Digital divide across the European Union and labour market resilience

ABSTRACT Using a regional evolutionary perspective and a cross-regional data panel for 278 European Union regions, this study investigates the relationship between regional digital development and labour market resilience. To address a fundamental concern of regional studies, it proposes an analytical framework that assesses digital disparities in the spatial context and provides a nuanced understanding of digital dimensions impacting labour market resilience. The primary labour market outcome, the employment rate, was evaluated to investigate the regional resilience in the Great Recession. A gradient boosting method was used to identify the digital predictors in different resilience stages and to articulate policy-relevant conclusions.


INTRODUCTION
The extraordinary impact of the 2007-08 economic crisis and the spatial diversity of its effects have pushed both academics and policymakers to understand the ability of regions to resist and recuperate from recessionary shocks (Crescenzi et al., 2016;Lagravinese, 2015) and to better describe the complex spatial interdependencies of determinants that foster economic and labour market resilience.Despite national statistics exposing optimistic trends for the employment level, in the aftermath of the Great Recession, regional figures articulate a more dissimilar narrative and reveal increasing disparities between regions, among and within European Union (EU) countries (Martin, 2012), enforcing inequalities.Comprehending the asymmetric impact of recessionary shocks is of great importance, as it can drive a tailored policy layout, to improve the ability of a region to withstand future shocks and foster the recovery process.
The first wave of research papers, released mainly after the outbreak of the crisis, focused on the uneven regional reaction to exogenous shock (Cellini & Torrisi, 2014;Doran & Fingleton, 2016;Sensier et al., 2016).Studies from the second wave, enlarging the conceptualization from the first wave, have investigated the influencing factors underpinning the labour market in various stages.Moreover, they have identified distinguishing regional responses (Giannakis & Bruggeman, 2020), revealing internal and external factors that increasingly influence the labour market resilience.
The impressive progress in information and communication technology (ICT) has soundly boosted economic development.It has also conveyed a new form of inequality, entitled the digital divide, which impacts multiple socio-economic areas.Digital inequality is a research topic of increasing relevance, as many claims have been expressed regarding the influence of the digital divide on national or regional economy long-run evolution (Dasgupta et al., 2005).One of the noticeable forms of inequality, the digital divide, can model life chances in various directions, having an evident impact on the labour market (Robinson et al., 2015).Despite intensive discussions about the importance of digital skills and technology to support labour markets, we are still far from understanding if and how the digital level of a region affects the local labour market resilience.This theme is of major importance as the EU digital policy framework for 2021-27 expects to sustain developing economies in going digital (European Commission, 2020).
Additionally, the regional policy discourse has increasingly highlighted the prominent contribution of technology in general and the digital level of a region, in particular, to foster resilience or rapid recovery from the recession (Kiss, 2017).At a time of significant concern about labour market vulnerability, two tasks are required to address policy-relevant gaps and understand the differential ability of regions to master major shocks and accomplish resilience.First, there is a need for new empirical evidence derived from detailed and higher order insights (Wrigley & Dolega, 2011) that more complex academic investigations can provide.The second task requires theorizing the landscape of complex ongoing changes during various stages of the resilience process.From both perspectives, a general requirement in defining valuable policy measures is to identify the predictors of resilience.While a large body of research concentrates on exposing the determinants of labour market resilience, it commonly assesses their significance level and does not uncover the relative magnitude of factors and the complexity of interactions between them.Moreover, most studies presume a linear relationship between various predictors and levels of resilience.
Tackling the broadly acknowledged description of the digital divide provided by Organisation for Economic Cooperation and Development (OECD) (2001), which states differences between individuals, enterprises, and regions regarding their openings to access and use ICTs for a wide diversity of activities, this study is part of the second wave of economic resilience literature.Exploring the digital transformation encountered by regions during and in the aftermath of the recessionary period and their impact on the labour market, this analysis identifies digital dimensions that affect the regional labour market response when faced with shocks.Our assumption is that the regional digital level at the outbreak of the crisis and the growth ratio during the recession are not neutral in response to exogenous shocks.Measuring regional digital performance and growth across the EU regions is notoriously awkward due to shortcomings in data readiness and digital world complexity.
As reported by the European Commission's Digital Economy and Society Indicators, there is a wide variety of ICTs across EU states and regions.A complex and dynamic phenomenon, the digital divide is investigated as a multifaceted concept, using a three-tier approach.It evaluates the disparities in accessing ICTs and the Internet (first-order digital divide), in using digital tools (secondorder), and beneficial results of online activities (thirdorder digital divide) (Ferro et al., 2011).Engaging digital practices and endowment in a regional setting, this analysis gauge the regional digital capital.It dynamically assesses cross-regional panel data on the following four main dimensions: (1) user's access to digital technology, (2) user's digital practices, (3) human capital and (4) innovation capability, articulated by the employment rate in high-tech (HT) domains and expenditure in research and development (R&D).
This study contributes to the literature both conceptually and empirically.First, from a theoretical perspective, this paper enlarges the labour market resilience concept and theorizes adaptive resilience as a dynamic and evolutionary process, which weight the reactive ability of labour markets to minimize the effect of disrupting shocks.Unlike previous research, this analysis offers a valuable addition providing evidence on the significantly dissimilar capacity of EU regions to master the impact of the economic crisis on the whole business cycle, defined as expansion and contraction of economic activities (Holm & Østergaard, 2015).This study considers not only labour market resistance like a bouncing back to the previous state, as investigated in previous studies, but also approaches resilience as a dynamic, adaptive and evolutionary process.
Second, the current study extends the resilience research and offers novel insight into the impact of digital development on regional labour resilience at the NUTS-2 regional level in the EU-28 and analyses fourteen key quantitative digital indicators that generate inequality.Third, considering a time frame of 14 years , longer than in other studies, the interplay between digital development and employment is empirically studied during resistance, recovery, and reorganization stages, giving an overview of the regional labour market's growing paths and its adaptive capacity.Forth, from the methodological perspective, this study offers findings from a theory-driven gradient boosting decision tree model (GBDT) to supplement traditional spatial and mapping analysis.Finally, a potential instrument is proposed to draw policy implications based on advanced data-mining techniques.From the policymaking perspective, the awareness of the regional digital level foster tailored initiatives to encourage citizens in using ICTs in a wide array of activities, like job seeking and online accomplishments.The paper, therefore, concludes by introducing some policy recommendations to ensure that the research benefit is broadly shared.

