IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/64051.html
   My bibliography  Save this paper

US city size distribution revisited: Theory and empirical evidence

Author

Listed:
  • Ramos, Arturo
  • Sanz-Gracia, Fernando

Abstract

We develop a urban economic model in which agents locate in cities of different size so as to maximize the net output of the whole system of cities in a country. From this model two new city size distributions are exactly derived. We call these functions “threshold double Pareto Generalized Beta of the second kind” and “double mixture Pareto Generalized Beta of the second kind”. In order to test empirically the theory, we analyze the US urban system and consider three types of data (incorporated places from 1900 to 2000, all places in 2000 and 2010 and City Cluster Algorithm nuclei in 1991 and 2000). The results are encouraging because the new distributions clearly outperform the lognormal and the double Pareto lognormal for all data samples. We consider a number of different tests and statistical criteria and the results are robust to all of them. Thus, the new distributions describe accurately the US city size distribution and, therefore, support the validity of the theoretical model.

Suggested Citation

  • Ramos, Arturo & Sanz-Gracia, Fernando, 2015. "US city size distribution revisited: Theory and empirical evidence," MPRA Paper 64051, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:64051
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/64051/1/MPRA_paper_64051.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/67277/1/MPRA_paper_64051.pdf
    File Function: revised version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/71928/9/MPRA_paper_71928.pdf
    File Function: revised version
    Download Restriction: no

