Cities in a world of diminishing transport costs
CCities in a world of diminishing transport costs
Tomoya Mori a,b,1 and Minoru Osawa a a Institute of Economic Research, Kyoto University. Yoshida-Honmachi, Sakyo-Ku, Kyoto, Kyoto 606-8501, Japan.; b Research Institute of Economy, Trade and Industry, 11thfloor, Annex, Ministry of Economy, Trade and Industry 1-3-1, Kasumigaseki Chiyoda-ku, Tokyo 100-8901, Japan.This manuscript was compiled on January 11, 2021
Economic activities favor mutual geographical proximity and con-centrate spatially to form cities. In a world of diminishing trans-port costs, however, the advantage of physical proximity is fading,and the role of cities in the economy may be declining. To provideinsights into the long-run evolution of cities, we analyzed Japan’scensus data over the 1970–2015 period. We found that fewer andlarger cities thrived at the national scale, suggesting an eventualmono-centric economy with a single megacity; simultaneously, eachlarger city flattened out at the local scale, suggesting an eventualextinction of cities. We interpret this multi-scale phenomenon as aninstance of pattern formation by self-organization, which is widelystudied in mathematics and biology. However, cities’ dynamics aredistinct from mathematical or biological mechanisms because theyare governed by economic interactions mediated by transport costsbetween locations. Our results call for the synthesis of knowledge inmathematics, biology, and economics to open the door for a generalpattern formation theory that is applicable to socioeconomic phe-nomena. city size | spatial pattern | spatial scale | science of cities C ities are home to most of the population and economicactivities within developed countries and industrializedregions in developing countries (1). For instance, Japanesecities accounted for 80% of the total national population, butoccupied only 6% of the total land area in Japan in 2015according to our data. Agglomeration effects, or superlin-ear scaling in cities’ outputs (2), facilitate city existence andgrowth. The fundamental trade-off between the various ag-glomeration effects and the costs associated with the transferof goods, people, and information has been the key factor forunderstanding the spatial organization of economic activities(3). The advantage of physical proximity and the role of citiesin the economy might diminish in the near future, given thecontinued improvement in transport technology and the riseof Internet communication in recent decades (4). Instead,cities might continue to thrive even in the era of diminishingtransport costs because in-person exchange of ideas is at theheart of innovation (5).To gain insights into the fate of cities, we address the actualsituation of cities in Japan between 1970 and 2015. Japanesedata in this period have unique and ideal features for studyingthe impacts of transport costs on the population distribution.First, Japan experienced from-scratch development in its na-tionwide high-speed transport networks, which highlights therole of decline in transport costs in a relatively short period oftime compared to the situation in other developed economies.Second, the availability of high-geographic-resolution popu-lation data over the study period enables us to assemble anew bottom-up dataset of cities, which, in turn, allows us toevaluate the evolution of the spatial population distributionin detail without being affected by the municipal boundaries. Results
We identify Japanese cities in a bottom-up manner based ongrid-level population census data (see
Materials and Meth-ods ). Figs. 1A and B show the 503 and 450 cities respectivelyidentified in 1970 and 2015. Japan experienced significantdecline in interregional transport costs in this period. Trig-gered by the Tokyo Olympics of 1964, the total high-speedrailway (highway) length in Japan increased from 515 km(879 km) in 1970 to 5,345 km (14,062 km) in 2015. In 1970,the high-speed railway and highway networks connected onlyTokyo and Osaka, the two largest cities (Figs. 1C and D);four of the ten largest cities were located between Tokyo andOsaka in 1970 (Fig. 1A). However, in 2015, the largest citieswere geographically farther apart, as only one among the tenlargest cities (Nagoya) remained between Tokyo and Osaka(Fig. 1B).Figs. 2A–D show the 2015/1970 ratios for population size,area, highest population density, and average population den-sity, respectively, for the 302 cities that existed in both 1970and 2015. Population size increased by 21% on average(Fig. 2A), indicating that the population concentration inthe 302 cities increased during the analyzed period. Simulta-neously, the city area almost doubled, peak population densityhalved (Figs. 2B and C), and average population density de-creased by 35% (Fig. 