Spatial scale of agglomeration and dispersion: Theoretical foundations and empirical implications

Akamatsu, Takashi and Mori, Tomoya and Osawa, Minoru and Takayama, Yuki (2017): Spatial scale of agglomeration and dispersion: Theoretical foundations and empirical implications.

Abstract

This paper studies the theoretical properties of existing economic geography models with agglomeration and dispersion forces in a many-region setup, rather than their original two-region space, to investigate the spatial scale — global or local — of agglomeration and dispersion intrinsic to each model. We show that models in the literature reduce to two canonical classes that differ starkly in their engendered spatial patterns and comparative statics. Our formal results offer a consistent explanation for the set of various outcomes from the extant reduced-form regression analyses and also provide qualitative predictions of the treatment effects in the structural model-based studies on regional agglomeration.

• Item Type: MPRA Paper
• Language: English
• Keywords: Agglomeration, dispersion, spatial scale, multiple equilibria, bifurcation
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; F - International Economics > F1 - Trade > F15 - Economic Integration; F - International Economics > F2 - International Factor Movements and International Business > F22 - International Migration; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R13 - General Equilibrium and Welfare Economic Analysis of Regional Economies

References

Ahlfeldt, Gabriel M., Stephen J. Redding, Daniel M. Sturm, and Nikolaus Wolf, The economics of density: Evidence from the Berlin Wall, Econometrica, 2015, 83 (6), 2127– 2189.

Akamatsu, Takashi, Shota Fujishima, and Yuki Takayama, Discrete-space agglomeration models with social interactions: Multiplicity, stability, and continuous limit of equilibria, Journal of Mathematical Economics, 2017, 69, 22–37.

Akamatsu, Takashi, Yuki Takayama, and Kiyohiro Ikeda, Spatial discounting, Fourier, and racetrack economy: A recipe for the analysis of spatial agglomeration models, Journal of Economic Dynamics and Control, 2012, 99 (11), 32–52.

Alder, Simon, Chinese roads in India: The effect of transport infrastructure on economic development, December 2016. Unpublished manuscript.

Allen, Treb and Costas Arkolakis, Trade and the topography of the spatial economy, The Quarterly Journal of Economics, 2014, 129 (3), 1085–1140.

Alonso, Wiliam, Location and Land Use: Toward a General Theory of Land Rent, Cambridge, MA: Harvard University Press, 1964.

Àngel Garcia-López, Miquel, Urban spatial structure, suburbanization and transportation in Barcelona, Journal of Urban Economics, 2012, 72 (2-3), 176–190.

Àngel Garcia-López, Adelheid Holl, and Elizabet Viladecans-Marsal, Suburbanization and highways in Spain when the Romans and Bourbons still shpae its cities, Journal of Urban Economics, 2015, 85, 52–67.

Armington, Paul S., A theory of demand for product distinguished by place of production, International Monetary Fund Staff Papers, 1969, 16 (1), 159–178.

Arthur, W. Brian, Increasing Returns and Path Dependence in the Economy, Ann Arbor, MI: University of Michigan Press, 1994.

Baum-Snow, Nathaniel, Did highways cause suburbanization?, The Quarterly Journal of Economics, May 2007, 122 (2), 775–805.

Baum-Snow, Nathaniel, Urban transport expansions, employment decentralization, and the spatial scope of agglomeration economies, 2017. Unpublished manuscript.

Baum-Snow, Nathaniel, J. Vernon Henderson, Matthew A. Turner, Qinghua Zhang, and Loren Brandt, Highways, market access, and urban growth in China, January 2016. Unpublished manuscript.

Baum-Snow, Nathaniel, Loren Brandt, J. Vernon Henderson, Matthew A. Turner, and Qinghua Zhang, Roads, railroads and decentralization of Chinese cities, Review of Economics and Statistics, 2017, 99 (3), 435–448.

Beckmann, Martin J., Spatial equilibrium in the dispersed city, in Yorgos Papageorgiou, ed., Mathematical Land Use Theory, Lexington Book, 1976.

