Lara Abdel Fattah'

Giuseppe Arcuri

Aziza Garsaa+

Nadine Levratto°

Firm soundness and knowledge externalities: a comparative regional analysis

Keywords: Firm effects, regional effects, human capital, firm robustness, multilevel longitudinal model I25, L26, R11, C33

This paper investigates the role of regional context with regard to human capital and knowledge spillover effects in SMEs' financial soundness. Our empirical setting is based on the multilevel analysis for panel data, which better allows for the treatment of hierarchical data. It is applied to firms belonging to the industrial sector and operating in four European countries over the 2010-2015 period. We find that a combination of individual-and regionallevel characteristics explain firm soundness more accurately than individual features alone. Furthermore, we find that a higher local educational level and knowledge spillover improve the firm soundness.

Introduction

Firm heterogeneity has long been recognized to be caused by individual differences, but a growing literature presents evidence for the effect of location on firm survival, growth and profitability [START_REF] Audretsch | Location: A Neglected Determinant of Firm Growth[END_REF]Cassia andColombelli, 2010, Grillitsch and[START_REF] Grillitsch | Knowledge externalities and firm heterogeneity: Effects on high and low growth firms[END_REF]. International comparisons show that macroeconomic conditions and national institutions shape firms' trajectories [START_REF] Ipinnaiye | Drivers of SME performance: a holistic and multivariate approach[END_REF][START_REF] Mazzucato | High-growth firms in changing competitive environments: The US pharmaceutical industry (1963 to 2002)[END_REF] but that local characteristics matter as well.

Numerous papers have investigated the relationship between individual performance and local conditions, and the regional level has been identified as a relevant dimension in this field of research. The regional context especially influences small businesses for several reasons [START_REF] Karlsson | Entrepreneurship, Firm Growth and Regional Development in the New Economic Geography: Introduction[END_REF]. First, regional features facilitate the formation and transmission of social capital and constitute a local labour market from which firms can find and develop social capital [START_REF] Huggins | Culture and Place-Based Development: A Socio-Economic Analysis[END_REF], and different levels of social capital are linked to different levels of financial development within a region, which drives firm performance [START_REF] Guiso | Does local financial development matter[END_REF]. Second, research and innovation are created and developed at a local level, and knowledge regional spillovers tend to be localized. Regional innovation systems, clusters and, broadly speaking, smart regional innovation policies capitalize on this geographical proximity, which is considered a factor facilitating coordination between innovation actors [START_REF] Gerber | Spatial Dynamics of Vertical and Horizontal Intergovernmental Collaboration[END_REF]. Third, transaction costs, markets, and self-reinforcing growth have been found to be especially relevant at the regional level, as shown by the new economic geography literature [START_REF] Krugman | Increasing returns and economic geography[END_REF][START_REF] Krugman | Space: The final frontier[END_REF]. For all of these reasons, the present work fits into a local approach to firm performance and growth while shedding light on a barely studied topic: the relationship between the firm soundness perspective and local context.

This paper aims to determine to what extend the regional context shapes firm soundness, a question often considered from an institutional point of view [START_REF] Acs | Public policy to promote entrepreneurship: a call to arms[END_REF][START_REF] García-Posada | Entrepreneurship and enforcement institutions: disaggregated evidence for Spain[END_REF]. We enrich this field of research by paying attention to intangible resources made available at the regional level. This choice is relevant from knowledge economy and open innovation perspectives [START_REF] Cooke | Knowledge economies. Clusters, learning and cooperative advantage[END_REF][START_REF] Mina | Open service innovation and the firm's search for external knowledge[END_REF].

To shed light on the relationship between regional context and firm soundness, we mobilize a unique dataset of a panel of enterprises located in four European countries. The dataset includes accounting and financial information, as well as characteristics such as firm size, age, activity and location. These data are complemented with a series of indicators computed at the regional level to describe local context. The estimations are run using a multilevel model estimation technique [START_REF] Hox | Multilevel analysis: Techniques and applications[END_REF][START_REF] Hox | Handbook of advanced multilevel analysis[END_REF] that allows one to consider in a single equation various variables computed at different levels of aggregation (time, firm, and region) without bias.

Our results show that a combination of individual-and regional-level (NUTS 2) characteristics explains firm soundness more accurately than individual features alone. In particular, a higher level of education and employment in high-tech industries improve the robustness of small and medium-sized enterprises (SMEs).

This paper is novel in that to our knowledge, it represents a first attempt to correlate companies' financial soundness with local characteristics and more precisely to knowledge context. It also relies on the use of new multilevel estimation technique, making it possible to take into account the hierarchical structure of data (individual and regional variables).

Another contribution relates to the broadness of the empirical analysis, which focuses on 22,079 companies operating in 91 regions of four European countries from 2010 to 2015.

The remainder of the paper is structured as follows. Section 2 provides a review of related literature and formulates the hypotheses to be tested. Section 3 introduces the empirical strategy used. Section 4 presents the results, and section 5 concludes.