2D), indicating the apparent tendency oflocal dispersion or suburbanization within each city. Figs. 2E–L compare the population density distributions between 1970and 2015 in each of the largest eight cities as of 2015. Thedensity distributions shifted to the left, indicating that thelocal dispersion took place over a larger area in these cities,thus, decreasing the peak population density.Fig. 2A also suggests that, among the 302 cities, someattracted more population, and others less so. Fig. 2M showsthe population growth rates for the cities in Fig. 2A againsttheir population shares for 2015. There is a trend for largercities attract more residents, while the opposite holds forsmaller cities. Fig. 2N reports the tendency of increasingspatial separation for the top 100 cities (see the
SI Appendix for details). Specifically, it shows the ratio d r ≡ d r, /d r, ,where d r,t is an index of the distance between the r largestcities in year t , together with the significance levels of theirmagnitudes. If d r >
1, the r largest cities in Japan werespatially more distant from each other in 2015 than they werein 1970. We observe that d r is consistently greater than unity,with d r being larger for smaller r values. Generally, citiesbecame more distant from each other during 1970–2015, withthis tendency being stronger for larger cities. Author contributions: T.M. and M.O. equally contributed to the design and implementation of theresearch, to the analysis of the results, and to the writing of the manuscript.The authors declare no conflict of interest. To whom correspondence should be addressed. E-mail: [email protected]
Mori et al. a r X i v : . [ ec on . GN ] J a n ig. 1. Spatial patterns of the population and transport network in Japan. (A, B) Thered areas on each map indicate the 503 and 450 cities in 1970 and 2015, respectively.Otherwise, a lighter color corresponds to a larger population size per a 1km-by-1kmgrid. We consider four major islands (Honshu, Kyushu, Shikoku, and Hokkaido) aswell as other islands connected to one of these by road. The largest 12 cities areindicated with their population rankings between parentheses. (C) The high-speedrailway network in 2015 is indicated by the blue lines. The yellow circles indicatethe locations of stations and the red circles the stations at which express trainsstop. In 1970, only the segment between Tokyo and Osaka (the red arrow) wascompleted. (D) The highway network as of 1970 (red) and 2015 (blue). Highway andhigh-speed railway network data are obtained from Kokudo Suuchi Joho Download(https://nlftp.mlit.go.jp/ksj/index.html).
Discussion
We identified contrasting evolutions of the urban populationin Japan over the study period. First, fewer cities grew larger,and they became more spatially distant from each other. Sec-ond, the remaining cities on average flattened out towardsextinction.In extant economic models, spatial patterns are explainedthrough the interactions between agents’ positive and negativefeedback, mediated by the transport costs between locations.Three representative feedback mechanisms can be found inthe literature: (i) local positive agglomeration effects (i.e.,short-range positive feedback) such as knowledge exchanges,market sharing, and production (6); (ii) crowding effects (i.e.,short-range negative feedback), such as traffic congestion andlocal scarcity of land for housing and production, which pro-mote the flattening or suburbanization of a city (7); and (iii)competition between different cities (i.e., long-range negativefeedback) (8). In a model with all three effects, lower transportcosts promote long-range negative feedback by increasing thecompetition between more distant locations; therefore, onlythe larger and more distant cities enjoying more extensivelocal positive feedback, such as Tokyo and Osaka, can thrive.At the same time, better transport accessibility induces subur-banization within each city as it mitigates the crowding effects(9). Overall, the evolution of the urban system in Japan is con-sistent with these predictions: Japanese cities move towardsa mono-centric distribution around Tokyo, which is itself ex-periencing an evening out, partly confirming the “death ofdistance” (4).Since cities can be seen as peaks (spots) in the populationdistribution, our findings can be associated with the mathe-matical pattern formation theory (10). Several analogies existbetween our results and known facts in the literature. Namely,stationary multiple spots in reaction–diffusion systems arisefrom a combination of long-range negative and short-rangepositive feedback (11). When the diffusion coefficients in areaction-diffusion system become large, the number of spotsdeclines due to “overcrowding instability” that limits the pos-sible number of spots in the system (12). Economic models