Advertisement

I Dream of Gini: Measures of Population Concentration and Their Application to US Population Distribution

  • Peter A. RogersonEmail author
Chapter
Part of the New Frontiers in Regional Science: Asian Perspectives book series (NFRSASIPER, volume 40)

Abstract

The unevenness of population across space may be captured with various measures of inequality; the Lorenz curve, the Gini coefficient, and the Hoover index constitute prime examples of such measures. In this chapter, I first review the history of these measures and then provide a selective review of their use in examining population concentration and deconcentration. Next, I show how the Gini coefficient may be disaggregated to show how population concentration varies within different ranges of population densities. The Gini coefficient is written as a weighted sum of the Hoover indexes for each population density category, where the weights are the proportion of total area in that density category. This disaggregation is applied to the US population for the period 2000–2015. Results show that population deconcentration is occurring among the subset of counties that have high population density and concentration is occurring among counties that have medium population density.

Keywords

Gini coefficient Hoover index Population deconcentration 

Notes

Acknowledgments

I would like to thank Xiang Ye for his assistance with the figures.

References

  1. Berry BJL (1980) Urbanization and counterurbanization in the United States. Ann Am Acad Pol Soc Sci 451(1):13–20CrossRefGoogle Scholar
  2. Bourne LS (1980) Alternative perspectives on urban decline and population deconcentration. Urban Geogr 1:39–52CrossRefGoogle Scholar
  3. Ceriani L, Verme P (2012) The origins of the Gini index: extracts from Variabilitia e Mutabilita (1912) by Corrado Gini. J Econ Inequal 10:421–443CrossRefGoogle Scholar
  4. Cochrane SG, Vining DR Jr (1988) Recent trends in migration between core and peripheral regions in developed and advanced developed countries. Int Reg Sci Rev 11:215–243CrossRefGoogle Scholar
  5. Dalton H (1920) The measurement of the inequality of incomes. Econ J 30:348–461CrossRefGoogle Scholar
  6. Domina T (2006) What clean break? Education and nonmetropolitan migration patterns, 1989–2004. Rural Sociol 71(3):373–398CrossRefGoogle Scholar
  7. Duncan OD, Cuzzort R, Duncan B (1961) Statistical geography. Free Press, GlencoeGoogle Scholar
  8. Florence PS (1953) The logic of British and American industry: a realistic analysis of economic structure and government. Routledge and Kegan Paul, LondonGoogle Scholar
  9. Florence PS, Wensley AJ (1939) The location of industry in Great Britain. LondonGoogle Scholar
  10. Frey WH (March 26, 2018) US population disperses to suburbs, exurbs, rural areas, and “middle of the country” metros. https://www.brookings.edu/blog/the-avenue/2018/03/26/us-population-disperses-to-suburbs-exurbs-rural-areas-and-middle-of-the-country-metros/. Last accessed 2 Dec 2018
  11. Fuguitt G (1985) The nonmetropolitan population turnaround. Annu Rev Sociol 11:259–280CrossRefGoogle Scholar
  12. Geyer HS, Kontuly T (1993) A theoretical foundation for the concept of differential urbanization. Int Reg Sci Rev 15(2):157–177CrossRefGoogle Scholar
  13. Gini C (1912) Variabilit’a e Mutabilit’a. Contributo allo studio delle distribuzioni e delle relazioni statistiche, Studi economico-giuridici Anno III, Parte II. Facolt’a di giurisprudenza della Regia Universit’a di Cagliari. Cuppini, BolognaGoogle Scholar
  14. Gini C (1914) Sulla Misura della Concentrazione e della Variabilit’a dei Caratteri. Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti LXXIII(II):1203–1248Google Scholar
  15. Gini C (1921) Measurement of inequality of incomes. Econ J 31:124–126CrossRefGoogle Scholar
  16. Gini C (2005) On the measurement of concentration and variability of characters. METRON - Int J Stat LXIII(1):3–38Google Scholar
  17. Giorgi GM (2014) A couple of good reasons to translate papers of the Italian statistical tradition. Metro 72(1):1–3CrossRefGoogle Scholar
  18. Gordon P (1979) Deconcentration without a ‘clean break’. Environ Plan A 11(3):281–289CrossRefGoogle Scholar
  19. Hall SA, Kaufman JS, Ricketts TC (2006) Defining urban and rural areas in U.S. epidemiological studies. J Urban Health 83(2):162–175CrossRefGoogle Scholar
