Economic complexity of prefectures in Japan
EEconomic complexity of prefectures in Japan
Abhijit Chakraborty
1, 2, 3* , Hiroyasu Inoue , Yoshi Fujiwara Graduate School of Simulation Studies, The University of Hyogo, Kobe 650-0047,Japan Advanced Systems Analysis, International Institute for Applied Systems Analysis(IIASA), Schlossplatz 1, A-2361 Laxenburg, Austria Complexity Science Hub Vienna, Josefstaedter Strasse 39, 1080 Vienna, Austria* [email protected]
Abstract
Every nation prioritizes the inclusive economic growth and development of all regions.However, we observe that economic activities are clustered in space, which results in adisparity in per-capita income among different regions. A complexity-based method wasproposed by Hidalgo and Hausmann [PNAS 106, 10570-10575 (2009)] to explain thelarge gaps in per-capita income across countries. Although there have been extensivestudies on countries’ economic complexity using international export data, studies oneconomic complexity at the regional level are relatively less studied. Here, we study theindustrial sector complexity of prefectures in Japan based on the basic information ofmore than one million firms. We aggregate the data as a bipartite network ofprefectures and industrial sectors. We decompose the bipartite network as aprefecture-prefecture network and sector-sector network, which reveals the relationshipsamong them. Similarities among the prefectures and among the sectors are measuredusing a metric. From these similarity matrices, we cluster the prefectures and sectorsusing the minimal spanning tree technique. The computed economic complexity indexfrom the structure of the bipartite network shows a high correlation withmacroeconomic indicators, such as per-capita gross prefectural product and prefecturalincome per person. We argue that this index reflects the present economic performanceand hidden potential of the prefectures for future growth.
Introduction
An important characteristic of the economy is that economic activities areheterogeneously distributed over geographic locations. For example, the “blue banana”region, which stretches from southeastern England through the Benelux countries,northern France and southwestern Germany to northeastern Italy, has a high level ofincome compared to other regions in Europe. Similar disparities in economic activityhave also been observed at the national level. In Portugal, differences in developmentactivities are observed between Lisbon and the north of the country and the center andthe south of the country. Similar examples include Paris compared to the rest of France,northeastern Spain and Madrid compare to the south and west parts of Spain, and thesouthern versus northern UK. Moreover, Japan also follows this trend. Japaneseprefectures such as Tokyo and Osaka are much more developed than rural prefecturessuch as Akita and Kagoshima [1, 2].September 1, 2020 1/21 a r X i v : . [ ec on . GN ] A ug idalgo and Hausmann proposed a complexity-based method to analyze thestructural properties of bipartite world trade networks to explain large gaps inper-capita income across countries [3, 4]. They quantitatively measured the complexityindices of the countries and their export products from the trade network, as theseeconomic complexity indices are useful for explaining countries’ performance. In arecent work, Mealy et al. showed [5] that the complexity index is equivalent to aspectral clustering algorithm, which divides a similarity graph into two parts. Theyhave further shown that these indices are connected to various dimensionality reductionmethods. Subsequently, Tacchella et al. introduced the fitness-complexity algorithm [6]based on the conceptual framework of Hidalgo and Hausmann to calculate intangibleproperties such as the fitness of countries and the complexity of export products fromthe structure of the world trade network. This method is very similar to the Googlepage rank method for directed networks and applicable to bipartite networks. In thisalgorithm, the fixed point of coupled nonlinear maps provides the fitness of countriesand the complexity of products. The comparison of the complexity indices obtained byboth methods [4, 6] with standard monetary indices presents an indication for potentialfuture growth.Economic complexity has traditionally been studied considering the structure of thebipartite world trade network [3, 4, 6–11]. Recently, economic complexity has beenstudied at the regional level for China [12], Brazil [10], Mexico [13], Italy [14], Spain [15],Australia [16], the US and the UK [5]. Most of these regional complexity studies aredone at very coarse grain level. In case of China, the analysis is performed for 31provinces with 2690 firms, which is a tiny fraction of all Chinese firms. The complexityanalysis is performed at states level for Brazil, Mexico and Australia. The difference inour study is that it concerns supply-chain in which prefectures and industrial sectors arestudied. We are looking at process of value added starting from a giant network of firmsand by aggregating as a binary bipartite network of prefectures and industrial sectors.The investigation of the structure of bipartite networks of cities and their