SPATIAL INTERACTIONS ACROSS THE REGIONAL EU LABOR MARKETS AND THE ROLE OF THE EU ENLARGEMENT

SPATIAL INTERACTIONS ACROSS THE REGIONAL

EU LABOR MARKETS AND THE ROLE OF THE EU

ENLARGEMENT

This thesis analyzed the degree of spatial interactions in the regional EU labor markets and to what extent the EU enlargement of 2004 affected the spatial interactions. The results indicated a significant association between a given region and nearby regions. Specifically, changes in unemployment in a given region lead to similar changes in unemployment in nearby regions, i.e. an increase in the unemployment rate of a given region is expected to increase the unemployment rate of nearby regions. Moreover, the results showed that changes in employment in a given region lead to opposite changes in unemployment in nearby regions, i.e. an increase in the employment rate of a given region is expected to increase the unemployment rate of nearby regions. The latter outcome suggests the presence of regional competition across the labor markets. The EU enlargement was found to weaken the regional competition effect. This finding is consistent with the hypothesis that the EU enlargement modified spatial interactions.

JEL classification: C21, C23, J64, R23

Keywords: Regional labor markets, EU enlargement, Spatial interactions

2 I. INTRODUCTION

It has been acknowledged that it is of utmost importance to consider unemployment rates from a regional point of view for the following reasons; the magnitude of regional differences within and across countries; the lack of explanations for the existence of regional unemployment disparities in macroeconomic theory; and the inefficiency created by such disparities for the economy (Elhorst, 2003). The principal aims of research on regional unemployment are usually to examine the persistence of unemployment differentials and to develop a model that examines its determinants, as the substantial regional disparities are of major political concern (Geppert and Stephan, 2008). One element that has often been neglected is the degree of spatial interactions between neighboring regions. This appears to be critical, as theoretical considerations predict that regions have a high level of reciprocal interaction and influence the economic performance of nearby regions, defined as spatial dependence. Hence, regions can be viewed as small open systems (Patuelli et al., 2011). Consequently, the spatial econometrics literature has developed methods to estimate and analyze the observed interconnections. Previous studies that analyzed spatial interactions across labor markets pointed towards the presence of strong spatial interaction effects (e.g. Patacchini and Zenou, 2007; Molho, 1995; López‐Bazo et al., 2002).

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In what follows, the importance of spatial interactions will be investigated in the regional EU labor markets. The purpose of this thesis is to assess to what extent the enlargement in 2004 modified the impact of spatial interactions across the regional EU labor markets.2 This is a novel research because as far as I am aware, previous literature neglected the role of the EU enlargement in reshaping spatial interactions across the labor markets. The economic transformation and the westward orientation of the Central and Eastern European (CEE) countries have a significant spatial dimension as, in a political sense, the enlargement undoubtedly reshaped the nature of relations between countries (Petrakos, 2013). Hence, this is certainly a worthwhile case to examine because the Eastern enlargement is expected to have modified the degree of spatial interactions.

The following reasoning is provided to clarify the hypothesis. Büttner (2007) argued that differences in languages, cultural background and institutional barriers impede integration throughout the continent. Therefore, as the enlargement significantly reduced institutional barriers between CEE and Western Europe, through the obstacle-free market for goods and services, one would expect that this unique situation intensified the degree of spatial interactions. In particular, the integration between CEE and Western Europe led to significant opportunities for trans-frontier co-operation (e.g. in the form of joint ventures, subcontracting, free trade areas, regional policy coordination, expansion of cross-border communication infrastructure) (Petrakos, 2013). This, in turn, led to dramatic changes in the labor markets due to the increased co-operation between firms through the creation and increased use of cross-border networks (Smallbone et al., 2007).

This thesis was carried out by using regional labor market statistics for 211 EU NUTS-II regions over the period 1999- 2016. The results provided strong evidence in favor of spatial interactions with respect to the regional labor markets in the EU. This finding is in accordance with the empirical evidence reported by previous studies that pointed towards substantial spatial interaction effects across the labor markets. Specifically, the outcomes showed that changes in unemployment in a given region lead to similar changes in nearby regions, i.e. an increase in the unemployment rate of a given region is expected to increase the unemployment rate of nearby regions. Moreover, changes in employment in a given region lead to opposite changes in unemployment in nearby regions, i.e. an increase in the employment rate of a given region is expected to increase the unemployment rate of nearby regions. Based on the results, the global and local nature of these spillovers could be 2 _{The accession concerned the following countries; Cyprus, the Czech Republic, Estonia, Hungary, Latvia,}

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identified. The former outcome corresponds to global spillovers and the latter outcome corresponds to local spillovers. The global spillovers have a greater geographical coverage compared to the local spillovers.

The positive impact of an increase in employment in a given region on the unemployment in nearby regions indicates some degree of regional competition. The intuition behind the regional competition effect is as follows. Consider a given region that attracts high-skilled workers. Therefore, high-skilled workers will locate from the nearby regions to the given region for better job opportunities. This will lead to an employment increase in the given region but to negative side effects in the nearby regions, which will increase the unemployment rate. One reason for this is that, due to higher earnings, high-skilled workers have higher savings rates and are more likely to be investors than low-skilled workers (Abella, 2006). Moreover, human capital is an important driver of economic growth in developed (regional) economies, as many industries are reliant on human capital (Pepper and Nguyen, 2016). Therefore, there is a disadvantage of losing high-skilled labor.

In the context of the EU enlargement, it is found that the regional competition effect is weaker as a result of the enlargement. Indeed, the enlargement stimulated integration across the EU regions (Ertur and Koch, 2006). In particular, the European Commission adopted regional policies to address regional disparities across the enlarged EU (Petrakos, 2013). Moreover, as was mentioned above, the enlargement facilitated significant opportunities for trans-frontier co-operation across the labor markets. These processes are likely to have weakened regional competition and thereby the negative side effects. This finding provides evidence in favor of the hypothesis that the enlargement modified the degree of spatial interactions.

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characterized by a particular skill-level, do not modify the degree of local spillovers.

The remainder of this thesis is structured as follows. Section II presents some stylized facts and a literature overview. Section III describes the methodology that is used to analyze spatial interactions. The dataset is outlined in Section IV. Section V reports the main results, followed by the robustness checks in Section VI. Finally, Section VII summarizes the findings and concludes.

II. STYLIZED FACTS AND LITERATURE OVERVIEW

II.A. Unemployment rates in the EU

The analysis covers the period 1999 - 2016. During this period, the average unemployment rate of the EU15 decreased from 9.4% to 9.1%.3 _{The average unemployment rate of the EU28} decreased from 9.0% in 2002 to 8.6% in 2016. Among the member states, the unemployment levels and trends differ substantially. Several countries reported remarkable high unemployment rates in 2016. Greece reported the highest unemployment rate (23.6%), followed by Spain (19.6%). At the other end of the spectrum are the Czech Republic (4.0%) and Germany (4.1%).

Regional unemployment rates across the EU regions differ more dramatically compared to the national levels. In 2016, the highest unemployment rates were reported in Dytiki Makedonia (31.3%) in Greece, followed by Ciudad Autónoma de Melilla (30.8 %) in Spain and Dytiki Ellada (29.8 %) in Greece. At the other end of the spectrum are Niederbayern (2.1 %) in Germany, followed by Praha (2.2 %) in the Czech Republic and Oberbayern (2.4%) in Germany.

Fig. 1 and Fig. 2 present the regional unemployment rates in the EU across the NUTS-II regions for 2006 and 2016, respectively. The high persistence of regional differences within countries is evident from Fig. 1 and Fig. 2. For instance in Italy, the Southern provinces report substantially above-average unemployment rates compared to the Northern provinces. These differences became more pronounced in 2016. Similar patterns are observed in other member states (e.g. the Netherlands, Germany and Poland).