THEORETICAL FRAMEWORK
Regional labour market resilience A broadly adopted topic in regional research and among policymakers, regional resilience has been criticized for being a vague concept, without a standard definition, a universally accepted meaning, and well-defined methods or indicators to benchmark its evolution (Gong & Hassink, 2019;Martin & Sunley, 2015).Consequently, some challenges must be addressed, especially in a crosscomparative analysis.The evolutionary economic perspective of regional labour market resilience adopted for this analysis is defined by Boschma and Bristow (Boschma, 2015;Bristow & Healy, 2018) as the ability of the labour market to resist, recover, reorganize when affected by shocks.
As the resilience to economic shock varies by scale, the spatial scale selected for this study shapes the research results.Most cross-comparative research is investigated at the national level, mainly because of data availability.However, an economically resilient country does not imply that constituent regions will necessarily demonstrate resilience to a particular shock (Martin, 2012).Because the European regions unveiled a different regional developing trajectory after the Great Recession outbreak (Giannakis & Bruggeman, 2020), this analysis performs at the NUTS-2 regional level.
The regional employment level was preferred for the appraisal of labour market resilience because it provides a meaningful measure of labour markets (Fingleton et al., 2012), consistently available at the regional level, on a comparative approach across EU countries for a suitable timeframe (Kitsos & Bishop, 2018).Another related challenge is to establish whether resilience is being evaluated in absolute terms and to determine how investigated regions behaved in relation to a particular shock, or in relative terms disclosing regions that coped better and were more resilient than others.
Regional resilience can be assessed relative to the reference level, using pre-shock economic indicators and counting the variations in the accomplishment of selected variables, or it can be appraised comparatively to other regions in the same countries or areas.Following (Martin, 2012), the reference state used in the current analysis is based on quantifying absolute resilience and reveals whether a regional labour market is shock resistant, is recovered, or has not been recovered from the shock.Two main reasons support our decision.First, although one labour market may stand more resilient than another, none of them has essentially demonstrated to be resilient if both are stuck in decline.Second, comparative resilience measures, such as the sensitivity index proposed by Martin (2012), are difficult to operationalize in a cross-comparative analysis, owing to methodological limitations (Sensier et al., 2016).
Concerns about labour markets' ability to cope with challenges generated by the crisis have interrelated the analysis of resilience with concepts like vulnerability and adaptive capacity.Before a perturbation, every region runs a degree of vulnerability determined by the sensitivity (capacity to absorb shocks) or propensity to be hit by an external shock (Gong et al., 2020).Vulnerability is an inherent feature of systems that can potentially generate adverse effects, irrespective of the risk of a specific shock.In the case of economic shocks, the vulnerability of regions derives from the lack of features like economic diversity, availability of resources, innovation capacity, and adaptation potential (Briguglio et al., 2009).
A multidimensional concept with varying interpretations, adaptive resilience was adopted to leverage understanding of the evolutionary path of regional digital development influencing labour markets.In addition, this path-dependent process analysis investigates not only if a region reached its pre-shock level but also considered the adaptive capacity of the region to reorganize and develop new growth paths afterwards the shock (Boschma, 2015;Martin & Sunley, 2015;Sensier & Devine, 2020).Given the criticism of the engineering resilience approach, in its passive sense (DeVerteuil & Golubchikov, 2016), that presumes to return to the pre-shock state and to lack the transformative potential, this study embraces the evolutionary dimension of resilience.Evolutionary resilience considers the vulnerability to shock, the magnitude of the impact, the short-term reaction, the adaptive patterns, and the reconfiguration of a new trend spawning growth.
To investigate regional labour market resilience, some scholars proposed a basket of indicators (McInroy & Longlands, 2010), but this method would combine the causes and effects of resilience.Since the same shock can hit regions at different moments and with various intensities, a key challenge for gauging the predictors of regional resilience is to identify when the shock impacted each region.However, for some local phenomena, dating shocks can be relatively straightforward.In contrast, others, such as the Great Recession, influence larger territorial areas and make it difficult to establish the exact starting point for each region.
Moreover, even if shocks are recurrent phenomena, their occurrence and geography are highly varied.At the same time, only some of them can be classified as region-wide shocks, as they impact many regions with comparable intensity and consequently are appropriate for cross-comparative analysis.Against this background, whether a challenging mission, it is essential for our research purposes to identify the onset of a regional shock.Misleading the starting date of a shock can result in a mix-up of cause and effect by mistreating the situations of regions disturbed earlier than the others.A more accurate approach for our research would be to assess each region as a particular entity and determine its reply to the shock, considering its specific developing route.In agreement with Sensier et al. (2016), a business cycle-dating algorithm was approached for every region, as it allows flexibility in identifying regional turning points to illustrate both peaks and troughs during their business cycle.This method facilitated us to evaluate if the employment of each region was unaffected by the shock or whether it faced a recessional crisis.
There is a range of interlinked drivers determining the labour market resilience.In some cases, they act in divergent directions, while in other circumstances, they reinforce themselves.These drivers include economic, technology, environmental, societal, and attitudinal factors, likely to operate at the regional level for resilience and inclusive growth.This study focuses on digital technology and related drivers that stand as the most critical factors that have shaped the labour market in recent decades.Digital technology is a significantly important driver of the EU labour market resilience, as the demand for professionals with digital skills has grown annually by 4%, and almost half of the population lacks basic digital skills (European Commission, 2015).

