Cluster Space Among Labor Productivity, Urbanization, and Agglomeration of Industries in Hungary

Citation preview

Journal of the Knowledge Economy https://doi.org/10.1007/s13132-021-00726-9

Cluster Space Among Labor Productivity, Urbanization, and Agglomeration of Industries in Hungary Devesh Singh1 Received: 19 September 2020 / Accepted: 19 January 2021 © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021

Abstract Do labor productivity, industrial agglomeration, and urbanization coexist in cluster space? To examine this question, we used multiple methodologies. Density-based cluster mapping is used to create the cluster space, simultaneous equation in each cluster to verify the co-existence of agglomeration, LP, and urbanization and, Kohonen self-organizing maps to insightful analyses of these clusters. This article used 18-year county-based data from 2001 to 2018 and analyzes the cluster space in Hungary. Three things emerge out from this study: first, there are seven clusters in space; second, in all seven cluster agglomeration, LP, and urbanization are significantly co-exist and there is bidirectional causality among them; and third, Hungarian manufacturing regions can be classified into two phases of clusters. The manufacturing industrial structure in Hungary is group-specific where one group is in a declining phase and another is in the reindustrialization phase. Keywords Simultaneous equation · Cluster density · Self-organized map · Neural networks · Agglomeration · Labor productivity · Urbanization · Industrial space

Introduction The spatial study is a widely investigated topic in past decades, especially for the industrial agglomeration pattern. Agglomeration of industries can be driven by the different regional factors such as firms that are located near to the same type of secondary industry that are beneficial and so-called localization of industries. Further, the industry-specific productive employee attracts this type of cluster and brings new skill, knowledge, innovation, and expertise. These skilled laborers enhance productivity in that area and also positively contributed to the process of urbanization. The three factors industrial agglomeration, labor productivity (LP), and urbanization are co-existing together and, possibly create * Devesh Singh [email protected] 1

Kaposvar University, Guba Sandor, Utca-40, Somogy County, Kaposvar, Hungary 7400

13

Vol.:(0123456789)

Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

the cluster space. So, the essential question is worth examining whether there is a spatial concentration among LP, urbanization, and agglomeration of industries. To examine this relation, first, we explore the cluster space among the listed variables through density-based clustering methodology. The second step is the verifying stage since we assumed that all three variables are co-existing in space and form a cluster, to verify this co-existence there should be a significant relation among LP, urbanization, and agglomeration. Therefore, we use the cluster-wise simultaneous equation approach that we found through the spatial density pattern and signify the relation among LP, urbanization, and agglomeration of industries. Third, we used the Kohonen self-organizing maps of supervised and unsupervised machine learning to deeply examine the insight of cluster space, and further, we present the cluster for manufacturing industries in Hungary, for binary phase: the first phase of manufacturing cluster where the industries are in declining phase and gross value added (GVA) or LP is lower and another phase of manufacturing cluster where the industries are in growing phase and gross value added is above the national average according to (Lengyel et al., 2017). Lall et al. (2004) states that the agglomeration of economies has two types. First is the localization in which the firm tries to locate near to another firm of the same industry. Hence, high skilled labor attracts to these clusters and causes a specialized labor pool. Second is the case of agglomeration economies due to the external to the firm; these firms have proximity to the other industries so-called urbanization of economies. The concept among the LP urbanization and agglomeration easily understand by the theory of economic geography. Henderson et  al. (2001) stated that the net benefits of industrial agglomeration in dense urban areas are immensely accumulated by innovative and technology intensive sectors. This is because the benefit of sharing creative ideas and access to producer services (i.e., venture capital) is remarkably higher compared with low-end manufacturing, which engages in the standardized production process. So, as a result, these innovative sectors afford to locate in dense urban areas and ready to pay high wages and rent in dense urban location industry clusters if other factors (e.g., transport) are constant or have negligible effect. Therefore, in this industrial framework, low-end industry producing standardized product tries to locate in small urban centers where rent is lower. The spatial structure of Hungarian industries is the result of interactions of centripetal and centrifugal forces of industrial agglomeration. The literature has confirmed that industrial agglomeration contributes to the growth of LP and further LP leads to urbanization (Abel et al., 2010; Yang et al., 2009). So, LP and industrial agglomeration are mutually related (Ke, 2009). In another scenario, post-socialist economies became an indispensable part of the global economy and export become significant and modern industries emerged in Hungary, although the process became halted in 2008 global crises and the concept of reindustrialization (such as neighboring regions near to the Austrian border) and deindustrialization (such as the Buda-Pest region) emerged. Reorganization of center-periphery regions is already happening in post-socialist countries such as reindustrialization in Hungary (Lengyel et  al., 2017), which makes the Hungarian regions a perfect ground to analyze the cluster space among agglomeration, LP, and urbanization.