    References listed on IDEAS

    as
    1. Overman, Henry G. & Ioannides, Yannis M., 2001. "Cross-Sectional Evolution of the U.S. City Size Distribution," Journal of Urban Economics, Elsevier, vol. 49(3), pages 543-566, May.
    2. Pierre‐Philippe Combes & Gilles Duranton & Laurent Gobillon & Diego Puga & Sébastien Roux, 2012. "The Productivity Advantages of Large Cities: Distinguishing Agglomeration From Firm Selection," Econometrica, Econometric Society, vol. 80(6), pages 2543-2594, November.
    3. Yannis M. Ioannides & Henry G. Overman, 2004. "Spatial evolution of the US urban system," Journal of Economic Geography, Oxford University Press, vol. 4(2), pages 131-156, April.
    4. Rafael González‐Val, 2010. "The Evolution Of U.S. City Size Distribution From A Long‐Term Perspective (1900–2000)," Journal of Regional Science, Wiley Blackwell, vol. 50(5), pages 952-972, December.
    5. Glaeser, Edward L. & Kahn, Matthew E., 2010. "The greenness of cities: Carbon dioxide emissions and urban development," Journal of Urban Economics, Elsevier, vol. 67(3), pages 404-418, May.
    6. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Urban Structure and Growth," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 597-624.
    7. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, vol. 71(C), pages 193-208.
    8. Cirillo, Pasquale, 2013. "Are your data really Pareto distributed?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5947-5962.
    9. Sukkoo Kim, 2000. "Urban Development in the United States, 1690–1990," Southern Economic Journal, Southern Economic Association, vol. 66(4), pages 855-880, April.
    10. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    11. Kristian GIESEN & Jens SÜDEKUM, 2012. "The French Overall City Size Distribution," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 36, pages 107-126.
    12. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    13. Bosker, Maarten & Brakman, Steven & Garretsen, Harry & Schramm, Marc, 2008. "A century of shocks: The evolution of the German city size distribution 1925-1999," Regional Science and Urban Economics, Elsevier, vol. 38(4), pages 330-347, July.
    14. Luckstead, Jeff & Devadoss, Stephen, 2014. "Do the world’s largest cities follow Zipf’s and Gibrat’s laws?," Economics Letters, Elsevier, vol. 125(2), pages 182-186.
    15. Gilles Duranton, 2007. "Urban Evolutions: The Fast, the Slow, and the Still," American Economic Review, American Economic Association, vol. 97(1), pages 197-221, March.
    16. Albert Saiz, 2010. "The Geographic Determinants of Housing Supply," The Quarterly Journal of Economics, Oxford University Press, vol. 125(3), pages 1253-1296.
    17. Hernán D. Rozenfeld & Diego Rybski & Xavier Gabaix & Hernán A. Makse, 2011. "The Area and Population of Cities: New Insights from a Different Perspective on Cities," American Economic Review, American Economic Association, vol. 101(5), pages 2205-2225, August.
    18. Ioannides, Yannis M. & Overman, Henry G., 2003. "Zipf's law for cities: an empirical examination," Regional Science and Urban Economics, Elsevier, vol. 33(2), pages 127-137, March.
    19. Miguel Puente-Ajovín & Arturo Ramos, 2015. "On the parametric description of the French, German, Italian and Spanish city size distributions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 54(2), pages 489-509, March.
    20. Ioannides, Yannis & Skouras, Spyros, 2013. "US city size distribution: Robustly Pareto, but only in the tail," Journal of Urban Economics, Elsevier, vol. 73(1), pages 18-29.
    21. Lee, Sanghoon & Li, Qiang, 2013. "Uneven landscapes and city size distributions," Journal of Urban Economics, Elsevier, vol. 78(C), pages 19-29.
    22. Behrens, Kristian & Mion, Giordano & Murata, Yasusada & Suedekum, Jens, 2017. "Spatial frictions," Journal of Urban Economics, Elsevier, vol. 97(C), pages 40-70.
    23. Parr, John B., 1985. "A note on the size distribution of cities over time," Journal of Urban Economics, Elsevier, vol. 18(2), pages 199-212, September.
    24. Marcus Berliant & Hiroki Watanabe, 2015. "Explaining the size distribution of cities: Extreme economies," Quantitative Economics, Econometric Society, vol. 6(1), pages 153-187, March.
    25. Ferdinand Rauch, 2014. "Cities as spatial clusters," Journal of Economic Geography, Oxford University Press, vol. 14(4), pages 759-773.
    26. Blank, Aharon & Solomon, Sorin, 2000. "Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 279-288.
    27. Wen‐Tai Hsu, 2012. "Central Place Theory and City Size Distribution," Economic Journal, Royal Economic Society, vol. 122(563), pages 903-932, September.
    28. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    29. Yankow, Jeffrey J., 2006. "Why do cities pay more? An empirical examination of some competing theories of the urban wage premium," Journal of Urban Economics, Elsevier, vol. 60(2), pages 139-161, September.
    30. Reed, William J., 2003. "The Pareto law of incomes—an explanation and an extension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 469-486.
    31. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
    32. Vernon Henderson & Duncan Black, 1999. "Spatial Evolution of Population and Industry in the United States," American Economic Review, American Economic Association, vol. 89(2), pages 321-327, May.
    33. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    34. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    35. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    36. William J. Reed, 2002. "On the Rank‐Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17, February.
    37. Rafael González-Val & Arturo Ramos & Fernando Sanz-Gracia & María Vera-Cabello, 2015. "Size distributions for all cities: Which one is best?," Papers in Regional Science, Wiley Blackwell, vol. 94(1), pages 177-196, March.
    38. Luckstead, Jeff & Devadoss, Stephen, 2014. "A comparison of city size distributions for China and India from 1950 to 2010," Economics Letters, Elsevier, vol. 124(2), pages 290-295.
    39. Kwok Tong Soo, 2014. "Zipf, Gibrat and geography: Evidence from China, India and Brazil," Papers in Regional Science, Wiley Blackwell, vol. 93(1), pages 159-181, March.
    40. Diego Puga, 2010. "The Magnitude And Causes Of Agglomeration Economies," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 203-219, February.
    41. Edward L. Glaeser, 1998. "Are Cities Dying?," Journal of Economic Perspectives, American Economic Association, vol. 12(2), pages 139-160, Spring.
    42. B. D. McCullough & H. D. Vinod, 2003. "Verifying the Solution from a Nonlinear Solver: A Case Study," American Economic Review, American Economic Association, vol. 93(3), pages 873-892, June.