Behrens, Kristian and Frederic Robert-Nicoud, Agglomeration theory with heterogeneous agents, in Gilles Duranton, J. Vernon Henderson, and William C. Strange, eds., Handbook of Regional and Urban Economics, Vol. 5, Elsevier, 2015, pp. 171–245.

Behrens, Kristian, Giordano Mion, Yasusada Murata, and Jens Südekum, Spatial frictions, Journal of Urban Economics, 2017, 97, 40–70.

Blanchet, Adrien, Pascal Mossay, and Filippo Santambrogio, Existence and uniqueness of equilibrium for a spatial model of social interactions, International Economic Review, 2016, 57 (1), 36–60.

Brendan, J. Frey and Delbert Dueck, Clustering by passing messages between data points, Science, 2007, 315, 972–976.

Brown, George W. and John von Neumann, Solutions of games by differential equations, in Harold W. Kuhn and Albert W. Tucker, eds., Contributions to the Theory of Games I, Princeton University Press, 1950.

Brülhart, Marius and Rolf Traeger, An account of geographic concentration patterns in Europe, Regional Science and Urban Economics, 2005, 35 (6), 597–624.

Caliendo, Lorenzo, Fernando Parro, Esteban Rossi-Hansberg, and Pierre-Daniel Sarte, The impact of regional and sectoral productivity changes of the U.S. economy, 2016. Unpublished manuscript.

Combes, Pierre-Philippe and Laurent Gobillon, The empirics of agglomeration economies, in Gilles Duranton, J. Vernon Henderson, and William C. Strange, eds., Handbook of Regional and Urban Economics, Vol. 5, Elsevier, 2015, pp. 247–348.

Desmet, Klaus and Esteban Rossi-Hansberg, Spatial growth and industry age, Journal of Economic Theory, 2009, 144 (6), 2477–2502s.

Desmet, Klaus and Esteban Rossi-Hansberg, Spatial development, American Economic Review, 2014, 104 (4), 1211–1243.

Desmet, Klaus and Esteban Rossi-Hansberg, The spatial development of India, Journal of Regional Science, 2015, 55 (1), 10–30.

Desmet, Klaus, Dávid Krisztián Nagy, and Esteban Rossi-Hansberg, The geography of development, Journal of Political Economy, 2017, forthcoming.

Donaldson, Dave and Richard Hornbeck, Railroads and American economic growth: A ‘market access’ approach, The Quarterly Journal of Economics, 2016, 131 (2), 799–858.

Dupuis, Paul and Anna Nagurney, Dynamical systems and variational inequalities, Annals of Operations Research, 1993, 44 (1), 7–42.

Duranton, Gilles and Diego Puga, Micro-foundations of urban agglomeration economies, in J. Vernon Henderson and Jacques-François Thisse, eds., Handbook of Regional and Urban Economics, Vol. 4, North-Holland, 2004, pp. 2063–2117.

Duranton, Gilles and Henry G. Overman, Testing for localization using micro-geographic data, Review of Economic Studies, 2005, 72 (4), 1077–1106.

Duranton, Gilles and Matthew A. Turner, Urban growth and transportation, Review of Economic Studies, 2012, 79 (4), 1407–1440.

Ellison, Glenn D. and Edward L. Glaeser, Geographic concentration in U.S. manufacturing industries: A dartboard approach, Journal of Political Economy, 1997, 105 (5), 889–927.

Faber, Benjamin, Trade integration, market size, and industrialization: Evidence from China’s national trunk highway system, Review of Economic Studies, 2014, 81 (3), 1046– 1070.

Facchinei, Francisco and Jong-Shi Pang, Finite-dimensional Variational Inequalities and Complementarity Problems, Springer Science & Business Media, 2007.

Fajgelbaum, Pablo D. and Edouard Schaal, Optimal transport network in spatial equilibrium, March 2017. NBER Working Paper 19492.