ofcities are formulated on the basis of transport costs betweenlocations, which would be interpreted as the impedance forthe “diffusion” of positive and negative feedback effects.Despite the similarities, however, pattern formation in thecity system poses new challenges that call for the synthesisof knowledge in economics, biology, and mathematics. Citysizes exhibit significant variation; their distribution can beapproximated well by the power law within many countries(13). This fact invalidates the naïve interpretation of cities asmultiple-spot patterns in two-component reaction–diffusionmodels, as no significant variations in spot sizes can arise.Economic modeling with homogeneous agents also cannotexplain cross-sectional size variations of the cities by self-organization (9).An economic rationale for size diversity of cities lies in in-dustrial diversity, which gives rise to the diversity in the spatialextents of feedback effects. For example, how geographicallyfar a firm could locate while still serving customers’ needs isdifferent across industries, which leads to the characteristic“frequency” in the location of firms in each industry. Addi-tionally, many industries coordinate spatially in cities as theyseek short-range positive feedback (e.g., cities’ large labor and
Mori et al. ig. 2. (A–D) Population size, area, largest peak population density, average population density for the 302 Japanese cities existing both in 2015 and 1970. In graphs A, C, andD, the total national population is normalized be 1 in each year. (E–L) The distribution of population size in a 1km-by-1km cell (i.e., population density) in 1970 and 2015 in eachof the largest eight Japanese cities as of 2015. In each city, population densities are normalized by the highest 1970 value. The curves in the panels indicate Gaussian kerneldensities. (M) The log ratio of each city’s population share, between 2015 and 1970, against the log population share to the national population in 2015, with a fitted line by anordinary least squared regression. (N) The 2015/1970 ratio of the spacing between the r largest cities against the city’s population ranking in 2015. The dashed curve indicatesthe average random counterfactual ratios. The lower (upper) dash-dot curve indicates the 1% (99%) value of the random counterfactual ratio. The four largest cities ( r ≤ are omitted, as they remain the same between 1970 and 2015. consumer pools). This process leads to the simultaneous emer-gence of spatial fractal structure (or the urban hierarchy) and apower-law city size distribution (14); both are confirmed in thereal-world data (15). Thus, to explain the observed variationin city sizes and its long-run dynamics, inter-temporal changesin transport costs alone are not sufficient; we should model(industrial) diversity in the spatial extent of feedback effects.Research on reaction–diffusion models with more than twocomponents is relatively scarce in the literature owing to theirintractability. However, in light of the discussed analogies, itwould be possible to build a unified theory for the city systemand other socioeconomic phenomena. Materials and Methods
Cities.
The Grid Square Statistics of the Population Censuses ofJapan provides population count data for 1970–2015 in 30”-by-45” ( ≈ city as a set of contiguous cells, each with a density of at least 1,000people/km , that yields a total population of at least 10,000. Seethe SI Appendix for the data and codes.
Distance between cities.
The measurement of distance between the r largest cities used in Fig.2N is computed with the Open Source Rout-ing Machine (OSRM, http://project-osrm.org/ ) and OpenStreetMap( http://download.geofabrik.de/ ). See the SI Appendix for the formulafor d r,t and other details. Data availability.
All data and codes are provided in the
SI Appendix . ACKNOWLEDGMENTS.
This research was conducted as partof the project, “Agglomeration-based framework for empirical and policy analyses of regional economies,” undertaken at the ResearchInstitute of Economy, Trade and Industry. This research has alsobeen supported by the Kajima Foundation, and the Murata ScienceFoundation, the International Joint Research Center of AdvancedEconomic Theory of the Institute of Economic Research in Japan,and the Grant in Aid for Research Nos. 17H00987 and 19K15108 ofthe MEXT, Japan. Part of this research was conducted under theproject, “Research on the evaluation of spatial economic impacts ofbuilding bus termini” (Principal Investigator: Prof. Yuki Takayama,Kanazawa University), supported by the Committee on AdvancedRoad Technology, the MLIT, Japan.
1. United Nations, The 2018 revision of world urbanization prospects (2018).2. LMA Bettencourt, J Lobo, D Helbing, C Kühnert, GB West, Growth, innovation, scaling, andthe pace of life in cities.
