The inequality Quantile Ratio Index: estimation in complex surveys and small areas

Economic inequality is a heterogeneous and continuously expanding phenomenon nowadays. An increase in GDP per capita does not guarantee an improvement in the living conditions of all the households unless it is accompanied by policies that control the dominant rise in disparities in well-being among them. The provision of an exhaustive statistical methodology for the measurement of economic inequalities is a necessary premise to help policy makers reducing them. This dissertation proposes a complete framework for the estimation of the Quantile Ratio Index (QRI), an indicator based solely on quantiles and that considers the entire distribution of the variable of interest. A direct estimator is defined to this end, which uses only sample observations in the context of finite population inference. The problem of its measurement in small areas - where survey data may be insufficient to ensure the direct estimator reliabilit - is addressed by introducing a small area estimation model at the area-level. The proposed methodology is applied on Italy’s income and wealth data to measure the inequality in small areas defined on a socio-geographical basis. A comparison between small area estimation of the QRI and the Gini coefficient demonstrates the superior reliability of the QRI in measuring inequality.