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

There is literature that discusses the relationship between agglomeration and industrial productivity, agglomeration and LP, agglomeration and urbanization, and agglomeration and technology spillover. To the best of my knowledge, no study has included all three variables together at the regional/county level study especially in Central and Eastern Europe (CEE) countries. This work attempts to fill this gap contributes to the empirical literature and uses the county level data. Further, the present study aims to fill this literature gaps by addressing the two following questions: First, whether the LP, agglomeration, and urbanizations form a cluster space in Hungary for the post-socialist period from 2001 to 2018, and if so, then which variable dominance in the regions to form a cluster node. Second, what role does industrial development play in spatial integration? The main objectives of this article are as follow: (i) present the clusters space through the variables; (ii) examine the relationships among the variables; (iii) analyses the LP, urbanization, and agglomeration concerning industrial cluster space; and (iv) explore the Kohonen supervised and unsupervised machine learning approach. Further, this article is propagated as follows: (i) discuss the related literature on agglomeration, LP, and urbanization; (ii) data and methodology for this study; (iii) discussion of empirical results; and (iv) summarization and conclusion by offering suggestion and policy implications.

Literature Industrial Clusters in Different Regions While exploring the areas of spatial concentration, there are three types of induced agglomerations, urbanization (clustering of firms in urban areas to take advantage of lower rent, infrastructure cost, and access of large market, skill labor which has higher LP), localization (benefits from the clustering of firms because of same industries), and internal scale (economies of scale achieved by individual firm) of economies (Hoover, 1948). The spatial clustering allows variety of benefits like sharing of suppliers, labor pooling, ad specialization which turn to contribute in enhanced economic growth and productivity. In the decades of 1980, it was assumed that information and telecommunication technology (ICTs) reduced the necessity of physical proximity alternately influenced the agglomeration. Now currently we are in a better era of ICT infrastructure; however, we can observe the reappearance of core periphery regions, reindustrialization of industries, and urbanization. These recreational urbanizations are not just attracting skilled labor also attract niche labor (Giuliano et  al., 2019). For some industries proximity influenced higher extent compared with others; therefore, there is a spatial heterogeneity in the United States (US) (Craig et al., 2016; Yang et al., 2019). The research by Boasson (2011) investigates the temporal and spatial clustering of service industries in 62 counties of New York state. Results shows that there is a general tendency to form a cluster and has positive autocorrelation across all service industry. Lu and Cao (2019) examine the agglomeration of specific

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

service industry (Big data) in China. They find that financial support from the government and educated labor forces are main factors for industrial agglomeration and to attract big data enterprises. Gokan and Kuroiwa (2016) explored the spatial pattern of manufacturing industries in Vietnam using local density and global extent and shows that the spatial pattern is industry specific and spread throughout in countrywide. Chica (2016) analyzed the spatial cluster of knowledge-based industries in Finland and shows that specialization and diversified economies in core and specialization economies of periphery regions in Helsinki create the spatial cluster for knowledge-based industries. There are two knowledge-based industrial economies that are observed: first, finance and ICT based which has high economic diversity and second, high-tech manufacturing, education, and health which has low economic diversity. Kano and Vas (2013) analyzed the spatial concentration of knowledge industries in Hungary and the analyses explored that still there are high spatial concentrations of firm near to the Budapest region; it is noted that the spatial distribution depends on the level of territorial unit examined and socio-economic condition of regions. López and Páez (2017) find the significant spatial cluster at sub-regional level in Canada for both hi-tech manufacturing and knowledge intensive firms in a single study. Their results show that the skilled labor and transport infrastructure is the main reason to form the industrial cluster.