Theoretical framework

Firm and local context

Over the past decades, firms' trajectories have been widely investigated in reference to different factors. A significant proportion of these contributions has focused on firm-specific factors such as firm size and age [START_REF] Mueller | Economic failure and the role of plant age and size[END_REF] or on minimally efficient scales, the timing of entry [START_REF] Klepper | Entry, Exit, Growth, and Innovation over the Product Life Cycle[END_REF], intellectual assets [START_REF] Hormiga | The role of intellectual capital in the success of new ventures[END_REF], social networks (Abou-Moghli and Al-kasasbeh, 2012) and the development of firm-specific assets through advertising and R&D expenditures (Esteve-Pérez and [START_REF] Esteve-Pérez | The resource-based theory of the firm and firm survival[END_REF]. This heuristic approach has been complemented with research aiming to propose different statistical techniques with which to assess firms' exposure to default risk. Financial factors such as leverage, profitability, cash flow, and debt structures combined with the size and age of firms have finally been found to influence financial strength (See [START_REF] Altman | The success of business failure prediction models: An international survey[END_REF][START_REF] Freeman | The liability of newness: Age dependence in organizational death rates[END_REF][START_REF] Kale | Business failures: Liabilities of newness, adolescence, and smallness[END_REF]. Following the structure-conduct-performance paradigm [START_REF] Porter | The Structure within Industries and Companies' Performance[END_REF], another set of papers considers industrial-specific factors to complete this field of analysis, revealing the role of industry-specific factors such as market evolution [START_REF] Agarwal | The Evolution of Markets and Entry, Exit and Survival of Firms[END_REF][START_REF] Ilmakunnas | Microeconomic and macroeconomic influences on entry and exit of firms[END_REF], technological regimes [START_REF] Audretsch | New-Firm Survival and the Technological Regime[END_REF][START_REF] Kim | Technological regimes and firm survival[END_REF], intra-industry diversification [START_REF] Li | The effect of within-industry diversification on firm performance: Synergy creation, multi-market contact and market structuration[END_REF] and the stage of the industry life cycle [START_REF] Agarwal | Does Entry Size Matter? The Impact of the Life Cycle and Technology on Firm Survival[END_REF].

However, firm-and industry-level factors are not sufficient to explain why some companies have better financial health than others. In addition to studies examining variables depicting individual and sectoral characteristics, another part of the literature explains the empirical evidence related to firm soundness with attention to location-specific factors [START_REF] Klepper | Firm Survival and the Evolution of Oligopoly[END_REF][START_REF] Strotmann | Entrepreneurial survival[END_REF]. Geographical concentration or agglomeration [START_REF] Sorenson | The Social Structure of Entrepreneurial Activity: Geographic Concentration of Footwear Production in the United States, 1940-1989[END_REF], economies of scale [START_REF] Audretsch | Innovation and Industry Evolution[END_REF], unemployment rate, income level within each region [START_REF] Scott | Metropolis: From the Division of Labor to Urban Form[END_REF][START_REF] Backman | Regions, Human Capital and New Firm Formation[END_REF], business climate [START_REF] Ciccone | Productivity and the density of economic activity[END_REF], and institutional legitimacy [START_REF] Shane | New firm survival: Institutional explanations for new franchisor mortality[END_REF] are likely to have significant implications for the competitiveness of firms.

Despite the general belief that country effects should diminish and especially within groups of countries based on their core-periphery status or membership in trade blocs, due to globalization and institutional convergence, technologies, and institutions [START_REF] Berry | Is there convergence across countries? A spatial approach[END_REF][START_REF] Ramajo | Spatial heterogeneity and interregional spillovers in the European Union: Do cohesion policies encourage convergence across regions?[END_REF], recent studies show that regional specificities still prevail [START_REF] Huggins | Entrepreneurship and the determinants of firm survival within regions: human capital, growth motivation and locational conditions[END_REF][START_REF] Robert | Urban and Regional Horizons Culture and Place-Based Development : A Socio-Economic Analysis[END_REF].

Furthermore, some studies have analysed firm soundness within or across regions while considering indicators computed at the regional level: the financial context [START_REF] Arcuri | Early stage SME bankruptcy: does the local banking market matter?[END_REF][START_REF] Guiso | Does local financial development matter[END_REF], networks [START_REF] Littunen | Networks and Local Environmental Characteristics in the Survival of New Firms[END_REF], agglomeration economies [START_REF] Glaeser | Local industrial conditions and entrepreneurship: How much of the spatial distribution can we explain[END_REF] and, more generally speaking, local conditions [START_REF] Karlsson | Regional Characteristics and the Survival of New Firms[END_REF], whereas it has long been recognized that "performance differences between regions cannot be perceived as a direct result of macro-economic differences between regions.

Instead, they are a by-product of firms' individual behaviours" [START_REF] Van Oort | Multilevel approaches and the firm-agglomeration ambiguity in economic growth studies[END_REF]. These considerations lead us to formulate our first hypothesis:

H1: A combination of individual and local levels explains firm soundness more accurately than individual characteristics alone.

2.2

The role of human capital as a resource

From endogenous growth theory [START_REF] Krugman | Increasing returns and economic geography[END_REF], human capital has been shown to be a critical factor explaining the level of regional competitiveness, and the various endowments observed explain regional heterogeneity. This relation holds at the regional level as shown by [START_REF] Acs | The impact of geographic differences in human capital on service firm formation rates[END_REF] and [START_REF] Backman | Human capital in firms and regions: Impact on firm productivity[END_REF].

Indeed, employing a large number of highly educated and skilled workers benefits a firm through a productivity effect. From [START_REF] Barro | Economic growth in a cross section of countries[END_REF] this factor has long been identified as one of the main determinants of economic growth and plays an important role in the technological progress of countries. Moreover, a local labour market characterized by a significant share of highly educated and skilled workers increases the productivity of the whole work force through human capital externalities [START_REF] Moretti | Estimating the social return to higher education: evidence from longitudinal and repeated cross-sectional data[END_REF][START_REF] Rauch | Productivity Gains from Geographic Concentration of Human Capital: Evidence from the cities[END_REF], allowing local firms to be more efficient and profitable. These knowledge externalities tend to improve firm performance [START_REF] Audretsch | Mansfield's Missing Link: The Impact of Knowledge Spillovers on Firm Growth[END_REF] through direct hiring or thanks to easier access to knowledge intensive business services [START_REF] Doloreux | Knowledge-intensive business services: Geography and innovation[END_REF]. This thesis is confirmed by [START_REF] Cassia | Firms' growth: Does the innovation system matter?[END_REF], who in reference to a sample of UK public companies from 1995 to 2006, present evidence on the effects of external sources of knowledge on firm growth. [START_REF] Mcguirk | Measuring the impact of innovative human capital on small firms' propensity to innovate[END_REF] also present evidence on the beneficial influence of human capital on small firms, considering that this category of firms is more sensitive to the four components encapsulated in human capital, i.e., education, training, a willingness to change in the workplace and job satisfaction, and they in turn overcome the limitations of measurements used previously.

