-2 region and SIC2 (Standard Industrial Classification) industry level, such as employment, net entry rate and agglomeration index. To estimate vertical backward and forward linkages, we make use of the ONS input-output tables, estimating supply and demand for all sectors at the SIC2 level in the UK. In addition, the research and development (R&D) intensities at the NUTS-2 region and SIC2 industry level are estimated using the UK Innovation Survey database (ONS, 2018).

Fast-growth definitions
Thanks to these detailed and comprehensive data, we can identify the incidence and distribution of fast-growth firms across the UK regions and industries in the UK using alternative measures. There is an ongoing debate over the merits and drawbacks of different definitions of fast-growth firms based measures are only modestly correlated, and different definitions produce different subsets of the business population (Daunfeldt et al., 2014;Du & Bonner, 2017;Shepherd & Wiklund, 2009). Hence, in this study we examine two different fast-growth definitions, based on employment and productivity growth, to capture the top performers in terms of different growth mechanisms. 1 First, the employment-based high-growth-firms (HGFs) definition captures firms with at least 10 employees that have an annual average growth in employment of 20% or more over a three-year period (Eurostat-OECD, 2007). Also to include firms with fewer than 10 employees, we adopt the small HGFs definition introduced by Clayton et al. (2013), capturing firms with fewer than 10 employees which grow by more than eight new employees over a three-year period. Second, we follow Bonner (2016, 2017) to define productivity-based super-growth heroes (SGHs). This metric captures firms that have experienced a positive labour productivity growth over a three-year period, whereby both turnover and employment have grown relative to the base year, implying faster growth in turnover than in employment, and in addition with labour productivity levels above the SIC3 industry average. Firms are defined as fast-growth firms for the three years constituting the growth episode in order to identify precisely each of the years in which firms have registered particularly fast growth. Table 1 presents summary statistics about the characteristics and distribution of the overall sample of manufacturing firms, HGFs and SGHs in the UK. Fast-growth firms represent around 4-5% of manufacturing firms in the sample. During this period, about 150,000 manufacturing firms have experienced at least one SGH period, while almost 120,000 have registered at least one HGF period. By comparing these two groups, we observe that during this period only 15% of these firms have experienced both an SGH and an HGF episode. Fast-growth firms are usually larger than the average firm in terms of employment and turnover, and have higher labour productivity. It appears that the average firm age of SGHs or HGFs is around 12-14 years. Both SGHs and HGFs have a higher probability of being foreign owned and of being more likely to be part of a business group. However, in our sample, the percentages of small and medium-sized enterprises (SMEs), young and high-tech firms do not differ significantly between fast-growth firms and the average firms. 2 Figure 1 presents the geographical distribution of SGHs and HGFs employment as the average share of total employment for each NUTS-2 UK region during the period 1997-2013. The two maps highlight a different geographical distribution for these two groups of fastgrowth firms. In fact, the SGHs incidence rate is particularly high in large cities' regions, such as the Greater London area, Hampshire (Southampton), the East Midlands (with Nottingham and Derby), and the Leeds and Newcastle regions. These are thus mainly in highly agglomerated areas, as suggested by the positive correlation between this fast-growth metric and the Ellison and Glaeser (1997) agglomeration index, and thus in turn with productivity growth as shown in the previous literature (Bertinelli & Black, 2004;Duranton & Puga, 2004). HGFs instead seem more evenly distributed both in urban and rural regions, with relatively higher incidence in Surrey, Sussex, Cheshire and County Durham, but also in more agglomerated regions, such as the Greater Manchester area and the region of Edinburgh in Scotland. This is consistent with previous evidence suggesting that employment fast growth can happen everywhere (Moreno & Coad, 2015).