Agglomeration and Labor Productivity Brunow and Blien (2015) examine the agglomeration effect on LP. The urbanization and agglomeration of industries are an important factor for individual establishment especially in metropolitan areas which enhances the LP in the country. At regional level agglomeration appears due to the “Marshallian forces” such as the forwardbackward linkage between firm circulates the higher productivity in higher industrial agglomerated and urbanized areas, LP, and knowledge spillover. In urbanized areas, LP occurred at the highest level, while the less urbanized areas separated from the agglomeration are disadvantaged. Firms located within the core of the industrial agglomeration have an advantage compared with the firms located near to the agglomeration. Although some firms try to locate near the value chain, the productive labor pooling is the main factor to a conglomeration of industries (Diodato et  al., 2018). The research by Giuliano et  al. (2019) examines the agglomeration and re-evolution of urbanization and presented that the agglomeration attracts the labor workforces and enhances the productivity in that region. Numerous studies examined the importance of agglomeration in LP such as Ke (2009) examines the agglomeration, productivity, and spatial spillover through simultaneous equation at the regional level in China for the single year 2005 and determine the regional determinant of agglomeration of industries and urban productivity along with the spillover effect the neighboring city. Andersson and Lööf (2009) examine the relationship between agglomeration and productivity at the firm level in Sweden from 1997 to 2004 and employ the dynamic and static model.

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

There is a positive relation between LP and size of the urbanization at a firm level, and these firms become more productive by being located in agglomerated regions. Agglomeration and Urbanization The empirical literature suggests that urbanization is more productive in agglomerated areas, especially the case of the services sector because some activities seek complex actions to fulfill this complex requirement; industries require a critical mass of high skill workforces. Ciccone (2002) analyzes the spatial fixed effect and distribution of employment. The result shows that the agglomeration of industries increased the aggregated LP in Europe, but this increment is less compared with the U.S. Further, Yang et al. (2009) examine the effect of spatial agglomeration with the variation of LP in China from 2001 to 2005 and suggested that the spatial industrial agglomeration positively increment the LP in China and this increment is larger compare to the U.S and Europe. The research by Ke (2009) examines the causal linkage between LP and agglomeration of industries and shows that the agglomeration and LP are mutually related. Lall and Mengistae (2005) examine the relation between LP and agglomeration of industries. They employ the two-step GMM model and concluded that the agglomeration and LP are positively correlated with each other in Sweden and also agglomeration enhances the LP. There are two forces work behind urbanization: population growth due to the expansion of urban centers and migration of people from rural to urban areas. The larger number of urbanizations brings the skills, knowledge, and innovative ideas which increase the LP and enhance the firm profit. Therefore, there is a relation between LP and urbanization (Miller, 2014). On doubling the urbanization or the spatial distribution of population increases the productivity between 2 and 4% in the U.S. In the U.S urbanized areas with above standardized mean average, human capital stock yield higher productivity compared with below standardized mean average. Generally, these patterns occurred in areas where the sharing of information and exchange of ideas are an important part of the production process (Abel et al., 2010). Empirical literature indicating the causality among agglomeration, LP, and urbanization and all are important to industrial development. Despite the growing number of empirical studies focuses on the relation between agglomeration and LP and, agglomeration and urbanization and different sector industries cluster space in widely investigated regions of however, little attention has been paid to whether these variables are co-existing in a space and make the clusters. This research fills this gap by analyzing the county/regional level data from Hungary. Further, this study contributes to the literature in four aspects. First, a theoretical framework is explored to analyze the relationship between agglomeration and LP, agglomeration and urbanization and, spatial clusters of manufacturing and services industries. Second, this study contributes to the literature by identifying the co-existence of agglomeration, LP, and urbanization in the Hungarian cluster space. Third, this study provides empirical evidence of which counties can contribute prominently

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

in future re-industrialization and assist policymakers in the advancement of the 4th industrial revolution. Fourth, this study identifies the emerging cluster and influence of all three variables in different counties to make clusters.