Furthermore, it is illustrated that adjacent regions report similar unemployment rates. For instance, the regions in the North(west) of Italy reported the following unemployment rates in 2016; Provincia Autonoma di Trento (6.90%), Veneto (6.80%), Friuli-Venezia Giulia

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(7.60%) and Lombardia (7.40%). In addition, it is important to note that clusters are observed between neighboring countries. For instance, the regions in the French-Belgian border area reported the following unemployment rates in 2016; Nord - Pas-de-Calais (13.30%) and Champagne-Ardenne (11.30%) in France, Prov. Hainaut (11.80%) and Prov. Namur (9.70%) in Belgium. This is also observed in the German-Czech border area. These regions reported the following unemployment rates in 2016; Jihozápad (3.10%) and Severozápad (5.20%) in the Czech Republic, Oberpfalz (2.90%) and Dresden (4.90%) in Germany.

Hence, Fig. 1 and Fig. 2 indicate unemployment clusters. More specifically, regions with relatively low unemployment rates are close to regions with low unemployment rates more often than it would be observed if their locations were purely random (Patacchini and Zenou, 2007). This holds for regions with high unemployment rates as well. The most important takeaway from Fig. 1 and Fig. 2 is that analyses of regional labor markets must take spatial interactions into account.

7 Fig. 2. Regional unemployment rates (%) in the EU 2016. Source: Eurostat (2018).

II.B. Spatial interactions and common factors

The previous subsection showed that neighboring regions report similar unemployment rates. This is in line with the spatial dependence theory, which states that regions have a great level of reciprocal interaction and influence the economic performance of nearby regions. There are several reasons why spatial interactions occur across labor markets.

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each other if they are physically nearby (Conley and Topa, 2002). This effect generates unemployment clustering. Furthermore, housing patterns have a clear spatial pattern, because workers are likely to search for cheaper housing in nearby regions if the region in which they work is more expensive (Mitchell and Bill, 2004). This effect is stronger if mobility is high. In addition, interregional trade generates spatial interactions (Niebuhr, 2002). The reason for this is that demand and supply shocks could be transmitted across trading partners (Weinhold, 2002). Moreover, trade allows for the exchange not only of goods but also of new ideas and technologies (Weinhold, 2002). This has a clear spatial dimension as bilateral trade decreases strongly with distance. Finally, capital accumulation processes and knowledge externalities create agglomerations, which influence firm locational decisions (Audretsch and Feldman, 1996) and thereby spreading shocks to neighboring areas (Mitchell and Bill, 2004). Recently, researchers have begun to pay more attention to the issue of distinguishing spatial interactions from common factors (Vega and Elhorst, 2016). Observed regional dependencies can be due to common factors (e.g. aggregate shocks, business cycles) that affect different units, rather than being the result of spatial interactions that generate spillover effects. Regarding the labor markets, common factors suggest that regional unemployment rates change simultaneously as these factors change in the economy. Sarafidis and Wansbeek (2012) pointed out that mistaking spatial interactions for common factors leads to spurious inference and inconsistent results (Sarafidis and Wansbeek, 2012). In addition, Vega and Elhorst (2016) found that it is of utmost importance to control for spatial interactions and common factors simultaneously in the estimation model. Indeed, focusing only on spatial interactions or common factors can bias the outcomes.

II.C. Related literature

The present analysis differs from the previous literature. This study investigates to what extent the Eastern enlargement of 2004 modified the spatial interactions in the EU with respect to the regional labor markets. This appears to be of relative importance because of the general economic transformation in CEE and the trade integration with the EU after 2004 (Parteka, 2013), which may have strengthened cross-border clusters and altered spatial interactions within countries. In particular, it is well-known that the enlargement reshaped the nature of relations between countries. Prior to the enlargement, the accession countries were dealt with by the EU as part of external policies, but after the enlargement, new member states have been dealt as EU internal policies (Smallbone et al., 2007).

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CEE and Western Europe across the regional labor markets as follows. For CEE countries, the openness and westward orientation led to a rapid internationalization of the economy (Petrakos, 2013). The main characteristics were foreign direct investment inflows and increasing trade volumes, which are important determinants of gross capital formation with significant spatial implications (Petrakos, 2013). Moreover, the enlargement fostered significant opportunities for trans-frontier co-operation in the form of joint ventures, subcontracting, free trade areas, scientific and technological co-operation, regional policy coordination, development of cross-border transportation and communication networks (Petrakos, 2013). In particular, the enlargement affected the regional production structures. The removal of trade barriers resulted in access to new markets, thus creating opportunities for firms to expand their activities, as well as providing consumers with a wider range and higher-quality products and services. Additionally, it created conditions for higher competition after import duties, quantitative restrictions and physical barriers to trade were removed or reduced (Smallbone et al., 2007). Furthermore, the EU enlargement transformed labor market regulations in the EU member states (Afonso, 2012). Specifically, the new member states supported de-regulation in the EU in order to exploit their lower labor costs as a competitive advantage (Afonso, 2012). Altogether, the process of the enlargement indicates that the labor markets throughout the continent were significantly transformed. Furthermore, these transformations clearly have a spatial dimension.

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shaped relation between skill-level and spillovers, i.e. high-skilled and low-skilled workers are more likely to be employed in adjacent regions due to increasing demand. Hence, taking the skill-level into account appears to be crucial, as the labor markets might be different for high-skilled, middle-skilled and low-skilled labor.

Previous studies that investigated the spatial dimension of regional labor markets concluded that spatial interactions exist. For instance, Patacchini and Zenou (2007) analyzed the degree of spatial interactions across the regional labor markets in Great Britain. The authors concluded that spatial interactions exist and that an important driver of spatial interactions is the fact that workers can search and work in different regions, thereby creating commuting flows between regions. Moreover, the authors showed that these spillovers have a limited geographical coverage, implying that the spillovers decreased strongly with distance. In addition, Niebuhr (2002) provided information on the spatial interactions across the regional labor markets in the EU15 and concluded that spatial interactions are an important feature of labor markets. Moreover, the author attempted to identify the sources of the reported spillover effects. It was shown that the reported spillover effects were likely to be caused by commuting flows, migration and interregional trade.

In the same vein, Mitchell and Bill (2004) examined spatial interactions across the labor markets of major coastal regions of New South Wales in Australia. The results showed that spatial interactions exist and that they sharply decline with distance. Further, the authors argued that the spatial interactions between regions magnify local responses to national economic phenomena, which explains the observed disparities among Australian regions since the 1990s.

Moreover, López‐Bazo et al. (2002) focused on the spatial interactions across Spanish labor markets for the years 1985 and 1997. Between this time period, the Spanish economy underwent critical economic reforms (e.g. market liberalization, integration into the EU, labor market deregulation). The outcomes showed that spatial interactions increased in magnitude between 1985 and 1997. The authors concluded that the processes of economic integration and labor market deregulations have instigated regional cluster formation.

Likewise, Patuelli et al. (2012) investigated the spatial interactions in the German labor markets between 1996 and 2004. This is the period when the effects of reunification were fully realized, and before the labor market reforms. The findings showed that on average the unemployment rates are to a large degree persistent and that the labor markets have a clear spatial structure.

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of a shock to a given region in Great Britain and the U.S. The regional employment change in a given region was found to impact the regional unemployment rate of the given region and the unemployment rate of neighboring regions. Also, the outcomes showed that the spatial spillovers were highly localized.

Finally, Burgess and Profit (2001) investigated the effect of labor market conditions on neighboring regions in the UK. The outcomes showed that high unemployment in a certain region is expected to raise the unemployment rate in neighboring regions. Also, employment increases in a certain region are likely to reduce unemployment in neighboring regions.

In the context of the EU enlargement and spatial interactions, previous studies mostly focused on migration flows, wage and income convergence and investment decisions. For instance, Breuss et al. (2003) examined the degree of foreign direct investment (FDI) shifts from the old to the new EU member states as a result of Structural and Cohesion Funds (SCF). The SCF were designed to address the disparities among member states. The enlargement led to a reallocation of the SCF from the EU15 to the new member states. The authors accounted for spatial interactions in inward FDI stocks across EU host countries. The results showed that neighbors of SCF expenditure winners gained in FDI stocks as well, whereas SCF losers experienced a decline in inward FDI stocks.