Fast-growth externalities
Following the theoretical predictions discussed above, and the established empirical literature on the identification of agglomeration externalities developed since the seminal paper by Javorcik (2004), we consider three possible Note: Statistics are based on the Business Structure Database (BSD) between 1997 and 2013. Turnover is expressed in thousands of pounds. Super-growth heroes (SGHs): firms that have experienced a positive labour productivity growth over a three-year period with both turnover and employment growth and labour productivity is above three-year average labour productivity of its sector at the SIC3 level. High-growth firms (HGFs): the total employment of firms with more than 10 employees grows by more than 20% over a three-year period, or if the total employment of firms with fewer than 10 employees grows by more than eight new employees over a three-year period.
measures of fast-growth spillovers. First, fast-growth industrial externalities at the horizontal level (Horizontal FG rst ) relate to the spillover effects generating from fast-growth firms operating in the same SIC2 industry s and NUTS-2 region r, following MAR theory. This is measured by the share of fast-growth firms' employment FG EMPL rst over the total employment EMPL rst of each region and industry in a given year (t): Horizontal FG rst = FG EMPL rst /EMPL rst Second, we estimate backward and forward externalities along the vertical supply chain, considering the fast-growth spillovers originating from vertically integrated sectors which are part of the same value chain of production. To do so, we build two measures of vertical externalities for each sector: one for backward linkages with fast-growth suppliers, and the other for forward linkages with fastgrowth customers (Frenken et al., 2007;Javorcik, 2004). Following Javorcik's (2004) methodology, we use the average intermediate supply linkage between SIC2 industries pairs, with the 2005 UK input-output tables as a base year, as a measure of industrial integration between all sector pairs in the UK (a sj ). For each sector (s) we can then construct two measures of vertical externalities through backward linkages with the supplying sectors (j) and forward linkages with customer sectors (z). To do so, we weight the share of fast-growth firms' employment in each upstream (Horizontal FG rjt ) and downstream sector (Horizontal FG rzt ) of industry (s) within the same region (r) by the relative measure of vertical integration between each pair of sector (sj) and (sz), and averaging across all backward (j) and forward sectors (z): 3 In this way, we can comprehensively estimate the externalities of fast-growth firms, considering not only those operating within the same region and industry but also the spillovers spreading throughout vertically integrated industries located within the same region. SGHs are those firms that have experienced a positive labour productivity growth over a three-year period with both turnover and employment growth, and labour productivity is above the three-year average labour productivity of its sector at the SIC3 level. HGFs are the total employment of firms with more than 10 employees that grow by more than 20% over a three-year period, or if the total employment of firms with fewer than 10 employees grows by more than eight new employees over a three-year period.
Agglomeration externalities of fast-growth firms

METHODOLOGY
We model fast-growth externalities for other non-fastgrowth firms in the following way, controlling for firm, region and industry heterogeneity: In equation (1) the dependent variable DEMP irst represents the year-to-year employment growth of non-HGF firms (i) at time (t), while the key explanatory variable DHoriz.HGF rst indicates the horizontal externalities linked to an increased incidence of employment-based HGFs in SIC2 industry (s) and NUTS-2 region (r). The potential regional vertical externalities in the backward DBackw.HGF rst and forward sectors DForw.HGF rst are also included for the spillover effects in sector (s) and region (r) of an increased incidence of fast-growth firms in the upand downstream industries. Similarly, equation (2) models the spillover effects of a higher proportion of productivity-based SGHs on the labour productivity growth of non-SGH firms. In this case, the dependent variable DLP irst measures the yearto-year labour productivity growth of non-SGHs in region (r) and industry (s) at time (t) measured as total revenue per employee. 4 The key explanatory variables include DHoriz.SGH rst , an increase of the proportion of SGHs over total employment in region r and industry s, and the vertical externalities linked to an increase in proportion of SGHs in backward (DBackw.SGH rst ) and forward sectors (DForw.SGH rst ). 5 Both equations control for variables at different levels. First, the vector FIRM it−1 includes several firm-level characteristics, including lagged levels of employment, labour productivity, firm age, foreign and group ownership. Second, ENV rst−1 , represents the different control variables at the industry and region level. We control for the overall performance of sectors and regions where each firm operates at the NUTS-2 and SIC2 level, including lagged levels of employment, labour productivity growth and the net entry rate, in order to take into account the level of competition and the dynamism of the local industries. 6 In addition, we control for the region and industry R&D intensity and for the agglomeration index at the regionindustry level, using the Ellison and Glaeser (1997) definition. 7 We also interact each externality metric with the agglomeration index in order to estimate the relationship between fast-growth incidence rate and other firms' employment and productivity growth, while controlling for the self-selection of fast-growth and highly performing firms in industries and regions characterized by high levels of spatial agglomeration and industrial concentration (Autor et al., 2017;Combes & Gobillon, 2015).