Forslid, Rikard and Gianmarco I. P. Ottaviano, An analytically solvable core-periphery model, Journal of Economic Geography, 2003, 33 (3), 229–240.

Fujita, Masahisa and Hideaki Ogawa, Multiple equilibria and structural transformation of non-monocentric urban configurations, Regional Science and Urban Economics, 1982, 12, 161–196.

Fujita, Masahisa and Jacques-François Thisse, Economics of Agglomeration: Cities, Industrial Location, and Regional Growth (2nd Edition), Cambridge University Press, 2013.

Fujita, Masahisa and Paul R. Krugman, When is the economy monocentric?: von Thuünen and Chamberlin unified, Regional Science and Urban Economics, 1995, 25 (4), 505–528.

Fujita, Masahisa, Paul R. Krugman, and Anthony Venables, The Spatial Economy: Cities, Regions, and International Trade, Princeton University Press, 1999.

Fujita, Masahisa, Paul R. Krugman, and Tomoya Mori, On the evolution of hierarchical urban systems, European Economic Review, February 1999, 43 (2), 209–251.

Guckenheimer, John and Philip J. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, 1983.

Harris, Britton and Alan G. Wilson, Equilibrium values and dynamics of attractiveness terms in production-constrained spatial-interaction models, Environment and Planning A, 1978, 10 (4), 371–388.

Head, Keith and Terry Mayer, The empirics of agglomeration and trade, in JacquesFrançois Thisse and J. Vernon Henderson, eds., Handbook of Regional and Urban Economics, Vol. 4, Elsevier, 2004, chapter 59, pp. 2609–2669.

Helpman, Elhanan, The size of regions, in David Pines, Efrainm Sadka, and Itzhak Zilcha, eds., Topics in Public Economics: Theoretical and Applied Analysis, Cambridge University Press, 1998, pp. 33–54.

Henderson, J. Vernon, The sizes and types of cities, American Economic Review, 1974, 64 (4), 640–656.

Horn, Roger A. and Charles R. Johnson, Matrix Analysis, Cambridge University Press, 2012.

Hsu, Wen-Tai, Central place theory and city size distribution, The Economic Journal, 2012, 122, 903–932.

Ikeda, Kiyohiro and Kazuo Murota, Bifurcation Theory for Hexagonal Agglomeration in Economic Geography, Springer, 2014.

Ikeda, Kiyohiro, Kazuo Murota and Yuki Takayama, Stable economic agglomeration patterns in two dimensions: Beyond the scope of central place theory, Journal of Regional Science, 2017, 57 (1), 132–172.

Ikeda, Kiyohiro, Kazuo Murota, Takashi Akamatsu, and Yuki Takayama, Agglomeration patterns in a long narrow economy of a new economic geography model: Analogy to a racetrack economy, International Journal of Economic Theory, 2017, 13, 113–145.

Ikeda, Kiyohiro, Kazuo Murota, Takashi Akamatsu, Tatsuhito Kono, and Yuki Takayama, Self-organization of hexagonal agglomeration patterns in new economic geography models, Journal of Economic Behavior and Organization, 2014, 99, 32–52.

Ikeda, Kiyohiro, Takashi Akamatsu, and Tatsuhito Kono, Spatial period-doubling agglomeration of a core–periphery model with a system of cities, Journal of Economic Dynamics and Control, 2012, 36 (5), 754–778.

Ishioka, Tsunenori, Extended K-means with and efficient estimation of the number of clusters, Japanese Journal of Applied Statistics, 2000, 29 (3), 141–149.

Kerr, William R. and Scott Duke Kominers, Agglomerative forces and cluster shapes, Review of Economics and Statistics, 2015, 97 (4), 877–899.

Kondo, Shigeru and Takashi Miura, Reaction–diffusion model as a framework for understanding biological pattern formation, Science, 2010, 329 (5999), 1616–1620.

Krugman, Paul R., Increasing returns and economic geography, Journal of Political Economy, 1991, 99 (3), 483–499.