Moreover, Sardadvar and Rocha-Aksis (2016) aimed to explore the drivers of interregional migration within the EU as a result of the enlargements of 2004 and 2007. The authors accounted for spatial interactions because migration critically depends on ties between regions. The outcomes indicated that net-migration at the regional level is positively related to an increase in the average disposable household income, gross regional product growth, population density and human capital endowment, and negatively related to an increase in the regional unemployment rate. Also, the outcomes showed that intra-EU migration patterns were strongly shaped by distance.

Furthermore, Büttner (2007) examined the wage flexibility of regional labor markets in the new member states compared to the EU15. The author accounted for spatial interactions effects across the labor markets. The results showed that wages are more sensitive to changes in unemployment rates in the new member states compared to the EU15. This indicates that the because of the higher wage flexibility, the new member states were in a better position to respond to shocks in the labor markets.

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showed that the convergence in income levels was quite slow. In particular, the results showed that, prior to the enlargement, mainly the metropolitan areas experienced a large increase in income levels whereas income levels in rural areas remained approximately constant in the new member states. This implies that regional disparities grew in the EU25. The authors also found evidence in favor of significant spatial interactions and concluded that it might be inefficient to support only the poor regions, as the dynamics of the rich metropolitan areas will interact with the poor rural areas.

Lastly, Egger et al. (2008) estimated the attitude towards integration of the EU15 countries on the accession countries and the spatial clustering of the attitude across the EU15 citizens. Spatial interactions appear to be important, as opinions and attitudes are formed in a geographically clustered way. The estimated spatial spillovers showed that attitudes have a spatial dimension.

To sum up, the importance of spatial interactions across labor markets has been repeatedly emphasized by past studies, indicating that region are not isolated entities, but instead related to each other. Additionally, the aforementioned papers indicate that spatial interactions exist with respect to investment and income levels in the enlarged EU. The unique historic event of the enlargement significantly transformed the labor markets throughout the continent. These transformations reflect a spatial dimension, as the enlargement, for instance, facilitated trans-frontier co-operation across the regional labor markets. Moreover, it increased competition due to the access of new markets. Also, the increased earning differences in the EU signify a change in the labor markets. Therefore, it is interesting to explore the extent to which the enlargement modified the spatial interactions. As this is not previously investigated, this study will contribute to the literature.

III. METHODOLOGY

The general model to estimate the evolution of regional unemployment rates is as follows:

𝛥𝑢𝑖𝑡 = 𝛽0+ 𝛽1𝛥𝑒𝑖𝑡+ 𝛽2𝑎𝑖𝑡+ 𝜇𝑖+ 𝜑𝑡+ 𝜀𝑖𝑡 (1)

𝑖 = 1, … . , 𝑁; 𝑡 = 2, … . , 𝑇; 𝜀𝑖𝑡 ∼ 𝛮(0, 𝜎2)

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time 𝑡 − 1 and 𝛥𝑒_𝑖𝑡 denotes the change in the regional employment rate of region 𝑖 between time 𝑡 and time 𝑡 − 1. In addition, 𝑎𝑖𝑡 denotes the economic activity rate. The economic activity rate concerns the activity of producing, buying and selling products and services, which is used as a control variable to capture supply and demand factors in the labor markets. Region fixed effects and time fixed effects are captured by 𝜇_𝑖 and 𝜑_𝑡, respectively. Finally, 𝜀_𝑖𝑡 are independently and identically distributed error terms for all 𝑖 with zero mean and variance 𝜎2_.

The previous section emphasized the importance of spatial interactions in labor markets. In particular, Section II indicated that neglecting spatial interactions between neighboring regions will lead to biased regression results. This implies that equation (1) is misspecified and therefore, the next step is to include spatial interactions. The basic idea of spatial econometric models is that the standard OLS model is extended to include a spatial weight matrix. The spatial weight matrix 𝑊 captures the spatial arrangement of the units in the sample, i.e. the various directions of interactions. This is an 𝑁 × 𝑁 matrix of spatial weights, where element 𝑤𝑖𝑗 summarizes the interaction between regions 𝑖 and 𝑗.

𝑊 = (

𝑤₁₁ . 𝑤_1𝑁

. . .

𝑤𝑁1 . 𝑤𝑁𝑁 )

The row elements of the 𝑊 matrix display the impact of a given region by all other regions, while the column elements of the 𝑊 matrix display the impact of a given region on all the other regions (Elhorst, 2014). The most commonly 𝑊 matrix used is the 𝑝 - order binary contiguity matrix, whereby the element 𝑤_𝑖𝑗 = 1 - before being row-standardized - if regions 𝑖 and 𝑗 share a border and 𝑤𝑖𝑗 = 0 otherwise (if 𝑝 = 1 the first-order neighbors are considered, if 𝑝 = 2 first-order and second-order neighbors are considered and so on). Contiguity matrices reflect a restrictive distance measure, because it is assumed that interactions between regions only occur when regions share borders. However, it is possible that spatial interactions continue (Elhorst and Vega, 2013). For this reasoning, this study employs the inverse distance matrix based on latitude and longitude data and the binary contiguity matrix is used as a robustness check. Τhe weights are set equal to 0 at the diagonal of the matrix as a region cannot impact itself.

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explanatory variables or spatially lagged error terms. Table 1 displays the types of spatial econometric specifications with their corresponding spatially lagged variables. Where 𝑊𝑌 denotes the spatially lagged dependent variable, 𝑊𝑋 denotes the spatially lagged explanatory variables and 𝑊𝑢 denotes the spatially lagged error terms.

Table 1

Spatial econometric models.

Model Spatial effects

Spatial autoregressive model (SAR) 𝑊𝑌

Spatial error model (SEM) 𝑊𝑢

Spatial lag of X model (SLX) 𝑊𝑋

Spatial autoregressive combined model (SAC) 𝑊𝑌, 𝑊𝑢

Spatial Durbin model (SDM) 𝑊𝑌, 𝑊𝑋

Spatial Durbin error model (SDEM) 𝑊𝑋, 𝑊𝑢

General nesting model (GNS) 𝑊𝑌, 𝑊𝑋, 𝑊𝑢

The spatially lagged dependent variable captures the effect of the dependent variable of unit 𝑖 on the dependent variable of unit 𝑗 and vice versa, given that 𝑖 ≠ 𝑗. The spatially lagged explanatory variables capture the effect of the explanatory variables of unit 𝑖 on the dependent variable of unit 𝑗. The spatially lagged error terms capture the effect of the error term of unit 𝑖 on the error terms of unit 𝑗 and vice versa. It is important to note that the spillovers of the specifications that include a 𝑊𝑋 term - and not a 𝑊𝑌 term – are local in nature, as the spillover effects fall only on the regions for which the elements in 𝑊 are nonzero. The spillovers of specifications that include a 𝑊𝑌 term are global in nature, as the spillover effects fall on every region (even when the element in the 𝑊 matrix is zero) (Elhorst, 2014). Hence, the SEM model does not capture any spillover effects (Elhorst, 2014). The derivations behind this result are shown in Appendix A and are taken from Elhorst (2014).

By incorporating the spatial terms, equation (1) is augmented as follows:

𝛥𝑢𝑖𝑡 = 𝛽0+ 𝛽1𝛥𝑒𝑖𝑡+ 𝛽2∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 + 𝜌 ∑ 𝑤𝑖𝑗 𝛮 𝑗=1 𝛥𝑢𝑗𝑡+ 𝛽3𝑎𝑖𝑡+ 𝜇𝑖+ 𝜑𝑡 + 𝜐𝑖𝑡 (2) 𝜐𝑖𝑡 = 𝜆 ∑ 𝑤𝑖𝑗𝜐𝑗𝑡 𝛮 𝑗=1 + 𝜀𝑖𝑡 𝑖 = 1, … . , 𝑁; 𝑡 = 2, … . , 𝑇; 𝜀𝑖𝑡 ∼ 𝛮(0, 𝜎2)

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The autoregressive 𝜌 parameter measures the effect of a change in the unemployment rate of region 𝑖 on the change in the unemployment rate of region 𝑗 and vice versa. Moreover, the 𝛽₂ coefficient measures the effect of a change in the employment rate of region 𝑖 on the change in the unemployment rate of region 𝑗. It is important to highlight that the spatially lagged dependent variable covers all forms of spillovers, whereas the spatially lagged independent variable is restricted to those spatial effects that occur via the regional employment. In addition, the 𝜆 coefficient measures the effect of the error term of region 𝑖 on the error term of region 𝑗 and vice versa. Lastly, the effect of economic activity is captured by 𝛽3.