Framing the relationship between digital transformation and labour market resilience
The concept of digital transformation, which has reshaped the way people do business and work, has evolved during the last two decades from approaching digital equipment and software to automation of repetitive tasks and has started to be considered the digitization of everything (Dufva & Dufva, 2019).Digital technology, more broadly all that Industry 4.0 encompasses, plays a crucial role in the progress of today's society, with widespread impact and enormous transformational power (Brynjolfsson & McAfee, 2014).New economic sectors emerge or profoundly change, primarily but not exclusively driven by technological advancements (European Commission, 2015).Digital infrastructure and skills offer new and more flexible working (e.g., remote working), opportunities to strengthen connectivity, and inclusiveness has fostered labour workforce sustainability.However, while the digital transformation of the economy requires a level of digital skills for almost all new jobs, some routine jobs are replacing due to the key technologies that enable automation, like nanotechnology, robotics, and artificial intelligence.Consequently, the impact of automation on employment has spawned a lively debate (Agrawal et al., 2019;Frank et al., 2019), mainly due to the intelligent robots that emerged within Industry 4.0.
There is a growing concern regarding the negative impact of digital transformation on the labour market and groundless anxiety of the job losses that may trigger.This claim is valid for low-skilled workers performing routinized activities (Balsmeier & Woerter, 2019), impacting cognitive and non-routine ones (Agrawal et al., 2019;Frey & Osborne, 2017).Some studies have identified a negative influence of technological advancement on the number of jobs and wages (Acemoglu & Restrepo, 2020).Other analyses claimed a positive effect of digitalization on productivity and labour demand as the labour force becomes high-skilled (Agrawal et al., 2019;Piva & Vivarelli, 2005).However, technological development also forwards economic and social innovations, as it affects both the quantity of employment (number of jobs) and the quality of work (skills and wages) (Pianta, 2009).
The distinct patterns of regions' development under Industry 4.0 are due to numerous factors.Capello and Lenzi (2021b) argue that in regions with a dynamic and large productive sector, Industry 4.0 fits well and produces significant transformations.Moreover, regional development is deeper and faster in areas where Industry 4.0 finds a strong technological setting (Capello & Lenzi, 2021a, 2021c).De Propris and Bailey (2021) state that the impact of the fourth industrial revolution at the regional level depends on the specialization and diversification of every region and on the potential for attracting and absorbing new technologies, but they also highlight the overwhelming role of innovation in the transformational process.
This paper fits in the active debate generated by the enhancements in digital technologies that support the workforce, by inequalities in accessing (also stated the first level of digital divide), in use (known as the second level of digital divide), and to advance results created online and worthy in the offline economic space (also named the third level of digital divide) (van Dijk, 2005).Despite the increasing body of literature on resilience and new reasons for comprehending the implications of inequality, the research so far directed little interest to digital inequality as an influencing factor on labour market resilience.Few exploratory studies have scrutinized this correlation, irrespective of the hypothetical, theoretical causal influences.
This analysis considers digital development a predictor of labour market resilience because the acceleration of technological progress is the primary vector of the fastest change in the labour market (Agrawal et al., 2019).Moreover, it may represent a form of adaptation to a new, more interconnected, resourceful, and innovative environment in turbulent times.In relationship with regional labour market resilience, research focused mainly on Schumpeter's concept of creative destruction (Schumpeter, 1934) induced by technological progress, innovation being the driver of the adaptive evolution of the economy at the regional level (Bristow & Healy, 2018).
Four complementary indicators of digital capital were considered to successfully investigate all the facets through which the digital divide can influence labour market resilience.Each dimension refers to a digital determinate with a distinctive contribution, and all shape a complete picture of digital capital.Table 1 depicts regional digital infrastructure and effective use of digital technology (Goss & Phillips, 2002), which capture complementary dimensions of the digital labour market.The second group of determinants is related to human capital.Following diffusion theory, we can claim that staff with a higher level of education tend to be more disposed to adopt new technologies than workers with lower levels of instruction (Rogers, 2003), and educated workers should benefit from their e-skills (Crescenzi et al., 2016).Education in connection with ICT literacy is one of the main determinants of employment, with an essential contribution in the reverberation of regions to unexpected socio-economic shocks (Di Caro, 2015).
The third set of determinants gauges the innovative regional capacity.As a measure of innovativeness, the R&D expenditure was reported as a catalyst for online activities (Pick et al., 2015), with a positive spillover effect on labour market growth.Furthermore, R&D expenditure may be considered both a control variable and an enabler of regional digital development through the diffusion of innovation induced in the economy.Employment in the HT sector is used to investigate whether technological industries in a region generate positive effects and foster labour market growth.It indicates advanced skills, empowering the workforce to take advantage of technology.

RESEARCH METHODOLOGY
market resilience?, and the subsequential secondary questions: What digital dimensions count the most?How does the digital pattern change over the business cycle?A crosscomparative methodological approach is proposed to investigate distinct responses to economic shock and to explore the digital regional predictors in resistance, recovery, and reorganization periods.This analysis considers a top-down theoretically driven methodology that involves three main stages: (1) measuring regional labour market resilience, (2) ranking and quantifying the key digital predictors of resilience, using the GBDT model, and (3) quantifying and mapping the regional digital level and the spatial correlation between digital endowment and labour market resilience.
Using a methodological framework inspired by two well-established studies (Sensier et al., 2016;Martin, 2012), this paper first classified the EU regional labour markets as resistant, recovered in the short-term, recovered in the long run, and unrecovered by 2019.Taking advantage of our extensive data set, this study focused not only on the early phase of resistance or the shortterm recovery, as many other studies, but aimed to identify long-term adaptive changes in growth trajectories.The longstanding process of reconstruction and organization after the crisis depicts the capacity of regions to reinvent and recombine the resources and create a new model of development.
Second, a GBDT classifier was used to evaluate the multivariable effect of the fourteen indicators, and potential digital predictors had been gathered for 278 EU NUTS-2 regions.To define an operational measurement, this analysis breaks down the digital development concept into two dimensions: the level of digital endowment and digital growth.Indicators such as access, use, own, tertiary education, and expenditure in R&D reflect the regional digital level.In addition, digital transformations during various resilience phases are evaluated using the rate of change for the same indicators.Three leading principles were applied in indicators' selection: data drawn from the extant literature, availability at NUTS-2 level, and their relevance for labour market resilience.
Third, to determine the digital development score for 278 EU regions, the importance of each digital indicator in predicting the labour market resilience was considered, and weighted indicators were computed to determine the digital level of development during each stage of resilience for all EU regions.Finally, the scale of the digital divide in the EU and its correlation with labour market resilience, the importance and circumstances of differences in approaching digital technologies, spatial correlation patterns across the EU and policy-relevant conclusions were articulated.