  20. Hoover EM (1936) The measurement of industrial localization. Rev Econ Stat 18:162–171CrossRefGoogle Scholar
  21. Hoover E (1941) Interstate redistribution of population: 1850–1940. J Econ Hist 1:199–205CrossRefGoogle Scholar
  22. Johnson KM, Cromartie JB (2006) The rural rebound and its aftermath. In: Kandel WA, Brown DL (eds) Population change and rural society. Springer, Dordrecht, pp 25–49CrossRefGoogle Scholar
  23. Lichter DT (1985) Racial concentration and segregation across US counties, 1950–1980. Demography 22(4):603–609CrossRefGoogle Scholar
  24. Lichter DT, Fuguitt GV (1982) The transition to nonmetropolitan population deconcentration. Demography 19(2):211–221CrossRefGoogle Scholar
  25. Lichter DT, Johnson KM (2006) Emerging rural settlement patterns and the geographic redistribution of America’s new immigrants. Rural Sociol 71(1):109–131CrossRefGoogle Scholar
  26. Long J (1981) Population deconcentration in the United States. Department of Commerce, US Government Printing Office, Washington, DCGoogle Scholar
  27. Long L, Nucci A (1997a) The ‘clean break’ revisited: is US population again deconcentrating? Environ Plan A 29(8):1355–1366CrossRefGoogle Scholar
  28. Long L, Nucci A (1997b) The Hoover index of population concentration: a correction and update. Prof Geogr 49(4):431–440CrossRefGoogle Scholar
  29. Lorenz MO (1905) Methods of measuring the concentration of wealth. Q Publ Am Stat Assoc ix:209–20IGoogle Scholar
  30. McCarthy KF, Morrison PA (1977) The changing demographic and economic structure of nonmetropolitan areas in the United States. Int Reg Sci Rev 2(2):123–142CrossRefGoogle Scholar
  31. Morrill R (1979) Stages in patterns of population concentration and dispersion. Prof Geogr 31(1):55–65CrossRefGoogle Scholar
  32. Morrill R (1980) The spread of change in metropolitan and nonmetropolitan growth in the United States, 1940–1976. Urban Geogr 1(2):118–129CrossRefGoogle Scholar
  33. Parker K, Horowitz JM, Brown A, Fry R, Chon D, Igielnik R (May 22, 2018) What unites and divides urban, suburban, and rural communities. Pew Research Report. http://www.pewsocialtrends.org/2018/05/22/demographic-and-economic-trends-in-urban-suburban-and-rural-communities/ Last accessed 2 Dec 2018
  34. Pietra G (1915) Delle relazioni tra gli indici di variabilità (Nota I)” Atti del Reale Istituto Veneto di Scienze, Lettere e Arti. 1915, Vol. LXXIV, Part I, pages 775–792Google Scholar
  35. Pietra G (2014) On the relationships between variability indices (note I) (translated from the 1915 article) in Metron 72(1):5–16Google Scholar
  36. Plane DA, Mulligan GF (1997) Measuring spatial focusing in a migration system. Demography 34(2):251–262CrossRefGoogle Scholar
  37. Plane DA, Henrie CJ, Perry MJ (2005) Migration up and down the urban hierarchy and across the life course. Proc Natl Acad Sci 103(43):15313–15318CrossRefGoogle Scholar
  38. Rogers A, Raymer J (1998) The spatial focus of US interstate migration flows. Int J Popul Geogr 4:63–80CrossRefGoogle Scholar
  39. Rogers A, Sweeney S (1998) Measuring the spatial focus of migration patterns. Prof Geogr 50(2):232–242CrossRefGoogle Scholar
  40. Rogerson P (2013) The Gini coefficient of inequality: a new interpretation. Lett Spat Resour Sci 6(3):109–120.  https://doi.org/10.1007/s12076-013-0091-xCrossRefGoogle Scholar
  41. Rogerson PA, Plane DA (2013) The Hoover index of population concentration and the demographic components of change: an article in memory of Andrew M. Isserman. Int Reg Sci Rev 36(1):97–114CrossRefGoogle Scholar
  42. Schutz R (1951) On the measurement of income inequality. Am Econ Rev 41:107–122Google Scholar
  43. US Bureau of the Census (2012) United States summary: 2010. 2010 census of population and housing, population and housing unit counts, CPH-2-5. U.S. Government Printing Office, Washington, DCGoogle Scholar
  44. Vinci F (1934) Manuale di Statistica, I (Bologna), pp 113–118Google Scholar
  45. Vining D, Strauss A (1977) A demonstration that the current deconcentration of population in the United States is a clean break with the past. Environ Plan A 9:751–758CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Departments of Geography and Biostatistics, Wilkeson HallUniversity at BuffaloBuffaloUSA

Personalised recommendations