The next step is to include common factors in the estimation. This appears to be critical, as previous literature concluded that the absence of common shocks in the estimation can bias the outcomes. Thus, I proceed with an approach that simultaneously deals with both spatial interactions and common factors, as was proposed by Vega and Elhorst (2016). The same procedure is followed as Vega and Elhorst (2016). That is, the change in the national unemployment rate of country 𝑐 at time 𝑡 is added to the regression estimations, which is denoted by 𝛥𝑢_𝑐𝑡. This variable captures common shocks, such as domestic business cycle effects, that operate within countries. The authors pointed out that time fixed effects should not be included as they are highly correlated with the (changes in the) national unemployment rates and hence, only region fixed effects are included. The resulting empirical model takes the following form:

𝛥𝑢𝑖𝑡 = 𝛽0+ 𝛽1𝛥𝑒𝑖𝑡+ 𝛽2∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 + 𝜌 ∑ 𝑤𝑖𝑗 𝛮 𝑗=1 𝛥𝑢𝑗𝑡+ 𝛽3𝑎𝑖𝑡 + 𝛿𝛥𝑢𝑐𝑡+ 𝜇𝑖 + 𝜐𝑖𝑡 (3) 𝜐𝑖𝑡 = 𝜆 ∑ 𝑤𝑖𝑗𝜐𝑗𝑡 𝛮 𝑗=1 + 𝜀𝑖𝑡 𝑖 = 1, … . , 𝑁; 𝑡 = 2, … . , 𝑇; 𝜀𝑖𝑡 ∼ 𝛮(0, 𝜎2)

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interactions before and after the EU enlargement, equation (3) is extended to include a dummy variable that takes the value 1 if time 𝑡 > 2003 and 0 otherwise. This time dummy variable is denoted by 𝑇𝐷_𝑖𝑡 and interacted with the change in the employment rate (𝛽₁) and the spatially lagged independent variable (𝛽2). Hence, the following equation is estimated:

𝛥𝑢𝑖𝑡 = 𝛽0+ 𝛽1𝛥𝑒𝑖𝑡+ 𝛽2∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 + 𝜌 ∑ 𝑤𝑖𝑗 𝛮 𝑗=1 𝛥𝑢𝑗𝑡+ 𝛽3𝑎𝑖𝑡+ 𝛽4𝛥𝑒𝑖𝑡 ∗ 𝑇𝐷𝑖𝑡+ 𝛽5∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 ∗ 𝑇𝐷𝑖𝑡+ 𝛿𝛥𝑢𝑐𝑡+ 𝜇𝑖+ 𝜐𝑖𝑡 (4) 𝜐𝑖𝑡 = 𝜆 ∑ 𝑤𝑖𝑗𝜐𝑗𝑡 𝛮 𝑗=1 + 𝜀𝑖𝑡 𝑖 = 1, … . , 𝑁; 𝑡 = 2, … . , 𝑇; 𝜀𝑖𝑡 ∼ 𝛮(0, 𝜎2)

An alternative approach to estimate the effect of the Eastern and Western integration is to include a dummy variable that takes the value 1 if region 𝑖 is located in Central or Eastern Europe and 0 otherwise. The CEE countries are the Czech Republic, Hungary, Poland, Romania and Slovakia. The dummy variable is denoted by 𝐶𝐸𝐸𝑖𝑡 and the resulting empirical model takes the following form:

𝛥𝑢𝑖𝑡 = 𝛽0+ 𝛽1𝛥𝑒𝑖𝑡+ 𝛽2∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 + 𝜌 ∑ 𝑤𝑖𝑗 𝛮 𝑗=1 𝛥𝑢𝑗𝑡+ 𝛽3𝑎𝑖𝑡+ 𝛽4𝛥𝑒𝑖𝑡 ∗ 𝐶𝐸𝐸𝑖𝑡 + 𝛽5∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 ∗ 𝐶𝐸𝐸𝑖𝑡+ 𝛿𝛥𝑢𝑐𝑡+ 𝜇𝑖+ 𝜐𝑖𝑡 (5) 𝜐𝑖𝑡 = 𝜆 ∑ 𝑤𝑖𝑗𝜐𝑗𝑡 𝛮 𝑗=1 + 𝜀𝑖𝑡 𝑖 = 1, … . , 𝑁; 𝑡 = 2, … . , 𝑇; 𝜀𝑖𝑡 ∼ 𝛮(0, 𝜎2)

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variable (𝛽₁) and the spatially lagged independent variable (𝛽₂). The regions that have above-median levels of high education are referred to as high-skilled regions because a relatively large share of the population has completed tertiary education. This approach is repeated for low-skilled labor and middle-skilled labor. It is important to highlight that job opportunities for high-skilled and low-skilled workers are likely to have expanded both in the area of residence and in adjacent areas and therefore, this approach considers the change in the local spillovers only, as global spillovers are difficult to justify. Hence, the following equation is estimated: 𝛥𝑢𝑖𝑡 = 𝛽0+ 𝛽1𝛥𝑒𝑖𝑡+ 𝛽2∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 + 𝜌 ∑ 𝑤𝑖𝑗 𝛮 𝑗=1 𝛥𝑢𝑗𝑡+ 𝛽3𝑎𝑖𝑡+ 𝛽4𝛥𝑒𝑖𝑡 ∗ 𝐻𝐷𝑖𝑡+ 𝛽5∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 ∗ 𝐻𝐷𝑖𝑡+ 𝛿𝛥𝑢𝑐𝑡+ 𝜇𝑖+ 𝜐𝑖𝑡 (6) 𝜐𝑖𝑡 = 𝜆 ∑ 𝑤𝑖𝑗𝜐𝑗𝑡 𝛮 𝑗=1 + 𝜀𝑖𝑡 𝑖 = 1, … . , 𝑁; 𝑡 = 2, … . , 𝑇; 𝜀𝑖𝑡 ∼ 𝛮(0, 𝜎2)

It is expected that the interaction terms are significantly negative in equation (6), implying that high-skilled workers – captured by the level of educational attainment – induce larger spatial interaction effects and decrease the regional unemployment rates. The same is expected for low-skilled workers and the opposite for middle-skilled workers.

IV. DATA

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unemployment rates of the capital region and three adjacent regions of Germany. From observing the figure, it is apparent that the movements have been quite similar across the regions. The 2003-05 labor market reforms stimulated the decrease in the unemployment rates after 2004, giving rise to the well-known “labor market miracle” of Germany (Burda and Hunt, 2011). Albeit less clear, regarding the regions in France, comparable trends are observed in Fig. 4 indicating that neighboring regions report analogous unemployment rates and movements to a substantial degree. These similarities in temporal patterns are also observed in the UK and Italy, as can be seen in Appendix C.

Fig. 3. Unemployment rate in capital region and adjacent regions of Germany. Source: Eurostat (2018). Own presentation.

Fig. 4. Unemployment rate in capital region and adjacent regions of France. Source: Eurostat (2018). Own presentation.

5,00 10,00 15,00 20,00 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 U N E M PL O Y M E N T I N G E R M A N R E G I O N S Berlin Brandenburg Mecklenburg-Vorpommern Sachsen-Anhalt 5,00 7,00 9,00 11,00 13,00 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 U N E M PL O Y M E N T I N FR E N C H R E G I O N S

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Fig. 5 shows the unemployment movements of cross-border regions between CEE and Western Europe. Regarding the German-Polish border, the figure indicates that the regions report analogous unemployment trends. This result points towards the presence of spatial interactions across the border regions over the entire time-span. Similar results emerge from the German-Czech border regions and the Austrian-Czech border regions in Appendix C. Hence, the figures indicate strong cross-border clusters between CEE and Western Europe.

Fig. 5. Unemployment rate in the German-Polish border regions. Source: Eurostat (2018). Own presentation.

