Advertisement

Ageing and Labour Market Development: Testing Gibrat’s and Zipf’s Law for Germany

  • Marco Modica
  • Aura Reggiani
  • Nicola De Vivo
  • Peter Nijkamp
Chapter
Part of the Advances in Spatial Science book series (ADVSPATIAL)

Abstract

Gibrat’s law and Zipf’s law describe two very well-known empirical regularities on the distribution of settlements. Many studies have focused on the analysis of both these regularities, stimulated by the idea that an accurate description of the distribution of people in space is important for both policy-relevant purposes and for specifying more appropriate theoretical models. However, the existing literature provides an analysis of Gibrat’s and Zipf’s law without taking into account the demographic characteristics of the population under analysis. Given the fact that many countries, and especially those in Europe, will become ageing societies in the decades to come, the aim of this chapter is to provide a more accurate description of the distribution of people, taking into account the demographic differences between people. In this analysis, we focus on both municipal population (place of residence) and employment (place of work) data for Germany between the years 2001 and 2011. Here, we provide evidence of different behaviour in the cohorts of older people. Theoretical models of urban growth that aim to be more fit-for-purpose need to take this different behaviour into consideration.

References

  1. Barabási AL, Oltvai ZN (2004) Network biology: understanding the cell’s functional organization. Nat Rev Genet 5:101–113CrossRefGoogle Scholar
  2. Berry BJL, Okulicz-Kozaryn A (2011) An urban-rural happiness gradient. Urban Geogr 32:871–883CrossRefGoogle Scholar
  3. Black D, Henderson V (2003) Urban evolution in the USA. J Econ Geogr 3:343–372CrossRefGoogle Scholar
  4. Brakman S, Garretsen H, Schramm M (2004) The strategic bombing of German cities during WW II and its Impact on city growth. J Econ Geogr 4:201–218CrossRefGoogle Scholar
  5. Bures RM (1998) Migration and the life course: is there a retirement transition? Int J Popul Geogr 3:109–119CrossRefGoogle Scholar
  6. Cameron C, Trivedi PK (2005) Microenometrics: methods and applications. Cambridge University Press, New YorkCrossRefGoogle Scholar
  7. Chesher A (1979) Testing the law of proportionate effect. J Ind Econ 27:403–411CrossRefGoogle Scholar
  8. Cordoba JC (2003) On the distribution of city sizes. J Urban Econ 63:177–197CrossRefGoogle Scholar
  9. Cordoba JC (2008) A generalized Gibrat’s law. Int Econ Rev 49:1463–1468CrossRefGoogle Scholar
  10. Eeckhout J (2004) Gibrat’s law for (All) cities. Am Econ Rev 94:1429–1451CrossRefGoogle Scholar
  11. European Union (2015) Being young in Europe today – demographic trends, EuroStat – statistics explained. Publications Office of the European Union, LuxembourgGoogle Scholar
  12. Fazio G, Modica M (2015) Pareto or log-normal? Best fit and truncation in the distribution of all cities. J Reg Sci 55:736–756CrossRefGoogle Scholar
  13. Frey WH, Speare A Jr (1988) Regional and metropolitan growth and decline in the United States: a 1980 census monograph. Russell Sage Foundation, New YorkGoogle Scholar
  14. Gabaix X (1999) Zipf’s law for cities: an explanation. Q J Econ 114:739–767CrossRefGoogle Scholar
  15. Gabaix X, Ibragimov R (2011) Rank-1/2: a simple way to improve the OLS estimation of tail exponents. J Bus Econ Stat 29:24–39CrossRefGoogle Scholar
  16. Gabaix X, Ioannides Y (2004) The evolution of city size distribution. In: Henderson JV, Nijkamp P, Mills ES, Cheshire PC, Thisse JF (eds) Handbook of regional and urban economics, vol 4. Elsevier, North-Holland, pp 2341–2378Google Scholar
  17. Gibrat R (1931) Les Inégalités économiques; Applications: aux Inégalités des Richesses, à la Concentration des Enterprises, aux Popolations des Villes, aux Statistiques des Familles, d’une loi Nuvelle, la Loi d’Effet Proportionnel. Librairie du Recueil Sirey, ParisGoogle Scholar
  18. Giesen K, Suedekum J (2014) City age and city size. Eur Econ Rev 71:193–208CrossRefGoogle Scholar
  19. Giesen K, Suedekum J (2011) Zipf’s law for cities in the regions and the country. J Econ Geogr 11:667–686CrossRefGoogle Scholar
  20. Giesen K, Zimmerman A, Suedekum J (2010) The size distribution across all cities – double pareto log normal strikes. J Urban Econ 68:129–137CrossRefGoogle Scholar
  21. Glaeser EL, Ponzetto GAM, Tobio K (2014) Cities, skills and regional change. Reg Stud 48:7–43CrossRefGoogle Scholar
  22. Gonzalez-Val R (2012) A nonparametric estimation of the local Zipf exponent for all US cities. Environ Plann B Plann Des 39:1119–1130CrossRefGoogle Scholar
  23. Gonzalez-Val R, Lanaspa L, Sanz F (2013) Gibrat’s law for cities, growth regression and sample size. Econ Lett 118:367–369CrossRefGoogle Scholar