Data source and variable selection
One major constraint of regional research is the availability of longitudinal regional data.Despite the efforts devoted by the EU ICT directorate, there is still a lack of detailed, comprehensive, and comparable data concerning regional digital endowment.Therefore, the empirical analysis is based on a data panel collected from Eurostat for 28 EU member states and 278 NUTS-2 regions, running from 2006 to 2019.The cross-country panel dataset benefits from encapsulating the overall equilibrium effect of different drivers.The selection of variables is grounded in the literature on labour market resilience and the digital divide, as mentioned in the previous section.Digital

V_access G_access
Proxy for the availability of digital infrastructure that represents a precondition for digital activities Ratio of individuals who own a computer

V_own G_own
Computed using the ratio of individuals who never used a computer; is a proxy for the first-order digital divide Ratio of individuals regularly using the Internet

V_use G_use
Provides insights into Internet usage; represents a driver for labour market growth; is a proxy for the second-order digital divide Ratio of persons who purchased goods or services over the Internet

V_order G_order
Proxy for information technology (IT) literacy (Goss & Phillips, 2002); it fits in the third-order digital divide Enablers of regional development

Employment in the high-tech sector V_ehts G_ehts
An indicator of the advanced skills, empowering the workforce to take advantage of technology; represents the human capital Share of population with tertiary education and above

V_educ G_educ
Acts as a proxy of human capital and a catalyst for labour market growth (Crescenzi et al., 2016) Intramural R&D expenditure V_expenditure G_expenditure Captures the regional innovation spillover effect that is expected to positively affect labour market resilience Note: 'V_' variables refer to the indicator values at the beginning of a phase.The compound annual growth rate (CAGR) was used to compute growth values, which are prefixed by 'G_'.
Digital divide across the European Union and labour market resilience 2395 development indicators had been gathered from Eurostat's annual ICT survey that collects comparable information on the use of digital technologies by individuals in the EU regions, as reported in Table 1.
The annual employment rate is the dependent variable selected to measure regional resilience as it is independent of depreciation (Di Caro, 2015) and statistically trustworthy (Sensier et al., 2016).While some studies, such as Palaskasy et al. (2015), upheld that well-performing regions before the crisis were more susceptible to be hit by the crisis than lagging regions, other researchers (Martin, 2012) stated the contrary.Consequently, the digital level at the outbreak of each stage of resilience and the rate of change was elected to capture these effects.The trend indicator captures the rate of change and is calculated as the compound over resistance, recovery, and reorganization stages as the compound average growth rate (CAGR), while the level indicator exposes the digital stage at the onset of each period.

Measuring labour market resilience
Following Sensier et al. (2016), this study employs preand post-shock outcomes and individually dated business cycle turning points for 14 years, between 2006 and 2019, to assess the influence of the Great Recession on the labour market employment rate.Apart from previous studies that considered mainly a downturn in labour market resilience, this research approached both downturn and growth stages.The resistance and recovery for every region are distinguished based on employment dynamics.The business cycle dating algorithm allows us to capture the disparities between regions and helps identify the downturn date for each NUTS-2 region.This option was preferred because we are specifically interested in quantifying the responsiveness of each EU region to the triggers of crisis in terms of absolute changes rather than variations around the growth path.
Although resistance and recoverability are similar concepts, they encapsulate dissimilar dimensions.Both consider the depth of employment transformation; however, the significant difference between the two measurements is the direction of change; resistance is dedicated to the shrinkage of employment and only includes recessions, while recoverability describes the change and reflects upturns.As proposed by Sensier et al. (2016), a minimum duration of one year for a phase and three years for the whole business cycle was considered in this analysis, while no constraints were defined for the maximum length of the business cycle.Furthermore, the peak turn-off point was dated like the performance before the recession and the trough turn-off point as the performance before the expansion.Finally, we have determined the duration and amplitude for the business cycle's resistance, recovery and reorganization stages, at the regional level, using the peak and trough points.
Regions were classified by amending the procedure proposed by Sensier et al. (2016).A region is considered 'resistant' whether the employment growth rate remains positive during the shock.The regions that have experienced contraction and returned to their pre-shock peak within four years are named 'recovered in a short time'.Regions returned in a larger time frame are categorized as 'long-term recovered'.Non-recovered regions experimented with a downturn and have not recovered to the pre-shock peak level.The reorganization stage consists of the long-term evolution of the employment rate from the trough until the end of the investigated period: 2019.