V. RESULTS V. A. Spatial interactions and common factors

To begin with, the OLS specification of equation (1) is estimated. The results are presented in the first column of Table 2. The outcomes show that the explanatory variables are significant at the 1% level. The 𝛽₁ coefficient indicates that a one percentage point increase in the regional unemployment rate is expected to decrease the regional unemployment rate by 0.643 percentage points, ceteris paribus. Moreover, the 𝛽3 coefficient indicates that a one percentage point increase in regional economic activity is expected to increase the unemployment rate by 0.166 percentage points, ceteris paribus. This finding may be explained by the reasoning that an increase in economic activity, i.e. an economic boom, generates higher labor force participation, leading to an increase in the unemployment rate.

The next step is to estimate the specifications of Table 1 with the corresponding spatial interaction effects. The results are presented in Table 2, where each column corresponds to a different spatial econometric specification. The SAR model in column (2) reports a

5,00 10,00 15,00 20,00 25,00 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 U N E M PL O Y M E N T I N G E R M A N - PO L I S H B O R D E R R E G I O N S

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significantly positive autoregressive parameter (𝜌). This implies that an unemployment increase in a given region is expected to substantially increase the unemployment rate of nearby regions and vice versa. This finding is in accordance with Section II, where it was concluded that adjacent regions share analogous unemployment rates. In other words, the spatially lagged dependent variable of the SAR model suggests that regional unemployment rates directly impact each other. The resulting global spillovers suggest that a change in one of the independent variables of a particular region influences the regional unemployment in all regions, including regions that the 𝑊 matrix perceives as unconnected. The SEM model in column (3) reports a significantly positive 𝜆 coefficient. This implies that the error term of a given region positively affects the error term of nearby regions and vice versa. Furthermore, the SLX model in column (4) shows that the coefficient of the spatially lagged independent variable is significantly negative. This suggests that an increase in the employment rate of a given region is predicted to decrease the unemployment rate, more than proportionally, of the nearby regions. These effects are local because the spillovers only fall on the spatial regions for which the elements of the 𝑊 matrix are non-zero. The negative 𝛽₂ coefficient signifies the presence of positive local spillover effects.

The general econometric specifications, which include multiple spatial interaction effects, are consistent with the simple spatial econometric specifications which include only one spatial interaction effect. Precisely, the general specifications report significant spatial interaction terms with robust signs in the remaining columns.

Table 2

Model comparison of spatial interactions.

OLS SAR SEM SLX SAC SDM SDEM GNS

𝛽1 -0.643 -0.560 -0.595 -0.549 -0.555 -0.540 -0.554 -0.534 (0.03)*** (0.03)*** (0.03)*** (0.01)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** 𝛽2 -1.060 -0.244 -1.342 -0.450 (0.08)*** (0.10)** (0.22)*** (0.13)*** 𝜌 0.908 0.848 0.888 0.778 (0.01)*** (0.02)*** (0.01)*** (0.03)*** 𝛽3 0.166 0.125 0.164 0.125 0.140 0.117 0.150 -0.130 (0.02)*** (0.02)*** (0.02)*** (0.01)*** (0.01)*** (0.02)*** (0.02)*** (0.02)*** 𝜆 0.919 0.820 2.243 0.834 (0.01)*** (0.02)*** (0.02)*** (0.02)*** R-squared 0.563 0.313 0.490 0.586 0.383 0.320 0.547 0.402 Log- likelihood - -4879.92 -4921.13 - -4803.66 -4874.46 -4698.61 -4793.07 N 3587 3587 3587 3587 3587 3587 3587 3587

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To continue, equation (3) is estimated, which captures spatial interactions and common factors simultaneously, as both effects are expected to occur in the applied setting. The estimation results of equation (3) are presented in Table 3. Several important insights emerge from this. Firstly, the SDM, SDEM and GNS models report a significantly positive 𝛽2 coefficient, whereas the SLX model reports a significantly negative 𝛽₂ coefficient. Hence, in contrast to Table 2, the majority of specifications suggest a positive relationship between regional unemployment rates and the spatially lagged independent variable. More precisely, this indicates that an increase in the employment rate of a given region is predicted to increase the regional unemployment rate of nearby regions. This suggests some degree of regional competition. The following example is provided to clarify the regional competition effect. Consider a given region that attracts high-skilled workers due to better job opportunities because of e.g. a research institution. Therefore, high-skilled workers will locate from the nearby regions to the given region. This will lead to an employment increase in the given region. However, this will increase the unemployment rate in the nearby regions due to the negative side effects. Specifically, one reason is that, due to higher earnings, high-skilled workers have higher savings rates and are more likely to be investors than low-skilled workers (Abella, 2006). Moreover, human capital is an important driver of economic growth in developed (regional) economies, as many sectors are reliant on human capital, such as the high-tech and engineering sectors (Pepper and Nguyen, 2016). Therefore, the disadvantage of losing high-skilled labor is clearly present.

Secondly, the SAR and SAC specifications suggest that the effects of the spatially lagged dependent variable are insignificant. Whereas the SDM and GNS specifications show that the effects of the lagged dependent variable are significantly positive. Thus, the positive spatial correlation drops when common factors are added to the regression. This outcome draws attention to the importance of domestic business cycle effects, implying that the positive effect of the spatially lagged independent variable operates to a considerable degree within countries. Similarly, the 𝜆 coefficient and 𝛽₃ coefficient decreased substantially in magnitude.

At this point, it is important to observe that the empirical model does not include any regional structure characteristics. In order to capture these effects, the share of the manufacturing sector is added to the estimation, defined as the number of people working in the manufacturing sector divided by the total active population of region 𝑖 at time 𝑡.5 _These

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data are drawn from Eurostat. Table 4 presents the outcomes. The 𝛽₆ coefficient on the manufacturing share is insignificant in all estimations and hence, this variable is not included in the remaining section.

Altogether, the estimation results indicate the presence of spatial interaction effects. Specifically, when common factors are added, the majority of the model specifications report a significantly positive spatially lagged independent variable, implying that an increase in the employment rate of a given region is predicted to increase the unemployment rate of the nearby regions. This suggests a regional competition effect across the labor markets. Moreover, the SAR and SAC specifications report an insignificant spatially lagged dependent variable, whereas the SDM and GNS models report a significantly positive one. Therefore, the SDM and GNS specifications indicate that an increase in the unemployment rate of a given region is predicted to increase the unemployment of other regions, with a stronger effect on the neighboring regions. The significant spatial error term indicates spillovers among the error terms.

Table 3

Model comparison of spatial interactions with common factors.

OLS SAR SEM SLX SAC SDM SDEM GNS

𝛽1 -0.339 -0.339 -0.362 -0.347 -0.365 -0.363 -0.371 -0.367 (0.02)*** (0.02)*** (0.02)*** (0.02)*** (0.02)*** (0.02)*** (0.02)*** (0.02)*** 𝛽2 -0.165 0.480 0.308 0.485 (0.04)*** (0.08)*** (0.11)*** (0.09)*** 𝜌 0.019 -0.086 0.337 0.321 (0.03) (0.08) (0.06)*** (0.07)*** 𝛽3 0.045 0.046 0.063 0.042 0.065 0.117 0.068 0.049 (0.01)*** (0.02)*** (0.01)*** (0.01)*** (0.01)*** (0.02)*** (0.01)*** (0.01)*** 𝛿 0.735 0.727 0.712 0.782 0.732 0.722 0.760 0.724 (0.02)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** 𝜆 0.529 0.592 0.615 0.192 (0.08)*** (0.10)*** (0.11)*** (0.16) R-squared 0.727 0.728 0.727 0.729 0.727 0.732 0.726 0.731 Log- likelihood - -4270.30 -4253.80 - -4252.64 -4232.95 -4241.46 -4231.98 N 3587 3587 3587 3587 3587 3587 3587 3587

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Table 4

Model comparison of spatial interactions with common factors: controlling for the manufacturing share.