The role of human capital has been explored in the new-firm survival literature [START_REF] Acs | The determinants of new-firm survival across regional economies: The role of human capital stock and knowledge spillover[END_REF]. The influence of human capital has mostly been analysed from an internal point of view while focusing on the correlation between education and the skills and competencies of workers, managers, or entrepreneurs [START_REF] Blundell | Human capital investment: the returns from education and training to the individual, the firm and the economy[END_REF][START_REF] Rauch | Productivity Gains from Geographic Concentration of Human Capital: Evidence from the cities[END_REF] when the firm perspective is privileged. When the spatial perspective prevails such that human capital is aggregated at the regional level, the vast majority of papers aim to determine its influence on regional performance measured as a difference in GDP or in the number of workers computed at the region level [START_REF] Badinger | Trade, human capital and innovation: the engines of European regional growth in the 1990s[END_REF][START_REF] Florida | Inside the black box of regional development -Human capital, the creative class and tolerance[END_REF].

Due to the possibility of interactions occurring between a firm and its environment, we adopt a different view that combines individual and local dimensions. Following Huggins et al.

(2017), we take into account that "location of the firm may increase or decrease the likelihood of survival through the threats faced and opportunities available that originate from outside the firm" (p.5). The level of human capital is unequally distributed among regions [START_REF] Berry | The divergence of human capital levels across cities[END_REF]). Hence, depending on the location, firms have different access to external human capital and may acquire new knowledge by hiring individuals with large human capital [START_REF] Glaeser | Growth in Cities[END_REF], with a positive consequence on firm productivity [START_REF] Backman | Regions, Human Capital and New Firm Formation[END_REF].

Coherently with this last strand of the literature, we hypothesize that a higher level of human capital in a region could have a significant effect on the soundness of SMEs.

These considerations lead us to formulate our second hypothesis:

H2: A higher education level in a region positively influences firm soundness.

Agglomeration effects and knowledge spillovers

Agglomeration forces, geographical clustering and knowledge spillovers have been widely examined, and it is broadly recognized that advantages can arise when companies operate geographically close to one another.

The fist advantage of geographical clustering derives from agglomeration benefits that lead to higher levels of firm performance due to improved production and/or increased demand [START_REF] Harrison | Introduction: New Horizons in Regional Studies[END_REF][START_REF] Krugman | Increasing returns and economic geography[END_REF][START_REF] Storper | The resurgence of regional economies, ten years later: the region as a nexus of untraded interdependencies[END_REF]. Agglomeration economies arise primarily from the set of shared resources available to firms co-locating in the same area. This thesis is rooted in the so-called "diamond" theorized by [START_REF] Porter | Location, clusters and company strategy[END_REF], which links firm performance to the quality of a firm's environment. In a more dense and large local market, it is possible for a firm to obtain a greater variety of intermediate inputs, generating productivity gains through higher levels of vertical disintegration and specialization [START_REF] Henderson | Marshall's scale economies[END_REF].

The availability of a wider variety of consumer goods also attracts consumers and as a consequence increases the level of demand. In the case of increasing returns, companies benefit from the presence of a larger number of easily accessible consumers. The same holds for labour. In a broader employment area, workers tend to be more specialized and thus more productive since when faced with a larger number of job opportunities, they do not hesitate to specialize. Finally, any exchange of information between companies concerning the characteristics of demand or production technologies occurs more easily when the density of economic actors is higher. Thus, the creation, accumulation and dissemination of knowledge are facilitated in the most densely populated areas. Although the geographic scope of a cluster can range from county to country, its common resources and capabilities are generally shaped by geographic proximity.

Knowledge spillovers are also associated with Marshallian external economies. [START_REF] Van Der Panne | Agglomeration externalities: Marshall versus Jacobs[END_REF] estimates that the most frequent knowledge transfers are inter-industrial. The diversity of geographically concentrated industries and their specialization stimulates innovation as [START_REF] Jacobs | The economies of cities[END_REF] pointed out. Interactions between different sectors are at the heart of this process: a common scientific base facilitates the generation and exchange of existing ideas between distinct but complementary industries [START_REF] Feldman | Innovation in cities: Science-based diversity, specialization and localized competition[END_REF]. Local knowledge spillovers are all the more beneficial to a company, as they are able to capture ideas and inputs (competencies, technologies and underlying knowledge bases) from other related activities [START_REF] Boschma | Related variety,trade linkages, and regional growth in Italy[END_REF]. Positioning close from knowledge producers should allow a firm to benefit from other firms' spillovers. Since high-tech industries in which knowledge plays a key role as an input and output are usually identified as 'knowledge-intensive' and given that the marginal cost of transmitting knowledge increases with distance [START_REF] Audretsch | R&D Spillovers and the Geography of Innovation and Production[END_REF], we formulate the following third hypothesis:

H3: A higher concentration of high-tech firms in a region positively influences firm soundness.

3.

Empirical strategy

Data

We assess the influence of local context on firm soundness for a panel of SMEs operating in four European countries belonging to the industrial sector. We limit the sample to SMEs because they are more sensitive to local context than larger enterprises [START_REF] Carreira | Are Small Firms More Dependent on the Local Environment than Larger Firms? Evidence from Portuguese Manufacturing Firms[END_REF].

Our dataset is developed through the merging of two datasets. The first is the Amadeus dataset provided by Bureau Van Dijk, which contains comprehensive financial and nonfinancial information on European companies, and the second dataset includes regional information compiled by Eurostat and computed at the NUTS 2 level.

A technical constraint guided us to review four countries (Belgium, France, Italy, and Germany) covered most fully by Amadeus. Moreover, these countries are representative of the economic situation that prevails in Western Europe, present a diversity of regions ranging from high density regions to more rural regions and include a large variety of industrial profiles. The countries include 91 NUTS 2 regions.