By using an ordinary least squares (OLS) first-difference fixed-effects model, we can identify the relationship between fast-growth externalities and the economic performance of non-fast-growth firms. In particular, the first-difference model allows one to measure the effect of a standard deviation increase in the externalities of fastgrowth incidence rates on other firms' employment and productivity growth. In this way, we can identify the dynamic evolution of fast-growth firms and of their related spillovers, given their definition being based on rapid growth and of a volatile nature. In particular, we are interested in understanding how the variation in fast-growth firms agglomeration affects employment and productivity growth for other firms clustered within the same industry. 8 In addition, the firm, industry and regional control variables, together with firm-level (j i ), year (j t ) and regionindustry fixed-effects (j rs ), improve the estimation precision by accounting for a range of firm heterogeneities and controlling for time-invariant firm, industry and region specific effects. Standard errors are clustered at the region, industry and year level.

Robustness tests and heterogeneity analysis
To test the robustness of our baseline specifications we perform several checks. First, we adopt a multilevel (ML) firstdifference fixed-effects methodology in order to consider the hierarchical nature of the data, relaxing the stringent assumption that observations within subunits are uncorrelated and modelling the non-independence of units in the same cluster (i.e., region and industry), including variables in the model at different levels (Gelman & Hill, 2007;Raspe & Van Oort, 2007;Srholec, 2010).
Second, we implement a dynamic system generalized method of moments (GMM) instrumenting the possible endogenous variables with their three-period lagged values. In this case, we consider the fast-growth variables as predetermined and therefore not correlated with the error term, but expected to influence non-fast-growth firms' performance. System GMM has been found to be more efficient compared with difference GMM, particularly in the presence of heteroskedasticity (Arellano & Bond, 1991). To evaluate the overall goodness of fit of the GMM models, we report the Hansen test of overidentifying restrictions, which presents an evaluation of the exogeneity of the subset of instruments. We also test for the presence of firstand second-order serial autocorrelation, for potential inconsistency with predetermined variable regressions (Windmeijer, 2006). Results from these two methodologies are reported in Table A2 in Appendix A in the supplemental data online.
Third, it might be argued that the results, especially in terms of labour productivity, could be driven by firm exits, where less productive non-fast-growth firms exit the market in the face of mounting competition from fastgrowth firms, pushing up the overall productivity of surviving firms. To account for this possibility, in Table A3 in Appendix A online we have followed two different approaches. We have replicated our analysis on a balanced panel of firms always active throughout the sample period. We have also controlled for firm exits by implementing a Heckman (1979) selection model, in which the first stage of the procedure controls for survival selection using lagged levels of labour productivity as an additional selection variable.
