IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v75y2017i2d10.1007_s40300-017-0115-1.html
   My bibliography  Save this article

At the roots of Gini’s transvariation: extracts from “Il concetto di transvariazione e le sue prime applicazioni”

Author

Listed:
  • Maria Grazia Pittau

    (Sapienza Università di Roma)

  • Roberto Zelli

    (Sapienza Università di Roma)

Abstract

The paper provides the formulations of the concept of “Transvariation” as Gini originally conceived in his work published in Italian in 1916 and entitled “Il concetto di transvariazione e le sue prime applicazioni”. To offer a relatively easy reading, we selected all the main concepts and opted for a translation that sometimes deviates from the original text, but the structure and the main ideas of Gini’s original article are preserved. The paper emphasizes how Gini’s proposed measures of transvariation anticipated the modern analysis of distributions’ overlapping.

Suggested Citation

  • Maria Grazia Pittau & Roberto Zelli, 2017. "At the roots of Gini’s transvariation: extracts from “Il concetto di transvariazione e le sue prime applicazioni”," METRON, Springer;Sapienza Università di Roma, vol. 75(2), pages 127-140, August.
    • Handle: RePEc:spr:metron:v:75:y:2017:i:2:d:10.1007_s40300-017-0115-1
    DOI: 10.1007/s40300-017-0115-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40300-017-0115-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40300-017-0115-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Anderson, Gordon & Linton, Oliver & Whang, Yoon-Jae, 2012. "Nonparametric estimation and inference about the overlap of two distributions," Journal of Econometrics, Elsevier, vol. 171(1), pages 1-23.
    2. Giovanni Maria Giorgi, 2005. "A fresh look at the topical interest of the Gini concentration ratio," Econometrics 0511005, University Library of Munich, Germany.
    3. Deutsch, Joseph & Silber, Jacques, 1997. "Gini's "Transvariazione" and the Measurement of Distance between Distributions," Empirical Economics, Springer, vol. 22(4), pages 547-554.
    4. Lambert, Peter J & Aronson, J Richard, 1993. "Inequality Decomposition Analysis and the Gini Coefficient Revisited," Economic Journal, Royal Economic Society, vol. 103(420), pages 1221-1227, September.
    5. Lidia Ceriani & Paolo Verme, 2012. "The origins of the Gini index: extracts from Variabilità e Mutabilità (1912) by Corrado Gini," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(3), pages 421-443, September.
    6. St鰨ane Mussard & Luc Savard, 2012. "The Gini multi-decomposition and the role of Gini's transvariation: application to partial trade liberalization in the Philippines," Applied Economics, Taylor & Francis Journals, vol. 44(10), pages 1235-1249, April.
    7. Corrado Gini, 2005. "On the measurement of concentration and variability of characters," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 1-38.
    8. Yitzhaki, Shlomo, 1994. "Economic distance and overlapping of distributions," Journal of Econometrics, Elsevier, vol. 61(1), pages 147-159, March.
    9. Michele Costa, 2009. "Transvariation and inequality between subpopulations in the Dagum’s Gini index decomposition," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 229-241.
    10. Pittau, Maria Grazia & Zelli, Roberto & Johnson, Paul, "undated". "Mixture Models and Convergence Clubs," Vassar College Department of Economics Working Paper Series 91, Vassar College Department of Economics.
    11. Maria Grazia Pittau & Roberto Zelli & Riccardo Massari, 2016. "Evidence of Convergence Clubs Using Mixture Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(7), pages 1317-1342, August.
    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. Gordon Anderson & Oliver Linton & Maria Grazia Pittau & Yoon-Jae Whang & Roberto Zelli, 2021. "On unit free assessment of the extent of multilateral distributional variation," The Econometrics Journal, Royal Economic Society, vol. 24(3), pages 502-518.
    2. Gordon Anderson, Alessio Farcomeni, Maria Grazia Pittau and Roberto Zelli, 2019. "Multidimensional Nation Wellbeing, More Equal yet More Polarized: An Analysis of the Progress of Human Development Since 1990," Journal of Economic Development, Chung-Ang Unviersity, Department of Economics, vol. 44(1), pages 1-22, March.
    3. Gordon Anderson & Maria Grazia Pittau & Roberto Zelli & Jasmin Thomas, 2018. "Income Inequality, Cohesiveness and Commonality in the Euro Area: A Semi-Parametric Boundary-Free Analysis," Econometrics, MDPI, vol. 6(2), pages 1-20, March.