From Amadeus, we extracted a list of companies with complete accounting documents covering at least two consecutive years in the 2010-2015 period. The research period starts in 2010, following the global shock that hit European countries from 2008-2009 because, according to [START_REF] Sensier | Measuring Regional Economic Resilience across Europe: Operationalizing a complex concept[END_REF], some regions in Belgium, France, and Germany started to recover beginning in 2010. After applying a cleaning procedure to all companies presenting missing or faulty data, from the population we only examine companies with at least two successive years of data, a condition to respect when using a panel. After performing these operations, we obtain an unbalanced panel of 86,839 observations.

Definitions and sources of the variables used are presented in Table 1, while descriptive statistics and a correlation matrix for the variables are reported in the Appendix.

Dependent variable

Our dependent variable measuring the financial soundness of firms is the Altman Z-Score. As one of the most widely used indicators [START_REF] Altman | Corporate Financial Distress & Bankruptcy[END_REF], the Altman Z'-Score was selected as it can be adapted to non-publicly traded firms like those utilized in the present work. The index was elaborated by Altman through the use of a multiple discriminate analysis (MDA) where discrimination is determined by a score and the «Zscore» is calculated on the basis of accounting ratios. More specifically, as a dependent variable we used the Z''-Score (1983), which has been found to perform satisfactorily when applied to an international context for the prevision of bankruptcy [START_REF] Altman | Financial Distress Prediction in an International Context: A Review and Empirical Analysis of Altman's Z-Score Model[END_REF].

The variable is calculated as follows:

𝑍" 𝑠𝑐𝑜𝑟𝑒 = 3.25 + 6.56 X1 + 3.26 X2 + 6.72 X3 + 1.05 X4

X1 is defined as Working Capital/Total Assets (WC/TA).

The working capital/total assets ratio frequently used in studies on corporate problems is a measure of the net liquid assets of a firm relative to total capitalization. Working capital is defined as the difference between current assets and current liabilities. Liquidity and size characteristics are explicitly considered.

X2 is defined as Retained Earnings/Total Assets (RE/TA).

Retained earnings correspond to the total amount of reinvested earnings and/or losses of a firm over its entire lifecycle. The account is also referred to as an earned surplus. The age of a firm is implicitly considered in this ratio. For example, a relatively young firm is likely to have a low RE/TA ratio because it has not had sufficient time to build up its cumulative profits.

X3 is defined as Earnings before Interest and Taxes/Total Assets (EBIT/TA).

This ratio is a measure of the true productivity of a firm's assets independent of any tax or leverage factors. Since a firm's ultimate existence is based on the earning power of its assets, the ratio appears to be particularly appropriate for studies dealing with corporate failure.

X4 is defined as the Book Value of Equity/the Book Value of Total Liabilities (BVE/TL).

This measure shows to what extent a firm's assets can decline in value (measured by the market value of equity plus debt) before liabilities exceed assets and the firm becomes insolvent.

Independent variables

The explanatory variables considered in the models are designed to reflect firm characteristics on one hand and local characteristics on the other. All firm-level variables are drawn from the Amadeus dataset.

At the firm level, we first introduce two classical variables determining firm soundness, i.e., Size and Age [START_REF] Coad | The Growth of Firms: a Survey of Theories and Empirical Evidence[END_REF][START_REF] Hatem | Determinants of Firm Performance: A Comparison of European Countries[END_REF]. We include firm Size as a proxy of creditworthiness. [START_REF] Fama | Size and Book-to-Market Factors in Earnings and Returns[END_REF] show that small firms have persistently low earnings, higher levels of financial leverage, and more earnings uncertainty and are more likely to reduce dividends than large firms. Consistent with this view, many previous empirical findings state a positive effect of size on firm performance with the conclusion that larger firms are characterized by higher levels of profitability [START_REF] Hurst | What do small businesses do?[END_REF][START_REF] Fort | How firms respond to business cycles: The role of firm age and firm size[END_REF]) and consequently face less bankruptcy risk than small firms [START_REF] Arcuri | Spatial patterns and determinants of firm exit: an empirical analysis on France[END_REF].

To take into account a possible non-linear effect on firm performance at the local level [START_REF] Raspe | Firm growth and localized knowledge externalities[END_REF], we also introduce into the model the size squared. Following [START_REF] Coad | The Growth of Firms: a Survey of Theories and Empirical Evidence[END_REF], we adopt an accounting conception of firm size and define this variable (Size) by the logarithm of the annual turnover of a company.

The relationship between a firm's age and its growth rate has also been frequently investigated in the literature [START_REF] Coad | Like milk or wine: Does firm performance improve with age?[END_REF][START_REF] Strotmann | Entrepreneurial survival[END_REF]. [START_REF] Coad | Like milk or wine: Does firm performance improve with age?[END_REF] note that age influences firm performance in three ways (selection, learning-by-doing, and inertia effects) depending on whether firm performance remains the same, improves or declines over time. We thus introduce it into the equation to be estimated. Age is computed as the difference between the year of registration and the current year.

In addition to these classical individual characteristics and in line with [START_REF] Bridges | Financial constraints, global engagement, and firm survival in the United Kingdom: Evidence from micro data[END_REF] and [START_REF] Musso | The Impact of Financial Constraints on Firms Survival and Growth[END_REF], we introduce a variable denoting a firm's short term-capacity for repayment as an explanatory variable of its future robustness. The liquidity ratio can be used as a proxy for financial constraint since constrained firms tend to sell equipment and corporate assets to prevent credit rationing, especially during an economic crisis [START_REF] Campello | The real effects of financial constraints: Evidence from a financial crisis[END_REF]. Constrained firms thus adopt optimal cash policies to balance the profitability of current with future investments while reducing their investment plans, a cut that can have a negative impact on their growth path [START_REF] Chowdhury | Investment-cash flow sensitivity under changing information asymmetry[END_REF][START_REF] Kaplan | Do Investment-Cash Flow Sensitivities Provide Useful Measures of Financing Constraints[END_REF]. The liquidity ratio is also a signal of a better probability of repayment, an element that should provide better access to credit, which in turn reduces the risk of firm failure [START_REF] Arcuri | Early stage SME bankruptcy: does the local banking market matter?[END_REF]. We compute the liquidity ratio, liquidity, as (Current Assets -Stock)/Total Assets.

