Regional economic growth and unemployment in the European Union – a spatio-temporal analysis at the NUTS-2 level (2013–2019) 179Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192.DOI: 10.15201/hungeobull.72.2.6 Hungarian Geographical Bulletin 72 2023 (2) 179–192. Introduction The problem of unemployment is one of the essential issues in macroeconomic analy- ses. This is widely known that the persis- tent regional unemployment disparities in the European Union occur (Patuelli, R. et al. 2012; Halleck Vega, S. and Elhorst, J.P. 2016) Increasing the number of unem- ployed persons is a problem in both devel- oping and developed regions. A lot of deter- minants significantly influence the regional unemployment disparities. For example, regional demand and supply factors, the la- bour migration (Andrews, R. 2015; Lados, G. and Hegedűs, G. 2016) and amenities are the most important factors. Positive changes in these factors can disincentive to migration, compensating for relatively high unemploy- ment rates (Rios, V. 2017). Moreover, the in- stitutional decisions providing restrictions or incentives influence the individual deci- sions regarding labour demand, supply and wages paid, which changes the level of the unemployment rate (Boeri, T. 2011). Capital inadequacy can influence the decrease in the employed people above all in the developing countries. In turn, technological progress is the primary reason for the increased unem- ployment rate in developed regions (Soylu, Ö.B. et al. 2018). Moreover, the national la- bour market regulation and labour market institutional system play significant role in the creation of unemployment rate in every economy. Whereas, as the most important determinant of unemployment, economic growth is pointed out. Arthur M. Okun proved the negative relationship between Regional economic growth and unemployment in the European Union – a spatio-temporal analysis at the NUTS-2 level (2013–2019) Mateusz J A N K I E W I C Z 1 Abstract The study aims to verify the relationship between the unemployment rate and economic growth in European Union (EU) regions. As the most important macroeconomic relationship, the significance of the dependence between the labour market situation and the output growth is widely known and considered. Analysis in this research was conducted using data for 229 EU regions on the NUTS-2 level in the years 2013–2019. In order to verify the relationship between the unemployment rate and the output growth, the spatio-temporal models for pooled time series and cross-sectional data (TSCS) were estimated. The Fitted Trend and Elasticity Method of verifying Okun’s law was used in the analysis, wherein the deterministic trend factor was enriched with the spatial element. Educational attainment as the additional explanatory variable was included in the models. The neighbourhood between regions was quantified based on two criteria: (1) common border criterion – related to the possibility of population migrations, and (2) similarity of the unemployment rate criterion – related to the imitation effect in the issue of introduced rules and regulations on the labour market by regional governments. One of the hypotheses verified in the investigation is the superiority of the economic neighbourhood over the geographical neighbourhood. Keywords: economic growth, European Union, Okun’s law, spatio-temporal models, unemployment rate Received August 2022, accepted April 2023. 1 Department of Applied Informatics and Mathematics in Economics, Faculty of Economic Sciences and Management, Nicolaus Copernicus University in Toruń. Ul. Gagarina 13a, 87-100 Toruń, Poland. E-mail: m.jankiewicz@umk.pl – ORCID: 0000-0002-4713-778X mailto:m_jankiewicz@umk.pl Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192.180 the unemployment rate and Gross National Product (GNP) based on the data for the United States (US) in the years 1947–1960 (Okun, A.M. 1963). He concluded that each 1 percent increase in GNP led to a 0.3 percent decrease in the unemployment rate. Since that time, the relationship between the unemployment rate and economic growth has been widely concerned in mac- roeconomic analyses. This negative short- run dependence is known as Okun’s law. Previous studies conclude that the relation- ship formulated by Okun is stable in many countries (Ball, L. et al. 2017) and possible instability is visible in terms of the economic slowdown (Cazes, S. et al. 2011). In turn, in some studies, authors concluded that the discrepancy in Okun’s relationship between regions within one country occurs (Adanu, K. 2005; Binet, M. and Facchini, F. 2013; Durech, R. et al. 2014). There are three methods of verifying Okun’s relationship: (1) Trial Gaps Method, (2) First Differences Method, and (3) Fitted Trend and Elasticity Method (Barreto, H. and Howland, F. 1993). The first two methods treated analysed processes as the processes stationary in the variance. Instead, within the meaning of the third method, processes are stationary in the average. The First Differences Method is characterized by the greatest popu- larity in previous studies. In this research, the Fitted Trend and Elasticity method is used, but the deterministic trend factor is enriched with the spatial element (originally, only time tendency was considered). In this study, the relationship between the unemployment rate and its main determi- nants – economic growth and educational attainment – is analysed. The study’s main aim is to show that the economic growth and unemployment rate are significantly related in European Union regions. Moreover, the stronger importance of economic similarity between territorial units than their near geo- graphical location in the considered relation- ship is verified. As a space and time range of the research, the NUTS-2 European Union regions in the years 2013–2019 were chosen (due to lack of data for the unemployment rate, Croatian regions were omitted). In the verification of the mentioned relationship, the spatial and spatio-temporal dependencies were included. Many researchers pointed out the importance of spatial connections in the unemployment rate analyses (Overman, H. et al. 2002; Patacchini, E. and Zenou, Y. 2007; Halleck