Finally, we analyse the heterogeneous distribution of fast-growth externalities across regions, industries and firms' characteristics. We estimate the baseline models, splitting the sample by firms' age, size and industrial technological intensity. Recent studies suggest that small firms are more likely to rely on spillovers, especially because of their limited ability to invest significant resources in internal capabilities, and thus expecting a particularly strong influence of fast-growth externalities on their performance (Abukabarr & Mitra, 2017;Audretsch & Dohse, 2007). We then expect to find different effects of fast-growth externalities on younger, entrepreneurial and more dynamic firms in comparison with established companies. We also test whether fast-growth externalities are stronger in knowledge-intensive, where external collaborations are more developed and firms can rely on stronger absorptive capacity to internalize spillovers, or in lowtech industries because of the scope of catch-up for firms distant from the technological frontier (De Silva & McComb, 2012;Sena et al., 2013). Finally, we analyse the heterogeneous distribution of fast-growth externalities across NUTS-2 regions and SIC2 industries to compare the spatial and industrial differences in the strength of these spillovers. Table 2 reports the estimates of the effect of fast-growth externalities on employment growth. In column 1 we find an overall negative horizontal spillover effect of fastemployment growth rate on the employment growth of other firms operating within the same region and sector. This may be interpreted as a sign of competition-led crowding out effects when facing a strong expansion of employment in fast-growth firms. This evidence is consistent with theories of trade-offs faced by firms clustering in thick local markets, between benefits linked to labour pooling and specialized suppliers, and higher costs of labour poaching and competition (Combes & Duranton, 2006). In this regard, labour poaching effects might be particularly relevant, given the skills shortages experienced in the UK, in particular in manufacturing industries (Calvo & Coulter, 2017;Haskel et al., 2005;Kemeny, 2017;Morris et al., 2019). In addition, this finding seems consistent with the recent evidence of 'superstar firms' in manufacturing industries, where rapid growth of mark-ups leads to an increased concentration of labour and skills in few fast-growing firms (Autor et al., 2017). According to back-of-the envelope calculations, increasing the fast-growth incidence rate by 10% leads to an overall slower employment growth by 0.082% in the same manufacturing industry and region, ceteris paribus. This translates to more than 35,000 fewer jobs per year across UK regions, 9 a sizeable impact compared with the estimated number of around 400,000 new jobs created by fast-growth firms in a given year. 10 Turning to vertical externalities, while there is no statistically significant effect linked to backward fast-growth externalities, we observe a strong positive spillover effect of a higher proportion of forward fast-growth firms, both in high-and low-tech sectors, which stimulates demanddriven employment growth for supplying non-fast-growing firms. In addition, the interaction between agglomeration and spillover effects suggests a mediating role of agglomeration in determining the externalities impact, where the externalities are more pronounced in more agglomerated industries and regions, in line with the previous literature (Audretsch & Dohse, 2007). In particular, an increase in the proportion of fast-growth firms in downstream sectors will lead to a larger increase in the employment growth of non-fast-growth firms in more agglomerated upstream sectors. Furthermore, by comparing the results among firms of different ages and sizes, we find mostly that small and old firms drive the overall results. We observe that horizontal externalities and the moderating effects of agglomeration are stronger for small firms, probably because of their limited resources, while old non-fast-growth firms benefit more from forward fast-growth spillovers, presumably benefiting from established supply linkages, but they also suffer more from the competition within the same sector in agglomerated regions and industries (Abukabarr & Mitra, 2017). Table 3 presents the results of fast-growth spillovers on productivity growth, finding overall a positive and significant impact of horizontal externalities on the labour productivity growth of non-fast-growth firms, particularly in low-tech sectors. Higher proportions of fast-productivitygrowth firms seem to spill labour productivity growth to other non-fast-growth firms, both within the same sector and along the vertically integrated supply chains. Overall, a 10% increase in the incidence of fast-productivity-growth firms within the same industry and region would prompt a 0.12% increase in the average labour productivity of nonfast-growth manufacturers. Interestingly, the marginal effect of the spillovers is higher for low-tech firms (0.17%), suggesting that there is more scope for productivity catch up in low-tech sectors, possibly through demonstration effects (Grillitsch & Nilsson, 2019). In addition to knowledge spillover effects, positive productivity externalities within the same sector could be driven by competition-led efficiency improvement. This refers to the pressure from competitors which affect productivity levels within the same industry. Product-market competition could enhance within-industry productivity through selection processes (Foster et al., 2001;Syverson, 2011) or Agglomeration externalities of fast-growth firms Table 2. Region-industry spillovers effect of fast-growing firms (HGFs) on the employment growth of non-fast-growth firms in the manufacturing sectors.

Productivity growth
(1) Note: Estimations are based on the Business Structure Database (BSD) between 1997 and 2013 using an ordinary least squares (OLS) first-difference model with firm, region, industry and year fixed-effects. Robust standard errors clustered at the region, industry and year level are reported in parentheses. Statistical significance levels: ***p < 0.01, **p < 0.05, *p < 0.1. Other control variables included but not reported: firm employment, labour productivity, age, foreign ownership and group participation; region-industry employment growth, labour productivity growth, net entry rate, and research and development (R&D) intensity. Table 3. Region-industry spillovers effect of fast-growing firms (SGHs) on the productivity growth of non-fast-growth firms in the manufacturing sectors.