At the local level, we take into account human capital, agglomeration economies, and the demand side of market opportunities from variables provided by Eurostat. All of these variables are computed for the NUTS 2 regions of the four countries under review.

As a proxy of human capital, we consider educational attainment levels of the population. The variable Education is calculated by dividing the number of employed people aged 20-64 years having completed tertiary education (ISCED 2011 levels 5-8 1 ) by the total population of the same age group. Tertiary education includes what is commonly understood as academic education and advanced vocational or professional education and corresponds to a higher level of skill in the educational system. The second indicator used to proxy knowledge intensive spillovers is employment in technology and knowledge-intensive sectors of NUTS 2 regions (NACE Rév. 2). This approach rests upon the sectoral strategy adopted by Eurostat 2 and corresponds to the percentage of those older than 15 and younger than 74 working in high-tech sectors. In addition, we control for GDPpercapita as a measure of macroeconomic conditions calculated as the logarithm of GDP per thousand inhabitants. Finally, to measure the effect of external agglomeration economies at the regional level, we include the variable Density defined as the logarithm of the number of employees on the number of squared metres of each region. For the regions considered in this study, the variables that are at measured the local level are displayed in the following figures.

Industry and country dummies are also included to capture industry-and country-specific unobserved characteristics.

3.4

The model

Companies operate in a socio-economic context that significantly affects the performance of business processes [START_REF] Audretsch | Location: A Neglected Determinant of Firm Growth[END_REF][START_REF] Garsaa | Does the employment growth rate depend on local context? An analysis of French industrial establishments over the 2004-2010 period[END_REF].

This finding is highlighted, as apparently weak ties between an organization and external parties can have a relevant impact not only on competitiveness and business performance but also on institutional structures and entrepreneurial goals. In other words, firms operating in the same territory share the same external environment; consequently, they are likely to be more similar to one another than firms operating in different geographical areas. From an econometric perspective, the most important effect of this similarity relates to the fact that the assumption of independence of standard errors is violated. This problem is resolved by using a multilevel approach, which provides efficient estimates of coefficients since it controls for spatial dependence and correct standard errors of variables.

The analysis focuses on SMEs for the 2010-2015 period. Then, as SMEs are embedded in local markets, a hierarchy of three levels is used. Multiple measurements of the firm soundness index for different time points represent level 1 of the hierarchy. Punctual-time observations nested within SMEs represent level 2 of the model. Further, SMEs nested in local markets (NUTS 2) represent level 3 of the structure. This hierarchy is widely in multilevel model literature on panel data [START_REF] Steele | Multilevel models for longitudinal data[END_REF][START_REF] Aiello | Multilevel empirics for small banks in local markets[END_REF]. The basic model is:

𝑦 𝑡𝑖𝑗 = 𝛽 0𝑖𝑗 + 𝑒 𝑡𝑖𝑗 (1)
where 𝑦 𝑡𝑖𝑗 is the vector of a firm's soundness measure of the i-th corporation operating in the j-th region (with t=2010...,2015, I= 1..., Nj and j=1,…,p) at time t.

Erratic component 𝑒 𝑡𝑖𝑗 captures randomness due to time.

In Equation (1) element 𝛽 0𝑖𝑗 varies across firms and regions. It is composed of a constant (𝛾 000 ) and random variations due to the regional ( 𝜇 00𝑗 ) and firm levels ( 𝜇 0𝑖𝑗 ). Thus, Equation 1 becomes:

𝑦 𝑡𝑖𝑗 = 𝛾 000 + 𝜇 00𝑗 + 𝜇 0𝑖𝑗 + 𝑒 𝑡𝑖𝑗 (2)
Equation 2 represents the empty model, a multilevel model without explanatory variables. From Equation (2), it is possible to identify the overall intercept (𝛾 000 ) and three different components of the variance of 𝑦 𝑡𝑖𝑗 : the variance of random error 𝑒 𝑡𝑖𝑗 (𝜎 𝑒 2 ), the within group variance, the variance of 𝑢 00𝑗 (𝜎 𝑢𝑗 2 ), the between group variance of regions and the variance of 𝜇 0𝑖𝑗 (𝜎 𝑢𝑖 2 ) for the between group variance at the firm level.

A useful way to exploit this information involves computing the intra-class correlation (ICC), which represents the proportion of variance underlying each level of the model hierarchy and which thus explains to what extent the heterogeneity of the dependent variable can be attributed to each level. The ICC for the regional level is computed as the ratio between the regional and total variance as follows:

𝐼𝐶𝐶 𝑗 = 𝜎 𝑢𝑗 2 𝜎 𝑢𝑗 2 +𝜎 𝑢𝑖 2 +𝜎 𝑒 2 (3)
Consequently, the ICC for the firm and time level are respectively:

𝐼𝐶𝐶 𝑖 = 𝜎 𝑢𝑖 2 𝜎 𝑢𝑗 2 +𝜎 𝑢𝑖 2 +𝜎 𝑒 2 (4) 𝐼𝐶𝐶 𝑡 = 𝜎 𝑒 2 𝜎 𝑢𝑗 2 +𝜎 𝑢𝑖 2 +𝜎 𝑒 2 (5)
Since our data follow a panel structure, the multilevel specification controls for the effect of time. Consequently, time can be considered a variable to add to Equation 2, which becomes:

𝑦 𝑡𝑖𝑗 = 𝛾 000 + 𝜇 00𝑗 + 𝜇 0𝑖𝑗 + 𝛿 .𝑖𝑗 𝑇𝑖𝑚𝑒 + 𝑒 𝑡𝑖𝑗 (6)
Finally, the model allows for the simultaneous consideration of variables defined at the firm level (𝑋 ℎ𝑡𝑖𝑗 where h is the number of covariates) and of regional variables (𝑅 𝑘𝑡.𝑗 where k is the number of local covariates). Thus, the final econometric specification can be written as follows:

𝑦 𝑡𝑖𝑗 = 𝛾 000 + ∑ 𝛽 ℎ 𝑟 ℎ=1 𝑋 ℎ𝑡𝑖𝑗 + ∑ 𝜌 𝑘 𝑠 𝑘=1
𝑅 𝑘𝑡.𝑗 + 𝜇 00𝑗 + 𝜇 0𝑖𝑗 + 𝛿 .𝑖𝑗 𝑇𝑖𝑚𝑒 + 𝑒 𝑡𝑖𝑗 (7)

Results

4.1 From the empty model to the effect of local features.

This section refers to estimations obtained from applying the multilevel model to our data. First, we consider the empty model, which allows us to evaluate how much of the variation in outcomes can be strictly attributed to unobserved factors operating at each level.