Vega, S. and Elhorst, J.P. 2016). In this study, two types of neighbourhood con- nections were considered. The first is the geo- graphical neighbourhood (associated with the possibility of migration), and the second is the economic neighbourhood (associated with the unemployment rate similarity). Two research hypotheses were verified in this investiga- tion: (1) Output growth and education have a significant positive impact on the labour market conditions in the EU regions, and (2) Economic similarity of regions is more impor- tant than a geographical neighbourhood in the formation of Okun’s relationship. There are many studies considering Okun’s relationship at the regional level, and different methods are used in order to verify it. A couple of studies pertain to Okun’s relationship in the Spanish prov- inces (Villaverde, J. and Maza, A. 2007, 2009; Clar-Lopez, M. et al. 2014; Cháfer, C.M. 2015; Bande, R. and Martín-Román, Á. 2018; Guisinger, A.Y. et al. 2018; Cutanda, A. 2023). All of these investigations are based on non-spatial analysis, and only Villaverde, J. and Maza, A. (2007) considered the Fitted Trend and Elasticity Method with the quad- ratic trend. Bande, R. and Martín-Román, Á. (2018) estimated a simple model for the first differences of processes and also for tri- al gaps. The same method of research took Clar-Lopez, M. et al. (2014). The subject of the investigations in terms of the relation- ship between unemployment rates were also regions from other European countries, e.g., Italian provinces (Salvati, L. 2015), Finnish regions (Kangasharju, A. et al. 2012), Greek regions (Apergis, N. and Rezitis, A. 2003), and also Czech and Slovak regions (Durech, R. et al. 2014). Most of these studies under- line the regional disparities in the unemploy- 181Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192. ment rate formation rely on their economic development. In turn, Yerdelen, F. and İçen, H. verified Okun’s relationship for NUTS- 2 level regions from 20 European countries using panel data models (Yerdelen, F. and İçen, H. 2019). Apart from the studies for European countries, it is possible to find analyses of the mentioned relationship at the regional level in the United States (Huang, H.C. and Yeh, C.C. 2013; Guisinger, A.Y. et al. 2018), Canada (Adanu, K. 2005), Indonesia (Sasongko, G. et al. 2020), and South Africa (Kavese, K. and Phiri, A. 2020). The spatial factor in the analysis of the de- pendence between the unemployment rate and output growth is also included in pre- vious studies. Duran, H.E. considered this dependence using spatial panel data models using data for 26 Turkish NUTS-2 regions (Duran, H.E. 2022). Spatial regression mod- els were used in the analyses concerning the unemployment rate in the United States (Montero-Kuscevic, C.M. 2011; Perreira, R.M. 2013), and EU15 NUTS-2 regions (Herwartz, H. and Niebuhr, A. 2011). In turn, Adolfo Maza conducted the analysis for the widest space range in the mentioned relationship (Maza, A. 2022). He considered the unemployment rate in 265 European re- gions between 2000 and 2019. Methodology In this research, spatial econometric methods were used in order to verify the Okun’s rela- tionship. Spatial econometric models contain the influence of process changes in the neigh- bouring regions on the same process in the established region. In the regional analyses, connections between nearby and also simi- lar (in the economic context) units are very important, in particular in case of the unem- ployment analysis. The economic conditions and possibilities of the neighbours can en- courage people to jobs migrations, changing the labour situation in the considered unit. In the first part of the investigation, the spatio-temporal structure of processes was analysed. The structure is composed of the spatio-temporal trend and spatio-temporal autocorrelation. Initially, spatio-temporal trend models were considered, which gen- eral form is as follows (Cressie, N.A.C. 1993): where si = [xi, yi] denotes unit’s location coor- dinates on the plane (longitude and latitude, respectively), i = 1, 2, ..., N are indexes of spa- tial units, and p means the polynomial trend degree (k + m + l ≤ p) but t indicates time. Simultaneously, the spatio-temporal auto- correlation presence as the second element of the spatio-temporal structure was checked. The spatial autocorrelation is tested using Moran statistics, which takes the following form (Moran, P.A.P. 1948; Schabenberger, O. and Gotway, C.A. 2005): where yi,t is the observation of the process in the ith region in time t, ӯ denotes the average value of the process, W* is the block matrix of spatio-temporal connections between units given as Szulc, E. and Jankiewicz, M. (2018): wherein W1 = W2 ··· = WT are standard spatial connectivity matrices quantified for a certain year. In this study, these matrices are the same for all years. In this research, two types of row-stand- ardized to unity matrices were adopted. The first of them is based on the common border criterion (marked as W). Therefore, two re- gions are neighbours if they have a common land border. In turn, the second defines the neighbourhood as the economic similarity (D) – regions are neighbours if the difference between their unemployment rate level in the last year of the investigation does not ex- ceed a certain specific value (established as 0.8% – the 15th percentile of differences be- tween the unemployment rate in all regions). The procedure of building the economic dis- (2) (1) (3) Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192.182 tance matrix is presented by Jankiewicz, M. and Szulc, E. in their study (Jankiewicz, M. and Szulc, E. 2021). Statistically significant Moran’s I coeffi- cient signalizes the presence of spatial au- tocorrelation. Its positive value denotes that territorial units create clusters of the regions with a similar level of the analysed phenom- enon. In turn, the negative sign of statistics points out that neighbouring regions are characterized by different values of the con- sidered process. Non-significant statistics tes- tifies to a random distribution of the process values in space. Next, the spatio-temporal models of the