Quantifying digital predictors of labour market resilience
Following the theoretical framework, the potentially relevant determinates of labour market resilience that may induce the digital inequality-resilience relationship were evaluated.The min-max technique was first used to make the data dimensionless and comparable across different measurements, and all digital metrics were normalized in the range [0, 100], based on beneficial/non-beneficial criteria.To assess the relationship between digital variables and to reduce the redundancy among covariates, the correlation matrices were computed, and then collinear variables were eliminated.
Inferential analysis based on mainstream statistical methods was performed further, and various determinants of regional resilience were investigated.The standard technique usually applied to define the relationship between drivers and effects is to identify and evaluate a narrow set of parametric models that engage latent variables, such as factorial analysis and structural equation modelling, or observed variables, like compound multivariate regression and canonical correlation analysis.However, data exploration using parametric models spawns significant problems (Miller et al., 2016).Besides the distributional assumption, these models involve the challenging hypothesis that a set of linear equations can adequately summarize the significant structure of the surveyed data, ignoring the non-linear influences and potential connections among predictors.
Hence, additional models have been applied, such as spatial regressionto master and surpass the spatial autocorrelation, the generalized additive regressionto apprehend non-linear effects, and the generalized linear regressionto overtake the non-Gaussian distribution.However, even when some non-linear effects are modelled, it can be difficult to simultaneously state the pertinent direct non-linear outcomes and interactions in a priorly defined parametric model, especially when the range of outcomes is significantly large.Meanwhile, a significant number of research papers disclose a non-linear relationship between economic development and the digital level of countries (Cruz-Jesus et al., 2017).
Against this background, to surmount most of the aforementioned drawbacks, machine learning algorithms have been recently involved in many studies, acknowledging their predictive power.A supervised machine learning algorithm, the GBDT method, was selected for this research due to its advantages compared with traditional multivariate linear regression models or other parametric 2396 Adriana Reveiu et al.

REGIONAL STUDIES
models.Primarily, the GBDT model can master the assumed non-linear relationship between predictors and our response variable (regional labour market resilience).Unlike linear regression algorithms, the GBDT technique does not presume the same type of connection between the outcome variable and the entire set of predictors during the whole processing time.As an alternative, it involves decision trees to rank the predictors and forecast the output variable by diminishing a loss function.
In contrast to other machine learning techniques considered black boxes, tree-based ensemble methods generate meaningful results and successfully handle different types of predictors (Hastie et al., 2009).Due to these advantages, the GBDT model has been widely applied in various research areas, such as predicting company failure (Jones & Wang, 2019), communication in disasteraffected areas (Raza et al., 2020), telework, and sustainable travelling (Wang & Ozbilen, 2020), factor sorting and the digital divide (Hidalgo et al., 2020).However, engaging the GBDT classifier in the study of regional resilience is still narrow.The GBDT method is approached here to fit a non-linear model and uncover hidden patterns, rank influential factors, and illustrate the contribution of various digital dimensions in predicting the labour market resilience.As regional level variables are included in our data panel, the model also involves the spatial dimension.
The GBDT model is a related statistical technique named gradient boosting because it uses a gradient descent technique to minimize the loss of information whenever new data models are appended and find the optimal combination of trees able to learn from previous predictions.Besides furnishing a prediction accuracy advantage, the GBDT model captures interactions among features without outlining them and is robust to outliers (Hastie et al., 2009).Although this model is extensively used in forecasting, for this analysis, model fitting was applied on the training data to estimate both linear and non-linear effects and interactions among digital predictors of labour market resilience, without any parametric assumption concerning the observed data.
A learning rate parameter controls the impact of newly added trees to avoid overfitting.A learning rate with a lower value generates a robust model with accurate outcomes, while it increases both the number of iterations and the processing time.The approximation function of the response variable is expressed as in equation (1) (Friedman, 2001): where z is the learning rate used to manage the effect of the newly added classification tree; a t is the average of the ending nodes of the tth classification tree; b t is the weight of the ending nodes of the tth tree; and h(.) is the growth of root function.
The predictors are seldom equally relevant in datamining analysis, so the next step of our analysis ranks the determinants and illustrates their relative influence in the predictive model.The influence of each predictor is defined as the sum of the squared errors generated by any split, computed over all model trees (Friedman, 2001).In contrast to traditional regression methods that determine a range of statistical coefficients, the gradient boosting technique features the relative weight of determinants in predicting the response variable.The most frequently a variable is used in making vital decisions, the higher its relative importance is in forecasting the output variable.The relative importance of variables is expressed as a ratio of the whole reduction in error, credited to the entire set of predictors.
The relative importance of digital predictors is then used as a weight to figure out the regional digital divide across the EU for all phases of resilience.For policymakers, accurately classifying factors that influence labour markets may be as important as revealing the extent to which the factors affect the outcome.Partial dependence is a global and model-agnostic method that explains the impact of digital factors on the target labour resilience, considering the overall data set.A comprehensive understanding of the contribution of digital capital in predicting labour market resilience is depicted by partial dependence plots (PDP).The PDP shows the marginal effect of one digital predictor on the labour market resilience, marginalizes all other predictors, and depicts their relationship (e.g., linear, monotonic or more complex).PDP is also used in this analysis to capture the non-linear relationships.
To control the GBDT model performance and to avoid overfitting, a set of hyper-parameters were evaluated, and the optimum set of values was identified, including the number of trees that determines the iteration number; the learning rate that establishes the influence of every tree on the result; and the maximum depth of interactions among variables (Hastie et al., 2009).Granger causality test and augmented Dickey-Fuller (ADF) cointegration test were conducted to create a clear picture of the inner causality between digital variables and regional labour market resilience and verify whether there is a long-term equilibrium relationship between them.
Finally, the bivariate spatial autocorrelation was performed between regional digital level and labour market resilience to supplement factor analysis.To develop a descriptive understanding of digital patterns and identify spatial clusters of resilient labour markets, we exploited Moran's index and local indicators of spatial association (LISA) (Anselin, 2019).The regional spatial dependence was mapped, and the type of interaction was colour coded.Positive local spatial correlations were categorized as highhigh or low-low spatial clusters.Spatial outliers represent negative spatial correlated areas.