economicactivities shows similarities with the nested ecological networks observed in mutualisticinteractions between species [17]. These complexity methods have also been studied inregard to ecological networks [18]. The quantification of complexity is found to beuseful for ranking active and passive species in ecological networks.Japan has been one of the most diversified country in the sense of the products.Therefore, it is important to reveal that whether such diversity comes from regionalstructures. We use information about more than one million Japanese firms for thisstudy. Similar Japanese firm-level data have been investigated in the past [19–25]. Paststudies on these datasets mostly aimed at uncovering the structure and dynamics of thesupply chain network and bank-firm credit network. However, the network thatrepresents the interactions of firms with geographic locations has not yet beenholistically studied. Here, we uncover the industrial sector complexity of prefectures inJapan from the structure of the bipartite network of prefectures and their economicactivities. The bipartite network is based on basic information of more than one millionJapanese firms. Using the locations of the firms and Japan Standard IndustrialClassification, we aggregate the data as a bipartite network of prefectures and industrialsectors. The monopartite projection of the bipartite network presents aprefecture-prefecture network and sector-sector network. The similarities amongprefectures and among industrial sectors are measured with these monopartite networks.Using the measured similarities, clustering among prefectures and sectors is shown withthe minimal spanning trees (MSTs). By employing the economic complexity framework,we calculate the economic complexity index (ECI) for the prefectures, which exhibit ahigh correlation with macroeconomic indicators, per-capita gross prefectural productand prefectural income per person. Furthermore, we have checked the robustness of theSeptember 1, 2020 2/21conomic complexity results using the fitness complexity method [6].The rest of this paper is structured as follows. In the Data section, we provide thedescriptions of the data. We explain the details of the methods in the Methods section.In the Results section, we present the results of our investigation, and in theConclusions section, we present our conclusions. Data
Our data are based on a survey conducted by Tokyo Shoko Research (TSR), one of theleading credit research agencies in Tokyo, which was supplied to us by the ResearchInstitute of Economy, Trade and Industry (RIETI). We use “TSR Kigyo Jouhou” (firminformation), which contains basic financial information on more than one million firms.The dataset was compiled in July 2016. We only considered “active” firms that haveinformation on employees and current year sales. The dataset contains N = 1 , , ,
455 industries (Japan StandardIndustrial Classification, November 2007, Revision 12). We aggregate the data as abipartite network of prefectures ( P = 47) and industrial sectors ( S = 91). We excludesome of the industrial sectors from the 99 major groups of the industrial sectorclassification, as these sectors skew the analysis in the following way: the excludedsectors are manufacturers of petroleum and coal products, services incidental to theinternet, financial product transaction dealers and future commodity transaction dealers,professional services, advertising services, and postal services. As these excluded sectorsare only linked to Tokyo, the inclusion of these sectors in our analysis results in thelargest value for the fitness of Tokyo, and the fitness of other prefectures become zero.The bipartite network is represented by the binary matrix M ps , where M ps = 1 ifthe industrial sector s has a significant amount of annual sales in prefecture p and 0otherwise. The Revealed Comparative Advantage (RCA) [26] is frequently used as aquantitative criterion to evaluate the relative dominance of a country, in the export ofcertain products by comparing it with the average export of those products. Recently,RCA has been measured from the ratio between the actual number of firms from anindustry in a province and the average number of firms from that industry in thatprovince [12]. Mealy et al. constructed a binary region-industry matrix based on thenumber of people employed in an industry in a region [5]. Here, we use annual sales ofindustrial sector s in prefecture p to measure the RCA, which is also a good indicator ofthe performance of a industrial sector. An industrial sector s is said to have asignificant amount of annual sales in prefecture p if its revealed comparative advantage(RCA) is greater than or equal to unity.The RCA is defined as RCA ps = w ps (cid:80) s w ps (cid:80) p w ps (cid:80) p,s w ps , where w ps is the aggregated annual sales of industrial sector s in prefecture p .To explain the heterogeneity in prefectural economic activities, we have examinedthe relationship between economic complexity and certain macroeconomic factorscharacterizing a prefectural economy. In particular, we find relationships betweeneconomic complexity and per-capita gross prefectural product and with prefecturalincome per person. The gross prefectural production is the total amount of value addedproduced in the prefecture and is calculated by subtracting raw material costs andutility costs from the total amount of services produced in the prefecture. Per-capitagross prefectural product is obtained by dividing the prefectural gross production by theSeptember 1, 2020 3/21refectural population. Prefectural income is the sum of employee compensation,property income and business income. The prefectural income per person is obtained bydividing the prefectural income by the prefectural population. We collected the grossprefectural product data, prefectural population data and prefectural income per persondata for the year 2015 from the Japanese government statistical portal site( ). Methods