relationship between the unemployment rate, economic growth, and educational at- tainment were considered. The general form of the TSCS model (pooled time series and cross-sectional data model) is as follows: where Yi,t denotes the unemployment rate in the ith region in time t, X1i,t, and X2i,t are levels of Gross Domestic Product per capita and edu- cational attainment, respectively (all expressed in natural logarithms). In turn, εi,t indicates the spatio-temporal random component, but β1 and β2 are the structural parameters. Loga- rithms of variables cause that parameter β1 is the elasticity parameter in the Fitted Trend and Elasticity Method in the Okun’s law veri- fication. Model (4) is deprived of constant due to all considered variables are filtered out from deterministic spatio-temporal trend, which is responsible for their average values. In terms of global spatial autocorrelation in the residuals of the model (4) the character of the spatial dependence was determined using Lagrange Multiplier (LM) tests in the basic and robust version (Anselin, L. et al. 2004). Including spatially lagged explanatory variables in the models, the spatio-temporal Durbin model (STDM) and spatio-temporal hybrid model (STHM) are given as follows: where Yi,t, X1i,t, X2i,t, εi,t , β1, β2 – as above, ∑j ≠ i wij,t Yj,t, ∑j ≠ i wij,t X1j,t, ∑j ≠ i wij,t X2j,t – spatially lagged variables, ∑j ≠ i wij,tŋj,t – spatially lagged random process, θ1, θ2, ρ, λ – structural parameters. Pa- rameters ρ and λ evidence the spatial depend- ence between neighbouring territorial units. Spatial and spatio-temporal structure of processes Data used in this study concern the unemploy- ment rate (marked as Y), Gross Domestic Prod- uct per capita (X1), and educational attainment level, understood as the percent of the popula- tion that graduated upper secondary and post- secondary (not tertiary) school (X2) in the Eu- ropean Union regions in the years 2013–2019. Better economic conditions in regions favour the creation of new workplaces, whereas the higher education level of society improves chances of getting a job. The indicators used in the research are only a few of many that sig- nificantly impact regional unemployment, but they are considered the most important. Apart from them, e.g., the innovation level and the economic structure of regions are important. The first is not included due to data unavail- ability for the whole considered area, while the second will be of interest for further research. Moreover, in case of unemployment, the age structure of the population and distance from main urban centres play an important role. The established period is the maximum period that can be analysed in light of the data availability. Moreover, due to a lack of data characterizing the unemployment level, Croatia’s regions were omitted. All data come directly from the European Statistical Office (EUROSTAT) database – https://ec.europa.eu/eurostat/data/ database (accessed: 04.07.2022). In the first part of the research, spatial dis- tributions of considered processes were pre- sented. These distributions were shown in three figures (for variable Y, for variable X1 and for (4) (5) (6) https://ec.europa.eu/eurostat/data/database https://ec.europa.eu/eurostat/data/database 183Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192. variable X2) in the extreme years of the analysis. In each figure, part (a) indi- cates the distribution in 2013, but part (b) refers to spatial differentiation in 2019. EU regions were divided into four groups using positional measures of the descriptive statistics (median and quarter de- viation). As we can see in Figure 1, the highest unemployment rate in 2013 was observed in the Iberian Peninsula regions, Greek regions, and the units located in Southern Italy. Moreover, relatively high unemploy- ment was noted in most of Eastern Europe NUTS- 2 level regions (above all in the regions located in Lithuania, Poland, and the Slovak Republic). On the other hand, Austrian and West German regions were characterized by the best labour market con- ditions – the unemploy- ment rate was relatively low. This is worth noting the low level of the con- sidered variable in the North Romanian regions. In 2019 the situation in the labour market in the EU was slightly different than in 2013. The unemploy- ment level in all Francian units was above the me- dian in the last year of the investigation. Instead, the Fig. 1. Spatial distribution of the unemployment rate in EU regions in the years 2013 (a) and 2019 (b) Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192.184 Fig. 2. Spatial distribution of the GDP per capita (PPS) in EU regions in the years 2013 (a) and 2019 (b) variable values in 2013 were more diversified between these regions. The relative deterioration of the situation concerns North Italian provinces and Scandinavian re- gions as well. In con- trast, most of the Polish provinces found them- selves in units with u n e m p l o y m e n t r a t e values below the me- dian, which denotes the relative improvement in this part of the European Community. Based on spatial distri- butions of the unemploy- ment level in the EU re- gions, it can be presumed that values of the consid- ered variable exhibit a certain tendency in space. Therefore, the spatial fac- tor in the analysis should be included. In this con- nection, the spatio-tem- poral trend models in the following part of the study were concerned. Seeing the spatial dis- tributions of GDP per capita (Figure 2), we can note that the spatial dif- ferentiation of process values in both analysed years was analogous. Relatively high economic growth (with the values of GDP per capita above median) was observed in the Central EU re- gions (located in Austria, 185Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192. Fig. 3. Spatial distribution of the educational attainment level in EU regions in the years 2013 (a) and 2019 (b) West Germany, North Italy, and Benelux coun- tries). Also, a high GDP level was noted in the Scandinavian and South Ireland regions. On the other hand, the relative- ly less developed units were located above all in the eastern part of the European Community, e x c e p t f o r r e g i o n s Bratislava (SK01), Praha ( C Z 0 1 ) , Wa r s z a w s k i stołeczny (PL91), Sostinės (LT01), and București- Ilfov (RO32). Three men- tioned units belonged to the group of regions with the highest values of the GDP per capita in 2019. A similar situa- tion was observed in the Iberian Peninsula prov- inces. Almost all regions were classified into the groups of very low and low economic growth levels. Only two regions were characterized by economic growth above the median – one Spanish a n d o n e P o r t u g u e s e (Madrid – ES30 and Área Metropolitana de Lisboa – PT17, respectively). As in the case of the unemploy- ment rate, certain spatial tendencies in the forma- tion of GDP per capita values were observed. F i g u r e 3 p r e s e n t s spatial distributions of educational attainment. Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192.186 The percent of graduates in the upper sec- ondary and post-secondary school (exclud- ing tertiary education) is considered. It is worth seeing the possibility of the division of EU regions into two parts in both extreme years of the study (more visible in 2019). The first was in the eastern part of the European Community, where almost all regions were characterized by a relatively high percentage of graduates in upper secondary and post- secondary school. Instead, the western part of the mentioned area was dominated by units with the values of the considered pro- cess below the median. It is worth noting the lowest level of the variable X2 in the French and Spanish regions, where the unemploy- ment rate was relatively high. Units with the low and high values of the educational at- tainment process created two almost coher- ent areas, which lead to presumption about a certain spatial tendency in their formation. The observations made based on the spatial distributions of all processes allowed us to con- sider the two-dimensional deterministic trend (with the spatial and time factors) in order to filter out long-term tendencies. Table 1 shows the results of estimation and verification of the spatio-temporal trend models for all variables. In the models, only the statistically significant parameters were left. It is a difference in the degree of trend ob- tained for the variable Y and the two remain- ing variables. The unemployment rate in the period 2013–2019 was shaped according to the second-degree spatio-temporal trend. Considering estimates of parameters θ100 and θ010 for variables X1 and X2 we can con- clude that their values averagely have been growing in the western-northern and east- ern-northern directions, respectively. This confirms the insights visible in figures 2 and 3. Moreover, positive estimates of parameter θ001 indicate the average increase of the GDP per capita and educational attainment in the years 2013–2019. In addition, an average de- crease of the variable Y towards the north and east should be noted (negative estimations of parameters θ010 and θ100, respectively). The low level of the determination coef- ficient R2 is the characteristic feature of the spatial and spatio-temporal trend models. However, we can see that the least coherent values formation in space and time was per- taining to Gross Domestic Product per capita. Additionally, the Moran test evaluating the dependence between neighbouring regions was conducted. In the spatial autocorrelation analysis, two types of neighbourhood matri- ces were used. First of them defines neigh- bouring regions as regions with a common land border (geographical neighbourhood – W). Instead, the second points out that two units are neighbours if they had a similar level of the unemployment rate in 2019 (eco- Table 1. The results of estimation and verification of the spatio-temporal trend models Parameter Unemployment (Y) GDP per capita (X1) Educational attainment (X2) Estimate p-value Estimate p-value Estimate p-value θ000 θ100 θ010 15.6290 -0.0185 -0.5110 0.0000 0.0000 0.0000 8.9967 -0.0190 0.0259 0.0000 0.0000 0.0000 3.8209 0.0120 0.0049 0.0000 0.0000 0.0000 θ001 – – 0.0301 0.0000 0.0023 0.0927 θ200 θ020 0.0008 0.0048 0.0000 0.0000 – – – – θ101 θ002 -0.0014 -0.0104 0.0123 0.0000 R2 0.5432 0.3315 0.5318 Moran test Matrix I p-value I p-value I p-value W D 0.4714 0.4953 0.0000 0.0000 0.3649 0.0466 0.0000 0.0019 0.4220 0.1096 0.0000 0.0000 187Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192. nomic distance matrix – D). The Moran’s I statistics for variable Y are very similar using both types of the connection matrix (0.4714 and 0.4953, respectively) with the proviso that units with a similar unemployment rate in 2019 showed slightly higher neighbour- hood dependence. In contrast, the Moran’s I coefficient evaluated considering the dis- tance matrix was relevantly lower than in the case of the first-order contiguity matrix W) for two remaining variables. It means that the dependence of GDP per capita and edu- cational attainment between neighbouring regions in a geographical space was stronger than between regions neighbouring in eco- nomic terms. Nonetheless, all determined Moran’s coefficients turned out statistically significant. This situation indicates the neces- sity of spatial dependence inclusion in the analysis of the relationship between the un- employment rate and economic growth, and educational attainment. Okun’s relationship models In the first part of the relationship analy- sis, the TSCS (pooled time series and cross- sectional) model was considered. Table 2 presents the results of the estimation and verification of the pooled spatio-temporal model. This is Okun’s model extended with the educational factor. The negative estimate of statistically signifi- cant parameter β1 denotes that an increase in the GDP per capita causes an average decrease in the unemployment rate. This confirms the observations made by Arthur M. Okun. The value of the elasticity parameter indicates that an increase in the GDP by 1 percent provides to decrease in the unemployment rate aver- agely by 0.41 percent ceteris paribus. A higher strength of the influence shows the education- al level, where an increase of 1 percent causes the average decrease in the unemployment rate averagely by 0.73 percent. Moran test