Statistical Inference for the Kakwani Inequality Index

We develop a comprehensive inferential framework for the Kakwani inequality index, a well-known generalisation of the Gini index that incorporates societal aversion to inequality through a parameter. Building on both the model-based and the design-based paradigms, we derive the influence functions of the Kakwani index in the two approaches, allowing for distribution-free inference in the model-based paradigm and accurate variance estimation in the design-based paradigm. The methodology is applied to the 2022 European Union Statistics on Income and Living Conditions (EU-SILC) data to assess income inequality across the European countries at both national (NUTS 0) and regional (NUTS 1) levels. The analysis includes comparisons at different values of inequality aversion, revealing consistent patterns of inequality distribution across Europe. Furthermore, the study explores the reliability of estimates using the corresponding dispersion estimation and introduces functional clustering to identify groups of countries with similar inequality profiles.