Data and Methodology This research using panel data of 19 county and including Budapest as a separate entity because of its identical administrative status equivalent to all the other 19 counties so, total 20 entities in our samples spanning the year 2001 to 2018. Data is extracted from the Hungarian statistical office (HSO) or Központi Statisztikai Hivatal (KSH) at NUTS-3 (Nomenclature des Unités Territoriales Statistiques) level and transformed into log form for analysis to makes the data usability and interpretation of results comparatively easier (HCSO, 2021). We used in this paper both the service and manufacturing sectors. The research by Hu et  al. (2019) examine the dual-core industry space in China and found that service and manufacturing industries are closely related to each other and both are important to regional industrial development. Therefore, we combinedly considered both the manufacturing and services sector data in the agglomeration of industries. Agglomeration directly influences the firm LP and because urbanization and localization both are important for individual establishment (Brunow & Blien, 2015; Graham & Melo, 2009). So, this research uses three variables agglomeration of industries, LP and urbanization. Where, AG = Agglomeration = number of active firms in a county. URB = Urbanization = urban population, as an indicator of urbanization measured in millions of persons. LP = Labor productivity in a county = all firm revenue in a county /economically active inhabitants in a county. CG = The growth rate of companies in a county = [(present revenue of the companies in a county – past revenue of the companies in a county)/past revenue of the companies in a county] × 100. There are three main analyses in this article. The first analysis is the densitybased clusters, to find the cluster space between agglomeration, urbanization, and LP. The second analysis is the three-stage least square simultaneous equation 3SLS method to examine the relationships among the variables in each cluster that we find in the first analysis. The third analysis is the supervised and unsupervised SOM (Self-Organized Map) to depict the cluster space and characteristics of the existing cluster in Hungary. The details of all three methodological approaches used in this research are given below in sub-sections.

Cluster Density Suppose in unknown density point p(x) is a mixture of k densities for (x) set of points. Sammut & Webb, (2011) and Hartigan (1975) suggested density-based cluster

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

definition a density contour cluster at level λ is expressed at (x) maximum connected data points where p(x) > λ, where p(x) at each point x, a density threshold λ, and links specified for some pairs of objects. Along with these conditions, distance function can be expressed as pairs of objects x and y through the following expression. { [ ] −min p(x), p(y) , x and y are linked, d(x, y) = 0 otherwise. This study uses the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm, which is based on density connectivity and density reachability. DBSCAN was first proposed by Ester et  al. (1996). To understand the algorithm behind the DBSCAN, let us suppose X =  {x1, x2, x3, …, xn} data points in our database (Kriegel et al., 2011): (1) start with unique arbitrary data points (2) extract the ε- neighbor from this unique arbitrary data points within ε distance (3) selected data points are marked as visited if there are sufficient data points near neighbor then a process of cluster started otherwise declare as noise (4) this procedure repeated from (2) until all points in a cluster is determined (5) further, to find a new cluster unvisited data points are selected and repeat steps from (2) to (4) (6) the process will continue until all data points are visited. Simultaneous Equation He and Zhu (2009) proposed that the agglomeration of industries positively associate with the LP. Ellison et  al. (2010) find that labor market pooling is the significant driver of industrial agglomeration. On the other side, Han et al. (2019) depict that urbanization is also a significantly associated with industrial agglomeration and industrial agglomeration is an important economic phenomenon in urban areas. Brunow and Blien (2015) found agglomeration effect exists because of urbanization and localization and, the concentration of firms positively affects the LP. So, trivariables are related to each other; disruption in one variable affects the other two variables and act as a system of equation. Based on empirical literature to test our research hypothesis, we decompose agglomeration, LP, urbanization, and growth rate of the companies in the following equation: ( ) AG l̇ = f LPl̇ , URBl̇ , CGl̇ (1) where i = 1, …, N denotes the county. Since our study is a panel data study, Eq. (1) can be written in panel data form as follows (Hun, 2011):