results indicate the presence of global spatio-temporal autocorrelation in the model residuals. Therefore, the significance of dependence between neighbouring regions in the light of both neighbourhood matrices was concluded. So the spatio-temporal models estimated considering geographical and eco- nomic neighbourhoods should be analysed. In order to determine the character of spatio-temporal dependence, the Lagrange Multiplier tests were conducted. Tests sta- tistics in the basic version (LMerr and LMlag) do not solve the problem of the model choice – both are statistically significant. Analysing LM statistics in the robust versions of tests, we can conclude that the model with spa- tial factor in the error term for the W matrix is better. In turn, for the economic distance matrix (marked as D), the model with a spa- tial lag of the dependent variable should be Table 2. The results of estimation and verification of the TSCS extended Okun’s model Parameter Estimate Standard error t statistics p-value β1 β2 -0.4194 -0.7301 0.0320 0.0925 -13.1190 -7.8960 0.0000 0.0000 R2 0.1353 Moran test Matrix W D I p-value 0.4363 0.0000 0.4257 0.0000 LM tests Statistics Estimate p-value Estimate p-value LMerr LMlag RLMerr 611.5708 575.7326 38.3835 0.0000 0.0000 0.0000 699.1660 859.9580 21.3310 0.0000 0.0000 0.0000 RLMlag 2.5453 0.1106 182.1230 0.0000 Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192.188 chosen. Regardless of the results of the ro- bust LM rests, both types of spatio-temporal models enriched with the spatial lags of ex- planatory variables were estimated. Table 3 presents the results of estimation and verification of the spatio-temporal Durbin models (STDM) and spatio-tempo- ral hybrid models (STHM), considering both connection matrices. Similar to the TSCS model, estimates of sta- tistically significant parameters β1 and β2 are negative, which confirms the positive influ- ence of the GDP per capita and educational attainment increase on the labour market conditions in the EU regions. Nonetheless, the strength of impact is lower. The highest difference is observed in the estimate of the parameter β2 in the models for the D matrix – the 1 percent increase in educational attain- ment provides the average decrease in the unemployment rate around 0.4 percent (less than for the TSCS model around 0.3%). In all models, parameters ρ and λ are statistically significant, which confirms the necessity of including spatial factors in the analysis. Values of estimates of the spatial parameters within one connection matrix are very simi- lar. Moreover, the estimates of both consid- ered parameters are slightly lower in the case of models for the economic distance matrix. This indicates that regions neighbouring in the geographical space were more similar in the unemployment rate than the neighbours determined by the economic terms. It is worth noting the statistical signifi- cance of the θ1 parameter in all estimated models. Except for the spatial Durbin model for the W matrix (SDM_W), the estimate of this parameter is negative. Considering the geographical neighborhood, changes in the unemployment rate in the neighboring re- gions had a different impact than changes in the random processes or processes omitted in the model. In turn, shocks like an increase in the unemployment rate level or in the ran- dom processes in the neighbouring (from the economic point of view) units caused a sig- nificant decrease in the unemployment rate in a certain region. However, shocks in the random processes or omitted explanatory variables were slightly stronger. The desirable characteristic of the mod- els with the W matrix is the lack of spatial autocorrelation in the models’ residuals. In the light of the Akaike Criterion (AIC) and the logarithm of likelihood values (Log-lik) Table 3. The results of estimation and verification of the spatial extended Okun’s model Parameter Model STDM_W STHM_W STDM_D STHM_D β1 -0.3094 (0.0000) -0.3289 (0.0000) -0.3111 (0.0000) -0.3296 (0.0000) θ1 0.1461 (0.0014) -0.1710 (0.0113) -0.2275 (0.0001) -0.3211 (0.0000) β2 -0.6009 (0.0000) -0.6310 (0.0000) -0.4030 (0.0000) -0.4448 (0.0000) θ2 0.2530 (0.0761) -0.2921 (0.1194) -0.0718 (0.6167) -0.2769 (0.1483) ρ 0.6204(0.0000) – 0.5642 (0.0000) – λ – 0.6249(0.0000) – 0.5822 (0.0000) Diagnostics Moran test -0.0155(0.2127) -0.0170 (0.1895) -0.0490 (0.0015) -0.0347 (0.0182) AIC 1,126.5000 1,118.9000 1,052.4000 1,095.5000 Log-lik -557.2697 -553.4698 -520.1802 -541.7608 189Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192. the best model is the spatial Durbin model estimated using connection matrix D based on the economic distance neighbourhood. Therefore, we can conclude about higher cog- nitive values of the models with the economic neighbourhood (regardless of the spatial auto- correlation presence in the model residuals). Statistical significance of the parameters ρ, β1 and θ1 allows for quantifying the short- term spatial spillovers. Nevertheless, this is- sue is not the subject of the study. The quan- tification of the spatial effects is one of the directions of further analysis. Discussion The analysis presented in this paper shows a large variation in the unemployment rate be- tween EU regions, which is a significant eco- nomic problem. The problem particularly re- fers to the southern and eastern parts of the Eu- ropean Union. The causes of this situation have a different character. The economic growth and education level of society are considered as the most important indicators influencing the labour market level. Estimated models confirm that the increase in Gross Domestic Product per capita and educational attainment (measured by the percentage of graduates in upper secondary and post-secondary school) significantly causes the decrease in the unem- ployment rate. Moreover, the other individual characteristics of regions influence the labour market situation. One of them is specific eco- nomic structure, i.e., if the considered regions are rural or industrial. A verification of Okun’s relationship for EU regions taking into account their specificity will be the subject of further research. Boďa, M. and Považanová, M. (2020) point out the necessity of diversifying