  24. Greenwood MJ (1985) Human migration: theory, models, and empirical studies. J Reg Sci 25(4):521–544CrossRefGoogle Scholar
  25. Guerin-Pace F (1995) Rank-size distribution and the process of urban growth. Urban Stud 32:551–562CrossRefGoogle Scholar
  26. Hunt GL (2006) Population-employment models: stationarity, cointegration and dynamic adjustment. J Reg Sci 46:205–244CrossRefGoogle Scholar
  27. Ioannides YM, Overman HG (2003) Zipf’s law for cities: an empirical examination. Reg Sci Urban Econ 32:127–137CrossRefGoogle Scholar
  28. Ioannides YM, Skouras S (2013) US city size distribution: Robustly Pareto, but only in the tail. J Urban Econ 73:18–29CrossRefGoogle Scholar
  29. Kapteyn JC (1903) Skew frequency curves in biology and statistics. Noordhoff, Astronomical Laboratory, GroningenGoogle Scholar
  30. Keyfitz N, Philipov D (1981) Migration and natural increase in the growth of cities. Geogr Anal 13(4):287–299CrossRefGoogle Scholar
  31. Lalanne A, Zumpe M (2015) Zipf’s law, Gibrat’s law and cointegration (No. 2015-27). Groupe de Recherche en Economie Théorique et AppliquéeGoogle Scholar
  32. Longino CF Jr, Biggar JC, Flynn CB, Wiseman RF (1984) The retirement migration project (Final report to the National Institute on Aging). University of Miami, Center for Social Research on Aging, Coral Gables, FLGoogle Scholar
  33. Mansfield E (1962) Entry, Gibrat’s law, innovation, and the growth of firms. Am Econ Rev 52:1023–1051Google Scholar
  34. Marin G, Modica M (2017) Socio-economic exposure to natural disasters. Environ Impact Assess Rev 64:57–66CrossRefGoogle Scholar
  35. Modica M (2014) Does the EU have a homogeneous urban structure area? The role of agglomeration and the impact of shocks on urban structure In: ERSA conference papers (No. ersa14p229). European Regional Science AssociationGoogle Scholar
  36. Modica M, Reggiani A (2014) An alternative interpretation of regional resilience: evidence from Italy. In: ERSA conference papers (No. ersa14p369). European Regional Science AssociationGoogle Scholar
  37. Modica M, Zoboli R (2016) Vulnerability, resilience, hazard, risk, damage, and loss: a socio-ecological framework for natural disaster analysis. Web Ecol 16(1):59–62CrossRefGoogle Scholar
  38. Modica M, Reggiani A, Nijkamp P (2013) Methodological advances in Gibrat’s and Zipf’s laws: a comparative empirical study on the evolution of urban systems. Research memorandum 2013–35. Faculty of Economics and Business AdministrationGoogle Scholar
  39. Modica M, Reggiani A, Nijkamp P (2017a) Are Gibrat and Zipf monozygotic or heterozygotic twins? A comparative analysis of means and variances in complex urban systems. In: Socioeconomic environmental policies and evaluations in regional science. Springer, Singapore, pp 37–59CrossRefGoogle Scholar
  40. Modica M, Reggiani A, Nijkamp P (2017b) Vulnerability, resilience and exposure: methodological aspects (forthcoming)Google Scholar
  41. Nadaraya EA (1964) On estimating regression. Theory Probab Appl 10:186–190CrossRefGoogle Scholar
  42. Peri G (2001) Young people, skills and cities, CESifo working papers, 610, CESifo Group MunichGoogle Scholar
  43. Reggiani A, Nijkamp P (2015) Did Zipf anticipate spatial connectivity structures? Environ Plann B Plann Des 42:468–489CrossRefGoogle Scholar
  44. Rosen KT, Resnick M (1980) The size distribution of cities: an examination of the Pareto law and primacy. J Urban Econ 8:165–186CrossRefGoogle Scholar
  45. Santarelli E, Audretsch DB, Klomp L, Thurik RA (2004) Gibrat’s law: are the services different? Rev Ind Organ 24:301–324CrossRefGoogle Scholar
  46. Scott AJ, Storper M (2003) Regions, globalization, development. Reg Stud 37:579–593CrossRefGoogle Scholar
  47. Soo KT (2005) Zipf’s law for cities: a cross-country investigation. Reg Sci Urban Econ 35:239–263CrossRefGoogle Scholar
  48. Storper M (2010) Agglomeration, trade, and spatial development: bringing dynamics back in. J Reg Sci 50:313–342CrossRefGoogle Scholar
  49. Watson GS (1964) Smooth regression analysis. Sankhya A 26:359–372Google Scholar
  50. Zipf GK (1949) Human behavior and the principle of least effort. Addison-Wesley, Cambridge, MAGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Marco Modica
    • 1
    • 2
  • Aura Reggiani
    • 3
  • Nicola De Vivo
    • 4
  • Peter Nijkamp
    • 5
    • 6
  1. 1.CNR –IRCrES, Research Institute on Sustainable Economic GrowthL’AquilaItaly
  2. 2.Gran Sasso Science InstituteL’AquilaItaly
  3. 3.Department of EconomicsUniversity of BolognaBolognaItaly
  4. 4.IMT Lucca – School for Advanced StudiesLuccaItaly
  5. 5.Adam Mickiewicz UniversityPoznańPoland
  6. 6.JADS (Jheronimus Academy of Data Science)’s-HertogenboschThe Netherlands

Personalised recommendations