OLS SAR SEM SLX SAC SDM SDEM GNS

𝛽1 -0.375 -0.375 -0.409 -0.388 -0.414 -0.415 -0.425 -0.419 (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** 𝛽2 0.191 0.588 0.429 0.594 (0.04)*** (0.09)*** (0.12)*** (0.10)*** 𝜌 0.012 -0.146 0.406 0.375 (0.03) (0.11) (0.06)*** (0.08)*** 𝛽3 0.034 0.034 0.054 0.031 0.058 0.033 0.062 0.042 (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** 𝛽6 -0.003 -0.002 -0.007 -0.004 -0.009 -0.000 -0.011 -0.004 (0.01) (0.01) (0.01) (0.01) (0.08) (0.01) (0.01) (0.01) 𝛿 0.713 0.707 0.682 0.764 0.713 0.692 0.740 0.697 (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.04)*** (0.03)*** 𝜆 0.597 0.682 0.698 0.259 (0.07)*** (0.09)*** (0.08)*** (0.20) R-squared 0.750 0.750 0.745 0.752 0.748 0.755 0.750 0.753 Log- likelihood - -3290.20 -3269.57 - -3267.25 -3246.74 -3253.26 -3245.20 N 2704 2704 2704 2704 2704 2704 2704 2704

Notes: (i) cluster-robust standard errors are in parentheses. (ii) *** significant at 1%.

V. B. The EU Enlargement Effect

In order to investigate the impact of the EU enlargement, equation (4) is estimated and the results are presented in Table 5. Consistent with the previous results, the explanatory variables are significant at the 1% level with constant signs. Moreover, the majority of specifications indicate a positive relationship between regional unemployment rates and the spatially lagged independent variable. The positive 𝛽2 coefficient signifies regional competition across the labor markets. The 𝛽₄ coefficient is insignificant in all specifications. Hence, the effect of a change in the employment rate of a particular region on the change in the unemployment rate of the same particular region does not change after the EU enlargement.

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rate of a given region on the change in the unemployment in nearby regions is larger after the enlargement. In other words, an increase in the employment rate of a given region is expected to decrease the unemployment rate of nearby regions to a larger degree. Hence, the majority of the specifications suggest that the regional competition effect is weaker as a result of the enlargement. One reasoning for this finding is that the European Commission adopted regional policies to address regional disparities across the enlarged EU (Petrakos, 2013), such as the Structural and Cohesion Funds (SCF). The SCF were designed to compensate for the effects of increasing competition, by providing less favored regions with the means to improve social and technical infrastructure, education and the competitiveness of industry (Petrakos, 2013). Moreover, the enlargement facilitated significant opportunities for trans-frontier co-operation in the form of joint ventures, subcontracting, free trade areas, scientific and technological co-operation, local or regional policy coordination as well as an expansion of cross-border transportation and communication infrastructure (Petrakos, 2013). These processes probably weakened the regional competition effect and thereby the negative side effects.

Similarly to Table 3, the 𝜌 parameter varies in its significance. The SDM and GNS report significantly positive coefficients, implying that an increase in the unemployment rate of a given region is expected to increase the unemployment rate of nearby regions.6 However, the SAR and SAC report insignificant coefficients. Finally, the interaction effects among the error terms are significantly positive, except for the GNS specification.

The next step is to determine which model gives the best performance. It is clear-cut that the OLS estimation is not considered as the spatial interaction effects appear significant and hence, the spatial econometric models are a useful and necessary extension to the OLS estimation. Throughout this subsection, the likelihood ratio (LR) is used to test the various model specifications against each other. The formula of this test is as follows; two times the difference between the value of the log-likelihood function in the unrestricted model and the value of the log-likelihood value in the restricted model 2 ∗ (ln 𝐿𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑 − ln 𝐿𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑). The test statistic follows a χ2 _{- distribution with the degrees of freedom} equal to the restrictions imposed. When testing whether GNS outperforms SDM, the LR test gives a value of (-4226.78 + 4228.54) ∗ 2 = 3.52. The null hypothesis states that the unrestricted model is not statistically different from the restricted model, i.e. the unrestricted model does not outperform the restricted model. As the test statistic is lower than the critical 6 _{Note again that the spillovers of the spatially lagged dependent variable are global in nature. Hence, regions}

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value of 3.84, the null hypothesis cannot be rejected. Following the same procedure, the outcomes show that the GNS model outperforms the SDEM model and the SAC model.7 Since the SDM and SDEM include an equal number of parameters, one cannot perform the LR test. The same holds for the SAC model. Moreover, the LR tests showed that SDM fits the data better than the SAR model and the SDEM model fits the data better than the SEM model.8 The SDM and SDEM models provide evidence that spatial effects are present beyond the spatially lagged independent variable, which in turn, indicates that the SLX model is not optimal.

Table 5

Model comparison of spatial interactions with common factors: Effect of EU enlargement (time dummy).

OLS SAR SEM SLX SAC SDM SDEM GNS

𝛽1 -0.338 -0.339 -0.361 -0.362 -0.362 -0.379 -0.389 -0.385 (0.03)*** (0.03)*** (0.04)*** (0.03)*** (0.04)*** (0.04)*** (0.04)*** (0.04)*** 𝛽2 -0.351 0.678 0.700 0.745 (0.10)*** (0.12)*** (0.18)*** (0.15)*** 𝜌 0.019 -0.086 0.339 0.311 (0.03) (0.07) (0.06)*** (0.07)*** 𝛽3 0.045 0.046 0.063 0.049 0.065 0.050 0.075 0.060 (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.03)*** (0.01)*** 𝛽4 -0.001 -0.000 -0.002 0.017 -0.003 -0.018 -0.021 0.020 (0.03) (0.03) (0.04) (0.04) (0.04) (0.04) (0.05) (0.04) 𝛽5 -0.210 -0.221 -0.480 -0.298 (0.09)** (0.21)** (0.18)*** (0.12)** 𝛿 0.735 0.727 0.712 0.782 0.732 0.721 0.759 0.725 (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.04)*** (0.03)*** (0.03)*** (0.03)*** 𝜆 0.529 0.592 0.610 0.256 (0.08)*** (0.10)*** (0.08)*** (0.15)* R-squared 0.728 0.728 0.727 0.730 0.727 0.732 0.727 0.731 Log- likelihood - -4270.30 -4253.80 - -4252.63 -4228.54 -4234.59 -4226.78 N 3587 3587 3587 3587 3587 3587 3587 3587

Notes: (i) cluster-robust standard errors are in parentheses.

(ii) *** significant at 1% ** significant at 5% * significant at 10%.

An alternative approach of estimating the integration with CEE is to estimate the effect of the CEE countries on the spatial interactions. The estimation results of equation (5) are presented in Table 6. These results are very similar to Table 5 with respect to the explanatory variables, the 𝜌 coefficient and the 𝜆 coefficient. Regarding the spatially lagged independent variable, the 𝛽2 coefficient is significantly positive in all models, whereas in

7 _{The LR test for the GNS vs. SDEM model test gives (-4226.78+4234.59)*2= 15.62. The LR test for the GNS}

vs. the SAC model gives (-4226.78+4252.63)*2=51.70. In both cases, the null hypothesis is rejected as the value is higher than the critical value of 3.84.

8 _{The LR test for the SDM vs. SAR model gives (-4228.52+4270.30)*2=83.56. The LR test for the SDEM vs.}

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Table 5, the SLX model reported a negative coefficient. This result reflects the presence of regional competition across the labor markets. As before, the 𝛽₄ coefficient is insignificant in the specifications, indicating that the effect of a change in the employment rate of a particular region on the change in the unemployment rate of the same region is not statistically different for the sample of the CEE countries. The SLX, SDEM and GNS specifications report an insignificant 𝛽₅ coefficient, implying that the positive effect of a change in the employment rate of a given region on the change in the unemployment rate of nearby regions in CEE is not statistically different from Western Europe. Hence, the hypothesis of equivalent spatial effects of the spatially lagged independent variable between CEE and Western Europe cannot be rejected. In contrast, the SDM model reports a significantly positive 𝛽₅ coefficient. However, as the majority of the specifications indicate an insignificant coefficient, this outcome cannot be interpreted.