(AG)it = 훽0 + 훽1 LPit + 훽2 (URB)it + 훽3 (CG)it + 휀it

(2)

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

In the above equations, all variables explained at the regional level where the subscript i = 1, …, N denotes the county, β0 is a constant term for model equation, and β1 − βn is constant terms for associated variables, ε is the error in the equation, and t  =  1, …, T denotes the time period. In Eq.  (2) agglomerations, LP, and urbanization are endogenous or dependent variables and growth of the companies is an exogenous variable. From, Eq. (2) derived in the form of simultaneous equations and taking log, since, we specify the three-way linkage therefore model following the multiple Eqs.  3–5 in log form (Kahouli, 2018). The final equations are as following in simultaneous form:

ln(AG)it = 훽0 + 훽1 lnLPit + 훽2 ln(URB)it + 훽3 ln(CG)it + 휀it

(3)

ln(LP)it = 훽0 + 훽1 ln(AG)it + 훽2 ln(URB)it + 훽3 ln(CG)it + 휀it

(4)

ln(URB)it = 훽0 + 훽1 ln(AG)it + 훽2 ln(LP)it + 훽3 ln(CG)it + 휀it

(5)

Self-Organizing Maps Another methodology we used in this article is SOM. The SOM is capable of analyzing high-dimensional data, able to find similarities between elements in a group of instances, and organizing the data neurons from computational layer to the associated cluster with a pattern, in the set of instances. Therefore, Kohonen self-organizing map is a depiction of learned structure that appears similar object to clusters and provide complex data into two-dimensional graphical visualization. The SOM is an unsupervised methodology of competitive learning introduced by the Kohonen (1982). Unlike other machine learning, SOM is a non-parametric and nonlinear analysis that does not depend on any strict assumption. The SOM consist of input and output layers where each output layer has one coordinate, facilitate to calculate the distance between the output layer, and appear into a two-dimension map based on the similarity of each output layer weight. The Fig. 1 Layout of SOM

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

neurons appear into SOM according to their weight so similar nodes are close to each other and unmatched weighted nodes located far from matched weighted nodes. Figure  1 depicts the SOM basic layout where WI(x) is the weight and x is the point in the input space mapping along with the I(x) output space. The SOM has five basic elements (initialization, competition, cooperation, adaptation, and continuation) to process the two-dimension complex informative maps. There is the following process for clustering and data visualization (Bullinaria, 2004; Demir & Cergibozan, 2018; Sarlin, 2011). 1. Initialization: each connection calculated with the initial weights. 2. Competitive: using discriminant function weight vector wj and input vector x for each neuron j calculated. The discriminant function is calculated through Euclidean distance where the smallest distance is the basis of competition and consider as the best fit value. The discriminant function is defined as: ∑D dj (X) = (x − wji )2 (6) i=1 i Suppose input space in D dimension and wji is the connection weight in the input unit i with the neurons j. 3. Cooperative: In biological neurons, if one neuron is malfunctioning, the closest neuron is active instead of further away neurons. Therefore, there is a topological neighbor decay with the distance. So, the nearest topological neighbor is located close to the input vector, the updated topological neighbor act cooperatively. 2 Tj.I(x) = exp(−Sj,I(x) 2∕휎 2 )

(7)

I(x) is winning neuron index, Tj.I(x) is a topological neighborhood, and the value of Tj.I(x) become zero for an infinite distance. So, σ is the decay function which is defined as

σ(t) = 휎0 exp(−t∕휏휎 )

(8)

4. Adaptive: To be self-organized SOM should be adaptive. It means after cooperation adaptive neurons also have to be updated their weight; therefore, the updated equation is