(1) Note: Estimations are based on the Business Structure Database (BSD) between 1997 and 2013 using an ordinary least squares (OLS) first-difference model with firm, region, industry and year fixed-effects. Robust standard errors clustered at the region, industry and year level are reported in parentheses. Statistical significance levels: ***p < 0.01, **p < 0.05, *p < 0.1. Other control variables included but not reported: firm employment, labour productivity, age, foreign ownership and group participation; region-industry employment growth, labour productivity growth, net entry rate, and research and development (R&D) intensity.
Agglomeration externalities of fast-growth firms through within-organization efficiency improvements (Abukabarr & Mitra, 2017;Schmitz, 2005). Along the vertical supply chain, higher incidence rates of backwards fast-growth firms seem to stimulate strong positive effects for non-fast-growth firms' productivity growth downwards, especially for small, old and hightech firms. The positive spillover effect of fast-growth incidence along supply chains echoes the recent evidence suggesting knowledge externalities between fast-growth suppliers and non-fast-growth customers (Isaksson, Simeth, & Seifert, 2016). In addition, we find a positive and significant moderating effect of agglomeration for the fast-productivity-growth backward externalities on non-fast-growth customers. Higher fast-growth among suppliers stimulates productivity improvement of other firms in more agglomerated industries-regions (De Silva & McComb, 2012;Sena et al., 2013).
Overall, the results highlight different externality channels through which fast-growth firms affect vertically integrated industries. On the one hand, employment growth externalities are linked to agglomeration economies and fast-growth-driven increased demand in downstream sectors. On the other hand, productivity spillovers through agglomeration economies seem more likely to be knowledge and technology driven, originating from fast-growth suppliers (Grillitsch & Nilsson, 2019).
The findings from our baseline specifications are robust and consistent with the results of the GMM and ML estimations provided in Table A2 in Appendix A in the supplemental data online. Even when considering the hierarchical nature of the main variables of interest, and after instrumenting the possible endogenous variables with their lagged values, we find consistent evidence that fast-growth firms have negative externalities for the employment growth of other firms, while there are positive spillovers in terms of productivity. Finally, the results are also robust in relation to potential selection-bias driven by the exit of less productive non-fast-growth firms. Both approaches, developed in Table A3 in Appendix A online to control for this issue, show consistent results with our baseline specifications, corroborating the overall robustness of our econometric methodology. 11 Spatial and industrial heterogeneity Based on the previous estimates, Figures 2 and 3 analyse the spatial and industrial heterogeneity of horizontal fast- Figure 2. Average marginal effect of horizontal fast-growth spillovers on employment and productivity growth per region (NUTS-2 level). Note: The marginal effects of the impact of horizontal fast-growth industry-region spillovers aggregated at the NUTS-2 level were estimated using an ordinary least squares (OLS) first-difference fixed-effects model. Fast-growth firms are defined as super-growth heroes (SGHs) for the productivity growth models and as high-growth firms (HGFs) for the employment growth models. growth externalities. At the regional level, Figure 2 shows that the negative externalities on the employment growth of non-fast-growth firms are stronger in peripheral areas, as the South West, Scotland and Cumbria, where local labour markets are less developed, and the costs of labour poaching and concentration are higher because of the particularly fierce competition of fast-growth firms (Sena et al., 2013). In contrast, the positive spillover effect of fast-productivity growth is more evenly scattered across the UK, with particularly strong positive externalities for productivity growth in the Greater Birmingham area, East Midlands, Yorkshire, Newcastle and South of Scotland, especially in highly agglomerated areas in line with previous evidence (Coad et al., 2014a;Stam, 2005).
