Prediksi Gini Rasio dan Komponen Penyusunnya Berdasarkan Model Ybarra-Lohr dengan Ragam Percontohan yang Diduga

Abstract

Gini ratio is one of the parameters used to measure income inequality, so it is necessary to know the value of the Gini ratio down to the level of smaller areas such as subdistricts. The Gini ratio classification is divided into three, those are very high (0,50 – 0,70), moderate (0,36 -0,49), and low (0,20 – 0,35). The components of the Gini ratio according to BPS for the subdistrict level are the average expenditure per capita 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 it is necessary to make estimates for the subdistrict expenditure class level. Direct estimation for small samples can cause large standard errors, therefore small area estimation with Logarithmic Transformation is used as a solution to fulfill the linearity assumption of the model to estimate the average per capita expenditure for each expenditure class for each subdistrict in Depok City in 2020. The expenditure class in this study was determined based on the BPS expenditure class and the distribution of response variable data. The Ybarra-Lohr model at the area level is used due to the availability of accompanying variables at the area level that contain errors which are also available in SUSENAS data. The area is the expenditure class in each subdistrict in Depok City. Estimation was also carried out in one sampleless area in one subdistrict. The sampling variance needed to estimate the average per capita expenditure, is estimated by comparing several methods of estimation, including direct estimation, probability distribution, and bootstrap repetitions of 1000, 10000 and 50000. Estimation of sampling variance and small area estimation analysis using the Ybarra-lohr model and logarithmic transformation done using R software with the help of the saeme package. The method of estimating the model variance with the probability distribution yields an estimate of the average expenditure per capita with the smallest RRMSE, and the random effect variance and the goodness of the YbarraLohr model are σ̂v 2 = 0.686, R 2= 0.929. The results of estimating the best average per capita expenditure for each expenditure class are used to obtain the gini ratio for each subdistrict in Depok City in 2020. Classification is based on the level of inequality, gini ratio with indirect results in all subdistricts in Depok City which are included in the low category are Bojongsari, Pancoran Mas, Cipayung, Sukmajaya, Cilodong, Tapos, Beji, and Limo subdistricts. The subdistricts included in the category of moderate inequality are Sawangan, Cimanggis, and Cinere subdistricts.