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Corrado Gini (1884–1965): Versatile Originator of Measures of Variability

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Great Minds in Regional Science, Vol. 2

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Abstract

Although the bulk of Corrado Gini’s career predated the beginnings of the field of regional science and recent developments in spatial econometrics, his ideas and contributions have been, and continue to be, influential in past and current work carried out in many areas of regional science research. While the coefficient of inequality that bears his name is by far his most well-known contribution, his other work has also had a lasting impact and influence on the development of important measures in regional science and geography. Much of what Gini contributed was rediscovered or reintroduced many years later. For example, in a very early contribution, he discussed subjective probability, beliefs, and inductive probability. In many ways, this anticipated the seminal work on inductive logic of (Carnap, Philosophy of Science 12:72–97, 1945) and Bayesian probability. In this chapter by Peter Rogerson, the measures of variability that Gini originated are reviewed, and applications to geography and regional science are emphasized. A detailed treatment of his well-known and eponymous measure of inequality is presented, and then four other areas of measurement that have been critical for progress in a variety of research areas in geography and regional science are detailed: locating centers of population; making international price comparisons; constructing indexes of agreement and classification accuracy; and measuring diversity.

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Notes

  1. 1.

    A recent study provides strong support for this hypothesis (Gellatly 2009). In particular, men who have many brothers are more likely to father sons; men with many sisters are more likely to father daughters.

  2. 2.

    Eells (1930) independently made the same point regarding the Census error in his own paper that appeared the next year. The Census error is discussed in an editor’s note in the Journal of the American Statistical Association that appeared later in 1930. The US Census Bureau continues to calculate the center of population incorrectly. Correct calculations that account for the proper map projection and great circle distances are described in Plane and Rogerson (2015).

References

  • Alkay, E., and G.J.D. Hewings. 2012. The determinants of agglomeration for the manufacturing sector in the Istanbul metropolitan area. The Annals of Regional Science 48: 225–245.

    Article  Google Scholar 

  • Arbia, G. 2001. The role of spatial effects in the empirical analysis of regional concentration. Journal of Geographical Systems 3: 271–281.

    Article  Google Scholar 

  • Aten, B. 1996. Evidence of spatial autocorrelation in international prices. Review of Income and Wealth 42: 149–163.

    Article  Google Scholar 

  • Aten, B.H. 1997. Does space matter? International comparisons of the prices of tradables and nontradables. International Regional Science Review 20 (1–2): 35–52.

    Article  Google Scholar 

  • Aten, B., and A. Heston. 2009. Are all Fishers equal? https://www.researchgate.net/publication/251695763_Are_All_Fishers_Equal. Last accessed April 28, 2022.

  • Benedetti, C. 1965. Ricordando Corrado Gini. Rivista Di Politica Economica 54: 3–9.

    Google Scholar 

  • Bickenbach, F., and E. Bode. 2008. Disproportionality measures of concentration, specialization and localization. International Regional Science Review 31: 359–388.

    Article  Google Scholar 

  • Blau, P. 1977. Inequality and heterogeneity. New York: Free Press.

    Google Scholar 

  • Carnap, R. 1945. On inductive logic. Philosophy of Science 12 (3): 72–97.

    Article  Google Scholar 

  • Castellano, V. 1965. Corrado Gini: A memoir. Metron 24 (1–4): 3–84.

    Google Scholar 

  • Ceriani, L., and P. Verme. 2012. The origins of the Gini index: Extracts from Variabilitia e Mutabilita (1912) by Corrado Gini. Journal of Economic Inequality 10: 421–443.

    Article  Google Scholar 

  • Cohen, J. 1960. A coefficient of agreement for nominal scales. Educational and Psychological Measurement 20 (1): 37–46.

    Article  Google Scholar 

  • Combes, P-P., and H.G. Overman. 2003. The spatial distribution of economic activity in the European Union.Handbook of Regional and Urban Economics 4: 2845–2909.

    Google Scholar 

  • Daskin, M.S., and K.L. Maass. 2015. The p-median problem. In Location science, ed. G. Laporte, S. Nickel, and F. da Gama, 21–45. Cham: Springer.

    Google Scholar 

  • David, H.A. 1968. Gini’s mean difference rediscovered. Biometrika 55: 573–575.

    Google Scholar 

  • David, H.A. 1998. Early sample measures of variability. Statistical Science 13 (4): 368–377.

    Article  Google Scholar 

  • Dawkins, C.J. 2004. Measuring the spatial pattern of residential segregation. Urban Studies 41 (4): 833–851.

