Welfare information is very important for policy makers and the government in order to improve the nation economic status. Most common welfare indicators widely used are expenditure and income. In practice, studying the two indicators separately could lead to different conclusions. Accordingly, to have precise viewpoints of the nation economic status, the two measurements should be simultaneously studied via a bivariate model. One of well-known models used in small area is the Fay-Herriot model. However, standard variance component estimation methods for the Fay-Herriot model frequently produce zero estimate of the strictly positive model variance. Therefore, Li and Lahiri proposed an adjusted method to prevent zero estimate of model variance for the univariate Fay-Herriot model. In this paper, we extend their technique to obtain an adjusted likelihood estimate for a bivariate Fay-Herriot model and apply the method to estimate income and expenditure in Thailand. In our study, simulation study is carried out to investigate the performance of our adjusted method comparing with the original profile likelihood method. The simulation results suggest that our adjusted profile likelihood estimates prevent zero estimates and outperform the profile likelihood estimates. Consequently, an empirical study is performed for the Thai income and expenditure welfare measurements using data from the 2017 Thailand Household Socio-Economic Survey (SES 2017) and the 2010 Thailand Population and Housing Census.
Keywords: Small area estimation, Bivariate Fay-Herriot model, Empirical best linear unbiased predictor, Adjusted maximum likelihood method, Income and Expenditure
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