Method for measuring economic complexity
Hidalgo and Hausmann introduced the idea of economic complexity for countries andproducts that they export [3, 4]. Here, we apply the method to Japanese prefectures andtheir industrial sectors. The economic complexity index (ECI) of prefectures andproduct complexity index (PCI) of industrial sectors can be calculated using thefollowing iterative equation: k p,N = 1 k p, (cid:88) s M ps k s,N − (1) k s,N = 1 k s, (cid:88) p M ps k p,N − , (2)where k p, = (cid:80) s M ps and k s, = (cid:80) p M ps . In network terms, k p, and k s, are known asthe average nearest neighbor degree.Substituting Eq. (2) into Eq. (1) obtains k p,N = 1 k p, (cid:88) s M ps k s, (cid:88) p (cid:48) M p (cid:48) s k p (cid:48) ,N − (3) k p,N = (cid:88) p (cid:48) k p (cid:48) ,N − (cid:88) s M ps M p (cid:48) s k p, k s, = (cid:88) p (cid:48) (cid:93) M pp (cid:48) k p (cid:48) ,N − , (4)where (cid:93) M pp (cid:48) = (cid:88) s M ps M p (cid:48) s k p, k s, (5)Eq. (4) is satisfied when k p,N = k p (cid:48) ,N − = 1, which is the eigenvector of (cid:93) M pp (cid:48) associated with the largest eigenvalue. Since this eigenvector is a vector with identicalcomponent values, it is not informative. The eigenvector associated with the secondlargest eigenvalue captures the largest amount of variance in the system. Therefore, wedefine the ECI as follows: ECI = −→ K − < −→ K >stdev ( −→ K ) , (6)where −→ K is the eigenvector of (cid:93) M pp (cid:48) associated with the second largest eigenvalue. < −→ K > and stdev ( −→ K ) indicate the mean and standard deviation of the components ofthe eigenvector −→ K , respectively.To further understand the matrix elements (cid:93) M pp (cid:48) , one can write Eq. (5) in thefollowing way: (cid:93) M pp (cid:48) = (cid:88) s M ps k p, M p (cid:48) s k s, = (cid:88) s P ( s | p ) P ( p (cid:48) | s ) = P ( p (cid:48) | p ) , (7)September 1, 2020 4/21here P ( s | p ) = M ps /k p, is the conditional probability that any industrial sector s ispresent in a given prefecture p , and P ( p (cid:48) | s ) = M p (cid:48) s /k s, is the conditional probabilitythat a particular industrial sector s is present in any prefecture p (cid:48) . From Eq. (7), wecan interpret (cid:93) M pp (cid:48) as the conditional probability of reaching p (cid:48) from p through commonindustrial sectors.Similarly, one can calculate the product complexity index (PCI) from the eigenvectorassociated with the second largest eigenvalue of the matrix: (cid:93) M ss (cid:48) = (cid:88) p M ps M ps (cid:48) k p, k s, . (8) Fitness-complexity algorithm
Based on the conceptual framework of Hidalgo and Hausmann [3] and inspired by theGoogle page rank algorithm, Tacchella et al. introduced the fitness-complexityalgorithm [6]. This method has been studied extensively in regard to countries and theirexport products [9–11]. Using this method, one can calculate the intangible propertiessuch as the fitness of countries and the complexity of products. Here, we use thismethod to study Japanese industrial sector and prefecture relationships.This method is based on the following three ideas. (i) The fitness of a prefecture ismeasured in terms of the diversity of the industrial sector set, weighted by thecomplexity of sectors. (ii) The more prefectures there are that have a particularindustrial sector, the lower the complexity of the industrial sector. (iii) The upperbound of the complexity of an industrial sector must be dominated by the prefectureswith the lowest fitness.The above facts are mathematically represented by the following self-consistentiterative coupled equations with fitness F p of prefectures and complexity Q s ofindustrial sectors: ˜ F ( n ) p = (cid:88) s M ps Q ( n − s , ˜ Q ( n ) s = 1 (cid:80) p M ps F ( n − p , (9)with normalization in each step: F ( n ) p = ˜ F ( n ) p < ˜ F ( n ) p > ; Q ( n ) s = ˜ Q ( n ) s < ˜ Q ( n ) s > . Here, n represents anyarbitrary iteration step.The initial conditions are ˜ Q (0) s = ˜ F (0) p = 1 for all p and s . The nature of the fixedpoint of the above equations depends on the structure of M ps [27].We use the fitness-complexity method to check the robustness of the ECI forprefectures. Results
Bipartite network projection is a useful technique to compress information aboutbipartite networks. The bipartite network of prefectures and industrial sectors can bedecomposed into two networks, namely, the network of prefectures and the network ofindustrial sectors.