Δwji = 휂(t).Tj.I(x) (t).(xi − wji )

(9)

and 휂(t) = 휂2 exp(−t∕휏n ) is the learning rate at t time. 5. Continuation: repeat cycle from step 2 until the feature map stops changing. The SOM is a type of neural network, and the algorithm is based on the principal dimension reduction where suppose input vector x which are similar and closed to each other in high dimension space are mapped close to each other in low dimensional discretized 2D map. All nodes in the map are associated by the weights (wj), not by the value, and each node has its coordinates (i, j); please see Eq. (6). The SOM algorithm is based on the following steps:

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

1) Each node weight vector wji initializes to a random value and chooses the random input vector wk 2) Connect with the first node where t, i, j = 0 through Euclidean distance of weight vector Wij and the input vector x(t), see Eq. (6) 3) Trace the node which has the smallest distance t 4) Calculate the Best Matching Unit (BMU), BMU select based on the similarity between the current input values and all the other nodes in the network 5) Find the best topological neighborhood based on Eqs. 7 and 8 6) Update the wji of the first node in the neighborhood of the BMU by involving a fraction of the difference between the input vector x(t) and the weight w(t) of the neuron repeat this step for all nodes in the BMU neighborhood 7) Repeat the complete iteration until reaching the selected iteration limit t = n.

Discussion In Hungary, ‘socialist industrialization’ materialized from 1949 to 1990 and this industry started to decline after regime change, large public companies were restructured or privatized, and most of them were closed down. It implies deindustrialization started right after the regime change. Diverse spatial patterns of reindustrialization have begun to develop in Hungary. New industrial activities and services deconcentrated, and new economic growth poles emerged in the countryside (Kovacs & Tosics, 2014). As a result, local institutional and infrastructural developments have been arise; new core regions appeared and diminish the cultural and economic role of the capital, Budapest. The counties where LP and agglomeration of industries and the LP and urbanization of industries spatially concentrated towards few counties however, weak concentration occur most of the regions. Agglomeration of industries is an important economic phenomenon in urban areas and has a significant effect on LP. Agglomeration of industries or a cluster of companies are united by the common interests in a region. Diversity and specialization are two main agglomeration of economies and indicate the external economy of scale of specialization. External economies of scale are due to the spatial clustering of industries, and knowledge spillover is the most significant externalities for agglomeration of industries (Cabral et al., 2018). Clusters are important part of regional economies in all stages of economic development in a country and also important to understand and addressing economic challenges. Thus, clusters support company to reach high level of productivity (Ketels & Sölvell, 2005). Moreover, such clustering improves the local economic performances because of leverage in technological expertise, broader access to markets, and supply of skilled labor. Thus, increasing concentration of industry in urban areas promoted the free exchange of information among firms and increases the productivity (Cruz Villamil, 2010). During post-socialist era, there were structural changes in Hungarian economy; significant shift from primary sector to the secondary sector and the tertiary sector manufacture growth were substantial in four counties (Szabolcs-SzatmárBereg, Győr-Moson-Sopron, Veszprém and Bács-Kiskun), and services industry were predominantly dominated by the central region of Hungary (Budapest and