Following the same procedure as above, the next step is to specify which model has the most superior fit of Table 6. The LR tests showed that the GNS model outperforms the SDEM model and the SAC model.9 _{In line with the previous results, the test indicates that the} GNS model does not fit the data better than the SDM model.10 _{This finding is not surprising,} as the GNS model is often overfitted. The parameters of the GNS model can be estimated, but they have the tendency either to blow each other up or to become insignificant, providing support in favor of simpler models with less spatial interaction effects, especially the SDM and SDEM specifications (Elhorst and Vega, 2013). Moreover, the LR test provided evidence in favor of the more general models against the simple models.11 Again, the SLX specification does not report a log-likelihood value, but the SDM and SDEM models provide evidence that spatial effects are present beyond the spatially lagged independent variable. This indicates that the SLX model is not optimal.

To briefly summarize this subsection, the analysis suggests that an increase in the employment rate of a given region is expected to increase the unemployment rate of nearby regions to a smaller degree, as a result of the enlargement. This indicates a weaker regional competition effect after the EU enlargement. Furthermore, the outcomes show that the effect of the spatially lagged independent variable is not different between CEE and Western Europe. In addition, both estimation regressions indicate, based on the LR test, that the SDM 9 _{The LR test for the GNS vs. SDEM model gives (-4225.89+4236.92)*2=22.06. The LR test for the GNS vs.}

SAC model gives (-4225.89+4248.00)*2=44.22. In both cases, the null hypothesis is rejected as the values are higher than the critical value of 3.84.

10 _{The LR test for the GNS vs. SDM model gives (-4225.89+4226.69)*2=1.60.}

11 _{The LR test for the SDM vs. SAR model gives (-4226.69+4266.06)*2=78.74. The LR test for the SDEM vs.}

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model provides the most superior fit to the data. This outcome suggests the presence of both global and local spillover effects across the regional labor markets.

Table 6

Model comparison of spatial interactions with common factors: Effect of EU enlargement (CEE countries dummy).

OLS SAR SEM SLX SAC SDM SDEM GNS

𝛽1 -0.326 -0.325 -0.347 -0.333 -0.349 -0.346 -0.355 -0.349 (0.02)*** (0.02)*** (0.03)*** (0.02)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** 𝛽2 0.155 0.474 0.292 0.488 (0.05)*** (0.09)*** (0.11)*** (0.09)*** 𝜌 0.028 -0.069 0.351 0.342 (0.03) (0.07) (0.06)*** (0.06)*** 𝛽3 0.047 0.048 0.064 0.044 0.066 0.043 0.068 0.051 (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.03)*** (0.01)*** 𝛽4 -0.060 -0.062 -0.071 -0.060 -0.069 -0.081 -0.073 -0.081 (0.04) (0.04) (0.04) (0.05) (0.04) (0.05)* (0.05) (0.05)* 𝛽5 0.024 -0.221 0.042 0.036 (0.09) (0.21)** (0.10) (0.09) 𝛿 0.733 0.721 0.708 0.778 0.724 0.714 0.754 0.716 (0.02)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** 𝜆 0.539 0.590 0.622 0.178 (0.07)*** (0.10)*** (0.10)*** (0.14) R-squared 0.728 0.728 0.728 0.730 0.727 0.733 0.727 0.732 Log- likelihood - -4266.06 -4248.77 - -4248.00 -4226.69 -4236.92 -4225.89 N 3587 3587 3587 3587 3587 3587 3587 3587

Notes: (i) cluster-robust standard errors are in parentheses.

(ii) *** significant at 1% ** significant at 5% * significant at 10%.

V. C. Skill-level and spillovers

28

job creation ability.12 This, in turn, leads to increases in the employment rate, but not necessarily to decreases in the unemployment rate. Hence, the skill-level influences the structural features of the regional economy, thereby altering the effect of employment on unemployment. The insignificant 𝛽5 coefficient indicates that the effect of the spatially lagged independent variable (i.e. the local spillovers) is not different between high-skilled regions and non-high-skilled regions.

Table 8 presents the results regarding the effects of low-skilled regions. The 𝛽₄ coefficient is insignificant in all model specifications. This indicates that the positive impact of a change in the employment rate of a particular region on the unemployment rate of the same region is not statistically different between low-skilled regions and non-low-skilled regions. In other words, this means that an increase in the employment rate of a particular region is expected to decrease the unemployment rate of the same region, and that this effect is not statistically different compared to non-low-skilled regions. Again, the insignificant 𝛽₅ coefficient indicates that the effect of the spatially lagged independent variable (i.e. the local spillovers) is not different between low-skilled regions and non-low-skilled regions .

This analysis was repeated for middle-skilled regions and the results are presented in Appendix D. The outcomes are similar to Table 8. Precisely, the outcomes report insignificant 𝛽₄ and 𝛽₅ coefficients. The former indicates that an increase in the employment rate of a particular region is expected to decrease the unemployment rate of the same region, and that this effect is not statistically different compared to non-middle-skilled regions. Moreover the latter indicates that the effect of the spatially lagged independent variable (i.e. the local spillovers) is not different between middle-skilled regions and non-middle-skilled regions. Finally, with respect to the spatial interaction variables and control variables, this subsection presents qualitatively equivalent results as the previous subsections.

Altogether the results show that the local spillovers across high-skilled, middle-skilled and low-skilled labor markets do not differ. Precisely, the outcomes indicate that regions, characterized by a particular skill-level, do not modify the degree of local spillovers.

29

Table 7

Model comparison of spatial interaction with common factors: Effect of high-skilled regions.

OLS SAR SEM SLX SAC SDM SDEM GNS

𝛽1 -0.381 -0.382 -0.404 -0.394 -0.406 -0.408 -0.418 -0.415 (0.03)*** (0.03)*** (0.03)*** (0.02)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** 𝛽2 0.189 0.547 0.340 0.523 (0.04)*** (0.11)*** (0.12)*** (0.10)*** 𝜌 0.028 -0.071 0.343 0.329 (0.03) (0.07) (0.06)*** (0.06)*** 𝛽3 0.044 0.044 0.062 0.042 0.064 0.042 0.068 0.049 (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** 𝛽4 0.091 0.092 0.090 0.101 0.089 0.094 0.101 0.105 (0.03)*** (0.03)*** (0.03)*** (0.02)*** (0.03)*** (0.05)*** (0.04)*** (0.04)*** 𝛽5 -0.073 -0.133 -0.079 -0.090 (0.06) (0.12) (0.07) (0.07) 𝛿 0.735 0.721 0.711 0.778 0.727 0.718 0.756 0.719 (0.02)*** (0.03)*** (0.03)*** (0.02)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** 𝜆 0.523 0.580 0.621 0.180 (0.07)*** (0.10)*** (0.11)*** (0.15) R-squared 0.730 0.730 0.729 0.731 0.729 0.734 0.728 0.733 Log- likelihood - -4257.32 -4241.93 - -4241.12 -4220.36 -4229.42 -4219.05 N 3587 3587 3587 3587 3587 3587 3587 3587

Notes: (i) cluster-robust standard errors are in parentheses. (ii) *** significant at 1%.

Table 8

Model comparison of spatial interactions with common factors: Effect of low-skilled regions.

OLS SAR SEM SLX SAC SDM SDEM GNS

𝛽1 -0.362 -0.362 -0.382 -0.367 -0.384 -0.379 -0.392 -0.390 (0.02)*** (0.02)*** (0.03)*** (0.02)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** 𝛽2 0.143 0.400 0.309 0.477 (0.05)*** (0.08)*** (0.11)*** (0.08)*** 𝜌 0.018 -0.080 0.346 0.329 (0.03) (0.07) (0.06)*** (0.06)*** 𝛽3 0.048 0.048 0.064 0.046 0.066 0.053 0.068 0.050 (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** (0.01)*** 𝛽4 0.038 0.038 0.033 0.032 0.032 0.021 0.035 0.039 (0.03) (0.03) (0.03) (0.02) (0.03) (0.03) (0.11) (0.04) 𝛽5 0.049 0.149 -0.013 0.023 (0.06) (0.09) (0.07) (0.06) 𝛿 0.734 0.727 0.712 0.782 0.731 0.722 0.759 0.723 (0.02)*** (0.03)*** (0.03)*** (0.02)*** (0.03)*** (0.03)*** (0.03)*** (0.03)*** 𝜆 0.521 0.581 0.605 0.137 (0.08)*** (0.10)*** (0.11)*** (0.16) R-squared 0.728 0.728 0.727 0.730 0.727 0.733 0.727 0.732 Log- likelihood - -4268.29 -4252.36 - -4251.31 -4225.74 -4240.08 -4229.30 N 3587 3587 3587 3587 3587 3587 3587 3587

30 VI. ROBUSTNESS

VI. A. Alternative 𝑊 matrices

In order to test the sensitivity of the results regarding the EU enlargement, alternative 𝑊 matrices are introduced for the estimations. The previous section showed that the SDM specification provides the most superior fit to the data and hence, only the SDM specification is considered. The results are presented in Table 9. The first 𝑊 matrix, referred to as 𝑊𝐼𝐷2, is based on the inverse distance, where regions are considered as neighbors within the range of the ten closest regions. The second 𝑊 matrix, referred to as 𝑊𝐵𝐶, represents the 10th _order binary contiguity matrix. Panel A and Panel B correspond to estimation equations (4) and (5), respectively.