The network of prefectures
The projection network of prefectures is represented by the ( N p × N p )prefecture-prefecture matrix P = M M T . The nondiagonal element P pp (cid:48) corresponds toSeptember 1, 2020 5/21 ig 1. The MST for prefectures. The colors red, yellow, green, cyan, blue, orange,purple and light gray are used for the Hokkaido, Tohoku, Kanto, Chubu, Kansai,Chugoku, Shikoku and Kyushu regions, respectively. The codes of the prefectures arelisted in Table S1 of Appendix S1. The eight regions of Japan are shown in a map usingthe same color code in Fig S1 of Appendix S1.the number of industrial sectors that prefecture p and p (cid:48) have in common. The diagonalelement P pp corresponds to the number of industrial sectors belonging to prefecture p and is a measure of the diversification of prefecture p . To quantify the competitionamong two prefectures, we can define the similarity matrix among prefectures asΘ Ppp (cid:48) = 2 × P pp (cid:48) P pp + P p (cid:48) p (cid:48) , where 0 ≤ Θ Ppp (cid:48) ≤
1. The values of Θ
Ppp (cid:48) indicate a correlation between the industrialsectors of prefectures p and p (cid:48) .We have investigated the interrelation between the different prefectures byconsidering how similar they are in terms of their industrial sectors. The MST is awidely used method to visualize the similarities between nodes. Given a set of nodeswith a matrix specifying the similarity between them, the method of MST involves thefollowing steps: (i) initially, an arbitrary node is set as a tree; (ii) the tree is grown witha link that has maximum similarity; and (iii) step (ii) is repeated until all nodes aremerged with the tree. We have shown the clustering of prefectures by the MST in Fig. 1.By visual inspection, we can observe that three different clusters on the tree consist offour prefectures of the Kanto, Chubu, and Kyushu regions. There is also a cluster offour prefectures of the Tohoku region and Hokkaido. Moreover, we observe varioushighly correlated pairs of geographically closely located prefectures, such asEhime-Kochi, Niigata-Nagano, Okayama-Hiroshima, Mie-Wakayama, and Hyogo-Osaka.This finding indicates a strong similarity among the regional industries and also reflectsthe cooperative and competitive nature of the regional industries in Japan.September 1, 2020 6/21 ig 2. The MST for industrial sectors. Different colors represent nineteendivisions of industrial sectors. For example, red (ID: 9 to 31), light green (ID: 48 to 59),and brown (ID: 6 to 8) represent the manufacturing, wholesale and retail, andconstruction industrial sectors, respectively. The node IDs, sectors and divisions aregiven in Tables S2 and S3 of Appendix S1.
The network of industrial sectors
The bipartite network can also be projected as a network of industrial sectors. Similarto the prefecture network, the industrial sector network is represented by the ( N s × N s )sector-sector matrix S = M T M . The nondiagonal element S ss (cid:48) corresponds to thenumber of prefectures having both sectors s and s (cid:48) . The diagonal element S ss corresponds to the number of prefectures having sector s , which is a measure of theubiquity of sector s . The similarity matrix among the sectors can be defined asΘ Sss (cid:48) = 2 × S ss (cid:48) S ss + S s (cid:48) s (cid:48) , where 0 ≤ Θ Sss (cid:48) ≤
1. Θ
Sss (cid:48) = 1 indicates that whenever industrial sector s is present in aprefecture, industrial sector s (cid:48) is also present.Similar to prefectures, we show the clustering of industrial sectors using the MST inFig. 2. Most of the manufacturing industrial sectors, except for manufacturers of food,chemical products, ceramic products, and information and communication electronics,form a single cluster among themselves, which may indicate that one manufacturingindustrial sector depends on other manufacturing industrial sectors. We also observe acluster of the construction sector and a cluster consisting of agriculture, forestry,fisheries and manufacturers of food industrial sectors. However, other sectors arescattered on the tree, and clusters are formed by the mixed composition of industrialsectors. For example, we observe that wholesale and retail trade industrial divisions donot appear together; rather, they are scattered all over the tree. This analysis showsSeptember 1, 2020 7/21 KAOIWMG AK YTFS IBTCGM STCH TKKNNITY ISFI YNNN GFSZAI MESHKYOSHGNRWKTTSM OYHSYCTS KGEHKC FOSGNSKMOTMZ KSON
20 30 40Diversity (k p, 0 ) 102030 U b i qu it y ( k p , )
We quantitatively measure the economic complexity of prefectures in Japan using themethod of Hausmann and Hidalgo [3]. For the method details, see the Methods section.The industrial diversification of a prefecture is represented by k p, , and the ubiquity ofits industrial sectors is indicated by k p, . We show the location of the prefectures in thespace defined by k p, and k p, in Fig. 3. k p, and k p, are slightly negatively correlated(Pearson correlation coefficient r = − .
230 and p-value = 0 . r = − . . × − [12].The ECI is a quantitative measure of the complexity of a prefecture and anonmonetary variable and can capture the economic development of a region [3, 4, 12].For prefectures, we can compare the ECI with macroeconomic variables such asper-capita gross prefectural product and prefectural income per person. We show therelationship between the ECI and per-capita gross prefectural product and prefecturalincome per person in Fig. 4. The ECI has a strong positive correlation with per-capitagross prefectural product (Pearson correlation coefficient r = 0 .
661 with a p-value= 4 . × − ) and prefectural income per person (Pearson correlation coefficient r = 0 .