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

Fig. 2 Cluster space in Hungary

Pest) (Mariš, 2015). Current data indicated that manufacturing industry continues in decline phase only on metropolitan region Budapest and its agglomeration. Nevertheless, this region is still the major cluster of manufacturing and 23.9% manufacturing employee work in this central region as on 2014. Cluster density result shows in Fig.  2 and observed seven clusters in space through the mutually collective variable’s agglomeration, LP, and urbanization. Further, we depicted that all clusters are hetrogenous and are in different shape and size and, no outlier point density detected. Possibly, this hetroginity is due to the development differences in Hungarian regions. Dusek et  al. (2014) characterized the development differences based on the living and income conditions, labor market situation, allocation of population, and some other economic indicators such as Gross Domestic Product (GDP). There are mainly eight pole cities based on contribution of Hungarian economic growth Győr, Szeged, Veszprém, Debrecen, Székesfehérvár, Miskolc, Pécs, and Budapest. Szanyi et  al. (2010) said clusters like Győr are specialized for automotive industries, Szeged for food processing, and Székesfehérvár specialized for information technology. Central Hungary is the biggest cluster in Hungarian spatial cluster space; Budapest and Pest regions are specialized in secondary and tertiary industries such as education, information technology, pharmaceutical, and knowledge intensive (Czabán, 2015). The city Debrecen, Pécs, and Szeged are potential knowledge cluster, and after Budapest, the second largest city of Hungary which is Debrecen also has the presence of micro cluster of medical devices and pharmaceuticals sectors. We assumed that the industrial agglomeration is not the stand-alone factor; there is a co-existence between agglomeration, LP, and urbanization that causes the formation of density cluster space in Hungary. Therefore, with significant contribution in cluster space, there should be a significant relationship among the

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

Journal of the Knowledge Economy

variables. To align this argument, we considered the hypothesis for the simultaneous equation. H1: If there is a significant relationship among the variables, the agglomeration of industries, LP, and urbanization are co-existing together in cluster space and have a complete necessary condition to form a cluster space in Hungary. Further, to observe the significance of three-way linkage among variable, three-stage least square simultaneous equation (3SLS) is perfectly suitable to our requirement. Since, in cluster space, we found seven clusters through density-based clustering; so, to perform the 3SLS, first, we ranked the counties in seven clusters based on the presence of the number of active firms in the counties and consider 2018 as a base year. Therefore, the classification of seven clusters based on the presence of active firms is as follow: Cluster 1: Budapest and Pest, a cluster where the number of active firms above 40,000. Cluster 2: Győr-Moson-Sopron, Bács-Kiskun, and Hajdú-Bihar, a cluster where the number of active firms between 35,000 to 40,000. Cluster 3: Csongrád, Borsod-Abaúj-Zemplén, Szabolcs-Szatmár-Bereg, cluster where the number of active firms between 35,000 and 30,000. Cluster 4: Baranya, Fejér, and Veszprém clusters where the number of active firms between 30,000 and 25,000. Cluster 5: Komárom-Esztergom, Zala, and Somogy clusters where the number of active firms between 25,000 and 20,000. Cluster 6: Vas, Heves, Jász-Nagykun-Szolnok, and Békés clusters where the number of active firms between 20,000 and 15,000. Cluster 7: Tolna and Nógrád clusters where the number of active firms less than 15,000. There had been significant changes in a spatial cluster of industries in the post-socialist era; in Budapest manufacturing industries, concentration had been decreased and depended on the services sector but still contributing largely to country’s growth. A new division of labor has been emerged surrounding the capital region (Barta et  al., 2008). Organization of cluster strongly depends on the size of the region, which plays a significant role in interregional competition: industrial complex (local but not urban), pure agglomeration (urban), and social networks (local but not urban). The smaller regions can achieve by associating to their hinterland to secure denser and large networks. The capital region (Budapest and surrounded region) of Hungary shown faster growth compared with the rest of the country. Urban agglomeration in Hungary leads to higher productivity through a deep labor market, greater specialization, and robust network effect (Karlsson, 2008). Most spatial concentrations in Hungary are located in the same areas where industrial activity was associated before the transition period (Szanyi et al., 2010). In the simultaneous equation, we consider the growth rate of the companies in a county as an exogenous variable. Table 1 shows the relation among agglomeration of industries, LP, and urbanization. Now, there are several things to observe in the results. First, please notice the first cluster of the results in the second column. Three

13 Content courtesy of Springer Nature, terms of use apply. Rights reserved.

(4)

***

1.656*** (0.265)

Cluster

0.079 0.20 84.17

2116.51

13.54

0.028

(0.143)

***

(0.00896) − 0.171

0.97

***

***

(5)

***

1.301*** (0.172)

(0.311)

93.38

0.28

0.182

17.38

***

p