Krugman, Paul R., On the number and location of cities, European Economic Review, 1993, 37 (2), 293–298.

Krugman, Paul R. and Anthony J. Venables, Globalization and the Inequality of Nations, The Quarterly Journal of Economics, 1995, 110 (4), 857–880.

Kuznetsov, Yuri A., Elements of Applied Bifurcation Theory (3rd Eds.), Springer-Verlag, 2004.

Lucas, Robert E. and Esteban Rossi-Hansberg, On the internal structure of cities, Econometrica, 2002, 70 (4), 1445–1476.

Marshall, John Urquhart, The Structure of Urban Systems, The University of Toronto Press, 1989.

Matsuyama, Kiminori, Geography of the world economy, 1999. Unpublished manuscript.

Meinhardt, Hans and Alfred Gierer, Pattern formation by local self-activation and lateral inhibition, Bioessays, 2000, 22 (8), 753–760.

Monte, Ferdinando, Stephen J. Redding, and Esteban Rossi-Hansberg, Commuting, migration and local employment, 2016. Unpublished manuscript.

Mori, Tomoya, A modeling of megalopolis formation: The maturing of city systems, Journal of Urban Economics, 1997, 42, 133–157.

Mori, Tomoya and Kohei Takeda, Highways, high-speed railways and the growth of cities, November 2017. Unpublished manuscript, Institute of Economic Research, Kyoto University.

Mori, Tomoya and Tony E. Smith, A probabilistic modeling approach to the detection of industrial agglomeration, Journal of Economic Geography, 2014, 14 (3), 547–588.

Mori, Tomoya and Tony E. Smith, On the spatial scale of industrial agglomerations, Journal of Urban Economics, 2015, (89), 1–20.

Mori, Tomoya, Koji Nishikimi, and Tony E. Smith, A divergence statistic for industrial localization, Review of Economics and Statistics, 2005, 87 (4), 635–651.

Mori, Tomoya, Se-il Mun, and Shosei Sakaguchi, Industrial agglomeration and transport costs, 2017. Unpublished manuscript.

Mossay, Pascal and Pierre M. Picard, On spatial equilibria in a social interaction model, Journal of Economic Theory, 2011, 146 (6), 2455–2477.

Murata, Yasusada, Product diversity, taste heterogeneity, and geographic distribution of economic activities: Market vs. non-market interactions, Journal of Urban Economics, 2003, 53 (1), 126–144.

Murata, Yasusada and Jacques-Frano ̧is Thisse, A simple model of economic geography à la Helpman–Tabucbi, Journal of Urban Economics, 2005, 58 (1), 137–155.

Nagy, Dávid Krisztián, City location and economic growth, January 2017. Unpublished manuscript.

Nash, John, Non-cooperative games, Annals of Mathematics, 1951, 54 (2), 286–295.

Osawa, Minoru, Takashi Akamatsu, and Yuki Takayama, Harris and Wilson (1978) model revisited: The spatial period-doubling cascade in an urban retail model, Journal of Regional Science, 2017, 57 (3), 442–466.

Ota, Mitsuru and Masahisa Fujita, Communication technologies and spatial organization of multi-unit firms in metropolitan areas, Regional Science and Urban Economics, 1993, 23 (6), 695–729.

Ottaviano, Gianmarco I. P., Takatoshi Tabuchi, and Jacques-François Thisse, Agglomeration and trade revisited, International Economic Review, 2002, 43, 409–436.

Owens, Raymond III, Esteban Rossi-Hansberg, and Pierre-Daniel Sarte, Rethinking Detroit, 2017. Unpublished manuscript.

Oyama, Daisuke, Agglomeration under forward-looking expectations: Potentials and global stability, Regional Science and Urban Economics, 2009, 39 (6), 696–713.

Oyama, Daisuke, History versus expectations in economic geography reconsidered, Journal of Economic Dynamics and Control, 2009, 33 (2), 394–408.