668 with a p-value = 9 . × − ). Following [28], we can argue that thecorrelation between the macroeconomic factors and the ECI is observed because incomegrowth rates are similar for prefectures with similar industrial sectors. An exponentialfit to the data reflects the expected values of per-capita gross prefectural product andSeptember 1, 2020 8/21 KAOIW MGAKYTFSIBTCGM STCH TKKNNI TYISFIYNNN GFSZ AIMESH KY OSHGNRWKTTSM OYHSYCTS KGEHKC FOSGNSKM OTMZKS ON -1 0 1 2 3 4ECI3000500070009000 G r o ss p r e f ec t u r a l p r odu c t / ca p it a ( y e n ) HKAOIW MGAKYTFSIBTCGM STCH TKKNNI TYISFIYNNN GFSZ AIMESH KY OSHGNRWKTTSM OYHSYCTS KGEHKC FOSGNSKM OTMZKS ON -1 0 1 2 3 4ECI200040006000 P r e f ec t u r a l i n c o m e p e r p e r s on ( y e n ) (a) (b) Fig 4. Variation in (a) per-capita gross prefectural product and (b)prefectural income per person in with the ECI.
The straight lines in bothplots represent an exponential fit to the data, indicating the expected values of theper-capita gross prefectural product and prefectural income per person.prefectural income per person at their level of economic complexity. The deviations inreal per-capita gross prefectural product and prefectural income per person data fromthe expected values are informative and provide an indication of the economicperformance of the prefectures. Prefectures such as Osaka, Kanagawa, Hyogo, Fukuoka,and Okinawa, appearing below the expected values of per-capita gross prefecturalproduct and prefectural income per person, may have the potential to more quicklygrow in the future. An interpretation of the above results for the regions in Japan isgiven in the section “ the average prefectural economic complexity of regions in Japan”of Appendix S1.
Robustness of the ECI using the fitness-complexity algorithm
To check the robustness of the ECI, we compare it with the results obtained using thefitness-complexity method [6]. For detailed descriptions of the method, see the Methodssection. The convergence properties of the algorithm depend on the structure of M ps [27]. We investigate the triangular structure of binary matrix M ps by ordering therows and columns according to their fitness complexity rank. The structure of theordered M ps in Fig. 5 (a) shows that the diagonal line does not pass through the vacantregion, which ensures that the fitness values of the prefecture and complexity values ofthe industrial sectors will converge to nonzero fixed values with iterations [27]. Weindeed observe that the evolution of the fitness values of the prefectures reaches fixednonzero values with iterations, as shown in Fig. 5 (b).As seen from Fig. 6, similar to the ECI, the fitness of the prefectures also shows astrong positive correlation with the per-capita gross prefectural product (Pearsoncorrelation coefficient r = 0 .
742 and a p-value = 2 . × − ) and prefectural income perperson (Pearson correlation coefficient r = 0 .
746 and a p-value = 1 . × − ). Here, wealso observe that prefectures such as Osaka, Kanagawa, Hyogo, Fukuoka, and Okinawaappear below the expected values of the per-capita gross prefectural product andprefectural income per person. These prefectures may have the potential to morequickly grow in the future.The ECI method and fitness complexity method obtain quite similar results.Comparisons of the ranking of the prefectures and industrial sectors by the two methodsare listed in Tables S2 and S3 of Appendix S1, reflecting the fact that the nonmonetaryvariables ECI and fitness are good nonmonetary indicators for assessing theperformance of a prefecture.September 1, 2020 9/21
10 20 30 40Prefectures0102030405060708090 I ndu s t r i a l s ec t o r s l og (f it n e ss ) (a) (b) Fig 5. (a) Triangular structure of the ordered M matrix. (b) The evolutionof the fitness values of the prefectures with iterations.
The black dots in (a)represent that the industrial sector is present in the associated prefecture. There are atotal of 47 curves in (b), and each of them represents the evolution of fitness values of aprefecture.
HKAOIWMGAK YT FS IBTCGM ST CH TKKNNI TYISFIYNNN GFSZ AIMESH KY OSHGNRWKTTSM OYHSYCTSKGEHKC FOSGNSKM OTMZKS ON G r o ss p r e f ec t u r a l p r odu c t / ca p it a ( y e n ) HKAOIWMGAK YT FS IBTCGM ST CH TKKNNI TYISFIYNNN GFSZ AIMESH KY OSHGNRWKTTSM OYHSYCTSKGEHKC FOSGNSKM OTMZKS ON P r e f ec t u r a l i n c o m e p e r p e r s on ( y e n ) (a) (b) Fig 6. Variation in (a) per-capita gross prefectural product and (b)prefectural income per person in with fitness.
The straight lines in bothplots represent power law fit to the data, indicating expected values of the per-capitagross prefectural product and prefectural income per person.
Conclusions
We have studied the interactions of economic activities with prefectures in Japan usinginformation on one million firms. The economic relation between prefectures shows thatgeographically close prefectures are cooperative and competitive. The interrelationshipbetween industrial sectors shows the interdependence among them. The clustering ofindustrial sectors further shows that the clusters are formed by diverse industrialsectors, except the manufacturing and construction sectors. We have observed thatmost of the diversified Japanese prefectures have ubiquitous industrial sectors, which isvery different from the case of China [12] and in the international trades of countries [3].The economic complexity measured by the nonmonetary variables, ECI and fitness forthe prefectures shows a high correlation with macroeconomic indicators, such asper-capita gross prefectural product and prefectural income per person. Thesenonmonetary variables are very useful for understanding the economic activities in aprefecture. Our study will be helpful for understanding the economic health ofSeptember 1, 2020 10/21ndustries in a region. We have studied economic complexity of prefectures in Japanbased on the binary bipartite matrix. In the future, it will be interesting to see if onegets more valuable insights using a weighted matrix. Further studies on the dynamicevolution of economic complexity [29] in industrial sectors can predict themacroeconomic indicators for a prefecture.