Proc. Natl. Acad. Sci. United States Am . , 7301–7306 (2007).3. M Fujita, JF Thisse, Economics of Agglomeration: Cities, Industrial Location, and Globaliza-tion . (Cambridge University Press), (2002).4. F Cairncross,
The Death of Distance: How the Communications Revolution Will Change OurLives . (Harvard Business School Press Boston, MA), (1997).5. E Glaeser,
Triumph of the City: How Our Greatest Invention Makes Us Richer, Smarter,Greener, Healthier, and Happier . (Penguin Books), (2011).6. G Duranton, D Puga, Micro-foundations of urban agglomeration economies in
Handbook ofRegional and Urban Economics , eds. JV Henderson, JF Thisse. (Elsevier) Vol. 4, pp. 2063–2117 (2004).7. M Fujita,
Urban Economic Theory: Land Use and City Size . (Cambridge University Press),(1989).8. P Krugman, On the number and location of cities.
Eur. Econ. Rev . , 293–298 (1993).9. T Akamatsu, T Mori, M Osawa, Y Takayama, Endogenous agglomeration in a many-regionworld. arXvi:1912.05113v2 (2020).10. JD Murray, Mathematical Biology II: Spatial Models and Biomedical Applications . (Springer-Verlag), (1989).11. H Meinhardt, A Gierer, Pattern formation by local self-activation and lateral inhibition.
Bioes-says , 753–760 (2000).12. J Wei, M Winter, Stationary multiple spots for reaction–diffusion systems. J. Math. Biol . ,53–89 (2008).13. X Gabaix, YM Ioannides, The evolution of city size distributions in Handbook of Regional andUrban Economics , eds. JV Henderson, JF Thisse. (Elsevier) Vol. 4, pp. 2341–2378 (2004).14. WT Hsu, Central place theory and city size distribution.
Econ. J . , 903–932 (2012).15. T Mori, TE Smith, WT Hsu, Common power laws for cities and spatial fractal structures. Proc.Natl. Acad. Sci. United States Am . , 6469–6475 (2020). Mori et al. upplementary Information Distance between cities.
The distance between cities is computed asthe shortest-path road distance between the most densely populatedgrids within each city. We computed bilateral road distances byapplying an open-source routing engine, the Open Source RoutingMachine (OSRM, http://project-osrm.org/ ) to the geographic data ofOpenStreetMap ( http://download.geofabrik.de/ ). Specifically, we usedthe routing service version 1 of OSRM with driving mode; the othersettings of routing were taken from the OSRM default as describedin Supplementary Information of (15). The complete manual forthe distance computation is available from distance_computation.zip at https://datadryad.org/stash/dataset/doi:10.5061/dryad.8gtht76k5 . A measure of distance between the largest cities.
We define a mea-sure of distance between the r largest cities in year t by d r,t ≡ r X i ∈ U r,t min j ∈ U r,t \{ i } d ( i, j ) , [1]where U r,t is the set of the r largest cities in year t , and d ( i, j )be the road-network distance between cities i and j , where thelocation of a city is the grid cell with the highest population density.To gauge the significance of the magnitude of d r , we consider ahypothetical value ˜ d r obtained from Eq. (1) with U r,t replaced by r cities randomly selected from all the 886 cities existed in at leastone of every five years between 1970 and 2015. city_data.zip. The data set and Python programs for replicating theresults are available from . There are five comma-separated value files: (i) city_population.csv contains four column data. Column
CITY includesthe city indices,
POP the population size,
NORM_POP the populationshare in the national total population,
YEAR the year (1970 or 2015).(ii) balanced_city_set.csv contains the list of cities that existed inboth 1970 and 2015. (iii) cells_in_cities.csv contains four columndata of the 1 km-by-1 km grid level population size in each citythat existed both in 1970 and 2015. Column
CELL_ID includesunique indices for 1 km-by-1 km grids,
CITY the city indices,
POP the population sizes of cities,
NORM_POP the shares of cities inthe national total population,
YEAR the year (1970 or 2015). (iv) all_cities_1970-2015.csv contains the indices of the most populated 1km-by-1 km grid cells in the cities that existed any year between1970 and 2015 (every five years). (v) bilateral_distances.csv containsbilateral distances among the grid cells listed in (iv).There are three Python programs (Python version 3.8). (a)
CitySizeEvolution.py generates Fig. 2A-D. (b)
CitySpatialEvolution.py generates Fig. 2E-L. (c)
GlobalConcentration.py generates Fig. 2M-N.Put all programs and the data in the same folder.