Pelleg, Dan and Andrew Moore, X-means: Extending K-means with efficient estimation of the number of clusters, in Proceedings of the 17th International Conference on Machine Learning 2000, pp. 727–734.

Pflüger, Michael, A simple, analytically solvable, Chamberlinian agglomeration model, Regional Science and Urban Economics, 2004, 34 (5), 565–573.

Pflüger, Michael and Jens Südekum, Integration, agglomeration and welfare, Journal of Urban Economics, March 2008, 63 (2), 544–566.

Picard, Pierre M. and Takatoshi Tabuchi, On microfoundations of the city, Journal of Economic Theory, 2013, 148 (6), 2561–2582.

Puga, Diego, The rise and fall of regional inequalities, European Economic Review, 1999, 43 (2), 303–334.

Redding, Stephen J., Goods trade, factor mobility and welfare, Journal of International Economics, 2016, 101, 148–167.

and Daniel Sturm, The cost of remoteness: Evidence from German division and reunification, American Economic Review, 2008, 98 (5), 1766–1797.

and Esteban Rossi-Hansberg, Quantitative spatial economics, Annual Review of Economics, 2017, 9, 21–58.

and Matthew A. Turner, Transport costs and the spatial organization of economic activity, in Gilles Duranton, J. Vernon Henderson, and William C. Strange, eds., Handbook of Regional and Urban Economics, Vol. 5, Elsevier, 2015, pp. 1339–1398.

Rosenthal, Stuart and William C. Strange, Evidence on the nature and sources of agglomeration economies, in J. Vernon Henderson and Jacques-François Thisse, eds., Handbook of Regional and Urban Economics, Vol. 4, North-Holland, 2004, pp. 2119–2171.

Rozenfeld, Hernán D., Diego Rybski, Xavier Gabaix, and Hernán A. Makse, The area and population of cities: New insignts from a different perspective on cities, American Economic Review, 2011, 101 (5), 2205–2225.

Sandholm, William H., Population Games and Evolutionary Dynamics, MIT Press, 2010.

Solow, Robert M. and William S. Vickrey, Land use in a long narrow city, Journal of Economic Theory, 1971, 3 (4), 430–447.

Statistics Bureau, Ministry of Internal Affairs and Communications of Japan, Population Census, 1970.

Statistics Bureau, Ministry of Internal Affairs and Communications of Japan, Population Census, 2015.

Storeygard, Adam, Farther on down the road: Transport costs, trade and urban growth in sub-Saharan Africa, Review of Economic Studies, 2016, 83 (3), 1263–1295.

Tabuchi, Takatoshi, Urban agglomeration and dispersion: A synthesis of Alonso and Krugman, Journal of Urban Economics, 1998, 44 (3), 333–351.

Tabuchi, Takatoshi and Jacques-François Thisse, A new economic geography model of central places, Journal of Urban Economics, 2011, 69 (2), 240–252.

Tabuchi, Takatoshi, Jacques-François Thisse, and Dao-Zhi Zeng, On the number and size of cities, Journal of Economic Geography, 2005, 5 (4), 423–448.

Takatsuka, Hajime and Dao-Zhi Zeng, Dispersion forms: An interaction of market access, competition, and urban costs, Journal of Regional Science, 2009, 49 (1), 177–204.

Takayama, Yuki and Takashi Akamatsu, Emergence of polycentric urban configurations from combination of communication externality and spatial competition, Journal of JSCE Series D3: Infrastructure Planning and Management, 2011, 67 (1), 001–020.

Taylor, Peter D. and Leo B. Jonker, Evolutionarily stable strategies and game dynamics, Mathematical Biosciences, 1978, 40, 145–156.

Wilson, Alan G., Catastrophe Theory and Bifurcation: Applications to Urban and Regional Systems, University of California Press, 1981.

Yamasaki, Junichi, Railroads, technology adoption, and modern economic development: Evidence from Japan, 2017. Unpublished manuscript.