In our case, the three levels are as follows: time, firm and region. Second, we present results obtained when the model is augmented with firm-specific and local variables as the principal aim of our analysis.

Table 2 shows the results obtained when running the empty model. The empty multilevel model allows one to understand how much of the variation in outcomes may be attributable to unobserved factors at each level. The first result to be discussed is the value of the likelihood ratio test (LR test), which compares the empty multilevel model to the standard OLS regression, for which the null hypothesis states that there is no random intercept in the model. When the null hypothesis is true, the OLS regression can be used instead of a mixed model. According to our results, the test is highly significant for every specification of the empty model, supporting the use of the multilevel model. Consequently, intercepts related to the different clusters should be treated as group by group variant coefficients. The value of the ICC represents the proportion of variability underlying each level of the model hierarchy: unaccounted regional-specific features capture 12.4% of firm robustness, time-specific factors explain 11.8% of variability, while the remaining 75.8% is attributable to firm-specific features. The relevant percentage of heterogeneity explained by the regional level confirms hypothesis H1 stating that coherent with the SCP approach, a combination of individual-and local-level factors explains firm soundness more accurately than individual characteristics alone.

Column 2 of Table 2 shows the results obtained when we augment the empty model with the variable year. This variable has a positive sign and is statistically significant at 0.1%, showing that the robustness of European SMEs increases with time, and this finding shows that small and medium-sized enterprises have been able to absorb effects of the financial crisis that hit the global economy in 2008. This specification shows the same percentage of heterogeneity explained by regionally specific unobservable factors (12.4%). Column 3 shows the results for the empty model obtained when time is added as a source of randomness in regional intercepts and slopes, confirming the same percentage of heterogeneity influenced by the local level.

Table 3 shows the estimations obtained when we augment the multilevel model with a set of firm-and region-specific factors3 . Column 1 of Table 3 shows estimations obtained for the full model. We find a nonlinear relationship between firm Size and our proxy of firm robustness (Z-score''), confirming the results obtained by [START_REF] Kim | Technological regimes and firm survival[END_REF]. The linear component of this variable is positive and statistically significant at 0.1%, and therefore larger companies are characterized by a higher degree of financial robustness. The variable Age has a positive sign and is statistically significant at 0.1%. This finding confirms evidence from the literature showing that age and size increase the soundness of companies and as a consequence that young and very small firms are more likely to exit from the market than other firms [START_REF] Kale | Business failures: Liabilities of newness, adolescence, and smallness[END_REF][START_REF] Thornhill | Learning About Failure: Bankruptcy, Firm Age, and the Resource-Based View[END_REF]. The variable Year of the empty model has a positive sign and is statistically significant at 0.1%, confirming that small and medium-sized enterprises have been able to absorb the effects of the financial crisis that hit the global economy in 2008. The variable liquidity has a positive sign and is statistically significant, showing that the firms' short-term capacities for repayment are relevant in increasing firm soundness, as they can be considered an element that should provide a better access to credit, and this in turn reduces the risk of firm failure [START_REF] Arcuri | Early stage SME bankruptcy: does the local banking market matter?[END_REF].

In focusing on the specific objectives of this paper, it is worth discussing the empirical findings on how the regional features considered in this study affect firm robustness.

The variable Education has a positive sign and is statistically significant at 0.1%, suggesting that a higher level of tertiary education in a certain region tends to increase firm soundness. This finding confirms hypothesis H2 stating that a higher education level in a region positively influences firm soundness. This is coherent with previous empirical findings showing that a local market characterized by a significant share of highly educated and skilled workers increases the productivity of the whole work force through human capital externalities [START_REF] Moretti | Estimating the social return to higher education: evidence from longitudinal and repeated cross-sectional data[END_REF][START_REF] Rauch | Productivity Gains from Geographic Concentration of Human Capital: Evidence from the cities[END_REF], allowing firms to be more efficient. Thus, human capital can be considered a critical factor accounting for levels of regional success and competitiveness. We obtain the same effect for the variable HTEmploy, suggesting that a higher employment level in high-tech industries positively influences firm soundness, thus confirming hypothesis H3. Local knowledge spillovers are beneficial to a company, as they are able to capture ideas and inputs (competencies, technologies and underlying knowledge bases) from other related activities [START_REF] Boschma | Related variety,trade linkages, and regional growth in Italy[END_REF]. Proximity to knowledge producers allows a firm to benefit from other firms' spillovers.

To decode the spatial distribution of firm robustness across regions, we conduct cluster analyses to classify regions by degree of knowledge intensiveness. With regard to regional knowledge levels, we choose as our clustering variable a composite index of education and employment in high tech industries and thereby classify 91 NUTS 2 regions into three groups (A, B, C) for which we estimate our model separately4 . Each observation is assigned to the group whose median is the closest, and then based on this categorization new group medians are determined. These steps continue until observations no longer change groups. Low levels of knowledge intensity are found for the regions grouped under cluster A. The highest levels of knowledge intensity are measured for the regions of cluster C. Our aim is to ascertain if the effects of education and employment levels in high-tech industries at the local level depend on the initial level of knowledge that characterizes a certain region. Corresponding results are shown in Table 3, columns 2-4.

