Abordagem média geométrica para medir o Índice Composto
DOI:
https://doi.org/10.23882/rmd.24160Palavras-chave:
Índice composto, Monotonicamente crescente, Média geométrica, Teste de reversão de tempo, índices de cadeiaResumo
O Índice Composto (IC) combina medidas de indicadores sobre variáveis económicas, sociais, ambientais, iniciativas governamentais, bem-estar da saúde, psicológico, satisfação das necessidades básicas, social/cultural, etc. No entanto, as medidas existentes de IC sofrem de limitações. O presente documento propõe que a medida do IC seja a média geométrica (GM), que evita o escalonamento e a escolha de pesos. Esta medida ajuda a comparar melhor os países no tempo e no espaço e satisfaz as propriedades desejadas, como a função contínua monotonicamente crescente, a elasticidade constante, a identificação de áreas-chave, a redução do nível de substituibilidade, a formação de índices em cadeia para mostrar o crescimento do IC de um país e é menos afetada por valores atípicos. O índice, com ampla aplicabilidade, pode ser utilizado para a classificação de países e facilita o cálculo da média e da variância de uma amostra de países. Além disso, o índice satisfaz o teste de inversão temporal, ajuda a identificar as áreas críticas e a encontrar a contribuição dos indicadores componentes, a estimar os parâmetros populacionais e a testar hipóteses estatísticas. Podem ser construídos índices separados por domínios, considerando indicadores relevantes para um domínio. Trata-se, portanto, de uma melhoria em relação aos métodos existentes. Sugerem-se estudos futuros.
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