Índice de Theil

O Índice de Theil é uma medida estatística da distribuição de renda. O índice de Theil é dado pelo logaritmo neperiano da razão entre as médias aritméticas e geométricas da renda familiar per capita média. Se a razão entre as médias for igual a 1, Theil será igual a zero, indicando perfeita distribuição.[1] Quanto maior a razão entre as médias, maior será o valor para o índice de Theil, e pior será a distribuição de renda [2]

O índice de Theil é dado pela seguinte formula: Theil = 1 - exp(-R). Este valor esta entre 0 e 1 e quanto maior este valor, pior a distribuição. O Índice de Theil, calculado por Theil em 1967 [3], é baseado no conceito de entropia de uma distribuição. Entre suas qualidades enumeram-se que é simétrico (tem a propriedade de invariância em caso de permuta de indivíduos), é invariante à replicação (é independente de replicações de população), independente da média (tem a propriedade de ser invariante em caso de alteração da escala da renda), e satisfaz o Princípio de Pigou-Dalton (a desigualdade cresce como resultado de transferências regressivas).[4] Inclusive países do G8+5, como Estados Unidos estão sendo descritos como altamente desiguais.[5]

Matemática

As fórmulas [6] para os indices T e L são

onde é a renda da -ésima pessoa, é a renda média, e é a quantidade de pessoas. O primeiro termo dentro da soma pode ser considerada a fatia do indivíduo na renda agregada, e o segundo termo indica a renda desta pessoa em relação à média. Se todos os indivíduos tiverem a mesma renda - ou seja, na média - o índice é 0. Se uma pessoa tem toda a renda, o índice é .

O índice de Theil é derivado da medida de entropia de uma distribuição de Claude Shannon. Se é o T é o Índice de Theil, e S é a medida de entropia de uma distribuição de Claude Shannon [7]

Ver também

Bibliografia

  • THEIL, H. (1967). Economics and information theory. North-Holland: Amsterdam.
  • ROGERS, F. H. The Measurement and Decomposition of Achievement Equity. Unpublished doctoral dissertation. Columbus, Ohio: Ohio State University  http://www.ohiolink.edu/etd/send-pdf.cgi?acc_num=osu1092419197  Em falta ou vazio |título= (ajuda)
  • DALTON, H. The measurement of the inequality of incomes, Economic Journal, 30 (1920), pp. 348–461.
  • PIGOU, Arthur Cecil. Wealth and Welfare, 1912.
  • SEN, A.K. (1973), On Economic Inequality, Oxford University Press, London.

Referências

  1. ↑ THEIL, Henry. The Development of International Inequality 1960 – 1985. North-Holland: Journal of Econometrics, 42, 1989, p. 145-155.
  2. ↑ IGNACZAK, João Carlos et al. Dinâmica da produção de trigo no Brasil no período de 1975 a 2003., Materiais e Métodos, in Boletim de Pesquisa e Desenvolvimento n° 36, Passo Fundo, RS: Embrapa Trigo, Dezembro, 2006, ISSN 1677-8901
  3. ↑ THEIL, H. Economics and information theory. Amsterdam: North-Holland, 1967.
  4. ↑ CAVACANTE, Luiz Ricardo. Desigualdades Regionais no Brasil: Uma Análise do Período 1985 – 1999. Salvador, BA: Universidade Federal da Bahia (UFBA), Escola de Administração, p. 6[ligação inativa]
  5. ↑ America is an oligarchy, not a democracy or republic, university study finds
  6. ↑ «Cópia arquivada» (PDF). Consultado em 28 de setembro de 2008. Arquivado do original (PDF) em 25 de março de 2009 
  7. ↑ http://www.poorcity.richcity.org (Redundancy, Entropy and Inequality Measures)
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