Acknowledgments
This research was supported by MEXT as Exploratory Challenges on Post-K computer(Studies of Multilevel Spatiotemporal Simulation of Socioeconomic Phenomena). Wealso acknowledge computational resources IDs: hp160259, hp170242, hp180177, andhp190148.
References
1. L´opez-Rodr´ıguez J, Nakamura D. Mind the remoteness! income disparities acrossJapanese prefectures. Estudios de Econom´ıa. 2010;38(2):394.2. Porter ME. Location, competition, and economic development: Local clusters ina global economy. Economic development quarterly. 2000;14(1):15–34.3. Hidalgo CA, Hausmann R. The building blocks of economic complexity.Proceedings of the national academy of sciences. 2009;106(26):10570–10575.4. Hausmann R, Hidalgo CA, Bustos S, Coscia M, Simoes A, Yildirim MA. Theatlas of economic complexity: Mapping paths to prosperity. Mit Press; 2014.5. Mealy P, Farmer JD, Teytelboym A. Interpreting economic complexity. Scienceadvances. 2019;5(1):eaau1705.6. Tacchella A, Cristelli M, Caldarelli G, Gabrielli A, Pietronero L. A new metricsfor countries’ fitness and products’ complexity. Scientific reports. 2012;2:723.7. Caldarelli G, Cristelli M, Gabrielli A, Pietronero L, Scala A, Tacchella A. Anetwork analysis of countries’ export flows: firm grounds for the building blocksof the economy. PloS one. 2012;7(10):e47278.8. Mariani MS, Vidmer A, Medo M, Zhang YC. Measuring economic complexity ofcountries and products: which metric to use? The European Physical Journal B.2015;88(11):293.9. Pugliese E, Chiarotti GL, Zaccaria A, Pietronero L. Complex economies have alateral escape from the poverty trap. PloS one. 2017;12(1):e0168540.10. Operti FG, Pugliese E, Andrade Jr JS, Pietronero L, Gabrielli A. Dynamics inthe Fitness-Income plane: Brazilian states vs World countries. PloS one.2018;13(6):e0197616.11. Utkovski Z, Pradier MF, Stojkoski V, Perez-Cruz F, Kocarev L. Economiccomplexity unfolded: Interpretable model for the productive structure ofeconomies. PloS one. 2018;13(8):e0200822.12. Gao J, Zhou T. Quantifying China’s regional economic complexity. Physica A:Statistical Mechanics and its Applications. 2018;492:1591–1603.September 1, 2020 11/213. Ch´avez J C, Mosqueda M T, G´omez-Zald´ıvar M. Economic complexity andregional growth performance: Evidence from the Mexican Economy. Review ofRegional Studies. 2017;47(2):201–219.14. Basile R, Cicerone G, Iapadre, L. Economic complexity and regional laborproductivity distribution: evidence from Italy. 2019.15. Balsalobre S J P, Verduras C L, Lanchas J D. Measuring the EconomicComplexity at the sub-national level using international and interregional trade.2017.16. Reynolds C, Agrawal M, Lee I, Zhan C, Li J, Taylor P, Mares T, Morison J,Angelakis N, Roos G. A sub-national economic complexity analysis of Australia’sstates and territories. Regional Studies. 2018;52(5):715–726.17. Garas A, Rozenblat C, Schweitzer F. The network structure of city-firm relations.arXiv preprint arXiv:151202859. 2015;.18. Dom´ınguez-Garc´ıa V, Munoz MA. Ranking species in mutualistic networks.Scientific reports. 2015;5:8182.19. Fujiwara Y, Aoyama H. Large-scale structure of a nation-wide productionnetwork. The European Physical Journal B. 2010;77(4):565–580.20. Krichene H, Chakraborty A, Inoue H, Fujiwara Y. Business cycles’ correlationand systemic risk of the Japanese supplier-customer network. PloS one.2017;12(10):e0186467.21. Chakraborty A, Kichikawa Y, Iino T, Iyetomi H, Inoue H, Fujiwara Y, et al.Hierarchical communities in the walnut structure of the Japanese productionnetwork. PloS one. 2018;13(8):e0202739.22. Chakraborty A, Krichene H, Inoue H, Fujiwara Y. Characterization of thecommunity structure in a large-scale production network in Japan. Physica A:Statistical Mechanics and its Applications. 2019;513:210–221.23. De Masi G, Fujiwara Y, Gallegati M, Greenwald B, Stiglitz JE. An analysis ofthe Japanese credit network. Evolutionary and Institutional Economics Review.2011;7(2):209–232.24. Fujiwara Y, Aoyama H, Ikeda Y, Iyetomi H, Souma W. Structure and temporalchange of the credit network between banks and large firms in Japan. Economics:The Open-Access, Open-Assessment E-Journal. 2009;3:7.25. Chakraborty A, Krichene H, Inoue H, Fujiwara Y. Exponential random graphmodels for the Japanese bipartite network of banks and firms. Journal ofComputational Social Science. 2019;2(1):3–13.26. Balassa B. Trade liberalisation and “revealed” comparative advantage 1. Themanchester school. 1965;33(2):99–123.27. Pugliese E, Zaccaria A, Pietronero L. On the convergence of theFitness-Complexity Algorithm. The European Physical Journal Special Topics.2016;225(10):1893–1911.28. Kemp-Benedict E. An interpretation and critique of the Method of Reflections.MPRA Paper No 60705. 2014;.29. Tacchella A, Mazzilli D, Pietronero L. A dynamical systems approach to grossdomestic product forecasting. Nature Physics. 2018;14(8):861.September 1, 2020 12/21 upporting information
S1 Appendix. Appendix to the manuscript.