regions by their specific characters estimating Okun’s relationship. In turn, Bonaventura, L. et al. (2018) verified this relationship in two gender groups in Italy. They inferred differences in the sensitivity level of the unemployment rate on changes in GDP per capita between males and females depending on the geographic location of the region. Some of the authors so far analysed Okun’s relationship on the regional level. For exam- ple, Duran, H.E. (2022) showed its significance for Turkish provinces. He did not include ad- ditional explanatory variables apart from the economic growth level, the increase of which causes the decrease in the unemployment rate in all provinces. In turn, Melguizo, C. (2017) considered the connection between economic growth and the unemployment rate in Spanish provinces. She inferred the same type of rela- tionship (with different strengths) through- out the area. Also negative sign of Okun’s coefficient for all regions of Slovenia obtained Dajcman, S. (2018). Palombi, S. et al. (2017) showed the same for Great Britain, analys- ing data for regions at a NUTS-3 level. Their study is one of few using spatial econometric models as a research tool for the verification of Okun’s relationship. Other analyses based on the spatial econometric approach were con- ducted by Montero-Kuscevic, C.M. (2011), Perreira, R.M. (2013), and Maza, A. (2022). In this research, additionally, the educational at- tainment level was included in Okun’s model, which is not found in many other studies. The methodological approach used in this research differs from other approaches. Firstly, previous researches including spatial connec- tions between territorial units based on the First Differences Method of Okun’s law. This analy- sis used the Fitted Trend and Elasticity Method enriched with the spatial trend. It is a new ap- proach to establishing long-term dependencies in the formation of key indicators used in the investigation, which treats the trend wider than yet. In turn, the definition of one of the spatial connection matrices is new. It is an economic distance matrix built on the unemployment rate similarity between regions. As we saw in the results, changes in GDP per capita level in regions with similar unemployment rates influence stronger on the labour market con- ditions in the specific region, than changes in the regions directly adjacent. Spatial models in previous studies were estimated using neigh- bourhood matrices built based on the common land border or the geographic distance criteria. The weakness of this research is not consider- Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192.190 ing the specific characteristics of regions, for ex- ample, a population composition, an economic structure, and other important indicators, such as an innovation level. These aspects will be the subject of further research. Conclusions The regional approach to the verify of Okun’s relationship has become more and more pop- ular in macroeconomic analyses. Regardless of the regional disparities in the unemploy- ment rate and the economic growth between NUTS-2 level units, the general dependence among these processes was confirmed in the European Union. The Okun’s elasticity param- eter (β1) in the estimated spatial models took a value similar to this, considered to be a bench- mark around -0.3 (value received by Arthur M. Okun in his study). Moreover, the educational attainment turned out to be significant, and an increase in the percentage of graduates in upper secondary and post-secondary schools caused a decrease in the unemployment rate. In this connection, the first research hypoth- esis of the study was confirmed. The economic similarity included in the models in the form of a neighbourhood ma- trix turned out to be statistically significant, so the similarity between regions related to the unemployment rate is relevant in Okun’s relationship verification. So this is the second type of connection, next to the repeatedly confirmed significance of the geographical closeness (in this study, too), which allows for an understanding of the formation of the relationship between unemployment and output growth. A comparison of the esti- mated spatio-temporal models shows that models with the economic neighbourhood (regardless of the certain imperfections) bet- ter explain the mentioned dependence, which confirms the second research hypothesis. It means that the regions similar in the unem- ployment rate levels are connected stronger in case of the relationship between economic growth and labour market conditions than the regions directly adjacent to each other. The proximity in the sense of the similarity of the unemployment rate can explain the imita- tion effect related to regularities and rules in- troduced by the governments of regions. The patterning of the regional rulers’ behaviours from other provinces in the case of the labour market situation can provide similar changes in the labour market in a certain unit. It is also worth noting the policy of combating un- employment should be fitted to the regional specificity of the local labour market. It is worth noting that in the adopted time range (2013–2019), all crises are omitted: (1) financial crisis in 2007–2009, (2) economic slowdown in 2012, and (3) COVID-19 pan- demic from 2020 (due to lack of the data). In this connection, the relationship between the unemployment rate and output growth may be accepted as relatively stable in the European Union regions (which does not mean that not differentiated between units). In further research, this is worth concerning also the analysis of the regimes of the regions divided by the economic growth level and the impact of the COVID-19 pandemic on the mentioned relationship. This research will be enriched with the spatial effects quantified based on the estimated models and the use of other spatial connections matrices. R E F E R E N C E S Adanu, K. 2005. A cross-province comparison of Okun’s coefficient for Canada. Applied Economics 37. (5): 561–570. Doi: 10.1080/0003684042000201848 Andrews, R. 2015. Labour migration, communities and perceptions of social cohesion in England. European Urban and Regional Studies 22. (1): 