    Article  Google Scholar 

  • Dawkins, C. 2007. Space and the measurement of income segregation. Journal of Regional Science 47 (2): 255–272.

    Article  Google Scholar 

  • Devereux, M.P., R. Griffith, and H. Simpson. 2004. The geographic distribution of production activity in the UK. Regional Science and Urban Economics 34 (5): 533–564.

    Article  Google Scholar 

  • Donaldson, D., and K. Pendakur. 2010. Index-number tests and the common-scaling social cost-of-living index. Manuscript number SCWE-D-10–00032 http://www.sfu.ca/~pendakur/CSSCOL%202010-11.pdf. Last accessed April 28, 2022.

  • Drechsler, L. 1962. A használati érték és az érték szerepe a volumenindex számításánál. Budapest: Akadémiai Kiadó.

    Google Scholar 

  • Duncan, O.D. 1957. The measurement of population distribution. Population Studies 11 (1): 27–45.

    Article  Google Scholar 

  • Duncan, O.D., and B. Duncan. 1955. A methodological analysis of segregation indexes. American Sociological Review 20 (2): 210–217.

    Article  Google Scholar 

  • Eells, W. 1930. A mistaken conception of the center of population. Journal of the American Statistical Association 25: 33–40.

    Article  Google Scholar 

  • Ellerman, D. 2017. Logical information theory: New logical foundations for information theory. Logic Journal of the IGPL 25 (5): 806–835.

    Article  Google Scholar 

  • Ellison, G., and E. Glaeser. 1997. Geographical concentration in U.S. manufacturing industries: A dartboard approach. Journal of Political Economy 105 (5): 889–927.

    Google Scholar 

  • Eltetö, O., and P. Köves. 1964. On a problem of index number computation relating to international comparison. Statisztikai Szemle 42: 507–518.

    Google Scholar 

  • Fan, G.-Z., S.E. Ong, and H.C. Koh. 2006. Determinants of house prices: A decision tree approach. Urban Studies 43 (12): 2301–2315.

    Article  Google Scholar 

  • Fassio, C., S. Kalantaryan, and A. Venturini. 2015. Human resources and innovation: Total factor productivity and foreign human capital. Discussion Paper Series, IZA DP No. 9422, Institute for the Study of Labor, Bonn, Germany.

    Google Scholar 

  • Feng, T., and H.J.P. Timmermans. 2017. Using recurrent spatio-temporal profiles in GPSpanel datat for enhancing imputation of activity type. In Big data for regional science, ed. L.A. Schintler and Z. Chen, 121–130. London: Routledge.

    Chapter  Google Scholar 

  • Fisher, I. 1922. The making of index numbers. Boston, MA: Houghton Mifflin Company.

    Google Scholar 

  • Folch, D.C., and S.J. Rey. 2016. The centralization index: A measure of local spatial segregation. Papers in Regional Science 95 (3): 555–576. https://doi.org/10.1111/pirs.12145.

    Article  Google Scholar 

  • Folch, D.C. 2012. The centralization index as a measure of local spatial segregation. Ph.D. Dissertation, Arizona State University, School of Geographical Sciences and Urban Planning.

    Google Scholar 

  • Gellatly, C. 2009. Trends in population sex ratios may be explained by changes in the frequencies of polymorphic alleles of a sex ratio gene. Evolutionary Biology 36 (2): 190–200.

    Article  Google Scholar 

  • Gibbs, J.P., and W.T. Martin. 1962. Urbanization, technology and the division of labor. American Sociological Review 27 (5): 667–677. https://doi.org/10.2307/2089624.

    Article  Google Scholar 

  • Gini, C. 1921. Measurement of inequality of incomes. The Economic Journal 31 (121): 124–126.

    Article  Google Scholar 

  • Gini, C. 1924. Quelques considerations au sujet de la construction des nombres indices des prix et des questions analogues. Metron 4 (1): 3–162.

    Google Scholar 

  • Gini, C. 1931. On the circular test of index numbers. Metron 9 (9): 3–24.

    Google Scholar 

  • Gini, C. 2001. Induction and statistics. Bologna: Clueb.

    Google Scholar 

  • Gini, C., and L. Galvani. 1929. Di talune estensioni dei concetti di media ai caratteri qualitative. Metron 8: 3–209.

    Google Scholar 

  • Gini, C., L. Berardinis, and L. Galvani. 1933. Sulla selettività delle cause di morte durante l’infanzia. Metron 11 (1): 163–183.