September 1, 2020 13/21 ppendix S1: Economic complexity of prefectures inJapan
September 1, 2020 • Table S1 represents the code of the prefectures and the number of firms in the 47prefectures in Japan. • Fig S1 shows the 8 regions and 47 prefectures in Japan. • Table S2 and Table S3 represent the industrial sectors and their divisions. • Table S4 compare the ranking of prefecture by economic complexity index methodand fitness complexity method. • Table S5 is list of the top and bottom 10 industrial sectors ranked by economiccomplexity index method and fitness complexity method. • Section “the average prefectural economic complexity of regions in Japan” relatethe obtained ECI with the regions in Japan • Fig S2 shows the variation of average prefectural economic coplexity index withaverage gross prefectural product per capita and average prefectural income perperson in eight regions and Tokyo. 14 able S1. Prefectures, regions and the firm distribution
ID Code Prefecture Region ).September 1, 2020 15/21 ig S1. The regions and prefectures in Japan. The numbers represent IDsof the prefectures as given in Table S1. The map is created using https://mapchart.net/japan.html .September 1, 2020 16/21 able S2. Industrial sectors and divisions
ID Sectors Divisions1 Agriculture Agriculture & Forestry2 Forestry3 Fisheries, except Aquaculture Fisheries4 Aquaculture5 Mining and quarrying of stone Mining and quarrying of stone6 Construction work, general including public and private construction work7 Construction work by specialist contractor,except equipment installation work Construction8 Equipment installation work9 Manufacture of food10 Manufacture of beverages11 Manufacture of textile products12 Manufacture of lumber and wood products, except furniture13 Manufacture of furniture and fixtures14 Manufacture of pulp, paper and paper products15 Printing and allied industries16 Manufacture of chemical and allied product17 Manufacture of plastic products, except otherwise classified18 Manufacture of rubber products19 Manufacture of leather tanning,leather products and fur skins20 Manufacture of ceramic, stone and clay products Manufacturing21 Manufacture of iron and steel22 Manufacture of non-ferrous metals and products23 Manufacture of fabricated metal products24 Manufacture of general-purpose machinery25 Manufacture of production machinery26 Manufacture of business oriented machinery27 Electronic parts, devices and electronic circuits28 Manufacture of electrical machinery, equipment and supplies29 Manufacture of information and communication electronics equipment30 Manufacture of transportation equipment31 Miscellaneous manufacturing industries32 Production, transmission and distribution of electricity33 Production and distribution of gas Electricity, Gas, Heat & Water34 Heat supply35 Collection, purification and distribution of water and sewage collection, processing and disposal36 Communications37 Broadcasting Information & Communications38 Information services39 Video picture information, sound information, character information production and distribution40 Railway transport41 Road Passenger transport42 Road freight transport43 Water transport Transport & Postal service44 Air transport45 Warehousing46 Services incidental to transport47 Postal services, including mail delivery
September 1, 2020 17/21 able S3. Industrial sectors and divisions
ID Sectors Divisions48 Wholesale trade, general merchandise49 Wholesale trade (textile and apparel)50 Wholesale trade (food and beverages)51 Wholesale trade (building materials, minerals and metals, etc.)52 Wholesale trade (machinery and equipment)53 Miscellaneous Wholesale trade Wholesale & Retail trade54 Retail trade, general merchandise55 Retail trade (woven fabrics, apparel, apparel accessories and notions)56 Retail trade (food and beverage)57 Retail trade (machinery and equipment)58 Miscellaneous retail trade59 Nonstore retailers60 Banking61 Financial institutions for cooperative organizations62 Non-deposit money corporations, including lending and credit card business Finance & Insurance63 Financial auxiliaries64 Insurance institutions, including insurance agents brokers and services65 Real estate agencies66 Real estate lessors and managers Real estate & Goods rental67 Goods rental and leasing68 Scientific and development research institutes Scientific research & Technical services69 Technical services, N.E.C.70 Accommodations71 Eating and drinking places Accommodations & Eating services72 Food take out and delivery services73 Laundry, beauty, and bath services74 