77–91. Doi: 10.1177/0969776412457165 Anselin, L., Florax, R. and Rey, S.J. 2004. Advances in Spatial Econometrics. Methodology, Tools and Applications. New York, Springer Verlag. Apergis, N. and Rezitis, A. 2003. An examination of Okun’s law: Evidence from regional areas in Greece. Applied Economics 35. (10): 1147–1151. Doi: 10.1080/0003684032000066787 Ball, L., Leigh, D. and Loungani, P. 2017. Okun’s law: Fit at 50? Journal of Money, Credit and Banking 49. (7): 1413–1441. Doi: 10.1111/jmcb.12420 Bande, R. and Martín-Román, Á. 2018. Regional differ- ences in the Okun’s relationship: New evidence for https://www.tandfonline.com/doi/abs/10.1080/0003684042000201848 https://journals.sagepub.com/doi/10.1177/0969776412457165 https://journals.sagepub.com/doi/10.1177/0969776412457165 https://www.tandfonline.com/doi/abs/10.1080/0003684032000066787 https://www.tandfonline.com/doi/abs/10.1080/0003684032000066787 https://onlinelibrary.wiley.com/doi/10.1111/jmcb.12420 191Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192. Spain (1980–2015). Investigaciones Regionales – Journal of Regional Research 41. 137–165. Barreto, H. and Howland, F. 1993. There Are Two Okun’s Law Relationships between Output and Unemployment. Crawfordsville, Wabash College. Binet, M. and Facchini, F. 2013. Okun’s law in the French regions: A cross-regional comparison. Economics Bulletin 33. (1): 420–433. Boďa, M. and Považanová, M. 2020. Formal and statis- tical aspects of estimating Okun’s law at a regional level. Papers in Regional Science 99. (4): 1113–1136. Doi: 10.1111/pirs.12511 Boeri, T. 2011. Institutional reforms and dualism in European labour markets. In Handbook of Labour Economics Vol. 4b. Eds.: Ashenfelter, O. and Card, D., Elsevier Publication, 1173–1236. Bonaventura, L., Cellini, R. and Sambatato, M. 2018. Gender Differences in Okun’s Law across the Italian Regions. Munich, MPRA Paper No. 87557. Available at https://mpra.ub.uni-muenchen.de/87557/1/MPRA_ paper_87557.pdf Cazes, S., Verick, S. and Al Hussami, F. 2011. Diverging Trends in Unemployment in the United States and Europe: Evidence from Okun’s Law and the Global Financial Crisis. Employment Sector, Employment Working Paper No. 106. Geneva, ILO. Cháfer, C.M. 2015. An Analysis of the Okun’s Law for the Spanish Provinces. Working Paper 2015/01. Barcelona, Institut de Recerca en Economia Aplicada Regional i Pública. Clar-Lopez, M., López-Tamayo, J. and Ramos, R. 2014. Unemployment forecasts, time varying coefficient models and the Okun’s law in Spanish regions. Economics and Business Letters 3. (4): 247–262. Cressie, N.A.C. 1993. Statistics for Spatial Data. New York, John Wiley & Sons Inc. Cutanda, A. 2023. Stability and asymmetry in Okun’s law: Evidence from Spanish regional data. Panoeconomicus 70. (2): 219–238. Doi: 10.2298/PAN191203012C Dajcman, S. 2018. A regional panel approach to testing the validity of Okun’s law: The case of Slovenia. Economic Computation & Economic Cybernetics Studies & Research 52. (3): 39–54. Doi: 10.24818/18423264/52.3.18.03 Duran, H.E. 2022. Validity of Okun’s law in a spa- tially dependent and cyclical asymmetric context. Panoeconomicus 69. (3): 447–480. Doi: 10.2298/ PAN190529003D Durech, R., Minea, A., Mustea, L. and Slusna, L. 2014. Regional evidence on Okun’s law in Czech Republic and Slovakia. Economic Modelling 42. (C): 57–65. Doi: 10.1016/j.econmod.2014.05.039 Guisinger, A.Y., Hernandez-Murillo, R., Owyang, M.T. and Sinclair, T.M. 2018. A state-level analysis of Okun’s law. Regional Science and Urban Economics 68. (C): 239–248. Doi: 10.1016/j.regsciurbeco.2017.11.005 Halleck Vega, S. and Elhorst, J.P. 2016. A regional unemployment model simultaneously accounting for serial dynamics, spatial dependence and com- mon factors. Regional Science and Urban Economics 60. (C): 85–95. Doi: 10.1016/j.regsciurbeco.2016.07.002 Herwartz, H. and Niebuhr, A. 2011. Growth, unem- ployment and labour market institutions: evidence from a cross-section of EU regions. Applied Economics 43. (30): 4663–4676. Available at https://www.tand- fonline.com/doi/full/10.1080/00036846.2010.493142 Huang, H.C. and Yeh, C.C. 2013. Okun’s law in panels of countries and states. Applied Economics 45. (2): 191–199. Doi: 10.1080/00036846.2011.597725 Jankiewicz, M. and Szulc, E. 2021. Analysis of spatial effects in the relationship between CO2 emissions and renewable energy consumption in the context of economic growth. Energies 14. (18): 5829. Doi: 10.3390/en14185829 Kangasharju, A., Tavera, C. and Nijkamp, P. 2012. Regional growth and unemployment: The validity of Okun’s law for the Finnish regions. Spatial Economic Analysis 7. (3): 381–395. Doi: 10.1080/17421772.2012.694141 Kavese, K. and Phiri, A. 2020. A provincial perspective of nonlinear Okun’s law for emerging markets: The case of South Africa. Studia Universitatis „Vasile Goldis” Arad – Economics Series 30. (3): 59–76. Doi: 10.2478/sues-2020-0017 Lados, G. and Hegedűs, G. 2016. Returning home: An evaluation of Hungarian return migration. Hungarian Geographical Bulletin 65. (4): 321–330. Doi: 10.15201/hungeobull.65.4.2 Maza, A. 2022. Regional differences in Okun’s law and explanatory factors: Some insights from Europe. International Regional Science Review 45. (5): 555–580. Doi: 10.1177/01600176221082309 Melguizo, C. 2017. An analysis of Okun’s law for the Spanish provinces. Review of Regional Research 37. (1): 59–90. Doi: 10.1007/s10037-016-0110-7 Montero-Kuscevic, C.M. 2011. Spatial Features of Okun’s Law Using U.S. Data. Morgantown, WV, West Virginia University Libraries. Doi: 10.33915/etd.3386 Moran, P.A.P. 1948. The interpretation of statistical maps. Journal of the Royal Statistical Society: Series B (Methodological) 10. (2): 243–251. Doi: 10.1111/j.2517- 6161.1948.tb00012.x Okun, A.M. 1963. Potential GNP: Its Measurement and Significance. Cowles Foundation Paper 190. Cowles Foundation, New Haven, CT, Yale University. Overman, H.G., Puga, D. and Vanderbussche, H. 2002. Unemployment clusters across Europe’s regions and countries. Economic Policy 17. (34): 115–147. Palombi, S., Perman, R. and Tavéra, C. 2017. Commuting effects in Okun’s law among British areas: Evidence from spatial panel econometrics. Papers in Regional Science 96. (1): 191–209. Doi: 10.1111/pirs.12166 Patacchini, E. and Zenou, Y. 2007. Spatial depen- dence in local unemployment rates. Journal of Economic Geography 7. (2): 169–191. Doi: 10.1093/ jeg/lbm001 https://rsaiconnect.onlinelibrary.wiley.com/doi/10.1111/pirs.12511 https://rsaiconnect.onlinelibrary.wiley.com/doi/10.1111/pirs.12511 https://mpra.ub.uni-muenchen.de/87557/1/MPRA_paper_87557.pdf https://mpra.ub.uni-muenchen.de/87557/1/MPRA_paper_87557.pdf https://pdfs.semanticscholar.org/e97a/85d0b7d44ce42c92d563f734f50d1a72b965.pdf?