Turning to the industrial distribution, Figure 3 shows that the industries mostly negatively affected in terms of employment growth by fast-growth spillovers are the fuels, apparel, mineral products and food-processing sectors. On the contrary, the automotive industry, the sector producing medical and precision instruments, and electric machinery industries seem to benefit the most in terms of employment spillovers. These findings suggest an overall negative spillover effect, especially on employment growth in medium-low-tech sectors, highlighting a concentration of the labour share in these sectors to a smaller number of fast-growth companies (Autor et al., 2017). On the contrary, medium-high-tech manufacturing sectors seem to experience positive externalities from fast-growth firms in terms of employment growth, in line with previous predictions (Grillitsch & Nilsson, 2019;Moreno & Coad, 2015). Productivity spillovers seem to follow a similar pattern, with strong positive effects for the machinery, metals, computers and information technology equipment industries, and a negative effect for the medium-low-tech sectors of leather, apparel and oil. These findings suggest that positive fast-growth externalities are more relevant in high-tech sectors, propagated through external collaborations between firms, and strongly relying on the internal absorptive capacity of non-fast-growth firms needed to internalize the spillovers (De Silva & McComb, 2012;Sena et al., 2013).

CONCLUSIONS
This is the first study to evaluate the agglomeration externalities of fast-growth firms. Overall, we find that a higher incidence of fast-employment growth has negative spillover effects on employment growth at the horizontal level, while a higher incidence of fast-productivity growth generates positive spillover effects in terms of labour productivity.
Furthermore, we find positive inter-industry externalities: high-employment-growth firms in the downstream sectors have positive demand-driven spillover effects on employment in upstream sectors, while backwards productivity externalities from fast-growth firms in upstream sectors are mainly relevant to non-fast-growth customers. These findings are more pronounced among small and old firms, in both low-and high-tech sectors. In addition, agglomeration plays an important role in mediating these externalities, with spatially heterogeneous effects driven by stronger negative externalities on employment growth in peripheral regions, and with positive spillover effects, in terms of both employment and productivity growth, in densely agglomerated regions and industries.
The results highlight several policy implications. First, the policy goals of job creation and productivity growth might not always be complementary. While national and subnational policies might be designed to promote fast growth, it is important to understand the indirect implications for the employment and productivity growths of non-fast-growth firms.
Second, having more fast-productivity-growth firms in a region is beneficial for the productivity growth of other firms overall. However, more fast-employment-growth firms may put a strain on other firms' abilities to attract workers and to upscale. This points to the skills and labour competition between employers in places experiencing skill shortages, skill mismatches and the local labour marketsorting problems. The imbalance between skill supply and skill demand is a longstanding challenge faced by the UK. Reforms and investment have been put in place by all previous governments to address these issues, but with limited success (Payne & Keep, 2011;Sissons & Jones, 2016). More promising policy designs would lean towards subnational approaches that emphasize place-based strategies to diagnose local labour market imbalances (Green, 2012), emphasize demand-led skills development (Froy, 2013), and improve local skills utilization and integration (Sissons & Jones, 2016).
Third, the externalities of the fast-growth phenomenon are highly heterogeneous across industries, positions in the supply chains, firms and regional characteristics. This variability should be considered when designing specific policy instruments. This lends clear support to linking Figure 3. Average marginal effect of horizontal fast-growth spillovers on employment and productivity growth per industry (SIC2 level). Note: The marginal effects of the impact of fast-growth industry-region spillovers aggregated at the industry SIC2 level were estimated using an ordinary least squares (OLS) first-difference fixed-effects model. Fast-growth firms are defined as supergrowth heroes (SGHs) for the productivity growth models and as high-growth firms (HGFs) for the employment growth models.
Agglomeration externalities of fast-growth firms industrial strategy with skills policy, aiming to drive regional economic growth (Payne & Keep, 2011). However, demand-driven skills development is crucial in responding to specific needs of skills for workplace and fast-pacing technological changes.
