
@misc{hoffmann2024MeasuringMismeasuring,
  title = {Measuring and {{Mismeasuring Income Polarization}}},
  author = {Hoffmann, Rodolfo and Kassouf, Ana Lucia},
  year = {2024},
  month = mar,
  doi = {10.21203/rs.3.rs-4139220/v1},
  urldate = {2024-08-12},
  abstract = {The main contribution of this paper is to clarify some of the misconceptions about income polarization indices observed in the existing literature. Our analysis explores the domain of measures of polarization of the income distribution, with a specific emphasis on elucidating the importance of distinguishing between bipolarization and multipolarization measures. Additionally, we assert that a valid polarization metric must adhere to the principle of scale-invariance. Furthermore, in cases where the income distribution is categorized into relatively poor and relatively rich, a valid bipolarization measure should consistently increase when regressive transfers occur from poorer to richer individuals and when progressive transfers occur between two poorer or two richer individuals. The study identifies instances where bipolarization measures that fail to adhere to these criteria have been employed in previous research, leading to erroneous conclusions. The research also provides a succinct analysis of the challenges faced by scholars in employing Esteban and Ray's multipolarization measure and its adapted versions. Artificial numerical examples are used to illustrate the application of different polarization measures in various scenarios. Additionally, a real-world illustration is presented that depicts a declining trend of the bipolarization of income distribution in Brazil from 2001 to 2015, coinciding with a decrease in inequality during this period. The study concludes by pinpointing errors in previously published works.},
  copyright = {https://creativecommons.org/licenses/by/4.0/},
  langid = {english},
  file = {/home/serge/Zotero/storage/WM4696MT/Hoffmann and Kassouf - 2024 - Measuring and Mismeasuring Income Polarization.pdf}
}

@article{wolfson1994WhenInequalities,
  title = {When {{Inequalities Diverge}}},
  author = {Wolfson, Michael C.},
  year = {1994},
  journal = {The American Economic Review},
  volume = {84},
  number = {2},
  eprint = {2117858},
  eprinttype = {jstor},
  pages = {353--358},
  publisher = {American Economic Association},
  issn = {0002-8282},
  urldate = {2024-08-12},
  file = {/home/serge/Zotero/storage/8JYHLHTW/Wolfson - 1994 - When Inequalities Diverge.pdf}
}

@article{schutz1951MeasurementIncome,
  title = {On the {{Measurement}} of {{Income Inequality}}},
  author = {Schutz, Robert R.},
  year = {1951},
  journal = {The American Economic Review},
  volume = {41},
  number = {1},
  eprint = {1815968},
  eprinttype = {jstor},
  pages = {107--122},
  publisher = {American Economic Association},
  issn = {0002-8282},
  urldate = {2024-07-22},
  file = {/home/serge/Zotero/storage/B54Q8IH7/Schutz - 1951 - On the Measurement of Income Inequality.pdf}
}


@Article{Atkinson_1970_Measurement,
  title = {On the Measurement of Inequality},
  author = {Atkinson, Anthony B},
  year = {1970},
  journal = {Journal of Economic Theory},
  volume = {2},
  number = {3},
  pages = {244--263},
  issn = {00220531},
  doi = {10.1016/0022-0531(70)90039-6},
  urldate = {2024-08-09},
}


@Article{rey_interregional_2010,
  Title                    = {Interregional inequality dynamics in {Mexico}},
  Author                   = {Rey, Sergio J. and Sastr\'e-Guti\'errez, Myrna L},
  Journal                  = {Spatial Economic Analysis},
  Year                     = {2010},
  Number                   = {3},
  Pages                    = {277--298},
  Volume                   = {5}
}


@Article{rey_comparative_2015,
  Title                    = {Comparative spatial inequality dynamics: The case of {Mexico and the United States}},
  Author                   = {Rey, Sergio J. and Sastr\'e Guti\'errez, Myrna L.},
  Journal                  = {Applied Geography},
  Year                     = {2015},
  Month                    = {Jul},
  Pages                    = {70--80},
  Volume                   = {61},
  Bdsk-url-1               = {http://dx.doi.org/10.1016/j.apgeog.2015.01.012},
  Doi                      = {10.1016/j.apgeog.2015.01.012},
  ISSN                     = {0143-6228},
  Publisher                = {Elsevier BV},
  Url                      = {http://dx.doi.org/10.1016/j.apgeog.2015.01.012}
}


@Article{Rey_2013_sea,
  Title                    = {A spatial decomposition of the {Gini} coefficient},
  Author                   = {Rey, Sergio J and Smith, Richard J},
  Journal                  = {Letters in Spatial and Resource Sciences},
  Year                     = {2013},
  Pages                    = {55--70},
  Volume                   = {6},
  Keywords                 = {gini, inequality, space-time}
}