Cluster A corresponds to almost all Italian regions and to some remote French regions typically characterized by economic problems. In these regions, Education, HTEmploy and Density have a positive effect on firm soundness. These results confirm Krugman's theory on the role played by agglomeration and density in economic development. By contrast, in cluster C, one finds the richest European regions, most of which are located in Belgium and Germany with some exceptional regions in France. These regions correspond to the so-called blue-banana region, which differs from other European regions in demographic, economic, infrastructural and cultural-educational features [START_REF] Polese | The Wealth and Poverty of Regions: Why Cities Matter[END_REF]. In these regions, density, education and HT employment levels are already high, and thus, an increase in their value does not generate any improvement in firm soundness, as shown by non-significant coefficients associated with the local variables. This can correspond to a threshold effect beyond which the marginal effect exerted by agglomeration economies tends to be cancelled out. The intermediate cluster (B) is more diverse and includes the northern Italian regions, areas of former East Germany (except for major cities) and the remaining French regions. In this cluster, Density is no longer significant, while Education and HTEmploy still have a positive influence on firm soundness at the local level.

Robustness checks

Two checks of robustness are performed. The first robustness exercise, following the approach proposed by [START_REF] Fazio | A Spatial Multilevel Analysis of Italian SMEs' Productivity[END_REF], investigates to what extent our results are affected by the smallest and the largest groups. Hence, we created a classification of region size in terms of the number of firms, and we run separate regressions in which the smallest (5 th percentile) or largest regions (regions exceeding the 95 th percentile) are dropped from the sample. Again, as can be observed from columns 1 and 2 of Table 4, the results do not change significantly. Second, to test the robustness of our results, we run fixed effects 5 instrumental variable estimations with clustered-robust standard errors (two-step GMM-HAC) that correspond to the cluster-robust covariance matrix for the fixed-effects model developed by [START_REF] Arellano | Computing Robust Standard Errors for Within-Groups Estimators[END_REF]. In this context, the two-step GMM-HAC technique allows us to address at least four problems. First, correlations between firm fixed effects (the time-invariant 5 Overall, a fixed effect model is the most preferred estimation tool, as suggested by the Hausman test, which measures the difference between the FE and RE estimators of coefficients. This test yields a χ2 value of 794.35 and a p value of 0.00. These findings lead us to reject the null hypothesis (according to which differences in the coefficients are not systematic) and to conclude that the FE estimator is consistent. component of the composed error term) and explanatory variables can be controlled by fixed effects modelling. Second, correlations between the time-variant part of the composed error term and local variables, which can lead to endogeneity bias, can be controlled using the instrumental variables method 6 . Third, the clustering of standard errors allows us to control for within-region correlations 7 . Fourth, standard errors can be controlled for classical autocorrelations and heteroscedasticity bias. The estimations provided by this last model (column 3 of Table 4) confirm results obtained with the multilevel model for panel data. 6 Six instruments have been used for the four local variables: the annual rate of variation in the regional level of education, the rate of variation in the active population, the rate of variation in the economic weight of the region, variation in regional unemployment, the rate of variation in regional density, and educational level elasticity relative to regional gross value added. 7 In our case, the number of clusters (NUTS 2) is equal to 91, which is greater than the efficient threshold of 50 [START_REF] Kézdi | Robust Standard Error Estimation in Fixed-Effects Panel Models[END_REF].

Conclusion

This paper investigates the role of regional context with regard to the effect of human capital and knowledge spillovers on firm soundness.

We find that firm soundness is shaped by a combination of individual characteristics and local features. In particular, a higher level of education and knowledge spillovers at the regional level enhance the robustness of SMEs. These results could be of interest to policy makers at the national and European levels. In a context of budgetary constraints, less advantaged regions should be targeted by local development programmes that should focus on education and HT employment, whose effects are observable over the medium-term.

Notwithstanding the above findings and contributions, this study and its outcomes have some limitations. A first limitation relates to the nature of the dependent variable, the Z-score based on accounting data, which may be sensitive to national accounting practices and budget policies. Furthermore, our results may depend on the regional scale considered. By limiting the analysed local context, one may be able to consider spatial effects of agglomeration economies, which are typically bounded to a limited scale.

Appendices

Figure 1 :

 1 Figure 1: Level of Education (Mean values 2010-2015)

Figure 2 :

 2 Figure 2: Level of Employment in HT (Mean values 2010-2015)

Figure 3 :

 3 Figure 3: Level of GDP per capita (Mean values 2010-2015)

Figure 4 :

 4 Figure 4: Level of Density (Mean values 2010-2015)

Table 1

 1

	. Variables

Table 2 . Explaining heterogeneity in firm soundness: Empty model.

 2 Standard errors are shown in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001. Results of the multilevel regressions run with command xtmixed are available from Stata13 version.Column 1 of Table2refers to the random intercept empty model in which the second level is formed by 22,079 SMEs, while the third level is composed of 91 NUTS 2 regions.

		(1)	(2)	(3)
		No time effect	Time effect (intercept)	Time effect (intercept and
				level 3 slopes)
	Constant	5.980 ***	-126.0 ***	-118.5 ***
		(0.0778)	(3.455)	(9.206)
	year		0.0656 ***	0.0619 ***
			(0.00172)	(0.005)
	Variance
	Firm (intercept)	3.058***	3.064***	3.064 ***
		(0.031)	(0.031)	(0.031)
	Region (intercept)	0.502***	0.502***	0.501 ***
		(0.797)	(0.798)	(0.080)
	Region (slope)			0.00108 ***
				(0.000317)
	Residual	0.474***	0.464***	0.463 ***
		(0.003)	(0.003)	(0.080)
	ICC (%)
	Region	12.4	12.4	12.4
	Firm	75.8	76.0	76.2
	Time	11.8	11.6	11.4
	N observations	86,839	86,839	86,839
	N of groups
	Firm level	22,079	22,079	22,079
	Regional level	91	91	91
	Log likelihood	-126368.6	-125652.0	-125608.1
	LR test	1.1e+05***	1.2e+05***	1.2e+05***
	Note:

Table 3 : Model with firm-and region-specific variables

 3 Standard errors are shown in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001. Results of multilevel regressions run with the command xtmixed are available from Stata13 version.

