Small area estimation of economic inequality indices using GAMLSS in the absence of covariates

The goal of this study is to estimate inequality indices for foreigners living in Italy at the regional level, differentiating between urban, peri-urban, and rural areas. This issue requires a Small Area Estimation (SAE) model. We operate in the unit-level context that has brought forth two challenges: the identification of individual covariates and the reduction of computational time. We propose a unit-level Simplified SAE model based on Generalized Additive Models for Location, Scale, and Shape specified without covariates and able to reduce variability in comparison with the direct estimator. A non-parametric bootstrap, suitable without design information, is proposed to estimate the mean square error. The performance of the proposed model used to estimate three different inequality indices (Gini, Theil, and Atkinson) is evaluated based on design-based simulations. The results show that the proposed predictor reduces the variability of the direct estimates even when covariates are not available. This methodology has been adopted to estimated the three indices for foreigners in Italy at the regional level, distinguishing between urban, periurban, and rural areas, showing that relevant disparities emerge in inequality between foreigners compared to natives. These results can help to formulate place-based policies aimed at promoting equity and integration.