    43. Anderson, Gordon & Ge, Ying, 2005. "The size distribution of Chinese cities," Regional Science and Urban Economics, Elsevier, vol. 35(6), pages 756-776, November.
    44. Combes, Pierre-Philippe & Duranton, Gilles & Gobillon, Laurent, 2008. "Spatial wage disparities: Sorting matters!," Journal of Urban Economics, Elsevier, vol. 63(2), pages 723-742, March.
    45. Edward L. Glaeser & Matthew G. Resseger, 2010. "The Complementarity Between Cities And Skills," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 221-244, February.
    46. Rauch James E., 1993. "Productivity Gains from Geographic Concentration of Human Capital: Evidence from the Cities," Journal of Urban Economics, Elsevier, vol. 34(3), pages 380-400, November.
    47. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.),Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378, Elsevier.
    48. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
    49. Soo, Kwok Tong, 2005. "Zipf's Law for cities: a cross-country investigation," Regional Science and Urban Economics, Elsevier, vol. 35(3), pages 239-263, May.
    50. Melo, Patricia C. & Graham, Daniel J. & Noland, Robert B., 2009. "A meta-analysis of estimates of urban agglomeration economies," Regional Science and Urban Economics, Elsevier, vol. 39(3), pages 332-342, May.
    51. Parker, Simon C., 1999. "The generalised beta as a model for the distribution of earnings," Economics Letters, Elsevier, vol. 62(2), pages 197-200, February.
    52. Wen-Tai Hsu & Tomoya Mori & Tony E. Smith, 2014. "Spatial Patterns and Size Distributions of Cities," KIER Working Papers 882, Kyoto University, Institute of Economic Research.
    53. Edward L. Glaeser & Joshua D. Gottlieb & Kristina Tobio, 2012. "Housing Booms and City Centers," American Economic Review, American Economic Association, vol. 102(3), pages 127-133, May.
    54. repec:wiw:wiwrsa:ersa14p34 is not listed on IDEAS
    55. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2013. "The size distribution of US cities: Not Pareto, even in the tail," Economics Letters, Elsevier, vol. 120(2), pages 232-237.
    56. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ramos, Arturo, 2015. "Log-growth distributions of US city sizes and non-Lévy processes," MPRA Paper 66561, University Library of Munich, Germany.
    2. Ramos, Arturo, 2015. "Are the log-growth rates of city sizes normally distributed? Empirical evidence for the US," MPRA Paper 65584, University Library of Munich, Germany.
    3. Puente-Ajovin, Miguel & Ramos, Arturo, 2015. "An improvement over the normal distribution for log-growth rates of city sizes: Empirical evidence for France, Germany, Italy and Spain," MPRA Paper 67471, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ramos, Arturo & Sanz-Gracia, Fernando & González-Val, Rafael, 2013. "A new framework for the US city size distribution: Empirical evidence and theory," MPRA Paper 52190, University Library of Munich, Germany.
    2. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.),Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853, Elsevier.
    3. Rafael González-Val, 2019. "US city-size distribution and space," Spatial Economic Analysis, Taylor & Francis Journals, vol. 14(3), pages 283-300, July.
    4. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2019. "Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 87-103.
    5. Arturo Ramos, 2017. "Are the log-growth rates of city sizes distributed normally? Empirical evidence for the USA," Empirical Economics, Springer, vol. 53(3), pages 1109-1123, November.
    6. Miguel Puente-Ajovín & Arturo Ramos, 2015. "On the parametric description of the French, German, Italian and Spanish city size distributions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 54(2), pages 489-509, March.
    7. Valente J. Matlaba & Mark J. Holmes & Philip McCann & Jacques Poot, 2013. "A Century Of The Evolution Of The Urban System In Brazil," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 25(3), pages 129-151, November.
    8. Ramos, Arturo, 2015. "Are the log-growth rates of city sizes normally distributed? Empirical evidence for the US," MPRA Paper 65584, University Library of Munich, Germany.
    9. Rafael González‐Val, 2019. "Historical urban growth in Europe (1300–1800)," Papers in Regional Science, Wiley Blackwell, vol. 98(2), pages 1115-1136, April.
    10. Rafael Gonz�lez-Val & Luis Lanaspa, 2016. "Patterns in US Urban Growth, 1790-2000," Regional Studies, Taylor & Francis Journals, vol. 50(2), pages 289-309, February.
    11. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, vol. 71(C), pages 193-208.
    12. Ramos, Arturo, 2015. "Log-growth distributions of US city sizes and non-Lévy processes," MPRA Paper 66561, University Library of Munich, Germany.
    13. Behrens, Kristian & Robert-Nicoud, Frédéric, 2015. "Agglomeration Theory with Heterogeneous Agents," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.),Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 171-245, Elsevier.
    14. Rafael González-Val & Arturo Ramos & Fernando Sanz-Gracia & María Vera-Cabello, 2015. "Size distributions for all cities: Which one is best?," Papers in Regional Science, Wiley Blackwell, vol. 94(1), pages 177-196, March.
    15. Arturo, Ramos, 2019. "Have the log-population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century," MPRA Paper 93562, University Library of Munich, Germany.
    16. Kristian Giesen & Jens Suedekum, 2012. "The Size Distribution Across All 'Cities': A Unifying Approach," SERC Discussion Papers 0122, Spatial Economics Research Centre, LSE.
    17. Giorgio Fazio & Marco Modica, 2015. "Pareto Or Log-Normal? Best Fit And Truncation In The Distribution Of All Cities," Journal of Regional Science, Wiley Blackwell, vol. 55(5), pages 736-756, November.
    18. González-Val, Rafael & Lanaspa, Luis & Sanz, Fernando, 2008. "New Evidence on Gibrat’s Law for Cities," MPRA Paper 10411, University Library of Munich, Germany.
    19. Wu, Jian-Xin & He, Ling-Yun, 2017. "How do Chinese cities grow? A distribution dynamics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 105-118.
    20. Lee, Sanghoon & Li, Qiang, 2013. "Uneven landscapes and city size distributions," Journal of Urban Economics, Elsevier, vol. 78(C), pages 19-29.

    More about this item

    Keywords

    human capital; congestion costs; lower tail; body; and upper tail; Pareto and Generalized Beta of the second kind distributions;

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D39 - Microeconomics - - Distribution - - - Other
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:64051. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter). General contact details of provider: http://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.