_gl=1*1r00kt1*_ga*NjU0NDcxNzkwLjE2ODMzMzAyMTQ.*_ga_H7P4ZT52H5*MTY4MzMzMDIxNC4xLjAuMTY4MzMzMDIxNy4wLjAuMA.. https://ecocyb.ase.ro/nr2018_3/03%20-%20Silvo%20DAJCMAN%20(T)%20-3-.pdf https://panoeconomicus.org/index.php/jorunal/article/view/814 https://panoeconomicus.org/index.php/jorunal/article/view/814 https://www.sciencedirect.com/science/article/abs/pii/S0264999314002181?via%3Dihub https://www.sciencedirect.com/science/article/abs/pii/S0264999314002181?via%3Dihub https://deliverypdf.ssrn.com/delivery.php?ID=599110006119023031096102028102105117031092005021001065087062044127045107030011005111045005030051119011039064055095047095119076073095072036086025113093012086126068085091081116010086111016114007113116119025118080078091103&EXT=pdf&INDEX=TRUE http://Halleck Vega, S. and Elhorst, J.P. 2016. A regional unemployment model simultaneously accounting for serial dynamics, spatial dependence and common factors. Regional Science and Urban Economics 60. 85–95. https://www.tandfonline.com/doi/abs/10.1080/00036846.2010.493142?journalCode=raec20 https://www.tandfonline.com/doi/abs/10.1080/00036846.2010.493142?journalCode=raec20 https://www.tandfonline.com/doi/abs/10.1080/00036846.2011.597725 https://pdfs.semanticscholar.org/5685/5de5651b546a277a008214866788da5132de.pdf?_gl=1*1varsj3*_ga*NjU0NDcxNzkwLjE2ODMzMzAyMTQ.*_ga_H7P4ZT52H5*MTY4MzMzMDIxNC4xLjAuMTY4MzMzMTk4MS4wLjAuMA.. https://pdfs.semanticscholar.org/5685/5de5651b546a277a008214866788da5132de.pdf?_gl=1*1varsj3*_ga*NjU0NDcxNzkwLjE2ODMzMzAyMTQ.*_ga_H7P4ZT52H5*MTY4MzMzMDIxNC4xLjAuMTY4MzMzMTk4MS4wLjAuMA.. https://www.tandfonline.com/doi/abs/10.1080/17421772.2012.694141 https://www.tandfonline.com/doi/abs/10.1080/17421772.2012.694141 https://sciendo.com/article/10.2478/sues-2020-0017 https://sciendo.com/article/10.2478/sues-2020-0017 https://core.ac.uk/download/pdf/196255098.pdf https://core.ac.uk/download/pdf/196255098.pdf https://journals.sagepub.com/doi/10.1177/01600176221082309 https://diposit.ub.edu/dspace/bitstream/2445/61326/1/IR15-001_Melguizo.pdf https://researchrepository.wvu.edu/etd/3386/ https://rss.onlinelibrary.wiley.com/doi/10.1111/j.2517-6161.1948.tb00012.x https://rss.onlinelibrary.wiley.com/doi/10.1111/j.2517-6161.1948.tb00012.x https://rsaiconnect.onlinelibrary.wiley.com/doi/10.1111/pirs.12166 https://rsaiconnect.onlinelibrary.wiley.com/doi/10.1111/pirs.12166 https://academic.oup.com/joeg/article-abstract/7/2/169/887792?redirectedFrom=fulltext https://academic.oup.com/joeg/article-abstract/7/2/169/887792?redirectedFrom=fulltext Jankiewicz, M. Hungarian Geographical Bulletin 72 (2023) (2) 179–192.192 Patuelli, R., Schanne, N., Griffith, D.A. and Nijkamp, P. 2012. Persistence of regional unemploy- ment: Application of a spatial filtering approach to local labor markets in Germany. Journal of Regional Science 52. (2): 300–323. Doi: 10.1111/j.1467- 9787.2012.00759.x Perreira, R.M. 2013. Okun’s Law and Regional Spillovers: Evidence from Virginia Metropolitan Statistical Areas and the District of Columbia. College of William & Mary, Department of Economics, Working Paper Number 140. Williamsburg, VA, William & Mary. Rios, V. 2017. What drives unemployment disparities in European regions? A dynamic spatial panel approach. Regional Studies 51. (11): 1599–1611. Doi: 10.1080/00343404.2016.1216094 Salvati, L. 2015. Space matters: Reconstructing a local-scale Okun’s law for Italy. International Journal of Latest Trends in Finance & Economic Sciences 5. (1): 833–840. Sasongko, G., Artanti, N., Huruta, A. and Lee, C.- W. 2020. Reexamination of Okun’s law: Empirical analysis from Panel Granger Causality. Industrija 48. (4): 63–80. Doi: 10.5937/industrija48-29455 Schabenberger, O. and Gotway, C.A. 2005. Statistical Methods for Spatial Data Analysis. Boca Raton, Champion & Hall/CRC. Soylu, Ö.B., Çakmak, İ. and Okur, F. 2018. Economic growth and unemployment issue: Panel data analysis in Eastern European countries. Journal of International Studies 11. (1): 93–107. Doi: 10.14254/2071-8330.2018/11-1/7 Szulc, E. and Jankiewicz, M. 2018. Spatio-temporal modelling of the influence of the number of busi- ness entities in selected urban centres on unemploy- ment in the Kujawsko-Pomorskie voivodeship. Acta Universitatis Lodziensis. Folia Oeconomica 4. (337): 21–37. Doi: 10.18778/0208-6018.337.02 Villaverde, J. and Maza, A. 2007. Okun’s law in the Spanish regions. Economics Bulletin 18. (5): 1–11. Villaverde, J. and Maza, A. 2009. The robustness of Okun’s law in Spain, 1980–2004. Regional evidence. Journal of Policy Modeling 31. (2): 289–297. Doi: 10.1016/j.jpolmod.2008.09.003 Yerdelen, F. and İçen, H. 2019. Heterogeneous multi-dimensional panel data models: Okun’s law for NUTS2 level in Europe. In Selected Topics in Applied Econometrics. Eds.: Çaglayan, E. and Korkmaz, Ö., Istanbul, Peter Lang, 31–45. https://onlinelibrary.wiley.com/doi/10.1111/j.1467-9787.2012.00759.x https://onlinelibrary.wiley.com/doi/10.1111/j.1467-9787.2012.00759.x https://www.tandfonline.com/doi/abs/10.1080/00343404.2016.1216094?journalCode=cres20 https://www.tandfonline.com/doi/abs/10.1080/00343404.2016.1216094?journalCode=cres20 https://scindeks.ceon.rs/Article.aspx?artid=0350-03732004063S https://www.jois.eu/files/7_428_Soylu%20et%20al.pdf https://www.jois.eu/files/7_428_Soylu%20et%20al.pdf https://czasopisma.uni.lodz.pl/foe/article/view/2534 https://www.sciencedirect.com/science/article/abs/pii/S0161893808000756?via%3Dihub https://www.sciencedirect.com/science/article/abs/pii/S0161893808000756?via%3Dihub Hungarian Geographical Bulletin Vol 72 Issue 2 179-192 (2023) Mateusz Jankiewicz: Regional economic growth and unemployment in the European Union – a spatio-temporal analysis at the NUTS-2 level (2013–2019)