EU regional labour market resilience
Our empirical work disclosed four countrywide labour markets prepared to withstand the Great Recession shock that preserved or improved their employment level: Germany, Luxembourg, Poland and Malta.
Digital divide across the European Union and labour market resilience 2397 REGIONAL STUDIES However, there was considerable spatial variability, at the regional level, within the 28 EU countries.At the same time, only 40 (14.4%)NUTS-2 regions exhibited resistance, 60 (21.6%)EU's regions bounced back to the preshock employment level in the short-run (four years), and 75 (27%) regions proved long-term recoverability.
Even if there are 108 (38.8%) unrecovered NUTS-2 regions across the EU, they are on an ascending path.Nevertheless, considering the slower recoverability process, policy measures are needed to foster their upturn or resilience in the case of additional future shocks.The spatial distribution of the EU labour market regional resilience, in Figure 1, exposes significant differences between the Central part and the rest of the EU in the proficiency of regional labour markets to withstand economic shocks.Although informative, Figure 1 does not shed light on the causes of distinctive performance of labour markets across the EU regions, following a harmful shock.
Exploring digital predictors of labour market resilience Four GBDT models (Figure 2) were developed to investigate the influence of different digital dimensions on the labour market resilience, the underlying conceptual model, and to answer our research questions. Figure 2a portrays regions in the period immediately preceding the economic crisis.This model was built for two reasons: on the one hand, it encompasses digital capital influencing employment in a time of economic prosperity, and it may also disclose the level of vulnerability of regions to shocks.
On the other hand, this model is used as a basis for comparison to identify the changes of digital capital during crisis and post-crisis stages.Due to the lack of data availability, at the regional level, for the 2006-07 timespan, employment in the HT sector (variables V_ehts and G_ehts) was not included in Figure 2a.The remaining models distinctly assess various phases of the regional labour market resilience.Figure 2b explores digital predictors during resistance.Figure 2c depicts digital components influencing regional labour markets during recovery in the short-run (four years aftermath the crisis outbreak), while Figure 2d identifies the post-crisis longrun adaptive pattern.All models include structural and growth indicators for each NUTS-2 region, as described in Table 1.Four correlation matrices were first created to identify any latent relationship between digital predictors, as presented in Figure A1 in the supplemental data online.These outcomes suggest that most parameters are uncorrelated, except V_own and V_order that were eliminated from the predictive models in Figure 2b, d, as they are strongly correlated with other variables.Similarly, V_order was also removed from Figure 2a, c.Moreover, correlations also confirm the relationship among digital variables that fit the conceptual model.The outcome of the GBDT model exhibits a dissimilar impact of the regional digital capital in each phase of resilience.The magnitude variables expose the particular contribution of each digital dimension to the predictive models.Uncovering a diverse structure of predictors, Table 2 reports on the feature importance in each analytical model.Figure 2a, which provides an overview of the digital sensitivity of  Digital divide across the European Union and labour market resilience 2399

REGIONAL STUDIES
EU regions at the outbreak of the crisis, discloses that the level of digital capital forecasts 72.7% of the employment ratio, as figured in Table 2. Human capital and innovative capacity count the second, with 16.9% predictive power.Figure 2b uncovers the most important predictors of employment in the resistance phase: the use and access to the Internet, R&D expenditures, the ratio of the population with tertiary education or above, and employment in HT industries.These top five leading variables forecast 82.36% of the labour market resilience in this model.Moreover, the digital development level proves to be a significant predictor of resistance, as all variables measuring the digital level account for 91.2%, in Figure 2b. Figure 2c rates digital predictors of employment during the short-term recovery stage.Among the five shortlisted variables with the highest predictive power in the recovery model (almost 87%) are digital capital and human resource in digitally intensive sectors.This outcome evidences that regions able to extend their capacity to create plus value from digital technology and e-skills succeeded in the short-term recovery of their labour markets.
Finally, Figure 2d identifies significant factors influencing reorganization after the Great Recession shock.The growth rate variables are the most influential in fostering the labour market adaptation.Their aggregated relative contribution is almost 89%, demonstrating that the reorganization is done through changes and development, the structural components being insignificant in this phase.Moreover, only indicators describing digital infrastructure and technology are among the six shortlisted variables that forecast 82.36% of the labour market resilience.These findings advocate a key policy priority to foster digital and human development, boosting third-order digital activities.Our outcomes indicate that third-order digital indicators, particularly the growth of Internet usage and online ordering goods and services, are significant predictors of labour market reorganization (ranks 1 and 2).
Consequently, the frequency of Internet usage and online activity can influence regional labour market adaptive patterns.Interestingly, essential factors that are the top four resilience predictors in the reorganization phase are related to growth rates in Internet usage, ordering goods and services, tertiary education, and owning a computer.The weakest predictor, the growth of expenditure in the R&D sector during reorganization, has a limited influence (rank 12).Two important conclusions emerge from these results.First, the model highlights the importance of digital capital for the short-term recovery of regional labour markets, as the most influential predictors of resilience are directly related to digital capital, mainly with the third-order digital divide indicators.Second, contrary to the resistance phase, the adaptive phase is characterized by a mix of both level and growth variables.This result suggests that labour market recovery is not grounded only on high levels of digitalization but also on the adaptive capacity of regions to generate growth in this essential domain.
The adaptive capacity of the regional labour market following a shock also emerges when comparing Figure 2d with Figure 2a.It emphasizes a different hierarchy of labour market resilience predictors.These findings confirm what has been previously argued by Boschma (2015), Martin and Sunley (2015) and Sensier and Devine (2020): after a shock, the labour market does not simply return to its original state but develops new patterns of change, 'learns' from previous vulnerabilities and adapts to another context.Our results are in line with this theory, representing an imported gain in the literature, as the robust quantitative methods bring solid evidence favouring the adaptive resilience of the labour market.In Figures A2 2400 Adriana Reveiu et al.