    Google Scholar 

  • Gini, C. 1908. Il sesso dal punto di vista statistic: Le leggi della produzione dei sessi. Firenze: Sandron.

    Google Scholar 

  • Gini, C. 1911. Considerazioni sulle probabilità a posteriori e applicazioni al rapporto dei sessi alla nascita. Studi Economico-Giuridici, Facoltà di Giurisprudenza Della Regia Università di Cagliari anno III; reprinted in Metron, 1949, 15(1–4). English translation in Gini (2001).

    Google Scholar 

  • Gini, C. 1912. Variabilit’a e mutabilit’a. Contributo allo studio delle distribuzioni e dekke relazioni statistiche, Studio economico-giurdici Anno III Parte II. Facolt’a di giurrisprudenza della Regia Universit’a di Cagliari. Bologna: Cuppini.

    Google Scholar 

  • Gini, C. 1914–15a. Di una misura della dissomiglianza tra due gruppi di quantitA e delle sue applicazioni allo studio delle relazioni statistiche. Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, Series 8, 74 (2): 185–213.

    Google Scholar 

  • Gini, C. 1914–15b. Indice di omofilia e di rassomiglianza e loro relazioni col coefficiente di correlazione e con gli indici di attrazione. Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, Series 8, 74 (2): 583–610.

    Google Scholar 

  • Gini, C. 1937. Die Messung der Ungleichheit zweier Verteilungen, angewendet auf die Untersuchung von qualitativen Rassenmerkmalen. Archiv fur Mathematische Wirtschafts- und Sozialforschung, 3: 167–84, plus two appendixes by Vittorio Castellano.

    Google Scholar 

  • Giorgi, G.M. 2001. Corrado Gini. In Statisticians of the centuries, ed. C.C. Heyde, E. Seneta, P. Crépel, S.E. Fienberg, and J. Gani, 364–368. New York: Springer.

    Google Scholar 

  • Gluschenko, K. 2018. Measuring regional inequality: To weight or not to weight? Spatial Economic Analysis 13 (1): 36–59. https://doi.org/10.1080/17421772.2017.1343491.

    Article  Google Scholar 

  • Goodman, L.A., and W.H. Kruskal. 1959. Measures of association for cross-classifications. II. Further discussions and references. Journal of the American Statistical Association 54: 123–163.

    Article  Google Scholar 

  • Guimaraes, P., O. Figueiredo, and D. Woodward. 2009. Dartboard tests for the location quotient. Regional Science and Urban Economics 39 (3): 360–364.

    Article  Google Scholar 

  • Hagen-Zanker, A. 2009. An improved fuzzy Kappa statistic that accounts for spatial autocorrelation. International Journal of Geographical Information Science 23 (1): 61–73. https://doi.org/10.1080/13658810802570317.

    Article  Google Scholar 

  • Hale, T.S., and C.R. Moberg. 2003. Location science research: A review. Annals of Operations Research 123: 21–35.

    Article  Google Scholar 

  • Hand, D.J. 2012. Assessing the performance of classification methods. International Statistical Review 80 (3): 400–414.

    Article  Google Scholar 

  • Havrda, J., and F. Charvat. 1967. Quantification method of classification processes. Concept of structural α-entropy. Kybernetika 3 (1): 30–35.

    Google Scholar 

  • Helmert, F.R. 1876. Die Berechnung des wahrscheinlichen Beobachtungsfehlers aus des ersten Potenzen der Differenzen gleichgenauer director Beobachtungen. Astronomische Nachrichten 88: 113–132.

    Article  Google Scholar 

  • Herfindahl, C. 1950. Concentration in the US steel industry. Unpublished Ph.D. dissertation, New York: Columbia University.

    Google Scholar 

  • Hirschman, A.O. 1945. National power and the structure of foreign trade. Berkeley: University of California Press.

    Google Scholar 

  • Hirschman, A.O. 1964. The paternity of an index. American Economic Review 54 (5): 761–762.

    Google Scholar 

  • Hoover, E.M., Jr. 1941. Interstate redistribution of population, 1850–1940. Journal of Economic History 1: 199–205.

    Article  Google Scholar 

  • Hurlbert, S.H. 1971. The nonconcept of species diversity: A critique and alternative parameters. Ecology 52 (4): 577–586. https://doi.org/10.2307/1934145.

    Article  Google Scholar 

  • James, D.R., and K.E. Taeuber. 1985. Measures of segregation. Sociological Methodology 15: 1–32.