Miscellaneous living-related and personal services Living-related and personal services75 Services for amusement and recreation76 School education Education & Learning support77 Miscellaneous education, learning support78 Medical and other health services79 Public health and hygiene Medical health care and welfare80 Social insurance, social welfare and care services81 Cooperative associations, N.E.C Cooperative associations82 Waste disposal business83 Automobile maintenance services84 Machine, etc. repair services, except otherwise classified85 Employment and worker dispatching services Service, N.E.C.86 Miscellaneous business services87 Political, business and cultural organizations88 Religion89 Miscellaneous services90 National government services Government services91 Local government services
September 1, 2020 18/21 able S4. Ranking of the prefectures using Economic Complexity Index(ECI) and Fitness
Rank ECI Fitness1 Tokyo Tokyo2 Aichi Osaka3 Osaka Aichi4 Kanagawa Kanagawa5 Hyogo Hyogo6 Fukuoka Chiba7 Saitama Ibaraki8 Kyoto Saitama9 Toyama Fukuoka10 Hiroshima Okinawa11 Chiba Toyama12 Okinawa Mie13 Shizuoka Kyoto14 Okayama Shizuoka15 Ishikawa Hokkaido16 Fukui Oita17 Kagawa Okayama18 Nara Gifu19 Ehime Ehime20 Yamaguchi Hiroshima21 Mie Kagawa22 Gifu Nara23 Oita Tochigi24 Tochigi Yamaguchi25 Shiga Tokushima26 Ibaraki Ishikawa27 Wakayama Fukushima28 Tokushima Wakayama29 Hokkaido Niigata30 Fukushima Saga31 Yamanashi Shiga32 Nagano Kagoshima33 Gunma Yamanashi34 Miyagi Aomori35 Niigata Fukui36 Shimane Shimane37 Yamagata Tottori38 Saga Yamagata39 Tottori Nagasaki40 Nagasaki Nagano41 Aomori Gunma42 Kagoshima Kumamoto43 Kumamoto Miyazaki44 Miyazaki Miyagi45 Akita Akita46 Kochi Kochi47 Iwate IwateSeptember 1, 2020 19/21 able S5. Top and bottom 10 industrial sectors ranked by ProductComplexity Index (PCI) and Complexity.
Rank PCI Complexity1 Video picture, sound, character information production and distribution Video picture, sound, character information production and distribution2 Wholesale trade, general merchandise Communications3 Communications Insurance institutions, including insurance agensts, brokers and services4 Insurance institutions, including insurance agensts, brokers and services Wholesale trade, general merchandise5 Railway Transport Postal services including mail delivery6 Postal services including mail delivery National government services7 Wholesale trade (Building materials, Minerals and Metals, etc) Real estate lessors and managers8 Manufacture of iron and steel Railway Transport9 National government services Financial auxiliaries10 Real estate lessors and managers Information Services82 Manufacture of food Forestry83 Forestry Miscellaneous retail trade84 Wholesale trade (food and beverages) Medical and other health services85 Manufacture of lumber and wood products except furniture Construction work, general including public and private86 Services for amusement and recreation Road passerger transport87 Accommodations Automobile maintenance services88 Cooperative assocations, N.E.C. Retail trade (Machinery and equipment)89 Agriculture Waste disposal business90 Fisheries, except aquaculture Construction work by specialist contractor, except equipment installation work91 Miscellaneous services Local government services
September 1, 2020 20/21 < G r o ss p r e f ec t u r a l p r odu c t / ca p it a ( y e n ) > < P r e f ec t u r a l i n c o m e p e r p e r s on ( y e n ) > Tokyo TokyoKansai KansaiChubu ChubuKanto KantoChugoku ChugokuShikoku ShikokuKyushu KyushuHokkaido HokkaidoTohoku Tohoku
Fig S2. The variation of average prefectural economic coplexity index < ECI > with (a) average gross prefectural product per capita and (b)average prefectural income per person in eight regions and Tokyo.
Thestraight line in both plots represnts the best exponential fit to the data, indicating theexpected values of the average per-capita gross prefectural product and averageprefectural income per person. The average is taken over all the prefectures of a region.
The average prefectural economic complexity ofregions in Japan
To relate the observed ECI with the regions in Japan, we have measured the averagerefectural economic complexity < ECI > of each regions in Japan. The averageprefectural economic complexity < ECI > is found to be strongly correlated withaverage gross prefectural product per capita (Pearson’s product-moment correlation r = 0 .
979 and p − value = 4 . × − ) and average prefectural income per person(Pearson’s product-moment correlation r = 0 .
982 and p − value = 2 . × −06