REGIONAL STUDIES
and A3 in the supplemental data online, the PDP plots illustrate marginal values that prove a highly non-linear relationship between predictors and labour market resilience and outline that growth in digital capital, R&D expenditure and tertiary education increase the probability of resilience.Labour market resilience surges in regions with an increase in the adoption of second-order digital greater than 27%, but after a threshold of 30%, the effect is limited (see Figure A3a online).The most substantial improvement in partial dependence is observed when the increase in approaching third-order digital solutions exceeds 13% in a region.However, an advance larger than 17% generates a limited effect (see Figure A3b online).This PDP indicates small marginal changes in labour market resilience for low third-order digital divide variables.Another interesting result is the tertiary education growth rate that exhibited a similar highly non-linear positively associated with labour market resilience, with a considerable impact of up to 38% growth (see Figure A3c online).Once this threshold (38% growth rate) is achieved, no significant impact on labour market resilience can be expected.
The performance parameters demonstrate that all models perform well; the accuracy scores are between 0.995 and 0.99 considering a learning rate of 0.01, the logarithmic loss is in the range 1.10 and 0.92, and area under the curve (AUC) values are between 0.8 and 0.9.The AUC measures the ability of a classifier to discriminate between classes.The model was trained and tested on the original data set, randomly allocated into two parts.Using a grid search solution was detected the optimal set of parameters that generated the lowest prediction error.The optimum set of parameters used to train the models is: the learning rate ¼ 0.01, the number of trees ¼ 300, and the complexity of the tree is 10.
The Granger causality test applied to the original dataset rejected the null hypothesis that digital variables did not Granger-cause regional resilience, while p < 0.05 (the significance level).Our results, for all models, confirm that causality goes from digital dimensions and expenditure in R&D, as depicted in Table A4 in the supplemental data online.The ADF unit root test results show that all the variables except V_own, in Figure 2b, and respectively G_use, V_order and V_own, in Figure 2d were first-order integrated.First-order integrated variables were used to conduct a cointegration test that showed a long-term equilibrium relationship between predictors and the labour market resilience.

Geography of the digital divide and labour market resilience
The developmental role of digital technology in the regional economy and labour markets presumes a ubiquitous distribution of digital skills, infrastructure and services across regions.However, earlier studies suggest an uneven distribution of digital resources across European Union regions, on different dimensions, such as adopting e-services (Pérez-Morote et al., 2020) and digital skills (Gheorghe & Dârdală, 2020).Furthermore, a common attribute of the regional economy is the spill over effect among neighbour regions, so that performance of a region is likely to impact nearby areas.The predictive factors exposed by the GBDT technique have been involved in the next stage of our analysis to uncover digital spatial patterns over the adaptive resilience process and to determine digital level/scores for all NUTS-2 regions.This outcome allows us to reflect on spatial disparities, to discover the spillover effect that may spawn regional spatial clusters of digitally prone areas or, on the contrary, less developed regions.Moreover, this adds a significant dimension to our findings that can be a basis for further policies at the EU regional level, which links the geography of resilience and the geography of digitalization in a coherent framework.
The spatial distribution of the digital capital indicates substantial geographical variations across the EU regions, as featured in Figure 2. A significant spatial correlation between the digital development level and labour market resilience was uncovered during the pre-shock, resistance, and short-term recovery stages (global bivariate Moran's index ¼ 0.096, 0.159 and 0.127, respectively, with p < 0.0001), that confirms the importance of regional digital level in fostering labour market resilience.It also suggests a heterogeneous spatial pattern across EU regions, grounded in the digital divide theory.Furthermore, the four stages of labour market resilience can be explained in terms of regional adaptability.Before the crisis, the leaders were regions from the Central and the North of Europe.However, during the reorganization phase, regions from the South and the East illustrated their adaptive capacity.A highly heterogeneous landscape was exposed during the short-term recovery phase.Nevertheless, during the reorganization, most hit regions struggled to adapt the structure of digital capital to the new challenges.Moreover, the negative global bivariate spatial dependence between digital capital growth and regional resilience (global bivariate Moran's index ¼ -0.344, p < 0.0001) supports the previous remark.
Bivariate LISA plots (Figure 3) bring to light significant spatial clusters, the relationship between digital level and labour market resilience, and highlight different patterns across EU regions.In the pre-shock stage (Figure 3a), the different development levels between the North and the South of the EU emphasize a distinctive preparedness and vulnerability level.There were significant clusters of high digital endowment and a high degree of labour market resilience in Germany and some regions from Belgium, while in France, Italy, Spain and a part of Romania, low significant clusters were discovered.During the resistance phase (Figure 3b), high-level clusters are uncovered in the central part of Europe, in Germany, and some areas from Austria and Belgium, and low-level spatial clusters were in the South of Europe, in regions from Italy, Greece, Spain, Portugal, Romania and Croatia.In contrast, leaders in ICT adoption, Finland and France, are among the outliers because of a high employment level at the outbreak of the crisis, which is currently underway.Interestingly, resistance is the only stage with fewer outliers than the clustered regions, reinforcing the polarization between the North and the South of the EU.
Spatial positive clusters were only insular in the shortterm recovery stage; they are located in regions from Germany, Luxembourg, Poland, and Hungary, while negative clusters were discovered in Portugal, Spain, Italy, Bulgaria, and Finland, as illustrated in Figure 3c.However, many significant outliers in the short-term recovery stage (77 NUTS-2 regions) and in the reorganization phase (92 NUTS-2 EU regions) provide evidence on the adaptive capacity of EU to generate a spill over effect in neighbouring regions.In the reorganization phase, there were spatial clusters of regions with a high level of digital capital and high perspectives of labour market resilience in Hungary and Luxembourg.In contrast, clusters of regions with low digital development and a low degree of resilience were released in regions from France, Finland, Greece, and Romania (Figure 3d).Although supported by previous studies (Giannakis & Bruggeman, 2017), these findings on geographical disparities within the EU disclose new insights.Considering the digital gap is particularly important for cohesion policies in the effort to countervail the impact of the economic crisis, mainly in southern European countries.