    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. Stéphane Mussard & Françoise Seyte & Michel Terraza, 2006. "La décomposition de l’indicateur de Gini en sous-groupes : une revue de la littérature," Cahiers de recherche 06-11, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    2. Gordon Anderson & Alessio Farcomeni & Grazia Pittau & Roberto Zelli, 2014. "A new approach to measuring and studying the characteristics of class membership: The progress of poverty, inequality and polarization of income classes in urban China," Working Papers tecipa-521, University of Toronto, Department of Economics.
    3. Jurkatis, Simon & Strehl, Wolfgang, 2014. "Gini decompositions and Gini elasticities: On measuring the importance of income sources and population subgroups for income inequality," Discussion Papers 2014/22, Free University Berlin, School of Business & Economics.
    4. Edna Schechtman & Ricardas Zitikis, 2006. "Gini indices as areas and covariances: what is the difference between the two representations?," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 385-397.
    5. Gordon Anderson & Maria Pittau & Roberto Zelli, 2014. "Poverty status probability: a new approach to measuring poverty and the progress of the poor," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(4), pages 469-488, December.
    6. Anderson, Gordon & Farcomeni, Alessio & Pittau, Maria Grazia & Zelli, Roberto, 2016. "A new approach to measuring and studying the characteristics of class membership: Examining poverty, inequality and polarization in urban China," Journal of Econometrics, Elsevier, vol. 191(2), pages 348-359.
    7. Michele Costa, 2016. "Overlapping component and inequality decomposition: a simulation study for the Gini index," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 193-205, August.
    8. Xiaofeng Lv & Gupeng Zhang & Guangyu Ren, 2017. "Gini index estimation for lifetime data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 275-304, April.
    9. Allanson, Paul, 2014. "Income stratification and between-group inequality," Economics Letters, Elsevier, vol. 124(2), pages 227-230.
    10. Paul Johnson & Chris Papageorgiou, 2020. "What Remains of Cross-Country Convergence?," Journal of Economic Literature, American Economic Association, vol. 58(1), pages 129-175, March.
    11. Magne Mogstad, 2007. "Measuring Income Inequality under Restricted Interpersonal Comparability," Discussion Papers 498, Statistics Norway, Research Department.
    12. Mendez, Carlos, 2019. "Regional Efficiency Dispersion, Convergence, and Efficiency Clusters: Evidence from the Provinces of Indonesia 1990-2010," MPRA Paper 95972, University Library of Munich, Germany.
    13. Marco Ranaldi, 2016. "On the Measurement of Functional Income Distribution," Documents de travail du Centre d'Economie de la Sorbonne 16051, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. Mariateresa Ciommi & Chiara Gigliarano & Giovanni Maria Giorgi, 2019. "Bonferroni And De Vergottini Are Back: New Subgroup Decompositions And Bipolarization Measures," Working Papers 439, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    15. Allanson, Paul, 2014. "Income stratification and the measurement of interdistributional inequality between multiple groups," SIRE Discussion Papers 2015-34, Scottish Institute for Research in Economics (SIRE).
    16. Yan, Cheng & Cheng, Tingting, 2019. "In search of the optimal number of fund subgroups," Journal of Empirical Finance, Elsevier, vol. 50(C), pages 78-92.
    17. Claudio Ceccarelli & Giovanni Maria Giorgi, 2009. "Analysis of Gini for evaluating attrition in Italian survey on income and living condition," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 63(1-2), pages 49-69, January-J.
    18. Chiang, Yen-Sheng, 2015. "Inequality measures perform differently in global and local assessments: An exploratory computational experiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 1-11.
    19. Giorgio Di Maio & Paolo Landoni, 2015. "Beyond the Gini index: Measuring inequality with the Balance of Inequality index," a/ Working Papers Series 1506, Italian Association for the Study of Economic Asymmetries, Rome (Italy).
    20. Ignazio Drudi & Giorgio Tassinari & Fabrizio Alboni, 2017. "Changes in wealth distribution in Italy (2002-2012) and who gained from the Great Recession," PSL Quarterly Review, Economia civile, vol. 70(281), pages 129-153.

    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:spr:metron:v:75:y:2017:i:2:d:10.1007_s40300-017-0115-1. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.