Comparing panel A to column (6) of Table 5, the results are as follows. Firstly, the key finding is that the 𝛽₅ coefficient remained significantly positive. This provides evidence in favor of the previous finding, i.e. an increase in the employment rate of a given region is expected to decrease the unemployment rate of nearby regions to a smaller degree after the EU enlargement. Secondly, the coefficients of the spatial interaction terms remained significant but decreased in magnitude. In particular, the 𝑊 matrix based on the inverse distance matrix suggests the largest spatial interaction effects, followed by the 𝑊 based on the inverse distance within a particular range and the binary contiguity matrix, respectively.

Comparing panel B to column (6) of Table 6, the results are as follows. Firstly, the 𝛽₅ coefficient is insignificant. This contrasts with the results of the SDM specification in Table 6 and therefore, it can be concluded that the effect of the spatially lagged independent variable is not different between CEE and Western Europe. Secondly, the coefficients of the spatial interaction terms remained significant but decreased again in magnitude. Moreover, the estimation using the binary contiguity matrix reports a significantly positive 𝛽₄ coefficient Nevertheless, as this coefficient varies in its significance, it cannot be interpreted. Finally, the signs and significance of these control variables are robust for both panels.

31

Table 9

SDM specification for alternative W matrices.

Panel A Panel B SDM (𝑊𝐼𝐷2) SDM (𝑊𝐵𝐶) SDM (𝑊𝐼𝐷2) SDM (𝑊𝐵𝐶) 𝛽1 -0.398 -0.369 -0.349 -0.333 (0.04)*** (0.04)*** (0.03)*** (0.02)*** 𝛽2 0.534 0.428 0.361 0.274 (0.08)*** (0.09)*** (0.06)*** (0.09)*** 𝜌 0.244 0.202 0.270 0.218 (0.05)*** (0.05)*** (0.05)*** (0.05)*** 𝛽3 0.054 0.050 0.046 0.042 (0.01)*** (0.01)*** (0.01)*** (0.01)*** 𝛽4 0.033 0.018 0.033 -0.096 (0.04) (0.04) (0.04) (0.04)** 𝛽5 -0.193 -0.155 0.110 0.132 (0.06)*** (0.07)** (0.08) (0.07)* 𝛿 0.724 0.727 0.710 0.718 (0.03)*** (0.03)*** (0.03)*** (0.03)*** R- squared 0.735 0.732 0.735 0.733 Log- likelihood -4215.87 -4245.10 -4212.75 -4239.57 N 3587 3587 3587 3587

Notes: (i) cluster-robust standard errors are in parentheses. (ii) *** significant at 1% ** significant at 5% * significant at 10%.

VI. B. SDM Dynamics

By adding dynamics to equation (5), the analysis becomes more generalized and flexible. Specifically, equation (5) is augmented as follows:

𝛥𝑢𝑖𝑡 = 𝛽0+ 𝛽1𝛥𝑒𝑖𝑡+ 𝛽2∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 + 𝜌 ∑ 𝑤𝑖𝑗 𝛮 𝑗=1 𝛥𝑢𝑗𝑡+ 𝛽3𝑎𝑖𝑡+ 𝛽4𝛥𝑒𝑖𝑡 ∗ 𝑇𝐷𝑖𝑡+ 𝛽5∑ 𝑤𝑖𝑗𝛥𝑒𝑗𝑡 𝑁 𝑗=1 ∗ 𝑇𝐷𝑖𝑡+ 𝛿𝛥𝑢𝑐𝑡+ 𝜂1𝛥𝑢𝑖𝑡−1 + 𝜂2∑ 𝑤𝑖𝑗 𝛮 𝑗=1 𝛥𝑢𝑗𝑡−1+ 𝜇𝑖+ 𝜐𝑖𝑡 (7) 𝜐𝑖𝑡 = 𝜆 ∑ 𝑤𝑖𝑗𝜐𝑗𝑡 𝛮 𝑗=1 + 𝜀𝑖𝑡 𝑖 = 1, … . , 𝑁; 𝑡 = 2, … . , 𝑇; 𝜀𝑖𝑡 ∼ 𝛮(0, 𝜎2)

where 𝜂₁ denotes the effect of dependent variable lagged in time and 𝜂₂ denotes the dependent variable lagged in both space and time. The outcomes are summarized in Table 10. The first column reports the results obtained using the inverse distance matrix, the second column corresponds to the inverse distance matrix within the range of ten neighbors and the third column corresponds to the 10th order binary contiguity matrix. The results are as follows.

32

region is predicted to decrease the unemployment rate of the same region in the subsequent period. The intuition of this outcome is built around the natural unemployment rate hypothesis, which describes movements of unemployment as fluctuations around a particular value, i.e. the natural rate of unemployment. Secondly, the (𝜂2) coefficient of the dependent variable lagged in both space and time is significantly positive. This suggests that an increase in the regional unemployment rate of a particular region is expected to increase the unemployment rate of nearby regions in the subsequent period.13 This result is consistent with the observed persistence in unemployment clusters, as outlined in Section II. The findings indicate that the dynamic SDM outperforms its non-dynamic counterpart, as the coefficients of the dynamic variables are significant. The significance and signs of these variables do not change when alternative 𝑊 matrices are used.

Moreover, it can be observed that the coefficients of the spatially lagged independent variable increased in magnitude, compared to the results of the non-dynamic models. Hence, the dynamic SDM model suggests stronger local spillover effects. In addition, the outcomes show that the EU enlargement affected the degree of the local spillovers, which is consistent with the previous outcomes. Finally, with respect to the spatial lagged dependent variable and the control variables, the dynamic model presents qualitatively equivalent results compared to its non-dynamic counterpart. These results also hold when alternative 𝑊 matrices are used.

Table 10 Dynamic SDM. SDM (𝑊𝐼𝐷1) SDM (𝑊𝐼𝐷2) SDM (𝑊𝐵𝐶) 𝛽₁ -0.371 -0.379 -0.354 (0.02)*** (0.02)*** (0.02)*** 𝛽2 0.925 0.593 0.458 (0.14)*** (0.08)*** (0.09)*** 𝜌 0.299 0.221 0.174 (0.05)*** (0.04)*** (0.04)*** 𝛽3 0.052 0.052 0.050 (0.01)*** (0.01)*** (0.01)*** 𝛽4 0.014 0.018 0.006 (0.03) (0.03) (0.02) 𝛽5 -0.466 -0.241 -0.200 (0.13)*** (0.08)*** (0.09)** 𝛿 0.773 0.762 0.772 (0.02)*** (0.02)*** (0.02)*** 𝜂₁ -0.089 -0.100 -0.088 (0.01)*** (0.01)*** (0.01)*** 𝜂₂ 0.101 0.117 0.094 (0.02)*** (0.02)*** (0.02)*** R- squared 0.736 0.734 0.735 Log- likelihood -3869.40 -3854.07 -3889.21 N 3376 3376 3376

Notes: (i) cluster-robust standard errors are in parentheses. (ii) *** significant at 1% ** significant at 5%.

13 _{Note again that the spillovers of the dependent variable lagged in both space and time are global in nature.}