Research on fast-growth firms needs to go beyond the within-firm growth analysis to understand better the overall welfare effect of the fast-growth phenomenon on the economy. Future research needs to analyse further the specific mechanisms through which the agglomeration externalities related to fast-growth firms operate, both within and across industries and regions, given their increasing relevance in the economy. This will then help to design appropriate policies to promote long-term and balanced growth. Conference 2017, and the RSA Conference 2017. The views expressed in the paper are those of the authors and do not necessarily represent those of the funders. The UK statistical data used in this study are from the Office for National Statistics (ONS) and are Crown copyright and reproduced with the permission of the controller of HMSO and the Queen's Printer for Scotland. The use of the ONS statistical data in this work does not imply the endorsement of the ONS in relation to the interpretation or analysis of the statistical data. This work uses research data sets that may not exactly reproduce National Statistics aggregates.

DISCLOSURE STATEMENT
No potential conflict of interest was reported by the authors.   (Du & Bonner, 2016), high-growth entrepreneurs (Audretsch, 2012) and gazelles (Acs et al., 2008). 2. Manufacturing sectors include all industries with an SIC (2003) code between 15 and 36. Firms with more than 250 employees are considered to be large, otherwise they are SMEs. Firms operating for more than five years are considered old, and young otherwise. Following the Eurostat classification, manufacturing high-tech firms have SIC codes (2003) equal to: (24) chemicals and pharmaceuticals; (29) machinery and engineering; (30) computers and office machinery; (31) electrical machinery; (32) information technology (IT) and communication equipment; (33) medical, precision and optical instruments; (34) motor vehicles; and (35) transport equipment. 3. As a robustness check, we estimated the vertical industrial integration externalities also at the sector-country level, considering the incidence of fast-growth suppliers and customers located across the country. These results are consistent and are available from the authors upon request. 4. The Business Structure Database does not provide enough information to estimate total factor productivity (TFP) for the population of businesses in the UK, and thus we rely on labour productivity. Using the Annual Business Survey (ONS, 2019), we have replicated our baseline specifications estimating TFP, but only for a limited sample of firms (around 12,000). The results (available from authors upon request) are consistent with the main findings, indicating that turnover per employee can be used in this case as a good proxy for productivity. 5. We also estimate the spillover effects of HGFs' externalities on the labour productivity growth of non-HGFs and the impact of SGHs' externalities on the employment growth of non-HGFs. The results are robust with respect to the main findings and are available from the authors upon request. 6. To test the robustness of the results and to control for potential omitted variable bias, additional checks also included in the estimations the level of unemployment, the share of population with a tertiary education degree and the gross domestic product (GDP) growth at the NUTS-2 level, as well as region-year and industry-year fixed effects, in order to take into account further regionand industry-specific time trends. The results (available from the authors upon request) show that the inclusion of these additional control variables and fixed effects does not affect the precision and significance of the estimates. 7. The Ellison and Glaeser (1997) region-industry agglomeration index is measured as the difference between the squared share of employment of an industry (s) in a given region (r) and the squared share of employment of a region (r) in the country divided by the squared share of employment of the industry (s) in the country and by the Herfindhal index of industrial concentration. 8. Additional results (available from the authors upon request) show that the methodology is robust with regard to the use of variables in levels rather than differences. 9. Given the partial effect of the change in employment growth rate with respect to the change in the proportion of high growth is estimated at 0.082% and the known sample mean of employment growth at 0.477%, the predicted change in employment level is estimated at 0.48%, which is (1 + 0.082%)*0.477%. A rough calculation of the employment level with a decrease of 0.48% for an average firm size of 21 employees and an average number of firms in the sample of 352,000 a year is then 35,288 fewer jobs. 10. The existing evidence suggests that fast-employmentgrowth firms (HGFs) generate the majority of all new jobs in the UK. For the period 2006-08, of the 2.4 million new jobs created by businesses employing 10 or more people, about 1.3 million were created by fast-growth firms, equating to roughly 54% of the total (NESTA, 2009). 11. In additional robustness tests we controlled for the possibility of a time lag in the materialization of knowledge spillovers by lagging the main independent variables (the fast growth spillovers) by up to three years. In addition, we tested the sensitivity of the results using the levels of variables rather than first differences as the main regressors in the specifications. The results for both robustness tests are very similar and consistent with the main findings, and are available from the authors upon request. ORCID Jun Du http://orcid.org/0000-0002-0449-4437 Enrico Vanino http://orcid.org/0000-0002-4740-1501