Empirical best linear unbiased predictions of small area estimation with panel data for estimating household consumption per capita expenditure

This paper discusses the empirical best linear unbiased prediction (EBLUP) method that is applied in linear mixed models used for small area estimation (SAE). Parameter estimation in the SAE model using the EBLUP method is obtained by minimizing the mean square error (MSE) of the estimator. The SAE method was initially developed by Fay and Herriot, employing a linear mixed model with random area effects. Rao and Yu developed the model by integrating a random area-time effect component with a first-order autoregressive process, enabling its use for time series and panel data analysis. Moreover, this article focuses on the application of the Rao-Yu model for estimating household consumption per capita expenditure (HCPE) of food and non-food by sub-districts in Langkat Regency. Both datasets were sourced from the National Socioeconomic Surveys (Susenas), which is held regularly by Statistics Indonesia. The application to real data showed that model estimates derived from EBLUP have a lower MSE than those obtained from direct estimates. According to the model, the estimated food expenditures by sub-district in Langkat Regency are significantly higher than the non-food expenditures.