| dc.description.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. | id |
