Gini Ratio Prediction by Estimating the Components Based on the Ybarra-Lohr Model Small Area Estimation with Estimated Sampling Variance

Abstract

Gini ratio is one of the tools used to measure income inequality, so it is necessary to know the value of Gini ratio to a smaller regional level such as a subdistrict. According to Badan Pusat Statistik (BPS), the components of the Gini ratio are the average per capita expenditure and the relative frequency of households for each expenditure class in the subdistrict. Per capita expenditure data available through SUSENAS is designed to obtain national statistics down to the district level so that estimates are made for the level of subdistrict expenditure classes. Direct estimation for a small sample can cause significant standard errors therefore Small Area Estimation (SAE) with Logarithm Transformation is used to estimate the average per capita expenditure for each subdistrict expenditure class in Depok City 2020. The Ybarra-Lohr area-level model was used because of the availability of auxiliary data with measurement error. Previously, the sampling variance required for estimating the average per capita expenditure was estimated by comparing several estimation methods. As sampling variance estimation method, probability distribution produces an estimate of the average per capita expenditure with the smallest RRMSE, with a random effect variance and goodness of Ybarra-Lohr model are  = 0.686 and = 0.929. The best result of the average per capita expenditure estimation for each expenditure class is used to obtain Gini ratio for each subdistrict in Depok City 2020.