Small Area Estimation of Mean Years of Schooling Under Time Series and Cross-sectional Models

Small area estimation develops within the framework of time series and cross-sectional models. The restricted estimation maximum likelihood method was used to obtain the empirical best linear unbiased prediction for small areas and its mean squared error estimators. The model focuses on applying statistical models that permit borrowing strength over area and time. The process uses regularly conducted survey data, where the areas of interest are observed repeatedly under a predetermined scheme. The time series and cross-sectional models were able to capture heterogeneity across area and time, so it can be used to enhance sample size effectiveness, thereby minimizing mean squared error and producing a more accurate estimation. The simulation results show that the degree of correlation parameters significantly affects the efficiency of the model. The application to estimate mean years of schooling at the sub-district level in Langkat Regency, North Sumatra, Indonesia, for the period of 2018–2021 showed that the time correlation coefficient was 0.3758, the variance of the area random effect was 1.1125, and the variance of the area-time random effect was 0.3241. The estimations derived from time series and cross-sectional models had a lower mean squared error than those obtained from the Fay-Herriot models and direct estimation.