Small area estimation of consumption per capita expenditure under simultaneous equation Rao-Yu model

This article proposed a simultaneous equation model for small area estimation with random area and time-varying effects called the Simultaneous Equation Rao-Yu (SERY) model. In the context of small area estimation, many socioeconomic variables are likely to exhibit not only correlations but also causal relationships. Therefore, it is considered to use simultaneous equation model for indirect estimation method in a small-area. The SERY model was developed to accommodate causal relationships among the variables of interest in time series and cross-sectional data. The SERY model is a modification of the Rao-Yu model, which was constructed using simultaneous equation that allows endogenous variables as explanatory variables. For fitting linear mixed models, three-stage least squares restricted maximum likelihood method was proposed to derive the empirical best linear unbiased predictor and mean squared error estimator. Finally, the model was applied to estimate consumption per capita expenditure of food and non-food. Some highlights of the proposed method are: • We presented the SERY model, a small area estimation model, which was constructed using simultaneous equation to accommodate causal relationships among the variables of interest. • The parameter estimation method used three-stage least squares restricted maximum likelihood. • Applied to estimate consumption per capita expenditure of food and non-food.