    Article  Google Scholar 

  • Jordan, W. 1869. Ueber die Bestimmung der Genauigkeit mehrfach wiederholter Beobachtungen einder Unbekannten. Astronomische Nachrichten 74: 209–226.

    Article  Google Scholar 

  • Jost, L. 2006. Entropy and diversity. Oikos 113 (2): 363–375. https://doi.org/10.1111/j.2006.0030-1299.14714.x.

    Article  Google Scholar 

  • Journal of the American Statistical Association. 1930. Editor’s note on the center of population and point of minimum travel 25: 447–452.

    Google Scholar 

  • Kindleberger, C.P. 1962. Foreign trade and the national economy. New Haven: Yale University Press.

    Google Scholar 

  • Krugman, P. 1991. Geography and trade. Cambridge, MA: MIT Press.

    Google Scholar 

  • Light, R.J., and B.H. Margolin. 1971. An analysis of variance for categorical data. Journal of the American Statistical Association 66: 534–544.

    Article  Google Scholar 

  • Lorenz, M.O. 1905. Methods of measuring the concentration of wealth. Publications of the American Statistical Association 9 (70): 209–219. https://doi.org/10.2307/2276207.

  • Lu, Y., S. Laffan, C. Pettit, and M. Cao. 2020. Land use change simulation and analysis using a vector cellular automata (CA) model: A case study of Ipswich City, Queensland, Australia. Environment and Planning B: Urban Analytics and City Science 47 (9): 1605–1621.

    Google Scholar 

  • Macuglia, D. 2014. Corrado Gini and the scientific basis of fascist racism. Medicina Nei Secoli 26 (3): 821–855.

    Google Scholar 

  • Massell, B.F. 1964. Export concentration and fluctuations in export earnings. American Economic Review 54: 47–63.

    Google Scholar 

  • Michaely, M. 1958. Concentration of exports and imports: An international comparison. Economic Journal 68: 722–736.

    Article  Google Scholar 

  • Nelson, S.L.P., V. Ramakrishnan, P. Nietert, D.L. Kamen, P.S. Ramos, and B.J. Wolf. 2017. An evaluation of common methods for dichotimization of continuous variables to discriminate disease status. Communications in Statistics: Theory and Methods 46 (21): 10823–10834.

    Article  Google Scholar 

  • Nijkamp, P., and J. Poot. 2015. Cultural diversity: A matter of measurement, IZA Discussion Papers, No. 8782, Institute for the Study of Labor (IZA), Bonn.

    Google Scholar 

  • Olkin, I., and S. Yitzhaki. 1987. Gini regression analysis. International Statistical Review 60 (2): 185–196.

    Article  Google Scholar 

  • Panzera, D., and P. Postiglione. 2020. Measuring the spatial dimension of regional inequality: An approach based on the Gini correlation measure. Social Indicators Research 148: 379–394. https://doi.org/10.1007/s11205-019-02208-7.

    Article  Google Scholar 

  • Pietra, G. 1915. Delle relazioni tra gli inidic di variabilita (Nota I) Atti del Reale Istituto Veneto di Scienze, Lettere e Arti. Vl. LXXIV (Part 1): 775–792.

    Google Scholar 

  • Pietra, G. 2014. On the relationships between variability indices (note 1) (translated from the 1915 article) in Metron 72 (1): 5–16.

    Google Scholar 

  • Plane, D., and G. Mulligan. 1997. Measuring spatial focusing in a migration system. Demography 34: 251–262.

    Article  Google Scholar 

  • Plane, D., and P. Rogerson. 1994. The geographical analysis of population: With applications to planning and business. New York: Wiley.

    Google Scholar 

  • Plane, D., and P. Rogerson. 2015. On tracking and disaggregating center points of population. Annals of the American Association of Geographers 105 (5): 968–986.

    Article  Google Scholar 

  • ReVelle, C.S., H.A. Eiselt, and M.S. Daskin. 2008. A bibliography of some fundamental problem categories in discrete location science. European Journal of Operations Research 184: 817–848.

    Article  Google Scholar 

  • ReVelle, C.S., and T.R. Swain. 1970. Central facilities location. Geographical Analysis 2: 30–42.

    Article  Google Scholar 

  • Rey, S.J., and M.V. Janikas. 2005. Regional convergence, inequality, and space. Journal of Economic Geography 5: 155–176.

    Article  Google Scholar 

  • Rey, S., and R.J. Smith. 2012. A spatial decomposition of the Gini coefficient. Letters in Spatial and Resource Sciences 6 (2): 1–16.