		(1)	(2)	(3)	(4)
		Full	Cluster A:	Cluster B:	Cluster C:
		sample	Low knowledge	Medium knowledge	High
			intensive regions	intensive regions	knowledge intensive
					regions
	Size	0.237 ***	0.274 ***	-0.0249	0.578 ***
		(0.055)	(0.0669)	(0.105)	(0.170)
	Size 2	-0.0126 ***	-0.0130 ***	-0.00393	-0.0245 ***
		(0.002)	(0.00239)	(0.00354)	(0.00561)
	Liquidity	3.528 ***	3.005 ***	3.589 ***	4.204 ***
		(0.034)	(0.0545)	(0.0552)	(0.0724)
	Age	0.0164 ***	0.0269 ***	0.0132 ***	0.0132 ***
		(0.001)	(0.00120)	(0.000860)	(0.00109)
	Education	1.078 ***	2.126 ***	1.920 **	0.429
		(0.310)	(0.636)	(0.626)	(0.452)
	HTEmploy	0.809 **	0.989 *	1.041 *	0.293
		(0.277)	(0.399)	(0.515)	(0.624)
	Density	-0.0624	0.137 *	-0.0605	-0.0597
		(0.037)	(0.0588)	(0.0953)	(0.0515)
	GDPpercapita	0.0244	-0.113	0.591	-0.00514
		(0.124)	(0.162)	(0.304)	(0.201)
	year	0.0516 ***	0.0345 ***	0.0454 ***	0.0561 ***
		(0.005)	(0.00819)	(0.0106)	(0.00857)
	constant	-102.3 ***	-68.05 ***	-94.30 ***	-111.7 ***
		(9.875)	(16.15)	(20.12)	(16.89)
	Industry dummies	Yes	Yes	Yes	Yes
	Country dummies	Yes	Yes	Yes	Yes
	Number of	86,839	31,791	33,947	21,101
	observations
	N of regions	91	21	37	33
	Log likelihood	-120071.6	-40974.1	-47314.2	-31202.7
	Note:

Table 4 : Robustness checks

 4 Standard errors are shown in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001. Results from the multilevel regressions run with the command xtmixed available in Stata13 version. Results of the two-step GMM-HAC model run with command xtivreg2 with the robust, cluster and gmm2s options sets.

		(1)	(2)	(3)
		Excluding small regions	Excluding large regions	2 step-GMM
	Size	0.235 ***	0.385 ***	0.401 ***
		(0.0546)	(0.0707)	(3.47)
	Size 2	-0.0125 ***	-0.0177 ***	-0.0194 ***
		(0.00188)	(0.00243)	(-4.63)
	Liquidity	3.524 ***	3.696 ***	3.474 ***
		(0.0344)	(0.0440)	(21.93)
	Age	0.0165 ***	0.0135 ***	0.130 ***
		(0.000588)	(0.000688)	(5.99)
	Educ	1.054 ***	0.687 *	2.802 *
		(0.310)	(0.341)	(1.99)
	HTEmploy	0.802 **	0.679 *	6.759 ***
		(0.277)	(0.303)	(3.37)
	Density	-0.0544	-0.0423	-0.0253
		(0.0375)	(0.0384)	(-0.04)
	GDPpercapita	0.0338	-0.0684	-0.697
		(0.126)	(0.137)	(-0.56)
	year	0.0517 ***	0.0580 ***
		(0.00504)	(0.00547)
	cons	-102.6 ***	-115.3 ***
		(9.899)	(10.76)
	Industry dummies	YES	YES
	Country dummies	YES	YES
	Number of observations	86,644	54,503	54,283
	Log-likelihood	-119758.9	-78015.7
	Centred R 2			0.1169
	Fisher statistic			166.70***
	Underidentification test (Kleibergen-Paap)			13.463**
	Hansen J statistic			1.137
	Note:

Table 5 : List of regions by cluster (Name and NUTS 2 Code)

 5

	A1. Descriptive statistics
			mean	Standard	min	p10	p25	p50	p75	p90	max
					deviation
	Z score		5.828		2.008	0.021 3.376	4.351	5.657	7.192	8.580	12.348
	Size		15.657		1.048	2.773 14.477 15.063 15.638 16.325 16.940 19.946
	Liquidity		0.460		0.196	0.000 0.205	0.315	0.455	0.600	0.725	1.000
	Age		27.856		19.222	1.000 9.000 15.000 25.000 36.000 51.000 637.000
	Educ		0.234		0.082	0.110 0.141	0.162	0.222	0.290	0.349	0.557
	HTEmpl		0.787		0.050	0.572 0.723	0.764	0.791	0.826	0.844	0.873
	Density		5.293		0.753	3.584 4.234	4.782	5.264	5.929	6.058	8.910
	GDPperc		10.291		0.219	9.693 10.073 10.177 10.299 10.404 10.483 11.056
	Observations	86839
	A2. Correlation Matrix
	Variable	Zscore	Size		Liquidity	age	Educ	HTEmpl	Density GDPperc
	Z score		1.000
	Size		0.089	1.000
	Liquidity		0.342	0.191	1.000
	Age		0.153	0.143	-0.074	1.000
	Educ		0.334	0.188	0.109		0.096	1.000
	HTEmpl	-0.067	0.115	-0.009	0.073	-0.170	1.000
	Density	-0.139	0.048	-0.028	0.031	-0.008	0.204	1.000
	GDPperc		0.056	0.134	0.043		0.111	0.358	0.636	0.544	1.11.00010

All regressions control for country-and industry-specific unobserved characteristics.

The map and list of regions for the three clusters are available in Appendix 3.

Code Cluster B Code Cluster C Code Champagne-Ardenne

A3. Regions by cluster (map and list)