DISCUSSION AND CONCLUSIONS
As a contribution to the regional science literature, this paper comprehensively analysed labour market resilience, investigating multiple phases: resistance, recovery, and reorganization of EU regions disturbed by the Great Recession.This outcome is valuable as available research papers mainly considered the resistance phase because the recovery was an ongoing process for some European countries or focused on engineering resilience.This research proposed and validated a framework that evaluates the seminal impact of regional digital capital, human resource, and expenditure in R&D on labour market resilience in the European Union.We engaged GBDT to explicitly consider the adaptive perspective of resilience and quantify the relative importance of regional digital capital, which features a non-linear relationship between the regional digital level and labour market resilience.The factor analysis conducted on fourteen digital-related variables discloses that third-order digital indicators significantly contribute to labour market resilience in EU regions.Our findings suggest that the technological level of regions is a good predictor for all stages of resilience and illustrated a nuanced contribution of different dimensions of digital capital and their impact on the regional divide.
The results show that dimensions of digital capital are more important for predicting labour market resilience at the regional level in the EU than are human capital or R&D expenditure.This study has found that digital drivers of labour market resilience varied significantly between different stages of resilience, and the labour market in digitally disadvantaged regions is more vulnerable to recessionary shocks.While this paper provides new insights on predictors of labour market resilience with a regional focus, it suffers from some limitations, many of which open opportunities for further research.First, as a non-parametric model, the GBDT technique is not able to deliver statistical inferences like confidence intervals or significant tests.Consequently, perhaps variables with minor relative importance are statistically insignificant.However, this is not a big issue for this analysis because we are mainly interested in disclosing major predictors of resilience.
Furthermore, GBDT encounters overfitting and is considered a slightly black-box model.However, these drawbacks have been controlled involving tuning parameters and cross-validations and model-agnostic explainable techniques, like PDP.Nevertheless, our findings also prove that the GBDT model can handle ill-posed problems, scrutinizing quantities of data without substantial loss in estimation quality.The second limitation comes from the narrow range of digital variables included in the analysis ( 14), as data sets systematically collected at the NUTS-2 level are limited.This context is slightly explained by the fact that the digital dimension has been only recently incorporated in European statistical data collection.Moreover, this weakness diminished the potential to frame more fine-grained geography than NUTS-2 regions.However, depending on data availability, the proposed framework may incorporate a broader set of predictors.
Another constraint is due to the dissimilar path of the labour market evolution that may occur inside a NUTS-2 region.However, an analysis at the LAU level, even insightful, would not allow a causal interpretation of labour market shortcomings and to recommend adequate remediating policies.Despite these drawbacks, the paper has meaningful policy implications.Two major arguments for policy debates on the EU digital future can be derived from our results.First, regional-specific policy strategies aimed at improving the digital level when focused on the third-level digital dimension can foster labour market resilience, especially in the lagging regions.Because the EU regions encountered heterogeneous routes during their business cycle, tailored policies for each stage can improve labour market resilience and help to identify a tailored adaptive path.
The findings of this paper are also meaningful for further theoretical and empirical research.Technological development fosters productivity and growth but is also likely to redesign labour markets.Consequently, this study highlights the overwhelming effect of digital capital on the labour market resilience and contributes to filling a gap in the literature, as the link between regional digital level and labour market resilience is under-investigated.The geographic analysis that jointly considers digital capital and the labour market is becoming crucial as working activities turn digital.The empirical results depicted here indicate that labour market resilience to recessionary shocks varies over time, not only because of differences in the regional context at the outbreak of the crisis but due to the adaptive transformations that shape resilience and may change and evolve.
Consequently, more detailed research, performed at the regional level, for identifying profiles of well-performing regions in all stages would be worthwhile.Furthermore, the conceptual framework developed around adaptive resilience offers a fundamental, albeit limited, for further theoretical research and empirical investigation of this ruling research agenda.One way to cope with a crisis could be to intensify remote work, which requires digital skills, a high level of ICT equipment, and a good Internet connection.Our analysis indicated that some regions have not even overcome the Great Recession and face a new crisis.Consequently, adaptive behaviour must be developed, considering flexibility and digitalization as two critical concepts of the labour market resilience.Thus, current research proves to be an excellent starting point in designing policies intended to mitigate the impact of a crisis on the labour market and help its rapid recovery.

Figure 1 .
Figure 1.Labour market resilience across European Union NUTS-2 regions during the Great Recession.Note: Readers of the print article can view the figures in colour online at https://doi.org/10.1080/00343404.2022.2044465Source: Authors' elaboration of Eurostat data.

Figure 2 .
Figure 2. Models of the digital divide across European Union (EU) regions: (a) regional level of digital development in the EU at the outbreak of the Great Recession; (b) digital development at the EU NUTS-2 level during resistance; (c) EU digital development during the short-term recovery; and (d) regional digital development of EU during reorganization stage.Note: Applying the gradient boosting decision tree model (GBDT) technique, the importance of digital variables in predicting resilience was generated first and used to weight the regional level of digital development in each stage.Regions are split into four quintiles; a darker nuance indicates a higher quintile.Source: Authors' elaboration of Eurostat data.

Figure 3 .
Figure 3. Bivariate local indicators of spatial association (LISA) spatial correlation between digital development level and labour market resilience across the European Union: (a) relationship between labour market resilience and digital development during the pre-shock phase; (b) relationship between labour market resilience and digital development during resistance; (c) relationship between labour market resilience and digital development during short-term recovery; and (d) relationship between labour market resilience and digital development during reorganization stage.Note: Queen's contiguity spatial lag of order 1 and k-nearest neighbour weights symmetric matrix.Positive local spatial correlations were categorized as high-high or low-low.Spatial outliers represent negative local spatial correlations, named high-low and low-high, respectively.Source: Authors' elaboration of Eurostat data.

Table 1 .
Description of the 14 digital variables used in the GBDT model to predict labour market resilience.

Table 2 .
Relative importance of predictors of labour market resilience generated by the GBDT model b , like a four-stage adaptive resilience process including pre-shock, resistance, short-term recovery and reorganization.Percentages describing the weight of each factor in predicting labour market reliance.b Computation was completed in Python (ver.3.6), using the sklearn and statsmodels packages.