    Google Scholar 

  • Rokicki, B., and G.J.D. Hewings. 2016. Regional convergence within particular country—An approach based on the regional price deflators. Economic Modelling 57: 171–179. https://doi.org/10.1016/j.econmod.2016.04.019.

    Article  Google Scholar 

  • Rosenbluth, G. 1955. Measures of concentration. In Business concentration and policy, 57–99. Princeton: National Bureau of Economic Research.

    Google Scholar 

  • Saksena, S., J. Fox, M. Epprecht, C. Tran, M. Casternce, D. Nong, J. Spencer, N. Lam, M. Finucane, D. Vien, and B. Wilcox. 2014. Role of urbanization, land-use diversity, and livestock intensification in zoonotic emerging infectious diseases. Honolulu, HI: East-West Center Working Papers, Environment, Population, and Health Series, No. 6.

    Google Scholar 

  • Salvemini, T. 1968. Corrado Gini. In International Encyclopedia of statistics, ed. D.L. Sills, vol. 6, 187–191. New York: Macmillan and Free Press.

    Google Scholar 

  • Schechtman, E., and Yitzhaki S. 1987. A measure of association based on Gini's mean difference. Communication in Statistics—Theory and Methods 16 (1): 207–231.

    Google Scholar 

  • Simpson, E. 1949. Measurement of diversity. Nature 163: 688. https://doi.org/10.1038/163688a0.

  • Sviatlovsky, E.E., and W.C. Eells. 1937. The centrographical method and regional analysis. Geographical Review 27 (2): 240–254.

    Article  Google Scholar 

  • Szulc, B. 1964. Indeksy dla porownan wieloregionalnych. Przeglad Statystyczny 3: 239–254.

    Google Scholar 

  • Tinbergen, J. 1962. Sha** the world economy. New York: Twentieth Century Fund.

    Google Scholar 

  • Tsallis, C. 1988. Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics 52 (1–2): 479–487.

    Article  Google Scholar 

  • Von Andrae, C.G. 1869. Schreiben des Herrn Geheimen Etatsraths von Andra an den Herausgeber. Astronomische Nachrichten 74: 283–284.

    Article  Google Scholar 

  • Von Andrae, C.G. 1872. Ueber die Bestimmung des wahrscheinlichen Fehlers durch die gegebenen vom gleich genauen Beobachtungen einer Unbekannten. Astronomische Nachrichten 79: 257–272.

    Article  Google Scholar 

  • Warrens, M.J. 2013. A comparison of Cohen’s kappa and agreement coefficients by Corrado Gini. International Journal of Recent Research and Applied Studies 16 (3): 345–351.

    Google Scholar 

  • Warrens, M.J. 2015. Five ways to look at Cohen’s kappa. Journal of Psychology and Psychotherapy 5: 4. https://doi.org/10.4172/2161-0487.1000197.

    Article  Google Scholar 

  • White, M. 1983. The measurement of spatial segregation. American Journal of Sociology 88: 1008–1018.

    Article  Google Scholar 

  • Wilson, A. 1970. Entropy in urban and regional modelling. London: Pion.

    Google Scholar 

  • Wilson, A. 2010. Entropy in urban and regional modelling: Retrospect and prospect. Geographical Analysis 42 (4): 364–394.

    Article  Google Scholar 

  • Wong, D.W.S. 1993. Spatial indices of segregation. Urban Studies 30 (3): 559–572.

    Article  Google Scholar 

  • Wong, D. 2003. Spatial decomposition of segregation indices: A framework toward measuring segregation at multiple levels. Geographical Analysis 35 (3): 179–194.

    Article  Google Scholar 

  • Yitzhaki, S. 2003. Gini’s mean difference: A superior measure of variability for non-normal distributions. Metron—International Journal of Statistics 61 (2): 285–316.

    Google Scholar 

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Acknowledgment

I acknowledge the very helpful comments of David Plane on earlier drafts of this manuscript.

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  1. School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, AZ, 85287, USA

    Peter Rogerson

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  1. Department of Geography and Planning, University of Liverpool, Liverpool, UK

    Peter Batey

  2. School of Geography, Development and Environment, University of Arizona, Tucson, AZ, USA

    David Plane

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Rogerson, P. (2023). Corrado Gini (1884–1965): Versatile Originator of Measures of Variability. In: Batey, P., Plane, D. (eds) Great Minds in Regional Science, Vol. 2. Footprints of Regional Science(). Springer, Cham. https://doi.org/10.1007/978-3-031-13440-1_5

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